‫ﺟﺎﻣﻌﺔ اﻟﻤﻮﺻﻞ‬ ‫آﻠﻴﺔ اﻟﺘﺮﺑﻴﺔ‬

‫ﻣﺤﺎآﺎة ﺣﺎﺳﻮﺑﻴﺔ ﺟﺪﻳﺪة ﻷﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬ ‫)1-‪ (IBM‬ﻟﺪراﺳﺔ اﻻﻧﺤﻨﺎء اﻟﺨﻠﻔﻲ ﻓﻲ ﻧﻈﺎﺋﺮ‬ ‫‪ 120-126Xe‬اﻟﺰوﺟﻴﺔ - اﻟﺰوﺟﻴﺔ‬ ‫ﻣﺸﺘﺎق ﻋﺒﺪ داؤد اﻟﺠﺒﻮري‬
‫رﺳﺎﻟﺔ ﻣﺎﺟﺴﺘﻴﺮ‬ ‫اﻟﻔﻴﺰﻳﺎء‬ ‫ﺑﺈﺷﺮاف‬ ‫ﻋﻤﺎد ﻣﻤﺪوح اﺣﻤﺪ‬ ‫أﺳﺘﺎذ ﻣﺴﺎﻋﺪ‬ ‫8002م‬ ‫9241هـ‬

‫ﳏﺎﻛﺎﺓ ﺣﺎﺳﻮﺑﻴﺔ ﺟﺪﻳﺪﺓ ﻷﳕﻮﺫﺝ ﺍﻟﺒﻮﺯﻭﻧﺎﺕ ﺍﳌﺘﻔﺎﻋﻠﺔ‬
‫621-021‬

‫)1-‪ (IBM‬ﻟﺪﺭﺍﺳﺔ ﺍﻻﳓﻨﺎء ﺍﳋﻠﻔﻲ ﰲ ﻧﻈﺎﺋﺮ ‪Xe‬‬ ‫ﺍﻟﺰﻭﺟﻴﺔ - ﺍﻟﺰﻭﺟﻴﺔ‬

‫ﺭﺳﺎﻟﺔ ﺗﻘﺪﻡ ﲠﺎ‬

‫ﻣﺸﺘﺎﻕ ﻋﺒﺪ ﺩﺍﺅﺩ ﺍﳉﺒﻮﺭﻱ‬
‫ﺇﱃ‬

‫ﳎﻠﺲ ﻛﻠﻴﺔ ﺍﻟﱰﺑﻴﺔ ﰲ ﺟﺎﻣﻌﺔ ﺍﳌﻮﺻﻞ‬ ‫ﻭﻫﻲ ﺟﺰﺀ ﻣﻦ ﻣﺘﻄﻠﺒﺎﺕ ‪￿‬ﻴﻞ ﺷﻬﺎﺩﺓ ﻣﺎﺟﺴﺘﲑ ﻋﻠﻮﻡ ﰲ ﺍﻟﻔﻴﺰﻳﺎﺀ‬
‫ﺑﺈﺷﺮﺍﻑ‬

‫ﻋﻤﺎﺩ ﳑﺪﻭﺡ ﺍﲪﺪ‬

‫ﺃﺳﺘﺎﺫ ﻣﺴﺎﻋﺪ‬
‫8002 م‬ ‫9241 هـ‬

‫ﺑﺴﻢ ﺍ‪ ‬ﺍﻟﺮﲪﻦ ﺍﻟﺮﺣﻴﻢ‬

‫‪‬ﻧﺮﻓﻊ‪ ‬ﺩﺭﺟـﺖ ﻣﻦ ‪‬ﻧﺸﺂﺀ ُ‬ ‫‪‬ﹶ ‪  ٍ ٰ   ‬‬ ‫ﻭﻓﻮﻕ ﻛ ﹼ ِﺫﻯ ﻋﻠﻢ ﻋﻠِﻴﻢ‪‬‬ ‫‪ ‬ﹶ ‪  ‬ﹸﻞ ِ ِ ﹾ ٍ ‪ ‬‬
‫ﺻﺪﻕ ﺍﷲ ﺍﻟﻌﻈﻴﻢ‬

‫)ﺳﻮﺭﺓ ﻳﻮﺳﻒ :ﻣﻦ ﺍﻵﻳﺔ 67 (‬

‫ﺍﻹﻫﺪﺍء‬
‫إﻟﻰ ﻣﻦ أﺿﺎء اﻟﻄﺮﻳﻖ ﻧﻮرا ﻓﻲ ﺳﺒﻴﻞ ﻣﺒﺘﻐﺎي‬ ‫وﻣﺪ ﻟﻲ ﻳﺪ اﻟﻤﺴﺎﻋﺪة‬ ‫واﻟﺪي‬ ‫إﻟﻰ ﻣﻦ ذرﻓﺖ اﻟﺪﻣﻊ ﺳﺒﻴﻼ ﻟﺮﻋﺎﻳﺘﻲ‬ ‫وهﻲ ﻣﺼﺪر ﻗﻮﺗﻲ وﻋﻮﻧﻲ ﻓﻲ اﻟﺤﻴﺎة‬ ‫وﺟﻌﻠﺖ ﻟﻲ ﻓﻲ هﺬﻩ اﻟﺪﻧﻴﺎ ﻣﻘﺎﻣﺎ‬ ‫واﻟﺪﺗﻲ‬ ‫إﻟﻰ ﻣﻦ أﺣﺒﻬﻢ‬ ‫ﺑﻜﻞ ﻣﺎ ﺧﻠﻖ اﷲ ﻣﻦ ﺣﺐ‬ ‫إﺧﻮﺗﻲ وأﺧﻮاﺗﻲ‬ ‫إﻟﻰ آﻞ ﻣﻦ ﻋﻠﻤﻨﻲ آﻞ ﺣﺮف ﺑﺈﺗﻘﺎن‬ ‫إﻟﻰ ﻣﻦ ﺻﻘﻞ اﻟﻔﻜﺮ ﻋﻠﻤﺎ ﻓﻲ ﺳﺒﻴﻞ ﻧﺠﺎﺣﻲ‬ ‫أﺳﺎﺗﺬﺗﻲ‬ ‫إﻟﻰ ﺗﻠﻚ اﻟﻜﻠﻤﺔ اﻟﺘﻲ ﺗﻨﻤﻮ ﻓﻲ أﺳﻤﺎﻋﻲ‬ ‫وﺗﻔﻴﺾ ﺑﻌﻄﺮهﺎ ﻓﻲ ﻧﻔﺴﻲ‬ ‫زﻣﻼﺋﻲ وزﻣﻴﻼﺗﻲ‬

‫ﺍﻟﺤﻤﺩ ﷲ ﺍﻟﺫﻱ ﻫﺩﺍﻨﺎ ﺍﻟﻰ ﻁﺭﻴﻕ ﺍﻟﻌﻠﻡ ﻭﻤﺎ ﻜﻨﺎ ﻟﻨﻬﺘﺩﻱ ﻟﻭﻻ ﺍﻥ ﻫﺩﺍﻨﺎ ﺍﷲ ﻭﺍﻟﺼﻼﺓ ﻭﺍﻟـﺴﻼﻡ‬ ‫ﻋﻠﻰ ﻤﻌﻠﻡ ﺍﻟﺒﺸﺭﻴﺔ ﺍﻷﻭل ﺴﻴﺩﻨﺎ ﻤﺤﻤﺩ )ﺼﻠﻰ ﺍﷲ ﻋﻠﻴﻪ ﻭﺴﻠﻡ( ﻭﻋﻠﻰ ﺍﻟـﻪ ﻭﺍﺼـﺤﺎﺒﻪ ﺃﺠﻤﻌـﻴﻥ‬ ‫ﻭﺒﻌﺩ:‬ ‫ﻴﻁﻴﺏ ﻟﻲ ﻭﺍﻨﺎ ﺃﻨﻬﻲ ﻫﺫﺍ ﺍﻟﺠﻬﺩ ﺍﻟﻤﺘﻭﺍﻀﻊ ﺍﻥ ﺍﺘﻭﺠﻪ ﺒﻭﺍﻓﺭ ﺍﻟﺸﻜﺭ ﻭﺍﻟﺘﻘﺩﻴﺭ ﻷﺴﺘﺎﺫﻱ ﺍﻟﻔﺎﻀل‬ ‫ﺍﻟﺴﻴﺩ ﻋﻤﺎﺩ ﻤﻤﺩﻭﺡ ﺃﺤﻤﺩ ﻷﻗﺘﺭﺍﺤﻪ ﻤﻭﻀﻭﻉ ﺍﻟﺒﺤﺙ ﻭﻟﻤﺎ ﺒﺫﻟﻪ ﻤﻌﻲ ﻤﻥ ﺠﻬﻭﺩ ﻋﻠﻤﻴـﺔ ﻤﺨﻠـﺼﺔ‬ ‫ﻭﻨﺼﺎﺌﺢ ﻭﺘﻭﺠﻴﻬﺎﺕ ﺴﺩﻴﺩﺓ ﻭﻴﺴﻌﺩﻨﻲ ﺍﻥ ﺃﺘﻘﺩﻡ ﺒﻭﺍﻓﺭ ﺍﻷﻤﺘﻨﺎﻥ ﺍﻟﻰ ﻤﻨﺘﺴﺒﻲ ﻗﺴﻡ ﺍﻟﻔﻴﺯﻴﺎﺀ ﻭﺍﺨـﺹ‬ ‫ﺒﺎﻟﺫﻜﺭ ﺍﻟﺩﻜﺘﻭﺭ ﻤﻤﺘﺎﺯ ﻤﺤﻤﺩ ﺼﺎﻟﺢ ﻭﺍﻟﻰ ﻜل ﻤﻥ ﻋﻠ ‪‬ﻨﻲ ﻓﻲ ﻓﺘﺭﺓ ﻤﺴﻴﺭﺘﻲ ﺍﻟﻌﻠﻤﻴﺔ.‬ ‫ﻤ‬ ‫ﻭﻴﺸﺭﻓﻨﻲ ﺃﻥ ﺃﺘﻘﺩﻡ ﺒﻭﺍﻓﺭ ﺍﻟﺸﻜﺭ ﻭﺍﻟﺘﻘﺩﻴﺭ ﺍﻟﻰ ﻜل ﻤﻥ ﺍﻟﺩﻜﺘﻭﺭ ﺃﺤﻤﺩ ﺨﻠﻑ ﻤﺤﻴﻤﻴﺩ ﺍﻟﺫﻱ ﻟـﻡ‬ ‫ﻴﺒﺨل ﻋﻠﻲ ﺒﻌﻠﻤﻪ,ﻭﺍﻟﺩﻜﺘﻭﺭ ﺴﻌﻴﺩ ﺤﺴﻥ ﺴﻌﻴﺩ ﺍﻟﺫﻱ ﻁﺎﻟﻤﺎ ﻗﺩﻡ ﻟﻲ ﻤﺴﺎﻋﺩﺘﻪ ﻭﺍﻟﺩﻜﺘﻭﺭ ﺃﻨﻭﺭ ﻨـﺎﻓﻊ‬ ‫‪‬‬ ‫ﻋﺒﻭﺩ ﻟﻤﺂﺯﺭﺘﻪ ﻟﻲ ﻭﻭﻗﻭﻓﻪ ﺒﺠﺎﻨﺒﻲ ﻁﻴﻠﺔ ﻓﺘﺭﺓ ﺍﻟﺒﺤﺙ,ﻭﺍﻟﺩﻜﺘﻭﺭ ﺨﻠﻴـل ﺍﺒـﺭﺍﻫﻴﻡ.ﻭﻻ ﻴﻔـﻭﺘﻨﻲ ﺃﻥ‬ ‫ﺍﺸﻜﺭ ﺍﻟﺴﻴﺩ ﺠﻤﻌﺔ ﻤﺤﻤﺩ ﺠﺎﺴﻡ,ﻭﺍﻟﺴﻴﺩ ﺤﺴﻴﻥ ﻋﻠﻲ ﺤﺴﻥ,ﻭﺍﻟﺴﻴﺩ ﻴﺎﺴﺭ ﻴﺤﻴﻰ ﻗﺎﺴﻡ, ﻭﺍﻟﺴﻴﺩ ﻤﺎﻟـﻙ‬ ‫ﺤﺴﻴﻥ ﺨﻀﺭ,ﻭﺍﻟﺴﻴﺩ ﺴﻌﺩ ﻭﺴﻤﻲ,ﻭﺴﻭﺯﺍﻥ ﺸﻜﺭ ﻨﻭﺭﻱ,ﻭﻤﺼﻁﻔﻰ ﺍﺤﻤﺩ ﻤﺤﻤـﺩ,ﻭﺍﺤﻤـﺩ ﻋﻠـﻲ‬ ‫ﺤﻤﺎﺩﻱ ﻷﻋﺎﻨﺘﻬﻡ ﻟﻲ ﻁﻴﻠﺔ ﻓﺘﺭﺓ ﺍﻨﺠﺎﺯ ﻫﺫﺍ ﺍﻟﺒﺤﺙ.‬ ‫ﻭﺃﺠﻼﻻ ﻤﻨﻲ ﻭﺃﺤﺘﺭﺍﻤﺎ ﻭﺘﻘﺩﻴﺭﺍ ﺃﻗﺩﻡ ﺸﻜﺭﻱ ﻭﺘﻘﺩﻴﺭﻱ ﻷﺴﺭﺘﻲ ﺍﻟﻔﺎﻀﻠﺔ ﻟﻤﺎ ﻗﺩﻤﻭﻩ ﻟـﻲ ﻤـﻥ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺘﺸﺠﻴﻊ ﻭﻤﺴﺎﻋﺩﺓ ﺨﻼل ﻓﺘﺭﺓ ﺍﻟﺩﺭﺍﺴﺔ ﻭﺍﻟﻰ ﻜل ﻤﻥ ﻭﻗﻑ ﺒﺠﺎﻨﺒﻲ ﻭﻓﺎﺘﻨﻲ ﺃﻥ ﺍﺫﻜﺭ ﺍﺴﻤﻪ ﺠـﺯﺍﻫﻡ‬ ‫ﺍﷲ ﻋﻨﻲ ﺨﻴﺭ ﺍﻟﺠﺯﺍﺀ .‬

‫ﻤﺸﺘﺎﻕ‬

‫ﺍﻟﺨﻼﺼﺔ‬
‫ﺍﺴﺘﺨﺩﻡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ )1-‪ (IBM‬ﺍﻟﺘﺤﺩﻴﺩ ﻜﺎﻤـﺎ ﻏﻴـﺭ ﺍﻟﻤـﺴﺘﻘﺭ )6(‪O‬‬ ‫ـﻭﻥ‬ ‫ـﺎﺌﺭ ﺍﻟﺯﻴﻨــ‬ ‫ـﻰ )‪ (Yrast levels‬ﻟﻨﻅــ‬ ‫ـﺔ ﺍﻷﺩﻨــ‬ ‫ﻟ ـﺴﺎﺏ ـﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗــ‬ ‫ﻤــ‬ ‫ﺤــ‬ ‫ﺍﻟﺯﻭﺠﻴﺔ – ﺍﻟﺯﻭﺠﻴﺔ.ﺍﺫ ﺍﺴﺘﺨﺩﻤﺕ ﻁﺭﻴﻘﺔ ﺠﺩﻴﺩﺓ ﻟﺤﺴﺎﺏ ﻤﻌﻠﻤـﺎﺕ ﺍﻟﺘﺤﺩﻴـﺩ )6(‪O‬‬
‫621-021‬

‫‪Xe‬‬

‫4‪ K‬ﻭ 5‪ K‬ﻟﻤﺭﺘﻴﻥ:ﻤﺭﺓ ﻟﻠﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﻭﺍﺨﺭﻯ ﻟﻠﺤﺯﻤﺔ ﺍﻟﻤﺜﺎﺭﺓ ‪ S‬ﺒﺩﻻ ﻤﻥ ﺤﺴﺎﺒﻬﻡ ﻟﻤـﺭﺓ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻭﺍﺤﺩﺓ ﻟﻠﺤﺎﻟﺘﻴﻥ. ﺒﻌﺩ ﺍﻴﺠﺎﺩ ﺍﻟﻤﻌﻠﻤﺎﺕ 4‪ K‬ﻭ 5‪ K‬ﻴﺘﻡ ﺍﺴﺘﺨﺩﺍﻤﻬﻤﺎ ﻓـﻲ ﻤﻌﺎﺩﻟـﺔ ﺍﻟﺘﺤﺩﻴـﺩ )6(‪O‬‬ ‫ﻟﺤﺴﺎﺏ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻷﺩﻨﻰ ﺤﻴﺙ ﺘﺒﻴﻥ ﺍﻥ ﻫﻨﺎﻙ ﺍﺘﻔﺎﻕ ﺠﻴﺩ ﺒﻴﻥ ﺍﻟﻘﻴﺎﺴﺎﺕ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﺤﺴﺎﺒﺎﺕ‬ ‫ﺍﻟﺤﺎﻟﻴﺔ.ﻜﻨﺘﻴﺠﺔ ﻟﺫﻟﻙ ﺤﺩﺩ ﻤﻭﻗﻊ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻤﻥ ﺤﺴﺎﺒﺎﺕ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗـﺔ ﻭﻗﻭﺭﻨـﺕ ﻤـﻊ‬ ‫ﺍﻟﻨﺘﺎﺌﺞ ﺍﻟﻌﻤﻠﻴﺔ ﻭﻜﺎﻥ ﺍﻟﺘﻁﺎﺒﻕ ﺠﻴﺩﺍ ﺍﻴﻀﺎ.ﻟﻘﺩ ﺍﻋﺩ ﺒﺭﻨﺎﻤﺞ ﻤﺤﺎﻜﺎﺓ ﺒﻠﻐﺔ 7-‪ MATLAB‬ﻟﻐـﺭﺽ‬ ‫‪‬‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺘﺤﺩﻴﺩ ﻗﻴﻡ ﻤﻌﻠﻤﺎﺕ ﺍﻟﺘﺤﺩﻴﺩ )6(‪ O‬ﻭﻤﻥ ﺜﻡ ﺤﺴﺎﺏ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﺎﺌﺭ ﺒﺩﻻ ﻤـﻥ ﺍﺴـﺘﺨﺩﺍﻡ‬ ‫ﹰ‬ ‫ﺍﻟﺒﺭﻨﺎﻤﺞ ﺍﻟﺠﺎﻫﺯ ‪ PHINT‬ﺍﻟﻤﻌﺘﺎﺩ ﺍﺴﺘﺨﺩﺍﻤﻪ ﻤﻥ ﻗﺒل ﺍﻻﺨﺭﻴﻥ ﻟﻬـﺫﺍ ﺍﻟﻐـﺭﺽ. ﻟﻘـﺩ ﺤـﺴﺒﺕ‬ ‫ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎل ﺍﻟﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﻤﺨﺘﺯل )2‪ B(E‬ﺒﻁﺭﻴﻘﺘﻴﻥ:ﺍﻻﻭﻟﻰ ﺍﻋﺘﻤﺩﺕ ﻋﻠـﻰ‬ ‫ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻟﻠﻌﻤﺭ ﺍﻟﻨﺼﻔﻲ ﻟﻸﻨﺘﻘﺎل 2/1‪ T‬ﻭﻋﻠﻰ ﻁﺎﻗﺔ ﺍﻷﻨﺘﻘﺎل ‪ Eγ‬ﺒﻴﻥ ﻤﺴﺘﻭﻴﻴﻥ ﻤﺘﺘﺎﻟﻴﻥ ﻤﻌﻴﻨـﻴﻥ‬ ‫ﻭﻋﻠﻰ ﻤﻌﺎﻤل ﺍﻟﺘﺤﻭل ﺍﻟﺩﺍﺨﻠﻲ ‪ α‬ﺍﻟﺫﻱ ﺤﺴﺏ ﺒﻁﺭﻴﻘﺔ ﺍﻷﺴﺘﻜﻤﺎل ﺒﺎﺴﺘﺨﺩﺍﻡ ﺒﺭﻨﺎﻤﺞ ﺨﺎﺹ ﻟﻬـﺫﺍ‬ ‫ﺍﻟﻐﺭﺽ ﻭﻜﺎﻨﺕ ﺍﻟﻨﺘﺎﺌﺞ ﻤﺘﻁﺎﺒﻘﺔ ﻤﻊ ﺍﻟﻘﻴﺎﺴﺎﺕ ﺍﻟﻌﻤﻠﻴﺔ.ﺍﻤﺎ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﺜﺎﻨﻴﺔ ﻟﺤـﺴﺎﺏ )2‪ B(E‬ﻓﻘـﺩ‬ ‫ﺍﻋﺘﻤﺩﺕ ﻋﻠﻰ ﻤﻌﺎﺩﻟﺔ ﺍﻟﺘﺤﺩﻴﺩ )6(‪ O‬ﻓﻲ ﺃﻨﻤﻭﺫﺝ )1-‪ (IBM‬ﻭﻜﺎﻨﺕ ﺍﻟﻨﺘﺎﺌﺞ ﺒﺸﻜل ﻋـﺎﻡ ﻤﺘﻔﻘـﺔ‬ ‫ﻭﺒﺸﻜل ﺠﻴﺩ ﻤﻊ ﺍﻟﻨﺘﺎﺌﺞ ﺍﻟﻌﻤﻠﻴﺔ ﻭﻤﻊ ﻨﺘﺎﺌﺞ ﺍﻟﺤﺴﺎﺒﺎﺕ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻻﻭﻟﻰ. ﻓﻀﻼ ﻋـﻥ ﺫﻟـﻙ ﻓﻘـﺩ‬ ‫ﹰ‬ ‫,‬
‫+‬ ‫+‬ ‫) 12 → 14;2 ‪B( E‬‬ ‫‪‬ﺭﺱ ﺘﺄﺜﻴﺭ ﺯﻴﺎﺩﺓ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻋﻠﻰ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﻨﺴﺏ ﺍﻟﺘﻔـﺭﻉ‬ ‫ﺩ ‪‬‬ ‫+‬ ‫+‬ ‫) 10 → 12;2 ‪B ( E‬‬ ‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫) 16 → 18;2 ‪B ( E‬‬ ‫) 14 → 16;2 ‪B( E‬‬ ‫,‬ ‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫) 10 → 12;2 ‪B ( E‬‬ ‫) 10 → 12;2 ‪B( E‬‬

‫. ﺍﻥ ﺍﻫﻤﻴﺔ ﺫﻟﻙ ﺘﻜﻤﻥ ﻓـﻲ ﺘﺤﺩﻴـﺩ ﻤﻭﻗـﻊ ﺍﻟﻨﻅـﺎﺌﺭ‬

‫ﻨﺴﺒﺔ ﺍﻟﻰ ﺍﻟﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ )5(‪ SU‬ﻭ )3(‪ SU‬ﻭ )6(‪ , O‬ﻭﻗـﺩ ﺍﺸـﺎﺭﺕ ﻨﺘـﺎﺌﺞ‬

‫621-021‬

‫‪Xe‬‬

‫ﺍﻟﺩﺭﺍﺴﺔ ﺍﻟﺤﺎﻟﻴﺔ ﺍﻥ ﺍﻟﻨﻅﺎﺌﺭ ﺍﻟﻤﺩﺭﻭﺴﺔ ﺘﻘﻊ ﻀﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ ﻜﺎﻤﺎ ﻏﻴﺭ ﺍﻟﻤﺴﺘﻘﺭ)6(‪. O‬‬

‫ﺍﻟﻔﻬﺭﺴﺕ‬
‫ﺭﻗﻡ‬ ‫ﺍﻟﺼﻔﺤﺔ‬ ‫‪I‬‬ ‫‪IV‬‬ ‫‪V‬‬ ‫ﺍﻟﻤﻭﻀﻭﻉ‬ ‫ﻗﺎﺌﻤﺔ ﺍﻟﻤﺤﺘﻭﻴﺎﺕ‬ ‫ﻗﺎﺌﻤﺔ ﺍﻟﺠﺩﺍﻭل‬ ‫ﻗﺎﺌﻤﺔ ﺍﻻﺸﻜﺎل‬

‫ﻗﺎﺌﻤﺔ ﺍﻟﻤﺤﺘﻭﻴﺎﺕ‬
‫ﺭﻗﻡ‬ ‫ﺍﻟﺼﻔﺤﺔ‬ ‫ﺍﻟﻤﻭﻀﻭﻉ‬ ‫ﺍﻟﺘﺴﻠﺴل‬

‫ﺍﻟﻔﺼل ﺍﻻﻭل: ﺍﻟﺩﺭﺍﺴﺎﺕ ﺍﻟﺴﺎﺒﻘﺔ‬
‫1‬ ‫2‬ ‫7‬ ‫01‬ ‫ﺍﻟﻤﻘﺩﻤﺔ‬ ‫ﺍﻟﺩﺭﺍﺴﺎﺕ ﺍﻟﺴﺎﺒﻘﺔ‬ ‫ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ‬ ‫ﺍﻟﻬﺩﻑ ﻤﻥ ﺍﻟﺩﺭﺍﺴﺔ‬ ‫1-1‬ ‫2-1‬ ‫3-1‬ ‫4-1‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ: ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬
‫11‬ ‫41‬ ‫61‬ ‫81‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ‬ ‫ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ ﻷﺸﻌﺔ ﻜﺎﻤﺎ‬ ‫ﺍﻟﺘﺸﻭﻩ ﻭﺍﻟﻌﺯﻡ ﺍﻟﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﻨﻭﻭﻱ‬ ‫ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬ ‫1-2‬ ‫2-2‬ ‫3-2‬ ‫4-2‬

‫‪I‬‬

‫ﺭﻗﻡ‬ ‫ﺍﻟﺼﻔﺤﺔ‬

‫ﺍﻟﻤﻭﻀﻭﻉ‬

‫ﺍﻟﺘﺴﻠﺴل‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻟﺙ: ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ )1-‪(IBM‬‬
‫22‬ ‫32‬ ‫52‬ ‫62‬ ‫92‬ ‫23‬ ‫73‬ ‫83‬ ‫83‬ ‫93‬ ‫93‬ ‫ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ‬ ‫ﻤﺅﺜﺭ ﻫﺎﻤﻠﺘﻭﻥ‬ ‫ﺍﻟﺘﻨﺎﻅﺭﺍﺕ ﺍﻟﺤﺭﻜﻴﺔ‬ ‫ﺍﻟﺘﺤﺩﻴﺩ ﺍﻷﻫﺘﺯﺍﺯﻱ‬ ‫ﺍﻟﺘﺤﺩﻴﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ‬ ‫ﺍﻟﺘﺤﺩﻴﺩ ‪ γ‬ﻏﻴﺭ ﺍﻟﻤﺴﺘﻘﺭﺓ )6(‪O‬‬ ‫ﺍﻟﻤﻨﺎﻁﻕ ﺍﻻﻨﺘﻘﺎﻟﻴﺔ ﻓﻲ ﺍﻨﻤﻭﺫﺝ )1-‪(IBM‬‬ ‫ﺍﻟﺼﻨﻑ ‪A‬‬ ‫ﺍﻟﺼﻨﻑ ‪B‬‬ ‫ﺍﻟﺼﻨﻑ ‪C‬‬ ‫ﺍﻟﺼﻨﻑ ‪D‬‬ ‫3‬ ‫1-3‬ ‫2-3‬ ‫1-2-3‬ ‫2-2-3‬ ‫3-2-3‬ ‫3-3‬ ‫1-3-3‬ ‫2-3-3‬ ‫3-3-3‬ ‫4-3-3‬

‫ﺍﻟﻔﺼل ﺍﻟﺭﺍﺒﻊ: ﺍﻟﺤﺴﺎﺒﺎﺕ ﻭﺍﻟﻨﺘﺎﺌﺞ‬
‫04‬ ‫34‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ‬ ‫ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺍﻟﻤﺨﺘﺯﻟﺔ )2‪B(E‬‬ ‫1-4‬ ‫2-4‬

‫ﺍﻟﻔﺼل ﺍﻟﺨﺎﻤﺱ: ﺍﻟﻤﻨﺎﻗﺸﺔ ﻭﺍﻻﺴﺘﻨﺘﺎﺠﺎﺕ ﻭﺍﻟﻤﻘﺘﺭﺤﺎﺕ‬
‫96‬ ‫07‬ ‫ﻤﻘﺩﻤﺔ‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ‬ ‫1-5‬ ‫2-5‬

‫‪II‬‬

‫ﺭﻗﻡ‬ ‫ﺍﻟﺼﻔﺤﺔ‬ ‫27‬ ‫57‬ ‫67‬

‫ﺍﻟﻤﻭﻀﻭﻉ‬ ‫ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺍﻟﻤﺨﺘﺯﻟﺔ‬ ‫ﺍﻷﺴﺘﻨﺘﺎﺠﺎﺕ‬ ‫ﺍﻟﻤﻘﺘﺭﺤﺎﺕ‬

‫ﺍﻟﺘﺴﻠﺴل‬ ‫3-5‬ ‫4-5‬ ‫5-5‬

‫ﺍﻟﻤﺼﺎﺩﺭ‬
‫77‬ ‫87‬ ‫ﺍﻟﻤﻠﺤﻕ‬ ‫58‬ ‫ﺍﻟﻤﻠﺤﻕ )1(‬ ‫ﺍﻟﻤﺼﺎﺩﺭ ﺍﻟﻌﺭﺒﻴﺔ‬ ‫ﺍﻟﻤﺼﺎﺩﺭ ﺍﻻﺠﻨﺒﻴﺔ‬

‫‪III‬‬

‫ﻗﺎﺌﻤﺔ ﺍﻟﺠﺩﺍﻭل‬
‫ﺭﻗﻡ‬ ‫ﺍﻟﺼﻔﺤﺔ‬ ‫14‬ ‫14‬ ‫54‬ ‫64‬ ‫74‬ ‫84‬ ‫94‬ ‫05‬ ‫15‬ ‫25‬ ‫35‬ ‫45‬ ‫2/1‪T‬‬ ‫ﻋﻨﻭﺍﻥ ﺍﻟﺠﺩﻭل‬ ‫ﻗﻴﻡ 2 ‪ E‬ﻭ 4 ‪ E‬ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﺴﺒﺔ ﺒﻴﻨﻬﻤﺎ ﻟﻜل ﻨﻅﻴﺭ‬
‫1‬ ‫1‬

‫ﺭﻗﻡ‬ ‫ﺍﻟﺠﺩﻭل‬ ‫1-4‬ ‫2-4‬ ‫3-4‬ ‫4-4‬ ‫5-4‬ ‫6-4‬ ‫7-4‬ ‫8-4‬ ‫9 -4‬ ‫01-4‬ ‫11-4‬ ‫21-4‬

‫ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻭﻗﻴﻡ ﻜل ﻤـﻥ 4‪ K‬ﻭ 5‪ K‬ﻟﻠﺤـﺯﻤﺘﻴﻥ ‪ g‬ﻭ ‪ S‬ﻟﻠﻨﻅـﺎﺌﺭ‬ ‫‪.120-126Xe‬‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪.120Xe‬‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪.122Xe‬‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪.124Xe‬‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪.126Xe‬‬ ‫ﻁﺎﻗﺎﺕ ﺍﻷﻨﺘﻘﺎل ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻅﻴﺭ ‪.120Xe‬‬ ‫ﻁﺎﻗﺎﺕ ﺍﻷﻨﺘﻘﺎل ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻅﻴﺭ ‪.122Xe‬‬ ‫ﻁﺎﻗﺎﺕ ﺍﻷﻨﺘﻘﺎل ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻅﻴﺭ ‪.124Xe‬‬ ‫ﻁﺎﻗﺎﺕ ﺍﻷﻨﺘﻘﺎل ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻅﻴﺭ ‪.126Xe‬‬ ‫ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ ﻋﻤﺭ ﺍﻟﻨﺼﻑ 2/1‪T‬‬ ‫ﻟﻠﻨﻅﻴﺭ ‪. 120Xe‬‬ ‫ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴـﺘﺨﺩﺍﻡ ﻋﻤـﺭ ﺍﻟﻨـﺼﻑ‬ ‫.‬
‫221‬

‫ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫55‬ ‫65‬ ‫65‬ ‫75‬ ‫85‬

‫ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴـﺘﺨﺩﺍﻡ ﻋﻤـﺭ ﺍﻟﻨـﺼﻑ 2/1‪T‬‬ ‫ﻟﻠﻨﻅﻴﺭ ‪. 124Xe‬‬ ‫ﻗﻴﻡ 22 ‪ α‬ﻟﻠﻨﻅﺎﺌﺭ ‪.120-124Xe‬‬ ‫ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ 1-‪ IBM‬ﻟﻠﻨﻅﻴﺭ ‪.120Xe‬‬ ‫ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ 1-‪ IBM‬ﻟﻠﻨﻅﻴﺭ ‪.122Xe‬‬ ‫ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ 1-‪ IBM‬ﻟﻠﻨﻅﻴﺭ ‪.124Xe‬‬

‫31-4‬ ‫41-4‬ ‫51-4‬ ‫61-4‬ ‫71-4‬

‫‪IV‬‬

‫ﻗﺎﺌﻤﺔ ﺍﻻﺸﻜﺎل‬
‫ﺭﻗﻡ‬ ‫ﺍﻟﺼﻔﺤﺔ‬ ‫ﻋﻨﻭﺍﻥ ﺍﻟﺸﻜل‬ ‫ﺭﻗﻡ‬ ‫ﺍﻟﺸﻜل‬

‫ﺍﻟﻔﺼل ﺍﻻﻭل‬
‫8‬ ‫9‬ ‫ﺤﺴﺏ ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ.‬ ‫.‬
‫621‬ ‫621‬

‫ﺘﻭﺯﻴﻊ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫1-1‬ ‫2-1‬

‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬
‫21‬ ‫31‬ ‫71‬ ‫81‬ ‫02‬ ‫12‬ ‫ﻨﻤﻭﺫﺝ ﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻷﻫﺘﺯﺍﺯﻴﺔ .‬ ‫ﺤﺎﻻﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﺤﺯﻤﺔ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﺍﻻﺭﻀﻴﺔ ﻟﻠﻨﻭﻯ ﺍﻟﺯﻭﺠﻴﺔ – ﺍﻟﺯﻭﺠﻴﺔ .‬ ‫ﺍﺸﻜﺎل ﺍﻟﺘﺸﻭﻩ.‬ ‫ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ.‬ ‫ﺘﺭﺍﺼﻑ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ.‬ ‫ﺘﻘﺎﻁﻊ ﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ ﻤﻊ ﺍﻟﺤﺯﻤﺔ ﺍﻟﻤﺜﺎﺭﺓ )‪. (S-band‬‬ ‫1-2‬ ‫2-2‬ ‫3-2‬ ‫4-2‬ ‫5-2‬ ‫6-2‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻟﺙ‬
‫82‬ ‫ﺍﻟﻁﻴﻑ ﺍﻟﻨﻤﻭﺫﺠﻲ ﻟﻠﺘﺤﺩﻴﺩ )5(‪ SU‬ﻟــ )6 = ‪ (N‬ﻤـﻊ ﻗـﻴﻡ )∆‪(ν, n‬‬ ‫ﻭﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻟﻜل ﻤﺴﺘﻭ.‬ ‫ٍ‬ ‫ﺍﻟﻁﻴﻑ ﺍﻟﻨﻤﻭﺫﺠﻲ ﻟﻠﺘﺤﺩﻴﺩ )3(‪ SU‬ﻟــ )6 = ‪ (N‬ﻤـﻊ ﻗـﻴﻡ )‪(λ , µ‬‬ ‫ﻭﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻟﻜل ﻤﺴﺘﻭ‬ ‫ٍ‬ ‫ﺍﻟﻁﻴﻑ ﺍﻟﻨﻤﻭﺫﺠﻲ ﻟﻠﺘﺤﺩﻴﺩ )6(‪ O‬ﻟــ )6 = ‪ (N‬ﻤـﻊ ﻗـﻴﻡ )∆‪(σ , ν‬‬ ‫ﻭﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻟﻜل ﻤﺴﺘﻭ .‬ ‫ٍ‬ ‫73‬ ‫ﻤﺜﻠﺙ ‪ Casten‬ﻴﺒﻴﻥ ﺍﻟﻤﻨﺎﻁﻕ ﺍﻻﻨﺘﻘﺎﻟﻴﺔ ﺒﻴﻥ ﺍﻟﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ.‬ ‫1-3‬

‫03‬

‫2-3‬

‫63‬

‫3-3‬ ‫4-3‬

‫‪V‬‬

‫ﺭﻗﻡ‬ ‫ﺍﻟﺼﻔﺤﺔ‬

‫ﻋﻨﻭﺍﻥ ﺍﻟﺸﻜل‬

‫ﺭﻗﻡ‬ ‫ﺍﻟﺸﻜل‬

‫ﺍﻟﻔﺼل ﺍﻟﺭﺍﺒﻊ‬
‫95‬ ‫06‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﻟﺤﺯﻤﺔ ‪Yrast‬‬ ‫ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻤﺴﺘﻭﻱ ﺍﻟﻁﺎﻗﺔ ) 12(‪ E‬ﻤـﻊ ﻋـﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ ﻟﻠﻨﻅـﺎﺌﺭ‬ ‫‪.120-126Xe‬‬
‫+‬ ‫+‬ ‫ﺘﻐﻴﺭ ﻗﻴﻡ ﻨﺴﺒﺔ ﺍﻟﻁﺎﻗﺔ ) 12(‪ E(41 ) / E‬ﻤﻊ ﻋـﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ ﻭﺍﻟﻘـﻴﻡ‬

‫1-4‬ ‫2-4‬

‫+‬

‫06‬

‫ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻟﻜل ﺘﺤﺩﻴﺩ.‬
‫+‬ ‫+‬ ‫ﺘﻐﻴﺭ ﻗﻴﻡ ﻨﺴﺒﺔ ﺍﻟﻁﺎﻗﺔ ) 12(‪ E(61 ) / E‬ﻤﻊ ﻋـﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ ﻭﺍﻟﻘـﻴﻡ‬

‫3-4‬

‫16‬

‫ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻟﻜل ﺘﺤﺩﻴﺩ.‬
‫+‬ ‫+‬ ‫ﺘﻐﻴﺭ ﻗﻴﻡ ﻨﺴﺒﺔ ﺍﻟﻁﺎﻗﺔ ) 12(‪ E(81 ) / E‬ﻤﻊ ﻋـﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ ﻭﺍﻟﻘـﻴﻡ‬

‫4-4‬

‫16‬ ‫26‬ ‫26‬ ‫36‬ ‫36‬ ‫46‬ ‫56‬ ‫66‬ ‫76‬

‫ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻟﻜل ﺘﺤﺩﻴﺩ.‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻠﻨﻅﻴﺭ ‪.120Xe‬‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻠﻨﻅﻴﺭ ‪.122Xe‬‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻠﻨﻅﻴﺭ ‪.124Xe‬‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻠﻨﻅﻴﺭ ‪.126Xe‬‬ ‫ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻭﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ.‬ ‫ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ.‬ ‫ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻁﺎﻗﺔ ﺍﻻﻨﺘﻘﺎل ‪ Eγ‬ﻭﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ .‬ ‫ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ.‬
‫421-021‬

‫5-4‬ ‫6-4‬ ‫7-4‬ ‫8-4‬ ‫9-4‬ ‫01-4‬ ‫11-4‬ ‫21-4‬ ‫31-4‬ ‫41-4‬

‫86‬

‫ﺘﻐﻴﺭ ﻗﻴﻤﺔ ‪ R‬ﻟﻼﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎل ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻟﻠﻨﻅﺎﺌﺭ ‪Xe‬‬ ‫ﻭﺍﻟﻘﻴﻡ ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻟﻜل ﺘﺤﺩﻴﺩ.‬

‫‪VI‬‬

‫ﺭﻗﻡ‬ ‫ﺍﻟﺼﻔﺤﺔ‬

‫ﻋﻨﻭﺍﻥ ﺍﻟﺸﻜل‬ ‫ﺍﻟﻔﺼل ﺍﻟﺨﺎﻤﺱ‬

‫ﺭﻗﻡ‬ ‫ﺍﻟﺸﻜل‬

‫37‬

‫ﺯﺍﻭﻴ ـﺔ ﺍﻟﺘﻘ ـﺎﻁﻊ ﺒ ـﻴﻥ ﺍﻟﺤﺯﻤ ـﺔ ﺍﻻﺭﻀ ـﻴﺔ ‪ g‬ﻭﺍﻟﺤﺯﻤ ـﺔ ﺍﻟﻤﺜ ـﺎﺭﺓ ‪S‬‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻟﻠﻨﻅﻴﺭ ‪. 120Xe‬‬ ‫ﺯﺍﻭﻴ ـﺔ ﺍﻟﺘﻘ ـﺎﻁﻊ ﺒ ـﻴﻥ ﺍﻟﺤﺯﻤ ـﺔ ﺍﻻﺭﻀ ـﻴﺔ ‪ g‬ﻭﺍﻟﺤﺯﻤ ـﺔ ﺍﻟﻤﺜ ـﺎﺭﺓ ‪S‬‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻟﻠﻨﻅﻴﺭ ‪. 122Xe‬‬ ‫ﺯﺍﻭﻴ ـﺔ ﺍﻟﺘﻘ ـﺎﻁﻊ ﺒ ـﻴﻥ ﺍﻟﺤﺯﻤ ـﺔ ﺍﻻﺭﻀ ـﻴﺔ ‪ g‬ﻭﺍﻟﺤﺯﻤ ـﺔ ﺍﻟﻤﺜ ـﺎﺭﺓ ‪S‬‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻟﻠﻨﻅﻴﺭ ‪. 124Xe‬‬ ‫ﺯﺍﻭﻴ ـﺔ ﺍﻟﺘﻘ ـﺎﻁﻊ ﺒ ـﻴﻥ ﺍﻟﺤﺯﻤ ـﺔ ﺍﻻﺭﻀ ـﻴﺔ ‪ g‬ﻭﺍﻟﺤﺯﻤ ـﺔ ﺍﻟﻤﺜ ـﺎﺭﺓ ‪S‬‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻟﻠﻨﻅﻴﺭ ‪. 126Xe‬‬

‫1-5‬

‫47‬

‫2-5‬

‫47‬

‫3-5‬

‫57‬

‫4-5‬

‫‪VII‬‬

‫ﺍﻟﻔﺼﻞ‬ ‫ﺍﻻﻭﻝ‬

‫ﺍﻟﺪﺭﺍﺳﺎﺕ ﺍﻟﺴﺎﺑﻘﺔ‬

‫1‬

‫‪Introduction‬‬

‫1-1 ﺍﻟﻤﻘﺩﻤﺔ‬

‫ﺘﻌﺩ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﺎﻤﻴﺔ ﻭﺍﺤﺘﻤﺎﻟﻴﺎﺘﻬﺎ ﻓﻀﻼ ﻋﻥ ﻋﺎﻤل ﺍﻟﺘـﺸﻭﻩ ﻭﺍﻟﻌـﺯﻡ‬ ‫ﹰ‬ ‫‪‬‬ ‫ﺍﻟﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﻓﻲ ﺍﻟﻨﻭﺍﺓ ﻤﻥ ﺍﻟﺨﺼﺎﺌﺹ ﺍﻟﻤﻬﻤﺔ ﻟﻠﺘﻌﺭﻑ ﻋﻠﻴﻬﺎ ﻭﺘﺤﺩﻴـﺩﻫﺎ ﻭﺒﻴـﺎﻥ‬ ‫ﻤﻭﺍﻗﻌﻬﺎ ﺒﻴﻥ ﺍﻟﻨﻭﻯ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻓﻀﻼ ﻋﻥ ﺒﻴﺎﻥ ﺨﺼﺎﺌﺹ ﺍﻟﺘﺭﻜﻴﺏ ﺍﻟﺫﻱ ﺘﻨﺘﻤﻲ ﺍﻟﻴـﻪ .ﻜـﺫﻟﻙ ﻴﻌـﺩ‬ ‫‪‬‬ ‫ﹰ‬ ‫ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻤﻥ ﺍﻟﻤﻌﺎﻟﻡ ﺍﻟﻤﻬﻤﺔ ﻓﻲ ﺘﺤﺩﻴﺩ ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻭﺍﺓ ﻟﻤﺎ ﻟﻪ ﻤـﻥ‬ ‫ﺘﺄﺜﻴﺭ ﻋﻠﻰ ﻫﺫﻩ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﻤﻥ ﺨﻼل ﺍﻟﻌﻼﻗﺔ ﺍﻟﺘﻲ ﺘﺭﺒﻁ ﻫﺫﺍ ﺍﻟﻤﻌﻠﻡ ﺒﻁﺎﻗﺔ ﺍﻟﻤﺴﺘﻭﻱ.ﻟﻘﺩ ﻭﻀـﻌﺕ‬ ‫ﺍﻟﻌﺩﻴﺩ ﻤﻥ ﺍﻟﻨﻤﺎﺫﺝ ﺍﻟﻨﻭﻭﻴﺔ ﻭﻓﻲ ﻓﺘﺭﺍﺕ ﺯﻤﻨﻴﺔ ﻤﺨﺘﻠﻔﺔ ﻟﺩﺭﺍﺴﺔ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﺤﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ‬ ‫ﻭﻤﻥ ﺍﻫﻤﻬﺎ ﺍﻷﻨﻤﻭﺫﺝ ﺍﻟﺠﻤﺎﻋﻲ ﺍﻟﺫﻱ ﻴﺼﻨﻑ ﺍﻟﻨﻭﻯ ﻭﻓﻕ ﺤﺭﻜﺘﻬﺎ , ﻓﻘﺩ ﺘﻜﻭﻥ ﺤﺭﻜﺘﻬﺎ ﺍﻫﺘﺯﺍﺯﻴـﺔ‬ ‫ﺍﻭ ﺩﻭﺭﺍﻨﻴﺔ ﻭﻟﻜل ﺤﺭﻜﺔ ﺤﺎﻻﺕ ﻁﺎﻗﺔ ﻤﻤﻴﺯﺓ.ﻭﻗﺩ ﺘﻜﻭﻥ ﺍﻟﻨﻭﺍﺓ ﺫﺍﺕ ﺨﺼﺎﺌﺹ ﺍﻨﺘﻘﺎﻟﻴﺔ ﻭﺍﻗﻌﺔ ﺒـﻴﻥ‬ ‫ﺤﺎﻟﺘﻲ ﺍﻟﺤﺭﻜﺘﻴﻥ ﺍﻟﺴﺎﺒﻘﺘﻴﻥ ﻭﻟﻬﺎ ﺤﺎﻻﺕ ﻁﺎﻗﺔ ﺘﺨﺘﻠﻑ ﻋﻥ ﺍﻟﺤﺎﻟﺘﻴﻥ ﺍﻟـﺴﺎﺒﻘﺘﻴﻥ]7891 , ‪[Krane‬‬ ‫ﻭ ِﻌﺕ ﻨﻤﺎﺫﺝ ﺍﺨﺭﻯ ﻟﻭﺼﻑ ﺤﺎﻻﺕ ﺍﻟﻁﺎﻗـﺔ ﻭﻤﻨﻬـﺎ ﺃﻨﻤـﻭﺫﺝ ﺩﺍﻓﻴـﺩﻭﻑ ﻭﻓﻴﻠﻴﺒـﻭﻑ ‪D-F‬‬ ‫ﻀ‬ ‫]8591 ,‪ [Davydov and Filippov‬ﻭﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ ‪ IBM‬ﻭﺃﻨﻤﻭﺫﺝ ﻋـﺯﻡ‬ ‫ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﺍﻟﻤﺘﻐﻴﺭ )‪ Varaiable Moment of Inertia Model (VMI‬ﻭﻏﻴﺭﻫﺎ ﻭﻟﻜل‬ ‫ﺃﻨﻤــﻭﺫﺝ ﻨﺠﺎﺤﺎﺘــﻪ ﻓــﻲ ﻭﺼــﻑ ﺍﻟﻨــﻭﻯ ﺫﺍﺕ ﺍﻟﺨــﺼﺎﺌﺹ ﺍﻟﻤﻨﺎﺴــﺒﺔ ﻟــﻪ.‬ ‫ﺍﻥ ﺍﻟﺘﻌﺭﻑ ﻋﻠﻰ ﺤﺎﻻﺕ ﺍﻟﻁﺎﻗﺔ ﻭﻤﻭﻗﻌﻬﺎ ﻭﺍﻻﻨﺘﻘﺎﻻﺕ ﺒﻴﻥ ﻫﺫﻩ ﺍﻟﺤﺎﻻﺕ ﻴﻌﻁﻲ ﻭﺼـﻔﺎ ﻤﻤﻴـﺯﺍ‬ ‫ﹰ‬ ‫ﹰ‬

‫ﻭﺤﺯﻤـﺔ ‪γ‬‬

‫ﹰ‬ ‫ﻟﻠﻨﻭﺍﺓ .ﻜﻤﺎ ﺍﻥ ﻟﺤﺎﻻﺕ ﺍﻟﻁﺎﻗﺔ ﺤﺯﻤﺎ ﻤﺨﺘﻠﻔﺔ ﻓﻬﻨﺎﻙ ﺍﻟﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﻭﺤﺯﻤـﺔ ‪β‬‬

‫ﻭﻟﻜل ﺤﺯﻤﺔ ﻤﻭﻗﻊ ﻁﺎﻗﻲ ﻤﻌﻴﻥ ﻴﺨﺘﻠﻑ ﻋﻥ ﺍﻟﺤﺯﻤﺔ ﺍﻷﺨـﺭﻯ ﻭﻗـﺩ ﺘﻜـﻭﻥ ﺍﻟﺤـﺯﻤﺘﻴﻥ ‪ β‬ﻭ ‪γ‬‬
‫ﻤﺘﻘﺎﺭﺒﺘﻴﻥ ﻋﻥ ﺒﻌﻀﻬﻤﺎ ﻭﻤﺘﺒﺎﻋﺩﺘﻴﻥ ﻋﻥ ﺍﻟﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﺒﻨﺴﺏ ﻤﻌﻴﻨﺔ . ﻭﻤﻥ ﺤـﺎﻻﺕ ﺍﻟﻁﺎﻗـﺔ‬ ‫ﺍﻟﻤﻬﻤﺔ ﻓﻲ ﺍﻟﺘﻌﺭﻑ ﻋﻠﻰ ﺨﺼﺎﺌﺹ ﺍﻟﻨـﻭﻯ ﻫـﻲ ﺤـﺎﻻﺕ ﺍﻟﻁﺎﻗـﺔ ﺍﻻﻭﻁـﺄ ﻟﺯﺨـﻭﻡ ﻤﻌﻴﻨـﺔ‬ ‫)‪ (Yrast Levels‬ﺍﻟﺘﻲ ﻗﺩ ﺘﺯﺩﺍﺩ ﻁﺎﻗﺔ ﻜل ﻤﺴﺘﻭ ﻓﻴﻬﺎ ﺒﺯﻴﺎﺩﺓ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻭﺒﻨـﺴﺒﺔ ﻤﻌﻴﻨـﺔ .‬ ‫ٍ‬ ‫ﻭﻟﻭﺤﻅ ﺍﻥ ﺤﺎﻻﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻻﻭﻁﺄ ﻟﺒﻌﺽ ﺍﻟﻨﻭﻯ ﻻﺘﺯﺩﺍﺩ ﺒﻨﺴﺏ ﻤﺘﺴﺎﻭﻴﺔ ﺤﻴﺙ ﻴﺤﺼل ﺯﻴﺎﺩﺓ ﻓـﻲ‬ ‫ﺍﻟﻁﺎﻗﺔ ﺍﻗل ﻤﻥ ﺍﻟﻨـﺴﺒﺔ ﺍﻟﻤﺘﻭﻗﻌـﺔ ﻋﻨـﺩ ﺯﺨـﻡ ﻤﻌـﻴﻥ ﻭﻫـﺫﺍ ﻤﺎﻴـﺴﻤﻰ ﺒﺎﻷﻨﺤﻨـﺎﺀ ﺍﻟﺨﻠﻔـﻲ‬ ‫]1791 , ‪ . [Johnson et al‬ﻟﻘﺩ ﻭﻀﻌﺕ ﺍﻟﻌﺩﻴﺩ ﻤﻥ ﺍﻟﺘﻔﺎﺴﻴﺭ ﻟﻬﺫﺍ ﺍﻻﻨﺤﻨـﺎﺀ ﺍﻫﻤﻬـﺎ ﻤـﺎﻴﺘﻌﻠﻕ‬ ‫ﺒﻌﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ‪ ϑ‬ﺍﻟﺫﻱ ﻴﺘﻐﻴﺭ ﺒﺯﻴﺎﺩﺓ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﺤﻴﺙ ﻟﻭﺤﻅ ﺯﻴﺎﺩﺓ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘـﺼﻭﺭ‬ ‫ﹰ‬ ‫ﺍﻟﺫﺍﺘﻲ ﻋﻨﺩ ﺯﺨﻡ ﺯﺍﻭﻱ ﻤﻌﻴﻥ ﻤﺴﺒﺒﺎ ﻨﻘﺼﺎﻨﺎ ﻓﻲ ﻗﻴﻤﺔ ﻁﺎﻗﺔ ﺫﻟـﻙ ﺍﻟﻤـﺴﺘﻭﻱ ﺤـﺴﺏ ﺍﻷﻨﻤـﻭﺫﺝ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺍﻟﺩﻭﺭﺍﻨﻲ . ﻜﻤﺎ ﻭﻀﻌﺕ ﺍﻟﻌﺩﻴﺩ ﻤﻥ ﺍﻟﺘﻔﺎﺴﻴﺭ ﻟﺘﻭﻀـﻴﺢ ﻫﺫﻩ ﺍﻟﺯﻴﺎﺩﺓ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘﺼـﻭﺭ ﺍﻟﺫﺍﺘـﻲ‬ ‫ﻭﺍﻟﻨﻘﺼﺎﻥ ﺍﻟﺤﺎﺼل ﻓﻲ ﺍﻟﻁـﺎﻗﺔ ﻨﺘﻴﺠﺔ ﻟﺫﻟﻙ , ﻜﻤﺎ ﻴﺯﺩﺍﺩ ﺘﺸﻭﻩ ﺍﻟﻨﻭﺍﺓ ﻋﻨﺩ ﺍﻟﺯﺨﻭﻡ ﺍﻟﺯﺍﻭﻴﺔ ﺍﻟﻌﺎﻟﻴﺔ‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫2‬

‫ﻤﺴﺒﺒﺎ ﺍﺨﺘﻼﻓﺎ ﻓﻲ ﻤﻌﺎﻤل ﺘﺸﻭﻩ ﺘﻠﻙ ﺍﻟﻨﻭﺍﺓ ﻭﺍﺨﺘﻼﻓﺎ ﻓﻲ ﻋﺯﻡ ﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﻟﻬﺎ ﺍﻀﺎﻓﺔ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺍﻟﻰ ﺍﺨﺘﻼﻑ ﻓﻲ ﻗﻴﻡ ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎل ﺒﻴﻥ ﻫﺫﻩ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ.‬ ‫ﺘﺤﺘﻭﻱ ﺍﻟﺭﺴﺎﻟﺔ ﻋﻠﻰ ﺨﻤﺴﺔ ﻓﺼﻭل ﺍﺫ ﻴﺘﻀﻤﻥ ﺍﻟﻔﺼل ﺍﻷﻭل ﻋﻠﻰ ﺍﻟﻤﻘﺩﻤﺔ ﻭﺍﻟﺩﺭﺍﺴـﺎﺕ‬ ‫ﺍﻟﺴﺎﺒﻘﺔ ﻭﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ﻭﺍﻟﻬﺩﻑ ﻤﻥ ﺍﻟﺩﺭﺍﺴﺔ ﻭﻴﺘﻁﺭﻕ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ ﺍﻟـﻰ ﻤـﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗـﺔ‬ ‫ﻭﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ ﻷﺸﻌﺔ ﻜﺎﻤﺎ ﻭﺍﻟﺘﺸﻭﻩ ﻭﺍﻟﻌﺯﻡ ﺍﻟﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒـﺎﺌﻲ‬ ‫ﺍﻟﻨﻭﻭﻱ ﻭﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻭﻴﺘﻡ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻟﺙ ﺍﻟﺘﺤـﺩﺙ ﻋـﻥ ﺃﻨﻤـﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨـﺎﺕ‬ ‫ﺍﻟﻤﺘﻔﺎﻋﻠﺔ ﺍﻟﻤﺴﺘﺨﺩﻡ ﻓﻲ ﺍﻟﺩﺭﺍﺴﺔ ﺍﻟﺤﺎﻟﻴﺔ ﻭﻴﺨﺘﺹ ﺍﻟﻔﺼل ﺍﻟﺭﺍﺒﻊ ﺒﺎﻟﺤﺴﺎﺒﺎﺕ ﻭﺍﻟﻨﺘﺎﺌﺞ ﺍﻤﺎ ﺍﻟﻔـﺼل‬ ‫ﺍﻟﺨﺎﻤﺱ ﻓﻴﺘﻀﻤﻥ ﺍﻟﻤﻨﺎﻗﺸﺔ ﻭﺍﺴﺘﻨﺘﺎﺠﺎﺕ ﻭﻤﻘﺘﺭﺤﺎﺕ ﺍﻟﺩﺭﺍﺴﺔ ﺍﻟﺤﺎﻟﻴﺔ.‬

‫‪Previous Work‬‬

‫2-1 ﺍﻟﺩﺭﺍﺴﺎﺕ ﺍﻟﺴﺎﺒﻘﺔ‬

‫ﺩﺭﺴﺕ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻤﻥ ﻗﺒل ﺍﻟﻌﺩﻴﺩ ﻤﻥ ﺍﻟﺒﺎﺤﺜﻴﻥ ﻨﻅﺭﻴﺎ ﻭﻋﻤﻠﻴـﺎ ﻭﺒﺄﺴـﺘﺨﺩﺍﻡ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻨﻤﺎﺫﺝ ﻨﻭﻭﻴﺔ ﻋﺩﺓ ﻓﻘﺩ ﺃﺴﺘﺨﺩﻡ ]9691,‪ [Mariscotti et al‬ﺃﻨﻤﻭﺫﺝ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﺍﻟﻤﺘﻐﻴﺭ‬ ‫)‪ Varaiable Moment of Inertia Model (VMI‬ﻟﺤﺴﺎﺏ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗـﺔ ﻟﻠﺤﺯﻤـﺔ‬ ‫ﻭﺒﻴﻨﻭﺍ ﺃﻥ ﻫﺫﺍ ﺍﻷﻨﻤﻭﺫﺝ ﻴﻌﻁﻲ ﺘﻭﺍﻓﻘﺎ ﺠﻴـﺩﺍ ﺒـﻴﻥ ﺍﻟﻘـﻴﻡ‬ ‫ﹰ‬ ‫ﹰ‬
‫031-021‬

‫ﺍﻷﺭﻀﻴﺔ ﻟﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ‪Xe‬‬

‫ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻜﻤﺎ ﺩﺭﺴﻭﺍ ﺘﻐﻴﺭ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻤﻊ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﺍﻟﻨﻭﻭﻱ ﺍﻟﻜﻠﻲ‬ ‫ﻟﻠﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﻟﻠﺤﺎﻻﺕ )+6 -+2=‪ (Jπ‬ﻭﺃﺴﺘﻨﺘﺠﻭﺍ ﺍﻥ ﺯﻴﺎﺩﺓ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ) ‪ ( ϑ‬ﻴﺯﺩﺍﺩ‬ ‫( ﺩﺍﻟـﺔ‬
‫‪EJ‬‬ ‫ﺒﺯﻴﺎﺩﺓ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﺍﻟﻨﻭﻭﻱ ﺍﻟﻜﻠﻲ )‪ (J‬ﻟﺤﺎﻟﺔ ﺍﻟﻨﻭﺍﺓ ﻭﺩﺭﺴﻭﺍ ﻜـﺫﻟﻙ ﺍﻟﻨـﺴﺒﺔ )‬ ‫1 2‪E‬‬

‫ﻟـ ) 2‪. ( E‬‬
‫1‬

‫ﺃﻜﺘﺸﻑ ]1791,.‪ [Johnson et al‬ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻭﻷﻭل ﻤﺭﺓ ﻓـﻲ ﻤـﺴﺘﻭﻴﺎﺕ‬ ‫ﻭﻨﺴﺒﻭﺍ ﺴﺒﺏ ﺤﺩﻭﺙ ﻫﺫﻩ ﺍﻟﻅﺎﻫﺭﺓ ﺇﻟﻰ ﺍﻟﺘﺤﻭل ﺍﻟﻁﻭﺭﻱ ﻤﻥ ﺤﺎﻟﺔ ﺍﻟﻤﻴﻭﻋﺔ‬
‫061‬

‫ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪Dy‬‬

‫ﺍﻟﻔﺎﺌﻘﺔ ﺍﻟﻰ ﺤﺎﻟﺔ ﺍﻟﻼﻤﻴﻭﻋﺔ ﻟﻠﻨﻭﺍﺓ .ﻭ ﻗﺎﻡ ]2791,.‪ [Johnson et al‬ﺒﻘﻴﺎﺱ ﻤـﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗـﺔ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﻟﻠﺤﺎﻟــﺔ ﺍﻷﺭﻀــﻴﺔ ﻓــﻲ ﺍﻟﻨــﻭﻯ )‪ (158Dy,160Dy,162Er,162Yb‬ﺍﻟﻨﺎﺘﺠــﺔ ﻋــﻥ‬ ‫ـ‬ ‫ـ‬ ‫ـﺎﻋﻼﺕ) ‪( 158 Gd (α , Xn)158 Dy,160 Gd (α , Xn)160 Dy,161Dy (α , Xn)162 Er ,167 Er (α , Xn)168 Yb‬‬ ‫ﺍﻟﺘﻔـ‬ ‫ﻋﻠﻰ ﺍﻟﺘﻭﺍﻟﻲ, ﺍﺫ ﻻﺤﻅﻭﺍ ﻅﻬﻭﺭ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﻫﺫﻩ ﺍﻟﻨﻭﻯ ﻓﻲ ﺤﻴﻥ ﺍﻥ ﻫﺫﺍ ﺍﻷﻨﺤﻨـﺎﺀ ﻟـﻡ‬ ‫ﻴﻅﻬﺭ ﻓﻲ ﺍﻟﻨﻭﺍﺓ )‪. (168Yb‬ﻭﺍﻋﻁﻭﺍ ﻟﺫﻟﻙ ﺍﻟﺘﻔﺴﻴﺭ ﺍﻟﺴﺎﺒﻕ ﻨﻔﺴﻪ )ﺍﻟﺘﺤﻭل ﺍﻟﻁـﻭﺭﻱ ﻤـﻥ ﺤﺎﻟـﺔ‬ ‫ﺍﻟﻤﻴﻭﻋﺔ ﺍﻟﻔﺎﺌﻘﺔ ﺍﻟﻰ ﺤﺎﻟﺔ ﺍﻟﻼﻤﻴﻭﻋﺔ ﻟﻠﻨﻭﺍﺓ(.‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫3‬

‫)‪ [122Sn (40Ar,4n‬ﻟﺩﺭﺍﺴﺔ ﻤـﺴﺘﻭﻴﺎﺕ‬

‫851‬

‫ﻭﺃﺴﺘﺨﺩﻡ ]7791,‪ [Lee et al‬ﺍﻟﺘﻔﺎﻋل ]‪Er‬‬
‫851‬

‫ﻭﻻﺤﻅﻭﺍ ﺤﺩﻭﺙ ﺍﻨﺤﻨﺎﺀ ﺨﻠﻔﻲ ﺜﺎﻥ ﻓﻀﻼ ﻋﻥ ﺍﻷﻭل ﻭﻴﻌﻭﺩ ﺴﺒﺏ ﺍﻷﻨﺤﻨـﺎﺀ‬ ‫ﹰ‬ ‫ٍ‬

‫ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻭﺍﺓ ‪Er‬‬

‫ﺍﻷﻭل ﺍﻟﻰ ﺍﻷﺼﻁﻔﺎﻑ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻟﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘﺸﺭﺓ 2/31‪, i‬ﺃﻤـﺎ ﺴـﺒﺏ ﺍﻷﻨﺤﻨـﺎﺀ‬ ‫ﺍﻟﺨﻠﻔﻲ ﺍﻟﺜﺎﻨﻲ ﻓﻌﺯﻭﻩ ﺍﻟﻰ ﺍﻷﺼﻁﻔﺎﻑ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻟﺯﻭﺝ ﻤﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘﺸﺭﺓ 2/11‪. h‬‬ ‫ﻭﻨﺴﺏ ]9791,‪ [Bengtsson and Frauendorf‬ﺴﺒﺏ ﺤﺩﻭﺙ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔـﻲ ﻋﻨـﺩ‬ ‫ﺤﺴﺎﺒﻬﻤﺎ ﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻭﻯ )07 ≤ ‪ (68 ≤ Z‬ﻭ )99 ≤ ‪ (89 ≤ N‬ﺇﻟﻰ ﻗﻭﺓ ﻜﻭﺭﻴـﻭﻟﺱ‬ ‫ﺍﻟﺘﻲ ﺘﻌﻤل ﻋﻠﻰ ﻓﻙ ﺍﻟﺘﺭﺍﺒﻁ ﺒﻴﻥ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻜﻠﻴﻭﻨﺎﺕ ﺃﻭ ﺃﻜﺜﺭ ﻭﺍﻟﺫﻱ ﻴﺅﺩﻱ ﺒﺩﻭﺭﻩ ﺍﻟﻰ ﻅﻬـﻭﺭ‬ ‫ﺤﺯﻤﺔ ﺸﺒﻴﻬﻲ ﺍﻟﺠﺴﻴﻤﻴﻥ )‪ Two- Qusiparticles (2qp‬ﺃﻭ ﺤﺯﻤﺔ ﺃﺸﺒﺎﻩ ﺃﻟﺠـﺴﻴﻤﺎﺕ ﺃﻷﺭﺒﻌـﺔ‬ ‫)‪.Four -Qusiparticles (4qp‬ﻭﺃﺴﺘﺨﺩﻡ ]9791,‪ [Lin and Chern‬ﺃﻨﻤﻭﺫﺝ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ‬ ‫ﻭﻨﺴﺒﺎ ﺴـﺒﺏ ﺤـﺩﻭﺙ ﻫـﺫﻩ‬ ‫ﻭﺒﻴﻨـﺎ‬
‫661‬

‫ﺍﻟﺫﺍﺘﻲ ﺍﻟﻤﺘﻐﻴﺭ )‪ (VMI‬ﻓﻲ ﺘﺤﺩﻴﺩ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻟﻠﻨﻅﻴﺭ ‪Yb‬‬

‫ﺍﻟﻅﺎﻫﺭﺓ ﺍﻟﻰ ﺘﻘﺎﻁﻊ ﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ ﻭﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻟﻤﺘﻬﻴﺠﺔ ‪(S-.band) 2qp‬‬

‫ﻜﺫﻟﻙ ﺍﻥ ﻫﺫﻩ ﺍﻟﻅﺎﻫﺭﺓ ﺘﺤﺩﺙ ﻋﻨﺩﻤﺎ ﻻﺘﺘﻐﻴﺭ ﺍﻟﺩﻭﺍل ﺍﻟﻤﻭﺠﻴﺔ ﺒﺸﻜل ﻤﺴﺘﻤﺭ ﻤﻊ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ .‬ ‫ﻜﻤﺎ ﺃﺴﺘﺨﺩﻡ ]0991 , ‪ [Hwang and Chung‬ﺃﻨﻤﻭﺫﺝ ﺴﻴﺯﺭ )‪ (Scissor model‬ﻓﻲ‬ ‫ﺍﺫ ﺃﻓﺘﺭﻀﺎ ﺍﻥ ﺍﻟﺘﺸﻭﻩ ﺍﻟﻨﺎﺘﺞ ﻋﻥ ﺍﻟﺒﺭﻭﺘـﻭﻥ ﻴـﺴﺎﻭﻱ‬
‫871‬

‫ﺘﺤﺩﻴﺩ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﺍﻟﻨﻅﻴﺭ ‪Os‬‬

‫ﺍﻟﺘﺸﻭﻩ ﺍﻟﻨﺎﺘﺞ ﻋﻥ ﺍﻟﻨﻴﺘﺭﻭﻥ ‪ β p = β n = β‬ﻭﻋﺯﻴﺎ ﺴﺒﺏ ﺤﺩﻭﺙ ﻫﺫﻩ ﺍﻟﻅﺎﻫﺭﺓ ﺍﻟـﻰ ﺘﺭﺍﺼـﻑ‬ ‫ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻟﺸﺒﻴﻬﻲ ﺍﻟﺠﺴﻴﻤﻴﻥ ﺍﻟﻨﺎﺘﺞ ﻤﻥ ﺘﺄﺜﻴﺭ ﻗﻭﺓ ﻜﻭﺭﻴﻭﻟﺱ.‬ ‫ﻭ ﺩﺭﺱ ]1991 , ‪ [Hara and Sun‬ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﻋﺩﺩ ﻤﻥ ﻨﻅﺎﺌﺭ ﺍﻟﻨﻭﻯ‬ ‫)‪ (Er , Yb , Hf‬ﻭﻓﺴﺭﺍ ﺴﺒﺏ ﺤﺩﻭﺙ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺒﺘﻘﺎﻁﻊ ﺍﻟﺤﺯﻡ ﻭﺍﻥ ﺸﻜل ﺍﻷﻨﺤﻨﺎﺀ ﻴﻌﺘﻤﺩ‬ ‫ﻋﻠﻰ ﺯﺍﻭﻴﺔ ﺍﻟﺘﻘﺎﻁﻊ ﺒﻴﻥ ﺍﻟﺤﺯﻤﺘﻴﻥ ﻓﻌﻨﺩﻤﺎ ﺘﻜﻭﻥ ﺯﺍﻭﻴﺔ ﺍﻟﺘﻘﺎﻁﻊ ﻜﺒﻴـﺭﺓ ﻴﻜـﻭﻥ ﺍﻷﻨﺤﻨـﺎﺀ ﺤـﺎﺩﺍ‬ ‫ﹰ‬ ‫ﻭﻜﺒﻴﺭﺍ, ﺍﻤﺎ ﺍﺫﺍ ﻜﺎﻨﺕ ﺯﺍﻭﻴﺔ ﺍﻟﺘﻘﺎﻁﻊ ﺼﻐﻴﺭﺓ ﺒﻴﻥ ﺍﻟﺤﺯﻤﺘﻴﻥ ﻓﺄﻥ ﺍﻷﻨﺤﻨﺎﺀ ﻴﻜﻭﻥ ﺼﻐﻴﺭﺍ .‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻭﺃﺴﺘﺨﺩﻡ ]4991,‪ [Chen‬ﺃﻨﻤﻭﺫﺝ ﺍﻟﻤﺯﺩﻭﺝ ﺍﻟﺒﺭﻭﺘﻭﻨﻲ ﺍﻟﻔﻴﺭﻤﻴﻭﻨﻲ ﻓﻲ ﺘﺤﺩﻴـﺩ ﺍﻷﻨﺤﻨـﺎﺀ‬ ‫ﺍﻟﺨﻠﻔﻲ ﻟﻌﺩﺩ ﻤﻥ ﻨﻅﺎﺌﺭ ﺍﻟﺘﻨﻜﺴﺘﻥ ‪ W‬ﻭﻗﺩ ﻜﺎﻥ ﺍﻟﺘﻁﺎﺒﻕ ﺠﻴﺩﺍ ﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻘـﻴﻡ ﺍﻟﻤﺤـﺴﻭﺒﺔ‬ ‫ﹰ‬ ‫ﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﻤﻭﻗﻊ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ,ﻭﻋﻠﻰ ﻭﻓـﻕ ﺃﺤﺘﻤﺎﻟﻴـﺔ ﺍﻷﻨﺘﻘـﺎل ﺭﺒﺎﻋﻴـﺔ ﺍﻟﻘﻁـﺏ‬ ‫ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﻤﺨﺘﺯﻟﺔ )2‪ B(E‬ﻭﻋﻼﻗﺘﻬﺎ ﺒﺎﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ‪. J‬‬ ‫ـﺫﻟﻙ ــﺎﻡ ]5991 , ‪ [Ahmed‬ﺒـﺎﺴـ ــﺩﺍﻡ ــﻤﻭﺫﺝ ﺩﺍﻓـ ــﺩﻭﻑ‬ ‫ﻴـ‬ ‫ﺃﻨـ‬ ‫ﺘﺨـ‬ ‫ﻗـ‬ ‫ﻜـ‬ ‫ﻭﻓـﻴﻠـﻴﺒﻭﻑ‪ Davydov-Fillippov‬ﻓﻲ ﺘﺤﺩﻴﺩ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺤﺎﻟﺔ ﺍﻟﺘﻬﻴﺞ ﺍﻷﻭﻟﻰ )12(*‪ E‬ﻭﻋﺩﺩ‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫4‬

‫ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ‪ N‬ﻭ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺤﺎﻟﺔ ﺍﻟﺘﻬﻴﺞ ﺍﻟﺜﺎﻨﻴﺔ )22(*‪ E‬ﺍﻟﻰ ﺤﺎﻟﺔ ﺍﻟﺘﻬﻴﺞ ﺍﻻﻭﻟﻰ )12(*‪ E‬ﺒﻌـﺩﺩ‬ ‫ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ,ﻭﺤﺴﺏ ﺃﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎل ﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﻤﺨﺘﺯﻟﺔ )2‪ b(E‬ﻭﺍﻟﻨﺴﺏ ﺒﻴﻨﻬﺎ‬ ‫‪‬‬ ‫ﻭﺤﺴﺏ ﺃﻴﻀﺎ ﻤﻌﻠﻡ ﺍﻟﻼﺘﻨﺎﻅﺭ ‪ γ‬ﻟﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ‪.114Xe,116Xe,120Xe‬‬ ‫ﹰ‬ ‫‪‬‬ ‫ﻭﻗﺩ ﺍﻜﺩ ]8991 , ‪ [Sun and Hara‬ﻋﻨﺩ ﺩﺭﺍﺴﺔ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓـﻲ ﺍﻟﻨﻅﻴـﺭ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ ﺍﻟﻤﺴﻘﻁﻲ )‪ (Project Shell Model‬ﺍﻥ ﺴﺒﺏ ﺤـﺩﻭﺙ ﻫـﺫﻩ‬
‫461‬

‫‪Er‬‬

‫ﺍﻟﻅﺎﻫﺭﺓ ﻴﻌﻭﺩ ﺍﻟﻰ ﺍﻷﺼﻁﻔﺎﻑ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻟﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘـﺸﺭﺓ 2/31‪. i‬ﻭﺃﺴـﺘﺨﺩﻡ‬ ‫]9991,‪ [Hara et al‬ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ ﺍﻟﻤﺴﻘﻁﻲ ﻟﺘﺤﺩﻴﺩ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻟﻠﻨﻅﻴﺭ ‪ 48Cr‬ﻋـﺎﺯﻴﻥ‬ ‫ﺴﺒﺏ ﻫﺫﻩ ﺍﻟﻅﺎﻫﺭﺓ ﺍﻟﻰ ﺍﻟﺘﻘﺎﻁﻊ ﺒﻴﻥ ﺍﻟﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﻭﺍﻟﺤﺯﻤﺔ ﺍﻟﻤﺜﺎﺭﺓ ﺍﻟﻨﺎﺘﺠﺔ ﻋﻥ ﻓﻙ ﺍﻷﺭﺘﺒﺎﻁ‬ ‫ﺒﻴﻥ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘﺸﺭﺓ ﺍﻟﺨﺎﺭﺠﻴﺔ ﻟﻠﻨﻭﺍﺓ.ﺒﻴﻨﻤﺎ ﻓـﺴﺭ ]9991,‪[Velazquez et al‬‬ ‫ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻋﻨﺩ ﺩﺭﺍﺴﺘﻬﻡ ﻨﻅﺎﺌﺭ ﺍﻟـ‪ Dy‬ﺒﺄﺴﺘﺨﺩﺍﻡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ ﺍﻟﻤـﺴﻘﻁﻲ ﺃﻟـﻰ‬ ‫ﺘﻘﺎﻁﻊ ﺍﻟﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﻤﻊ ﺍﻟﺤﺯﻤﺔ ﺍﻟﻤﺜﺎﺭﺓ )‪ (S-band‬ﺍﻟﻨﺎﺘﺠﺔ ﻤﻥ ﺍﻷﺼﻁﻔﺎﻑ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻟﺯﻭﺝ‬ ‫ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘﺸﺭﺓ ﺍﻟﺨﺎﺭﺠﻴﺔ ﻟﻠﻨﻭﺍﺓ 2/31‪. i‬‬ ‫ﻭﺃﺴــﺘﺨﺩﻡ]9991,‪ [Ahmed and Karim‬ﺃﻨــﻤﻭﺫﺝ ﺩﺍﻓــﻴﺩﻭﻑ ﻓﻴـﻠﻴـﺒــﻭﻑ‬ ‫‪ Davydov-Fillippov‬ﻓﻲ ﺤﺴﺎﺏ ﺃﺤﺘﻤﺎﻟﻴﺎﺕ ﺍﻷﻨﺘﻘﺎﻻﺕ ﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﻤﺨﺘﺯﻟﺔ‬

‫) 22 → 13, 2‪b(E2 ,21 → 01 ),b(E2 ,22 → 01 ),b(E2 ,22 → 21 ),b(E2 ,31 → 21 ),b(E‬‬
‫) 12 → 13, 2‪b( E2 ,2 2 → 21 ) b( E2 ,2 2 → 01` ) b( E2 ,2 2 → 21 ) b( E‬‬ ‫;‬ ‫;‬ ‫;‬ ‫ﻭﺍﻟﻨﺴﺏ ﺒﻴﻥ ﻫﺫﻩ ﺍﻷﻨﺘﻘﺎﻻﺕ‬ ‫) 2 2 → 13, 2‪b( E2 ,21 → 01 ) b( E2 ,21 → 01 ) b( E2 ,2 2 → 01 ) b( E‬‬

‫ﻭﺤﺴﺒﺎ ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻤﺨﺘﺯﻟﺔ )2‪ B(E‬ﺒﻭﺤﺩﺍﺕ 2‪ e2b‬ﻭﻋـﺯﻡ‬ ‫ﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﺫﺍﺘﻲ ‪ Qo‬ﻟﻠﻨﻅﻴﺭﻴﻥ ‪ .118Xe,120Xe‬ﻭﺍﺴﺘﺨﺩﻡ ﺍﻟﺒﺎﺤﺜـﺎﻥ ﻨﻔـﺴﻴﻬﻤﺎ‬ ‫ﻭﺍﻟﻨﺴﺒﺔ ﺒـﻴﻥ‬
‫]0002 , ‪ [Karim and Ahmed‬ﺍﻷﻨﻤﻭﺫﺝ ﻨﻔﺴﻪ ﺒﺤﺴﺎﺏ ﻤﻌﻠﻡ ﺍﻟﻼﺘﻨﺎﻅﺭ ‪γ‬‬
‫22 ‪E‬‬ ‫12 ‪E‬‬ ‫ﻤﺴﺘﻭﻴﻲ ﺍﻟﺘﻬﻴﺞ ﺍﻟﺜﺎﻨﻲ 22 ‪ E‬ﺇﻟﻰ 12 ‪E‬‬

‫= ‪ R‬ﻟﻠﻨﻅﺎﺌﺭ ‪ ,114-124Xe‬ﻭﺤـﺴﺒﺎ ﻜـﺫﻟﻙ ﻤﻌﺎﻤـل‬
‫-811‬

‫ﻟﻠﻨﻅﻴـﺭﻴﻥ‬

‫2‪β‬‬ ‫‪β 2 sp‬‬

‫ﻭﺍﻟﺘﺸﻭﻩ ﺍﻟﺠﺴﻴﻤﻲ ﺍﻟﻔﺭﺩﻱ ‪ β 2 sp‬ﻜﻤـﺎ ﺤـﺴﺒﺎ ﺍﻟﻨـﺴﺒﺔ‬

‫ﺍﻟﺘﺸﻭﻩ 2 ‪β‬‬

‫‪.120Xe‬‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫5‬

‫ﻭﻗﺎﺱ ]2002,‪ [Jungelus et al‬ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻓﻲ ﺍﻟﻨﻅﻴﺭﻴﻥ )‪ (160Dy&162Dy‬ﻋﻥ‬ ‫ـﺭ ﺍﻟﻜﺎﻤـ ـل ‪Incomplet fusion rection‬‬ ‫ـ‬ ‫ـل ﺍﻷﻨـ ـﺩﻤﺎﺠﻲ ﻏﻴــ‬ ‫ـ‬ ‫ﻁﺭﻴـ ـﻕ ﺍﻟﺘﻔﺎﻋــ‬ ‫ـ‬
‫061, 851‬ ‫) ‪Gd ( 7 Li, ( p, d , t ) Xn)160,162 Dy‬‬ ‫( , ﺍﺫ ﻗﺎﻤﻭﺍ ﺒﺄﺴﻘﺎﻁ ﺤﺯﻤﺔ ﻤﻥ ﺠـﺴﻴﻤﺎﺕ ‪ Li‬ﺒﻁﺎﻗـﺔ‬

‫)‪ (8MeV/nucleon‬ﻋﻠﻰ ﺍﻟﻨﻅﻴﺭﻴﻥ ‪,158,160Gd‬ﻭﺤﺩﺩﻭﺍ ﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ ﻭﺤﺯﻤﺘﻲ ﺒﻴﺘـﺎ‬ ‫ﻭﻜﺎﻤﺎ ﻭﺩﺭﺴﻭﺍ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﻫﺫﻴﻥ ﺍﻟﻨﻅﻴﺭﻴﻥ ﻭﻓﺴﺭﻭﺍ ﺴﺒﺏ ﺤﺩﻭﺙ ﻫﺫﻩ ﺍﻟﻅـﺎﻫﺭﺓ‬ ‫ﺒﺘﻘﺎﻁﻊ ﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ ﻤﻊ ﺤﺯﻤﺔ ﻤﺜﺎﺭﺓ ﻋﻠﻴﺎ )‪ (S-band‬ﺍﻟﻨﺎﺘﺠـﺔ ﻋـﻥ ﺍﻷﺼـﻁﻔﺎﻑ‬ ‫ﺍﻟﺩﻭﺭﺍﻨﻲ ﻟﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘﺸﺭﺓ 2/31‪.i‬‬ ‫ﻭﺃﺴﺘﺨﺩﻡ ]2002, ‪ [Higashiyama et al‬ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ ﺍﻟﻤﺴﻘﻁﻲ ﻟﺩﺭﺍﺴـﺔ ﻅـﺎﻫﺭﺓ‬ ‫ﻭﻨﺴﺒﻭﺍ ﺴﺒﺏ ﺤﺩﻭﺙ ﻫﺫﻩ ﺍﻟﻅﺎﻫﺭﺓ ﺍﻟـﻰ ﺘﻘـﺎﻁﻊ‬
‫631-031‬

‫ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ‪Xe‬‬

‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺩﺍﺭﺍﺕ ﻋﺎﻟﻴﺔ ﺍﻟﺯﺨﻡ ﻏﻴـﺭ ﺍﻟﻤﺸﻐﻭﻟﺔ ﻭﺍﻟﻤﺩﺍﺭﺍﺕ ﺍﻟﻤﺸﻐﻭﻟﺔ ﻤﻤـﺎ ﻴـﺴﺒﺏ‬ ‫ﺯﻴﺎﺩﺓ ﻤﻔـﺎﺠﺌﺔ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘﺼـﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻋﻠﻰ ﻁـﻭل ﺤﺎﻻﺕ ﺤﺯﻤــﺔ ﺍﻟﻁﺎﻗـﺎﺕ ﺍﻷﺩﻨــﻰ‬ ‫‪.Yrast Levels‬‬ ‫ﻭﻗﺎﻡ ]4002,‪ [Bucurescu et al‬ﺒﺘﺤﺩﻴﺩ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻋﻤﻠﻴﺎ ﻟﻠﻨﻅﻴﺭ ‪ 90Ru‬ﻭﻋﻥ‬ ‫ﹰ‬ ‫ﻁﺭﻴﻕ ﺍﻟﺘﻔﺎﻋل ‪ 40Ca + 58Ni‬ﻭﻗﺎﺭﻨﻭﺍ ﺍﻟﻨﺘﺎﺌﺞ ﺍﻟﻤﺴﺘﺤﺼﻠﺔ ﻤﻊ ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ ﺍﻟﻤﺴﻘﻁﻲ ﻭﻋﺯﻭﺍ‬ ‫ﺴﺒﺏ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻷﻭل ﻟﻌﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﺍﻟﻰ ﺘﻘﺎﻁﻊ ﺤﺯﻤﺔ ﺸﺒﻴﻬﻲ ﺍﻟﺠﺴﻴﻤﻴﻥ‪ 2-qp‬ﺍﻟﻨﺎﺘﺠﺔ ﻤﻥ‬ ‫ﺍﺼﻁﻔﺎﻑ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘﺸﺭﺓ 2/9‪ g‬ﻤﻊ ﺍﻟﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﻭﻴﺤـﺩﺙ ﺒـﻴﻥ ﺍﻟﺯﺨـﻭﻡ‬ ‫ﺍﻟﺯﺍﻭﻴﺔ 6,4=‪ J‬ﻭﻫﺫﺍ ﻴﻁﺎﺒﻕ ﺘﺭﺍﺼﻑ ﺍﻟﻨﻴﺘﺭﻭﻨﻴﻥ ﻓﻲ ﺍﻟﻘﺸﺭﺓ 2/9‪, g‬ﻜﻤﺎ ﺃﺸﺎﺭﻭﺍ ﺍﻟﻰ ﺃﻥ ﺍﻷﻨﺤﻨﺎﺀ‬ ‫ﺍﻟﺜﺎﻨﻲ ﻋﻨﺩ ﺍﻟﻘﻴﻡ 21=‪ J=10 & J‬ﻴﻌﻭﺩ ﺍﻟﻰ ﻭﺠﻭﺩ ﺘﻘﺎﻁﻊ ﺒﻴﻥ ﺤﺯﻤﺔ ﺸﺒﻴﻬﻲ ﺍﻟﺠـﺴﻴﻤﻴﻥ ‪2-qp‬‬ ‫ﻤﻊ ﺤﺯﻤﺔ ﺍﺨﺭﻯ ﺘﺘﻜﻭﻥ ﻤﻥ ﺘﺭﺍﺼﻑ ﺯﻭﺝ ﻤﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻓﻀﻼ ﻋﻥ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ‬ ‫ﹰ‬ ‫ﺍﻟﻘﺸﺭﺓ 2/9‪.g‬ﻭﻗﺩ ﺃﺴﺘﺨﺩﻡ ]4002, ‪ [Sun‬ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ ﺍﻟﻤﺴﻘﻁﻲ ﻓﻲ ﺘﺤﺩﻴﺩ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔـﻲ‬ ‫ﻟﻠﻨﻅﺎﺌﺭ )‪ (80-82Zr,84-86Mo,88-90Ru72-74&78Kr,76-78Sr‬ﻭﻻﺤﻅ ﻋﺩﻡ ﻅﻬﻭﺭ ﺍﻷﻨﺤﻨـﺎﺀ ﻓـﻲ‬ ‫ﻭﻅﻬﻭﺭﻩ ﻤﺭﺘﻴﻥ ﻓﻲ ﺍﻟﻨﻅﺎﺌﺭ ﺍﻷﺨﺭﻯ ﻭﻓﺴﺭ ﺴﺒﺏ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻷﻭل ﻋﻠـﻰ ﺍﻨـﻪ‬
‫87-67‬

‫ﺍﻟﻨﻅﻴﺭﻴﻥ ‪Sr‬‬

‫ﻨﺘﻴﺠﺔ ﻟﺘﻘﺎﻁﻊ ﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ‪ 0-qp‬ﻤﻊ ﺍﻟﺤﺯﻤﺔ ‪ 2-qp‬ﺍﻟﻨﺎﺘﺠﺔ ﺒﺴﺒﺏ ﺘﺭﺍﺼﻑ ﻨﻴﺘـﺭﻭﻨﻴﻥ‬ ‫2/9‪ g‬ﺃﻤﺎ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺜﺎﻨﻲ ﻓﻴﻅﻬﺭ ﺒﺴﺒﺏ ﺘﻘﺎﻁﻊ ﺍﻟﺤﺯﻤﺔ ﺍﻟﻤﺘﻜﻭﻨﺔ ﻤﻥ ﺯﻭﺝ ﻤﻥ ﺍﻟﺒﺭﻭﺘﻭﻨـﺎﺕ‬ ‫ﻋﻨﺩ‬ ‫ﻓﻀﻼ ﻋﻥ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ‪ 4-qp‬ﻤﻊ ﺤﺯﻤﺔ ‪.2qp‬‬ ‫ﹰ‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫6‬

‫ﻭﻗﺎﻡ ]ﻋﺒﺩﺍﻟﺭﺤﻤﻥ , 4002[ ﺒﺘﻁﻭﻴﺭ ﻤﻌﺎﺩﻟﺔ ﻟﺩﺭﺍﺴﺔ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﺎﺀ ﺍﻟﺨﻠﻔـﻲ ﻟﻌـﺩﺩ ﻤـﻥ‬ ‫≤ 3 ﻭﻫﻲ ﺘﺘﺒﻊ‬
‫14 ‪E‬‬ ‫12 ‪E‬‬ ‫ﺍﻟﻨﻭﻯ ﻭﻗﺩ ﺍﺘﻀﺢ ﺍﻥ ﺍﻟﻨﻭﻯ ﺍﻟﺘﻲ ﻗﺎﻡ ﺒﺩﺭﺍﺴﺘﻬﺎ ﻫﻲ ﻨﻭﻯ ﺩﻭﺭﺍﻨﻴﺔ ﻭﺍﻥ 3.3 ≤‬

‫ﺍﻟﺘﺤﺩﻴﺩ )3(‪ SU‬ﻭﻗﺩ ﺍﻅﻬﺭﺕ ﺍﻟﺩﺭﺍﺴﺔ ﺘﻭﺍﻓﻘﺎ ﺠﻴﺩﺍ ﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻤﺤـﺴﻭﺒﺔ ﺒﺎﺴـﺘﺨﺩﺍﻡ‬ ‫ﹰ ﹰ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ ﺍﻟﻤﻁﻭﺭﺓ.‬ ‫ﻭﺩﺭﺱ ]4002,‪ [Kvasil and Nazmitdinov‬ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﺍﻟﻨﻅﻴـﺭ‬ ‫‪162Yb‬ﻭﻗﺩ ﺒﻴﻨﺎ ﻤﻥ ﺨﻼل ﺩﺭﺍﺴﺘﻬﻤﺎ ﻟﻬﺫﺍ ﺍﻟﻨﻅﻴﺭ ﺃﻥ ﺴﺒﺏ ﻫﺫﻩ ﺍﻟﻅﺎﻫﺭﺓ ﻨﺎﺘﺞ ﻋﻥ ﻤﺤﺼﻠﺔ ﺃﻨﻔﻜﺎﻙ‬ ‫ﺒﺭﻭﺘﻭﻨﻴﻥ ﻭﺘﻜﻭﻴﻥ ﺤﺯﻤﺔ ﺸﺒﻴﻬﻲ ﺍﻟﺠﺴﻴﻤﻴﻥ )‪ (2qp‬ﻭﻭﺠﺩﺍ ﻜﺫﻟﻙ ﺍﻥ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ‬ ‫‪‬‬ ‫ﺘﻨﺘﺞ ﻋﻥ ﺍﻫﺘﺯﺍﺯ ‪ γ‬ﻏﻴﺭ ﺍﻟﻤﺴﺘﻘﺭﺓ.‬
‫651‬

‫ﺍﻟﻨﻅﻴﺭ ‪Dy‬‬

‫ﻭﻗﺎﻡ ]5002,‪ [Alharbi et al‬ﺒﺎﺴﺘﺨﺩﺍﻡ ﻨﻤﺎﺫﺝ ﻋﺩﺓ ,ﻤﻨﻬﺎ ﺍﻷﻨﻤﻭﺫﺝ ﺍﻷﺴﻲ ﺍﻟﻤﻁﻭﺭ ﻓـﻲ‬ ‫ﺩﺭﺍﺴﺔ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﺍﻟﻨﻅﺎﺌﺭ )‪ (224-234Th ,230-238U ,236-244Pu‬ﻭﻻﺤﻅﻭﺍ ﻅﻬﻭﺭ‬ ‫ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﺒﻌﺽ ﺍﻟﻨﻅﺎﺌﺭ ﻭﻋﺩﻡ ﻅﻬﻭﺭﻩ ﻓﻲ ﻨﻅﺎﺌﺭ ﺍﺨﺭﻯ ﻭﻋﺯﻭﺍ ﻋﺩﻡ ﻅﻬﻭﺭ ﺍﻷﻨﺤﻨﺎﺀ‬ ‫ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﻨﻅﺎﺌﺭ ﻤﻌﻴﻨﺔ ﺍﻟﻰ ﺜﺒﻭﺕ ﻤﻌﺎﻤل ﺍﻟﺘﺸﻭﻩ 2 ‪ β‬ﻓﻴﻬﺎ , ﺍﻤﺎ ﺴﺒﺏ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓـﻲ‬ ‫ﺍﻟﻨﻅﺎﺌﺭ ﺍﻷﺨﺭﻯ ﻓﻴﻌﻭﺩ ﺍﻟﻰ ﺘﺭﺍﺼﻑ ﺯﻭﺝ ﻤﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﺨﺎﺭﺝ ﺍﻟﻘﺸﺭﺓ 2/31‪ i‬ﻭﻜـﺫﻟﻙ ﺒـﺴﺒﺏ‬ ‫ﺘﺄﺜﻴﺭ ﻗﻭﺓ ﻜﻭﺭﻴﻭﻟﺱ .ﻭﺩﺭﺱ ]5002,‪ [Rani et al‬ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺒﺄﺴﺘﺨﺩﺍﻡ ﺍﻨﻤﻭﺫﺝ ﺍﻟﻘـﺸﺭﺓ‬ ‫ﻭﻻﺤﻅﻭﺍ ﺍﻥ ﺍﻻﻨﺤﻨﺎﺀ ﻴﺤﺩﺙ ﻋﻨﺩ ﺯﺨﻡ 41 .‬
‫421‬

‫ﺍﻟﻤﺴﻘﻁﻲ ﻓﻲ ‪Ce‬‬

‫ﻭﻗﺩ ﻗﺎﻤﺕ ]6002 , ‪ [Sirag‬ﺒﻭﺼﻑ ﺍﻟﺤﺯﻡ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﻭﺩﺭﺍﺴﺔ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻟـﺒﻌﺽ‬ ‫ﺍﻟﻨﻭﻯ ﺍﻟﻤﺸﻭﻫﺔ ﺍﻟﺯﻭﺠﻴﺔ – ﺍﻟﺯﻭﺠﻴﺔ ﻓﻲ ﻤﻨﻁﻘﺔ ﺍﻟﻌﻨﺎﺼﺭ ﺍﻷﺭﻀﻴﺔ ﺍﻟﻨﺎﺩﺭﺓ ﺒﺄﺴـﺘﺨﺩﺍﻡ ﺍﻟـﺼﻴﻐﺔ‬ ‫ﺍﻟﻤﺘﻌﺩﺩﺓ ﺍﻟﺒﺎﺭﺍﻤﺘﺭﺍﺕ ﻟﻌﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﺍﻟﺤﺭﻜﻲ .‬ ‫ﻭﺍﺴﺘﺨﺩﻡ ]6002,‪ [El-Kameesy et al‬ﺍﻷﻨﻤﻭﺫﺝ ﺍﻷﺴﻲ ﻓﻲ ﺘﺤﺩﻴﺩ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ‬ ‫ﺍﻟﻨﻭﻯ ﺍﻟﺨﻔﻴﻔﺔ ﺫﺍﺕ ﺍﻟﻌﺩﺩ ﺍﻟﻜﺘﻠﻲ 06~‪ A‬ﻭﻻﺤﻅﻭﺍ ﻅﻬﻭﺭ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺒﺼﻭﺭﺓ ﺠﻴﺩﺓ ﻓﻲ ﻫﺫﻩ‬ ‫ﺍﻟﻨﻭﻯ ﻋﻨﺩ ﺍﻟﺯﺨﻭﻡ ﺍﻟﺯﺍﻭﻴﺔ ‪ Jπ=(8+-12+) ħ‬ﻭﻗﺩ ﺃﺴﺘﻨﺘﺠﻭﺍ ﺍﻥ ﺯﻴﺎﺩﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔـﻲ ﺘﻜـﻭﻥ‬ ‫ﺒﺯﻴﺎﺩﺓ ﺍﻟﻌﺩﺩ ﺍﻟﻜﺘﻠﻲ ‪. A‬‬ ‫ﻭﺍﺴﺘﺨﺩﻡ ]7002 , ‪ [Bucurescu‬ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﻩ ﺍﻟﻤﺴﻘﻁﻲ ﻓﻲ ﺘﺤﺩﻴﺩ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔـﻲ‬ ‫ﻓﻲ ﺒﻌﺽ ﺍﻟﻨﻭﻯ ﺍﻟﻭﺍﻗﻌﺔ ﻓﻲ ﺍﻟﻤﻨﻁﻘﺔ 001 - 08=‪ A‬ﻭ ﻗﺎﻡ ﺒﻤﻘﺎﺭﻨﺔ ﻨﺘﺎﺌﺞ ﺘﺤﺩﻴﺩ ﺍﻷﻨﺤﻨـﺎﺀ ﻤـﻊ‬ ‫ﺍﻟﻨﺘﺎﺌﺞ ﺍﻟﻌﻤﻠﻴﺔ ﻭﻋﺯﺍ ﺴﺒﺏ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﻰ ﻨﻅﺭﻴﺔ ﺘﻘﺎﻁﻊ ﺍﻟﺤـﺯﻡ .ﻭﺩﺭﺱ ]7002 ,‪[Paul et al‬‬ ‫ﻭﻻﺤﻅﻭﺍ ﺍﻥ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺍﻷﻭل ﻴﺤﺩﺙ ﻋﻨﺩ‬
‫851‬

‫ﻋﻤﻠﻴﺎ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﺍﻟﻨﻅﻴﺭ ‪Er‬‬ ‫ﹰ‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫7‬

‫‪ J=14ħ‬ﻨﺘﻴﺠﺔ ﺍﻟﺘﺭﺍﺼﻑ ﺍﻷﻭل ﻟﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘﺸﺭﺓ 2/31‪,i‬ﻭﺍﻟﺘﺭﺍﺼﻑ ﺍﻟﺜﺎﻨﻲ ﻟﺯﻭﺝ‬ ‫ﻤﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻘﺸﺭﺓ 2/11‪ h‬ﻭﻤﻨﻪ ﻴﻨﺘﺞ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺍﻟﺜﺎﻨﻲ .‬

‫‪A‬‬ ‫‪54 Xe N‬‬

‫‪Xenon Istopes‬‬
‫801‬

‫3-1ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ‬
‫ﹰ‬ ‫ﺒـ)29-45=‪ (N‬ﻨﻴﺘﺭﻭﻨﺎ ﺍﺫ ﺃﻥ ﺍﻟﻨﻅﻴﺭ ‪Xe‬‬

‫ﻴﻭﺠﺩ ﻋﺩﺩ ﻜﺒﻴﺭ ﻤﻥ ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ‪ Xe‬ﺒـ 45 ﺒﺭﻭﺘﻭﻨﺎ ﻭﺍﻟﺘﻲ ﺘﻤﺘﺩ ﻤﻥ)641-801=‪(A‬‬ ‫ﹰ‬ ‫ﻟﻪ 45=‪ N=Z‬ﻗﺭﻴﺏ ﻤﻥ ﺍﻟﻌﺩﺩ ﺍﻟـﺴﺤﺭﻱ 05‬ ‫ﻭﻭﻓﻕ ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ ﻓﺎﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﺘﻤﻸ ﺍﻷﻏﻠﻔﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ﻭﺍﻷﻏﻠﻔﺔ ﺍﻟﺜﺎﻨﻭﻴﺔ ﺘﺒﻌﺎ‬ ‫ﹰ‬ ‫ﺍﻟﻰ ﺍﻟﻤﻭﻗﻊ ﺍﻟﻤﻨﺎﺴﺏ ﻓﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ﺍﻟﺘﻲ ﻟﻬﺎ 45 ﺒﺭﻭﺘﻭﻨﺎ ًﺘﻤﻸ ﺍﻷﻏﻠﻔﺔ ﺍﻟﺭﺌﻴـﺴﻴﺔ ﻭﺍﻷﻏﻠﻔـﺔ‬ ‫ﺍﻟﺜﺎﻨﻭﻴﺔ ﻭﺼﻭﻻ ﺃﻟﻰ ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ 2/9‪.1g‬ﻭﺘﻤﻸ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﺍﻟﻤﺘﺒﻘﻴﺔ ﺍﺭﺒﻌﺔ ﻤﻭﺍﻗﻊ ﻤﻥ ﺍﺼـل‬ ‫ﹰ‬ ‫ﺜﻤﺎﻨﻴﺔ ﻓﻲ ﺍﻟﻐﻼﻑ 2/7‪. 1g‬ﺒﻴﻨﻤﺎ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﺍﻟﺘﻲ ﺘﺒﺩﺃ ﻤﻥ 45 ﻨﻴﺘﺭﻭﻨـﺎ ﺍﻟـﻰ 29 ﻨﻴﺘﺭﻭﻨـﺎ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻓﺎﻨﻬﺎ ﺘﺸﻐل ﺃﻏﻠﻔﺔ ﻤﺨﺘﻠﻔﺔ ﺍﺒﺘﺩﺍﺀ ﻤﻥ ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ 2/7‪ 1g‬ﻟﻠﻨﻅﻴـﺭ ‪ 108Xe‬ﺍﻟـﻰ‬ ‫‪‬‬ ‫ﺍﻟـﺫﻱ ﻴﻤﺘﻠـﻙ 27‬
‫621‬ ‫641‬

‫ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫,ﻭﻋﻠﻰ ﺴﺒﻴل ﺍﻟﻤﺜﺎل ﺍﻟﻨﻅﻴـﺭ ‪Xe‬‬

‫641‬

‫ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ 2/9‪ 1h‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﻨﻴﺘﺭﻭﻨﺎ ﻭﺍﻟﻘﺭﻴﺏ ﻤﻥ ﺍﻟﻌﺩﺩ ﺍﻟﺴﺤﺭﻱ 28 ﺘﺸﻐل ﺠﻤﻴﻊ ﺍﻷﻏﻠﻔﺔ ﺍﻟﺜﺎﻨﻭﻴﺔ ﺍﻟـﻰ ﺍﻟﻐـﻼﻑ ﺍﻟﺜـﺎﻨﻭﻱ‬ ‫ﹰ‬ ‫2/11‪ ,1h‬ﺍﺫ ﺘﻤﻸ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﺍﻷﻏﻠﻔﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ﻟﻐﺎﻴﺔ ﺍﻟﻐﻼﻑ ﺍﻟﺨـﺎﻤﺱ ﻭﺍﻷﻏﻠﻔـﺔ ﺍﻟﺜﺎﻨﻭﻴـﺔ ﻓـﻲ‬ ‫ﺍﻟﻐﻼﻑ ﺍﻟﺴﺎﺩﺱ ﻭﺼﻭﻻ ﺍﻟﻰ ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ 2/1‪ 3s‬ﻭﺘﻤﻸ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﺍﻟﻤﺘﺒﻘﻴﺔ ﻤـﻭﻗﻌﻴﻥ ﻤـﻥ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺍﺼل ﺍﺜﻨﺎ ﻋﺸﺭ ﻤﻭﻗﻌﺎ ﻓﻲ ﺍﻟﻐﻼﻑ 2/11‪ 1h‬ﻭﻴﺒﻴﻥ ﺍﻟﺸﻜل )1-1( ﻜﻴﻔﻴﺔ ﺘﻭﺯﻴـﻊ ﺍﻟﺒﺭﻭﺘﻭﻨـﺎﺕ‬ ‫ﻭﺍﻟﺸﻜل )2-1( ﻴﺒﻴﻥ ﻤﺨﻁﻁ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ‬
‫621‬

‫ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻋﻠﻰ ﺍﻷﻏﻠﻔﺔ ﺍﻟﺜﺎﻨﻭﻴﺔ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫ﺍﻟﻌﻤﻠﻴﺔ ﻟﻠﻨﻅﻴﺭ ﻨﻔﺴﻪ.‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫8‬

‫45= ‪Protons‬‬

‫27= ‪Neutrons‬‬

‫6‬ ‫8‬

‫6‬ ‫8‬

‫ﺤﺴﺏ ﺃﻨﻤﻭﺫﺝ ﺍﻟﻘﺸﺭﺓ‬

‫621‬

‫ﺍﻟﺸﻜل )1-1(:ﺘﻭﺯﻴﻊ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻟﻠﻨﻅﻴﺭ‪Xe‬‬ ‫]7891,‪[Krane‬‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫9‬

‫]2002 , ‪[ENSDAT‬‬

‫621‬

‫ﺍﻟﺸﻜل )2-1(:ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ‪Xe‬‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫01‬

‫‪The Aim of the Present Work‬‬
‫ﺍﻟﺯﻭﺠﻴﺔ – ﺍﻟﺯﻭﺠﻴﺔ ﻤﻥ ﺨﻼل ﻤﺤﺎﻜـﺎﺓ‬
‫621-021‬

‫4-1 ﺍﻟﻬﺩﻑ ﻤﻥ ﺍﻟﺩﺭﺍﺴﺔ‬

‫ﺘﻬﺩﻑ ﺍﻟﺩﺭﺍﺴﺔ ﺍﻟﺤﺎﻟﻴﺔ ﺍﻟﻰ ﺍﺴﺘﺨﺩﺍﻡ ﺍﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠـﺔ 1-‪ IBM‬ﻓـﻲ ﺩﺭﺍﺴـﺔ‬ ‫ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ‪Xe‬‬

‫ﺤﺎﺴﻭﺒﻴﺔ ﺠﺩﻴﺩﺓ ﻟﻸﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ 1-‪ IBM‬ﺒﺎﺴﺘﺨﺩﺍﻡ ﺒﺭﻨﺎﻤﺞ ﺒﻠﻐﺔ 7-‪MATLAB‬‬ ‫ﻴﺘﻡ ﺍﻋﺩﺍﺩﻩ ﻟﻬﺫﺍ ﺍﻟﻐﺭﺽ ﺒﺩﻻ ﻤﻥ ﺍﻻﻋﺘﻤﺎﺩ ﻋﻠﻰ ﺍﻟﺒﺭﻨﺎﻤﺞ ﺍﻟﺠﺎﻫﺯ ‪ PHINT‬ﺍﻟﺫﻱ ﻴﺴﺘﺨﺩﻡ ﻋـﺎﺩﺓ‬ ‫ﹰ‬ ‫ﻓﻲ ﻤﺜل ﻫﺫﻩ ﺍﻟﺩﺭﺍﺴﺎﺕ, ﻭﺫﻟﻙ ﻜﻭﺴﻴﻠﺔ ﺠﺩﻴﺩﺓ ﻓﻲ ﻫﺫﻩ ﺍﻟﺩﺭﺍﺴﺔ ﻟﺤﺴﺎﺏ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻟﺘـﻲ‬ ‫ﺘﺴﺘﺨﺩﻡ ﻤﺒﺎﺸﺭﺓ ﻓﻲ ﺍﻴﺠﺎﺩ ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ .ﻜﺫﻟﻙ ﺘﻬﺩﻑ ﺍﻟﺩﺭﺍﺴﺔ ﺍﻟﻰ ﻤﺩﻯ ﻨﺠﺎﺡ ﻁﺭﻴﻘﺔ ﺤـﺴﺎﺏ‬ ‫ﻤﻌﻠﻤﺎﺕ ﺍﻟﺤﺯﻤﺘﻴﻥ ﺍﻻﺭﻀﻴﺔ ﻭﺍﻟﻤﺜﺎﺭﺓ ﻜل ﻋﻠﻰ ﺤﺩﺓ ﺒﺸﻜل ﻤﻨﻔﺼل ﻭﺒﻘـﻴﻡ ﻤﺨﺘﻠﻔـﺔ ﺒـﺩﻻ ﻤـﻥ‬ ‫ﹰ‬ ‫ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﻤﻌﺘﺎﺩﺓ ﻓﻲ ﺤﺴﺎﺏ ﺘﻠﻙ ﺍﻟﻤﻌﻠﻤﺎﺕ ﻟﻠﺤﺯﻤﺘﻴﻥ ﻟﻤﺭﺓ ﻭﺍﺤﺩﺓ ﻭﺒﻘﻴﻡ ﻤﺘﺴﺎﻭﻴﺔ, ﻓـﻀﻼ ﻋـﻥ‬ ‫ﹰ‬ ‫ﺩﺭﺍﺴﺔ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﻼﻗـﺔ ﻁﺎﻗـﺔ ﺍﻻﻨﺘﻘـﺎل ﺒـﺎﻟﺯﺨﻡ‬ ‫ﺍﻟﺯﺍﻭﻱ.‬

‫اﻟﺪراﺳﺎت اﻟﺴﺎﺑﻘﺔ‬

‫اﻟﻔﺼﻞ اﻻول‬

‫ﺍﻟﺜﺎﻧﻲ‬

‫ﺍﻟﻔﺼﻞ‬

‫ﻣﺴﺘﻮﻳﺎﺕ ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭﺍﻻﳓﻨﺎء ﺍﳋﻠﻔﻲ‬

‫ﺧﺼﺎﺋﺺ‬

‫11‬

‫‪Energy Levels‬‬

‫1-2 ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ‬

‫ﻤﻥ ﺍﻟﻤﻤﻜﻥ ﺍﻥ ﺘﻬﺘﺯ ﺍﻟﻨﻭﺍﺓ ﺍﻭﺘﺩﻭﺭ ﻋﻨﺩ ﺃﻜﺘﺴﺎﺒﻬﺎ ﻁﺎﻗﺔ ﻭﻴﻨﺘﺞ ﻋﻥ ﺫﻟﻙ ﺤﺎﻻﺕ ﺘﻬﻴﺞ ﻤﺨﺘﻠﻔـﺔ‬ ‫ﺍﺫ ﺍﻥ ﻁﺎﻗﺔ ﺍﻟﺘﻬﻴﺞ ﺍﻷﻭﻟﻰ 2 ‪ E‬ﻟﻠﻨﻭﻯ ﺍﻟﺯﻭﺠﻴﺔ – ﺍﻟﺯﻭﺠﻴﺔ ﺘﻜـﻭﻥ ﺒﺤـﺩﻭﺩ ‪ 500keV‬ﻟﻠﻨـﻭﻯ‬
‫1‬

‫ﺍﻻﻫﺘﺯﺍﺯﻴﺔ ﻭﺒﺤﺩﻭﺩ ‪ 100keV‬ﻟﻠﻨﻭﻯ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﻭﻟﻠﻨﻭﻯ ﺍﻻﻨﺘﻘﺎﻟﻴﺔ ﻜﺎﻤﺎ ﻏﻴـﺭ ﺍﻟﻤـﺴﺘﻘﺭﺓ ﺘﻜـﻭﻥ‬ ‫ﺒﺤﺩﻭﺩ ‪ [Regan et al, 2003] 300keV‬ﻓﺎﻟﻨﻭﺍﺓ ﻓﻲ ﺤﺎﻟﺘﻬﺎ ﺍﻟﻤﺴﺘﻘﺭﺓ ﺘﻜﻭﻥ ﻜﺭﻭﻴـﺔ ﺍﻟـﺸﻜل‬ ‫ﺘﺸﺒﻪ ﻗﻁﺭﺓ ﺍﻟﺴﺎﺌل ﻭﻤﺸﺤﻭﻨﺔ ﻭﺫﺍﺕ ﻜﺜﺎﻓﺔ ﻨﻭﻭﻴﺔ ﺜﺎﺒﺘﺔ ﻭﺍﻟﻤﺎﺩﺓ ﺍﻟﻨﻭﻭﻴﺔ ﺩﺍﺨﻠﻬﺎ ﺘﻜﻭﻥ ﻋﻠﻰ ﺸـﻜل‬ ‫ﻤﺎﺌﻊ,ﻭﻋﻨﺩ ﻤﺭﻭﺭ ﺠﺴﻴﻡ ﻤﺸﺤﻭﻥ ﺒﺎﻟﻘﺭﺏ ﻤﻥ ﺍﻟﻨﻭﺍﺓ ﻓﺄﻨﻬﺎ ﺘﻜﺘـﺴﺏ ﻁﺎﻗـﺔ ﻭﺘﻘـﻭﻡ ﺒﻌـﺩﺩ ﻤـﻥ‬ ‫ﺍﻻﻫﺘﺯﺍﺯﺍﺕ ﺤﻭل ﻤﺭﻜﺯ ﺘﻭﺍﺯﻨﻬﺎ ﻭﺘﻜﻭﻥ ﻫﺫﻩ ﺍﻟﺤﺭﻜﺔ ﻤﺘﻨﻭﻋﺔ ﺍﻋﺘﻤﺎﺩﺍ ﻋﻠﻰ ﺍﻟﻁﺎﻗﺔ ﺍﻟﺘﻲ ﺍﻜﺘﺴﺒﺘﻬﺎ‬ ‫ﹰ‬ ‫ﺍﻟﻨﻭﺍﺓ , ﻭﺤﺴﺏ ﺍﻷﻨﻤﻭﺫﺝ ﺍﻻﻫﺘﺯﺍﺯﻱ ﻓﺄﻥ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻓﻴﻤﺎ ﻴﺨﺹ ﺍﻟﻨﻭﻯ ﺍﻟﻜﺭﻭﻴﺔ ﺍﻟﺯﻭﺠﻴـﺔ‬ ‫– ﺍﻟﺯﻭﺠﻴﺔ ﺍﻟﻨﺎﺘﺠﺔ ﻤﻥ ﺍﻷﻫﺘﺯﺍﺯﺍﺕ ﺍﻟﺴﻁﺤﻴﺔ ﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺤﻭل ﺸﻜل ﻤﺘﻭﺍﺯﻥ ﺘﻌﻁـﻰ ﺒــ‬ ‫]5791 , ‪: [Greiner and Maruhan , 1996] , [Preston and Bhaduri‬‬

‫5‬ ‫) + ‪E N = hω(N‬‬ ‫2‬

‫)1-2(‬

‫ﺍﺫ ﺍﻥ ‪ hω‬ﻫﻲ ﻁﺎﻗﺔ ﺍﻟﻔﻭﻨﻭﻥ ﻭ ‪ N‬ﻋﺩﺩ ﺍﻟﻔﻭﻨﻭﻨﺎﺕ .‬ ‫ﺍﻟﻔﻭﻨﻭﻥ ﻫﻭ ﻭﺤﺩﺓ ﺍﻟﻜﻡ ﻓﻲ ﺍﻟﺤﺭﻜﺔ ﺍﻻﻫﺘﺯﺍﺯﻴﺔ ﺒﺯﺨﻡ ﺯﺍﻭﻱ )‪ (L‬ﻭﺘﻤﺎﺜـل ‪. (-1)L‬ﻴﻜـﻭﻥ‬ ‫ﻟﻠﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ ﺯﺨﻤﺎ ﻭﺘﻤﺎﺜﻼ ﻗﺩﺭﻩ )+0( ﻭﻴﻜﻭﻥ ﻟﺤﺎﻟﺔ ﺍﻟﺘﻬﻴﺞ ﺍﻷﻭﻟﻰ ﺯﺨﻤﺎ ﻭﺘﻤﺎﺜﻼ ﻗﺩﺭﻩ )+2(‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺍﻤﺎ ﺍﻟﺤﺎﻻﺕ ﺍﻟﻤﺘﻬﻴﺠﺔ ﺍﻷﺨﺭﻯ ﻓﺘﻨﺘﺞ ﻤﻥ ﺍﺯﺩﻭﺍﺝ ﻓﻭﻨﻭﻨﻴﻥ ﻤﺘﻬﻴﺠﻴﻥ ﺒـ )2=‪ (L‬ﻭﻫﺫﻩ ﺍﻟﺤـﺎﻻﺕ‬
‫ﻫﻲ ) 4 , 2 , 0( ﻭﺘﻜﻭﻥ ﻁﺎﻗﺔ ﻫﺫﻩ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﻀﻌﻑ ﻁﺎﻗﺔ ﺤﺎﻟﺔ ﺍﻟﺘﻬـﻴﺞ ﺍﻷﻭﻟـﻰ ) 12 ‪(2E‬‬
‫+‬ ‫+‬ ‫+‬

‫.ﻭﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺜﻼﺜﺔ ﻓﻭﻨﻭﻨﺎﺕ ﻤﺘﻬﻴﺠﺔ ﺒـ )2=‪ (L‬ﻋﻨﺩﻫﺎ ﻴﺘﻭﺍﺠﺩ ﺨﻤﺱ ﺤـﺎﻻﺕ ﻤﺘﻬﻴﺠـﺔ‬ ‫ﻫﻲ )+6 ,+4 , +3 ,+2 ,+0( ﻁﺎﻗﺘﻬﺎ ﺜﻼﺜﺔ ﺍﻀﻌﺎﻑ ﻁﺎﻗﺔ ﺤﺎﻟﺔ ﺍﻟﺘﻬﻴﺞ ﺍﻷﻭﻟﻰ ) 2 ‪ . (3E‬ﻭﻫﻨـﺎﻙ‬
‫1‬

‫ﻓﻭﻨﻭﻥ ﻤﺘﻬﻴﺞ ﺒـ)3=‪ (L‬ﻭﺘﻤﺎﺜل ﺴﺎﻟﺏ ﻭﻨﺘﻴﺠﺔ ﻟﻬﺫﺍ ﺍﻟﺘﺭﺘﻴﺏ ﻴﻨﺘﺞ ﻤﺴﺘﻭﻱ ﻟﻠﻁﺎﻗـﺔ )-3( ﺘﻜـﻭﻥ‬ ‫ﻁﺎﻗﺘﻪ ﺍﻭﻁﺄ ﻤﻥ ﻁﺎﻗﺔ ﻤﺠﻤﻭﻋﺔ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﺜﻼﺜـﺔ )+4 , +2 , +0( ﻜﻤـﺎ ﻓـﻲ ﺍﻟـﺸﻜل)1-2(‬ ‫]2691 , ‪. [Smith‬‬

‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫21‬

‫ﺍﻟﺸﻜل )1-2(: ﻨﻤﻭﺫﺝ ﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻻﻫﺘﺯﺍﺯﻴﺔ.‬ ‫ﺍﻤﺎ ﻓﻲ ﺤﺎﻟﺔ ﺍﻟﻨﻭﻯ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﺍﻟﺯﻭﺠﻴﺔ – ﺍﻟﺯﻭﺠﻴﺔ ﻓﺄﻥ ﺍﻟﻨﻜﻠﻴﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻨﻭﻯ ﺘﺭﺘﺒﻁ ﻟﻜﻲ ﺘﻌﻁـﻲ‬ ‫+0=‪ J‬ﻓﻲ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ ﺍﻤﺎ ﺍﻟﺤﺎﻻﺕ ﺍﻟﻤﺜﺎﺭﺓ ﻟﻬﺫﻩ ﺍﻟﻨﻭﻯ ﻓﺘﺄﺨﺫ ﺍﻟﻘـﻴﻡ )..,+6 , +4 , +2=+‪(J‬‬ ‫ﹰ‬ ‫ﻜﻼﺴﻴﻜﻴﺎ ﻓﺎﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻟﺠﺴﻴﻡ ﺩﻭﺍﺭ ﻴﺘﻨﺎﺴﺏ ﻤﻊ ﺍﻟﺴﺭﻋﺔ ﺍﻟﺯﺍﻭﻴﺔ ‪ ω‬ﻟـﻪ ﻭﻴﻌﻁـﻰ ﺒﺎﻟﻌﻼﻗـﺔ‬ ‫]8791 , ‪: [Lin‬‬
‫‪J = ϑ ω‬‬

‫)2-2(‬

‫ﺍﺫ ﺍﻥ ‪ ϑ‬ﻫﻭ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻭﺍﺓ ﻭﻴﻤﺜل ﺍﻟﻨﺴﺒﺔ ﺒﻴﻥ ‪ J‬ﻭ ‪ ω‬ﻭﺘﻌﻁﻰ ﺍﻟﻁﺎﻗـﺔ ﺍﻟﺩﻭﺭﺍﻨﻴـﺔ‬ ‫ﻟﻠﺠﺴﻡ ﺍﻟﺼﻠﺏ ﺍﻟﺩﻭﺍﺭ ﺒﺎﻟﻌﻼﻗﺔ ]7891, ‪[Krane‬‬
‫1‬ ‫‪ϑω‬‬ ‫2‬

‫)‪E(J‬‬

‫=‬

‫2‬

‫)3-2(‬

‫ﻭﺒﺎﻟﺘﻌﻭﻴﺽ ﻋﻥ ‪ ω‬ﻤﻥ ﺍﻟﻤﻌﺎﺩﻟﺔ )2-2( ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )3-2( ﻨﺤﺼل ﻋﻠﻰ‬

‫)‪E(J‬‬

‫=‬

‫1‬ ‫‪J‬‬ ‫2‪J‬‬ ‫= 2) ( ‪ϑ‬‬ ‫2‬ ‫‪ϑ‬‬ ‫‪2ϑ‬‬

‫)4-2(‬
‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫31‬

‫ﻭﺤﺴﺏ ﺍﻟﻤﻴﻜﺎﻨﻴﻙ ﺍﻟﻜﻤﻲ ﻓﺄﻥ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﺘﻭﻗﻌﺔ ﻟﻤﺭﺒﻊ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻫﻲ‬

‫2‪J‬‬

‫)1 + ‪= h 2 J(J‬‬

‫)5-2(‬

‫ﻭﺒﺘﻌﻭﻴﺽ ﺍﻟﻤﻌﺎﺩﻟﺔ )5-2( ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )4-2( ﻨﺤﺼل ﻋﻠﻰ ﺍﻟﻁﺎﻗﺔ ﺒﺩﻻﻟﺔ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ‬
‫2‪h‬‬ ‫)1 + ‪J(J‬‬ ‫‪2ϑ‬‬

‫= )‪E(J‬‬

‫)6-2(‬

‫ﻭﺍﻟﺸﻜل )2-2( ﻴﺒﻴﻥ ﺤﺎﻻﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﺤﺯﻤﺔ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﺍﻷﺭﻀﻴﺔ:‬

‫ﺍﻟﺸﻜل )2-2(: ﺤﺎﻻﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﺤﺯﻤﺔ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﺍﻷﺭﻀﻴﺔ ﻟﻠﻨﻭﻯ ﺍﻟﺯﻭﺠﻴﺔ – ﺍﻟﺯﻭﺠﻴﺔ‬ ‫]6991 ,‪[Greiner and Maruhn‬‬ ‫ﻟﻭﺤﻅ ﺍﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻨﻅﺭﻴﺔ ﻤﻥ ﺤﺴﺎﺒﺎﺕ ﺍﻟﻤﻌﺎﺩﻟﺔ )6-2( ﺍﻋﻠﻰ ﻤﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻻﺴﻴﻤﺎ ﻋﻨـﺩ‬ ‫8=‪ J‬ﻓﻤﺎ ﻓﻭﻕ ﺒﺴﺒﺏ ﺯﻴﺎﺩﺓ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﺒﺯﻴﺎﺩﺓ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻟﻠـﺩﻭﺭﺍﻥ ﻨﺘﻴﺠـﺔ ﺍﻟﻘـﻭﺓ‬ ‫ﺍﻟﻁﺎﺭﺩﺓ ﺍﻟﻤﺭﻜﺯﻴﺔ ﻭﻟﺫﻟﻙ ﺍﺩﺨل ﺤـﺩ ﺍﻟﺘـﺼﺤﻴﺢ 2)1+‪ BJ2(J‬ﺍﻟـﻰ ﺍﻟﻤﻌﺎﺩﻟـﺔ )6-2( ﻟﺘـﺼﺒﺢ‬ ‫]ﺍﻨﻜﺎ , 3891[‬
‫2‪h‬‬ ‫= )‪E(J‬‬ ‫2 )1 + ‪J(J + 1) − BJ 2 (J‬‬ ‫‪2ϑ‬‬
‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫)7-2(‬
‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫41‬

‫2-2 ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ ﻷﺸﻌﺔ ﻜﺎﻤﺎ‬ ‫‪Electromagnatic Transition Probability of Gamma-ray‬‬
‫ﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﺍﻟﻨﻭﺍﺓ ﻓﻲ ﺤﺎﻟﺔ ﺍﺜﺎﺭﺓ ﻓﺄﻨﻬﺎ ﺘﻨﺤل ﺒﻁﺭﻴﻘﺔ ﻤﺎ ﻟﺘﻌﻭﺩ ﻟﻠﺤﺎﻟﺔ ﺍﻷﺭﻀـﻴﺔ ,ﻓﻘـﺩ‬ ‫ﺘﺒﻌﺙ ﺠﺴﻴﻤﺎﺕ ﺍﻟﻔﺎ ﺃﻭ ﺒﻴﺘﺎ ﺃﻭ ﺘﻨﺸﻁﺭ ﻟﺘﺘﺤﻭل ﺇﻟﻰ ﻨﻭﺍﺓ ﺃﺨﺭﻯ ﺃﻭ ﺘﻨﺘﻘل ﻤﻥ ﻤـﺴﺘﻭ ﺇﺜـﺎﺭﺓ ﺇﻟـﻰ‬ ‫ٍ‬ ‫ﻤﺴﺘﻭ ﺁﺨﺭ ﺍﻗل ﺇﺜﺎﺭﺓ ﻭﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺘﻨﺒﻌﺙ ﺃﺸﻌﺔ ﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ ﻭﻫﻲ ﺃﺸﻌﺔ ﻜﺎﻤﺎ ﻨﺘﻴﺠﺔ ﻟﻬـﺫﺍ‬ ‫ٍ‬ ‫ﺍﻻﻨﺘﻘﺎل. ﺍﺫ ﺃﻥ ﺍﻟﻨﻭﺍﺓ ﺘﺘﻜﻭﻥ ﻤﻥ ﻨﻜﻠﻴﻭﻨﺎﺕ ﻨﻘﻁﻴﺔ ﻟﻬﺎ ﻋﺯﻡ ﻤﻐﻨﺎﻁﻴﺴﻲ ﺜﻨﺎﺌﻲ ﺍﻷﻗﻁﺎﺏ ﻓﻀﻼ ﻋﻥ‬ ‫ﹰ‬ ‫ﺃﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﺘﻤﺘﻠﻙ ﺸﺤﻨﺔ ﻭﺃﻥ ﺘﻭﺯﻴﻊ ﺍﻟﺸﺤﻨﺔ ﻤﻤﻜﻥ ﺃﻥ ﻴﺘﻔﺎﻋل ﻤﻊ ﺍﻟﻤﺠﺎل ﺍﻟﺨـﺎﺭﺠﻲ ﻤﻤـﺎ‬ ‫ﻴﺅﺩﻱ ﺇﻟﻰ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﺒﺎﺌﻴـﺔ )‪, (EL‬ﺃﻤـﺎ ﺍﻻﻨﺘﻘـﺎﻻﺕ ﺍﻟﻤﻐﻨﺎﻁﻴـﺴﻴﺔ )‪ (ML‬ﻓﺘﻨـﺘﺞ ﻤـﻥ‬ ‫ﺍﻟﻤﻐﻨﺎﻁﻴﺴﻴﺔ ﺍﻟﺫﺍﺘﻴﺔ ﻟﻜل ﻨﻜﻠﻴﻭﻥ ﻓﻀﻼ ﻋﻥ ﺍﻟﻤﻐﻨﺎﻁﻴﺴﻴﺔ ﺍﻟﻨﺎﺘﺠﺔ ﻋﻥ ﺤﺭﻜـﺔ ﺍﻟﺒﺭﻭﺘﻭﻨـﺎﺕ ﻓـﻲ‬ ‫ﹰ‬ ‫ﻤﺩﺍﺭﺍﺕ ﻤﻐﻠﻘﺔ ]ﺨﻠﻴل , 6991[.‬ ‫ﺇﻥ ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻨﺘﻘﺎل ﻜﺎﻤﺎ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﻟﻭﺤﺩﺓ ﺍﻟﺯﻤﻥ ﻤﻥ ﺤﺎﻟﺔ ﺯﺨﻡ ﺯﺍﻭﻱ ﺍﺒﺘﺩﺍﺌﻲ ‪ Ji‬ﺇﻟﻰ ﺤﺎﻟﺔ ﺯﺨـﻡ‬ ‫ﺯﺍﻭﻱ ﻨﻬﺎﺌﻲ ‪ Jf‬ﺘﻌﻁﻰ ﺒﺎﻟﻌﻼﻗﺔ ]0991 , ‪: [Yamamoto , 2004] , [Wong‬‬
‫1+ ‪2 L‬‬

‫⎞ ‪8π (L + 1) 1 ⎛ Eγ‬‬ ‫‪λ (σL; i → f ) = αhc‬‬ ‫⎟ ⎜‬ ‫⎠ ‪L[(2L + 1)!!]2 h ⎝ hc‬‬

‫) ‪B(σL; i → f‬‬

‫)8-2(‬

‫ﺍﺫ ‪ σL‬ﻨﻭﻉ ﻗﻁﺒﻴﺔ ﺍﻷﻨﺘﻔﺎل ﻭ ‪ Eγ‬ﻫﻲ ﻁﺎﻗﺔ ﺍﻻﻨﺘﻘﺎل ﺒﻴﻥ ﺍﻟﻤﺴﺘﻭﻴﻴﻥ ﻭ‪ L‬ﻫﻭ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻭ‬ ‫‪ h‬ﻋﺒﺎﺭﺓ ﻋﻥ ﺜﺎﺒﺕ ﺒﻼﻨﻙ ﻭ )‪ B(σL ; i→f‬ﻴﻤﺜل ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎل ﺍﻟﻤﺨﺘﺯﻟﺔ ﺒﻘﻁﺒﻴـﺔ ‪ L‬ﻭ‪c‬‬ ‫ﺴﺭﻋﺔ ﺍﻟﻀﻭﺀ. ﻤﻥ ﺍﻟﻤﻌﺎﺩﻟﺔ )8-2( ﺘﻌﻁﻰ ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎل ﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ )2‪λ(E‬‬ ‫ﺒﺎﻟﻌﻼﻗﺔ ]0991 ,‪:[Yamamoto , 2004] ,[Wong‬‬

‫)2 ‪λ ( E2) ≈ (1.225 ×109 ) Eγ5 B( E‬‬

‫)9-2(‬

‫ﺇﺫ ﺍﻥ ‪ Eγ‬ﻫﻲ ﻁﺎﻗﺔ ﺍﻨﺘﻘﺎل ﻜﺎﻤﺎ ﺒﻭﺤﺩﺓ ‪ MeV‬ﻭ )2‪ B(E‬ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺭﺒﺎﻋﻴﺔ‬ ‫ﺍﻟﻘﻁﺏ ﺍﻟﻤﺨﺘﺯﻟﺔ ﺒﻭﺤﺩﺓ 4‪ e2fm‬ﻭﺘﻌﻁﻰ )2‪ λ(E‬ﺒﻭﺤﺩﺓ 1-‪s‬‬

‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫51‬

‫ﻭﺍﻋﻁﻰ ﻭﺍﻴﺴﻜﻭﻑ ﺘﻘﺩﻴﺭﺍﺕ ﻟﺸﺩﺓ ﺍﻷﻨﺘﻘﺎﻻﺕ ﺍﻟﻨﺎﺘﺠﺔ ﻤﻥ ﺍﻟﺒﺭﻭﺘﻭﻥ ﺍﻟﻤﻨﻔﺭﺩ ﺍﻟﻤﺘﺤﺭﻙ ﻓـﻲ‬ ‫ﻤﺩﺍﺭ ﻤﺎ ﻭﻜﻤﺎ ﻴﺄﺘﻲ ]3002 , ‪: [Mark‬‬

‫‪(0.12) 2L ⎛ 3 ⎞ 2L/ 3 2 L‬‬ ‫= )‪BW ( EL‬‬ ‫‪eb‬‬ ‫⎜‬ ‫‪⎟A‬‬ ‫⎠3+‪4π ⎝ L‬‬

‫2‬

‫)01-2(‬

‫ﻭﺒﺠﻌل 2=‪ L‬ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )01-2( ﻟﻼﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺒﻴﺔ ﻨﺤﺼل ﻋﻠﻰ :‬

‫2‪B W ( E 2 ) = 5.943 ×10− 6 A4 / 3 e2b‬‬

‫)11-2(‬

‫‪γ‬‬ ‫ﻭﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎل ﻭﻋﻤﺭ ﺍﻟﻨﺼﻑ 2 /1‪ T‬ﻫﻲ ]5691 ,‪[Stelson and Grodzins‬‬

‫= )‪λ (σL‬‬

‫396.0‬ ‫2 /‪T1γ‬‬

‫)21-2(‬

‫ﻜﻤﺎ ﻴﻤﻜﻥ ﺍﻟﺘﻭﺼل ﺍﻟﻰ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ )2‪ B(E‬ﻭﻋﻤﺭ ﺍﻟﻨﺼﻑ ﻭﺫﻟﻙ ﺒﺘﻌﻭﻴﺽ ﺍﻟﻤﻌﺎﺩﻟـﺔ )21-2(‬ ‫ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )9-2( ﻟﻨﺤﺼل ﻋﻠﻰ ]2891 , ‪[Schrecknbach et al‬‬
‫75650. 0‬ ‫) 2 ‪(e 2 b‬‬ ‫5‬ ‫) ‪T1 / 2 ( ps ) E γ ( MeV‬‬
‫‪γ‬‬

‫= )2 ‪B ( E‬‬

‫)31-2(‬ ‫ﺍﺫ ﺍﻥ‬

‫‪γ‬‬ ‫) ‪T1/2 = T1/2 (exp)(1 + α tot‬‬

‫)41-2(‬ ‫ﺍﺫ ﺍﻥ ‪ α tot‬ﻫﻭ ﻤﻌﺎﻤل ﺍﻟﺘﺤﻭل ﺍﻟﺩﺍﺨﻠﻲ ﻭﻴﻌﻁﻰ ﺒﺎﻟﻤﻌﺎﺩﻟﺔ‬

‫..... + ‪α tot = α k + α L‬‬

‫)51-2(‬ ‫ﻭﻻﻨﺘﻘﺎل ﻭﺍﺤﺩ ﺨﺎﺭﺝ ﻤﻥ ﺍﻟﻤﺴﺘﻭﻱ‬

‫= )2‪B(E‬‬

‫75650.0‬ ‫) 2 ‪(e 2 b‬‬ ‫)‪T1/2 (exp)(1 + α tot )E 5 (MeV‬‬ ‫‪γ‬‬

‫)61-2(‬
‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫61‬

‫ﻭﺍﻟﻌﻼﻗﺔ ﺍﻟﺘﻲ ﺘﺭﺒﻁ )2‪ B(E‬ﺒﻭﺤﺩﺍﺕ ﻭﺍﻴﺴﻜﻭﻑ ﻭ)2‪ B(E‬ﺒﻭﺤﺩﺍﺕ 2‪ e2b‬ﻫﻲ‬
‫= ‪B ( E 2 ) w.u‬‬ ‫2 ‪B ( E 2) e 2 b‬‬ ‫2 ‪5.943 ×10 − 6 A 4 / 3 e 2 b‬‬

‫)71-2(‬

‫3-2 ﺍﻟﺘﺸﻭﻩ ﻭﺍﻟﻌﺯﻡ ﺍﻟﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﻨﻭﻭﻱ‬
‫ﺍﻟﻨﻭﻯ ﺍﻤﺎ ﺃﻥ ﺘﻜﻭﻥ ﻜﺭﻭﻴﺔ ﺍﻭ ﻤﺸﻭﻫﻪ ,ﻭﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻡ ﺍﻟﺘﻨﺎﻅﺭ ﻜﻤﻘﻴﺎﺱ ﻟﺘـﺸﻭﻩ ﺍﻟﻨـﻭﺍﺓ‬ ‫ﻓﺎﻟﺘﺸﻭﻩ ﻋﻥ ﺍﻟﺸﻜل ﺍﻟﻜﺭﻭﻱ ﻴﻨﺘﺞ ﻋﻥ ﺍﻟﺘﻔﺎﻋل ﺒﻴﻥ ﺍﻟﻁﺎﻗﺔ ﺍﻟـﺴﻁﺤﻴﺔ ﻟﻠﻨـﻭﺍﺓ ﻭﻁﺎﻗـﺔ ﻜﻭﻟـﻭﻡ ,‬ ‫ﻓﺎﻟﺘﻔﺎﻋل ﺍﻟﻜﻭﻟﻭﻤﻲ ﺒﻴﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻴﻜﻭﻥ ﺘﻨﺎﻓﺭﻴﺎ ﻤﻤﺎ ﻴﺅﺩﻱ ﺍﻟﻰ ﺍﺒﻌﺎﺩ ﺒﻌﻀﻬﺎ ﻋﻥ ﺍﻟﺒﻌﺽ ﺍﻷﺨﺭ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻤﺴﺒﺒﺎ ﺯﻴﺎﺩﺓ ﻓﻲ ﺤﺠﻡ ﺍﻟﻨﻭﺍﺓ ﻭﺘﺸﻭﻫﻬﺎ ,ﻭﻟﻜﻥ ﺍﻟﺸﺩ ﺍﻟﺴﻁﺤﻲ ﻴﺤﺎﻓﻅ ﻋﻠـﻰ ﺍﻟﻤـﺴﺎﺤﺔ ﺍﻟـﺴﻁﺤﻴﺔ‬ ‫ﻟﻠﻨﻭﺍﺓ.ﻓﺎﺫﺍ ﺘﻐﻠﺒﺕ ﻁﺎﻗﺔ ﻜﻭﻟﻭﻡ ﻋﻠﻰ ﺍﻟﻁﺎﻗﺔ ﺍﻟﺴﻁﺤﻴﺔ ﺘﻜﻭﻥ ﺍﻟﻨﻭﺍﺓ ﻤﺸﻭﻫﺔ ﺍﻤﺎ ﺍﺫﺍ ﺘﻐﻠﺒـﺕ ﺍﻟﻁﺎﻗـﺔ‬ ‫ﺍﻟﺴﻁﺤﻴﺔ ﻋﻠﻰ ﻁﺎﻗﺔ ﻜﻭﻟﻭﻡ ﻓﺴﺘﺤﺎﻓﻅ ﺍﻟﻨﻭﺍﺓ ﻋﻠﻰ ﺸﻜﻠﻬﺎ ﺍﻟﻜﺭﻭﻱ .ﻭﻋﻥ ﻁﺭﻴﻕ ﺍﻟﺘـﺸﻭﻩ ﻴﻤﻜـﻥ‬ ‫ﻤﻌﺭﻓﺔ ﺸﻜل ﺍﻟﻨﻭﺍﺓ ﻭﺍﻟﻌﺯﻡ ﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﻟﻬﺎ ﻭﺍﻟﺫﻱ ﻴﻤﻜﻥ ﺘﻌﺭﻴﻔﻪ ﻋﻠﻰ ﺃﻨﻪ ﺍﻻﻨﺤﺭﺍﻑ‬ ‫ﻋﻥ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻜﺭﻭﻱ ﺍﻟﻤﺘﻨﺎﻅﺭ ﻟﻠﺸﺤﻨﺔ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺩﺍﺨل ﺍﻟﻨﻭﺍﺓ ,ﺍﺫ ﻴﻜﻭﻥ ﺘﻭﺯﻴﻊ ﺍﻟﺸﺤﻨﺔ ﻓﻲ ﺍﻟﻨﻭﻯ‬ ‫ﺍﻟﻜﺭﻭﻴﺔ ﻤﺘﻨﺎﻅﺭﺍ ﻜﺭﻭﻴﺎ ﻭﺘﻘﻊ ﻫﺫﻩ ﺍﻟﻨﻭﻯ ﺒﺎﻟﻘﺭﺏ ﻤﻥ ﺍﻟﻘﺸﺭﺍﺕ ﺍﻟﻤﻐﻠﻘﺔ ﻭﺍﻟﺘـﻲ ﺘﺤـﺩﺩ ﺒﺎﻷﻋـﺩﺍﺩ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺍﻟﺴﺤﺭﻴﺔ ﻟﻠﺒﺭﻭﺘﻭﻨﺎﺕ ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ) 621 , 28 , 05 , 02 ,8 , 2 ( ﻭﻋﻨﺩﻫﺎ ﺘﻜﻭﻥ ﺍﻟﻨﻭﺍﺓ ﺃﻜﺜﺭ‬ ‫ﺍﺴﺘﻘﺭﺍﺭﺍ ﻭ ﺘﻜﻭﻥ ﻁﺎﻗﺎﺕ ﺭﺒﻁ ﺍﻟﻨﻜﻠﻴﻭﻨﺎﺕ ﻓﻲ ﻫﺫﻩ ﺍﻟﻨﻭﻯ ﻋﺎﻟﻴﺔ ﻭﻟﻬﺎ ﻋﺯﻡ ﺭﺒﺎﻋﻲ ﻗﻁﺏ ﻜﻬﺭﺒﺎﺌﻲ‬ ‫ﹰ‬ ‫ﺫﺍ ﻗﻴﻤﺔ ﺼﻐﻴﺭﺓ ﺘﺼل ﺍﻟﻰ ﺍﻟـﺼﻔﺭ ﻓﻲ ﺍﻟﻨﻭﻯ ﺍﻟـﺯﻭﺠﻴـﺔ – ﺍﻟـﺯﻭﺠﻴﺔ ]6691 , ‪ [Enge‬ﺍﻤﺎ‬ ‫ﺍﻟﻨﻭﻯ ﺍﻟﻤﺸﻭﻫﺔ ﻓﺘﻘﻊ ﻓﻲ ﻭﺴﻁ ﺍﻟﻤﺴﺎﻓﺔ ﺒﻴﻥ ﺍﻟﻘﺸﺭﺍﺕ ﺍﻟﻤﻐﻠﻘﺔ ﻭﻫﺫﻩ ﺍﻟﻨﻭﻯ ﺘﻤﺘﻠﻙ ﻋﺯﻭﻤﺎ ﻜﻬﺭﺒﺎﺌﻴﺔ‬ ‫ﹰ‬ ‫ﺫﺍﺕ ﻗﻴﻤﺔ ﻜﺒﻴﺭﺓ ﻭﻜﻠﻤﺎ ﺍﺯﺩﺍﺩ ﺍﻟﺘﺸﻭﻩ ﺍﺯﺩﺍﺩﺕ ﻗﻴﻤﺔ ﺍﻟﻌـﺯﻡ ﺍﻟﺭﺒـﺎﻋﻲ ﺍﻟﻘﻁـﺏ ﺍﻟﻜﻬﺭﺒـﺎﺌﻲ ﻟﻬـﺎ‬ ‫]1791 , ‪. [Cohen‬‬ ‫ﺍﻥ ﺘﻭﺯﻴﻊ ﺍﻟﺸﺤﻨﺎﺕ ﻭﺍﻟﺘﻴﺎﺭﺍﺕ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﻴﻨﺘﺞ ﻋﺯﻭﻤﺎ ﻜﻬﺭﺒﺎﺌﻴـﺔ ﻭﻤﻐﻨﺎﻁﻴـﺴﻴﺔ ﻤﺘﻌـﺩﺩﺓ‬ ‫ﹰ‬ ‫ﺍﻟﻘﻁﺒﻴﺔ ﺘﺘﺤﺩﺩ ﺒﻭﺍﺴﻁﺔ ﺍﻟﻌﺎﻤل ‪ (2) L‬ﻓﻌﻨﺩﻤﺎ ﻴﻜﻭﻥ )0=‪ (L‬ﺃﻱ ﺍﻥ ﺍﻟﺤﺭﻜﺔ ﺍﻟﻤﺩﺍﺭﻴﺔ ﺘﺴﺎﻭﻱ ﺼﻔﺭﺍ‬ ‫ﹰ‬ ‫ﻓﺄﻥ )1=02( ﻭﻫﺫﺍ ﻴﻌﻨﻲ ﻤﺠﺎﻻ ﻜﻬﺭﺒﺎﺌﻴﺎ ﺍﺤﺎﺩﻱ ﺍﻟﻘﻁﺒﻴﺔ )‪ (monople‬ﻴﻌﺭﻑ ﺒﺎﻟﻤﺠﺎل ﺍﻟﻜﻭﻟﻭﻤﻲ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺍﻟﻨﺎﺘﺞ ﻋﻥ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻜﺭﻭﻱ ﺍﻟﻤﻨﺘﻅﻡ ﻟﻠﺸﺤﻨﺔ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﻓﻲ ﺍﻟﻨﻭﺍﺓ , ﻭﻋﻨـﺩﻤﺎ ﻴﻜـﻭﻥ )1=‪ (L‬ﺃﻱ‬ ‫ﻫﻨﺎﻙ ﺤﺭﻜﺔ ﻤﺩﺍﺭﻴﺔ ﻟﻠﺸﺤﻨﺔ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﻓﻲ ﻤﺩﺍﺭﺍﺕ ﻤﻐﻠﻘﺔ ﻴﻨﺘﺞ ﻋﻨﻬﺎ ﻤﺠﺎل ﻤﻐﻨﺎﻁﻴـﺴﻲ ﺜﻨـﺎﺌﻲ‬ ‫ﹰ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ﺍﻟﻘﻁﺒﻴ ـﺔ )‪ , (dipole‬ﻭﻋﻨ ـﺩﻤﺎ ﻴﻜ ـﻭﻥ )2=‪ (L‬ﻴﻨ ـﺘﺞ ﻋﺯﻤ ـﺎ ﻜﻬﺭﺒﺎﺌﻴ ـﺎ ﺭﺒ ـﺎﻋﻲ ﺍﻟﻘﻁ ـﺏ‬ ‫ـ‬ ‫ﹰ ـ‬ ‫)‪ (Quadrupole‬ﻭﻫﻜﺫﺍ ]ﺨﻠﻴل ,6991[‬
‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬ ‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫71‬

‫ﻭﻴﻌﻁﻰ ﻋﺯﻡ ﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﺫﺍﺘﻲ ‪ Qo‬ﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﻷﺤﺩﺍﺜﻴﺎﺕ ﺍﻟﻜﺭﻭﻴـﺔ ﺒــ‬ ‫]0991 , ‪:[Singo , 2006] , [Wonge‬‬
‫‪Qo = ∫ ρ ch (3 z 2 − r 2 )dv‬‬

‫)81-2(‬

‫ﺤﻴﺙ ‪ ρch‬ﻫﻭ ﻜﺜﺎﻓﺔ ﺍﻟﺸﺤﻨﺔ ﻭ ‪ dv‬ﻋﻨﺼﺭ ﺍﻟﺤﺠﻡ ﻟﺘﻭﺯﻴﻊ ﺍﻟﺸﺤﻨﺔ ﻭ‪ z‬ﻫﻭ ﺇﺤﺩﺍﺜﻲ ﺍﻟﺘﻨﺎﻅﺭ ﻟﺘﻭﺯﻴﻊ‬ ‫ﺍﻟﺸﺤﻨﺔ ﻭ ‪ r‬ﻫﻭ ﻨﺼﻑ ﻗﻁﺭ ﺍﻟﻨﻭﺍﺓ ,ﻭﻗﺩ ﺘﻜﻭﻥ ﻗﻴﻤﺔ ‪ Q o‬ﻤﻭﺠﺒﺔ ﻋﻨﺩﻫﺎ ﺘﻜﻭﻥ ﺍﻟﻨـﻭﺍﺓ ﻤﺘﻁﺎﻭﻟـﺔ‬ ‫)‪ (Prolate‬ﺍﻤﺎ ﺍﺫﺍ ﻜﺎﻨﺕ ‪ Q o‬ﺴﺎﻟﺒﺔ ﻓﺄﻥ ﺍﻟﻨﻭﺍﺓ ﺘـﺼﺒﺢ ﻤﻔﻠﻁﺤـﺔ )‪ (Oblate‬ﻭﺍﻟـﺸﻜل )3-2(‬ ‫ﻴﻭﻀﺢ ﺍﺸﻜﺎل ﺍﻟﺘﺸﻭﻩ ﻭﻗﻴﻤﺔ ‪[Martin , 2006] Q o‬‬

‫‪Prolate‬‬

‫‪Oblate‬‬

‫ﺸﻜل )3-2( ﺍﺸﻜﺎل ﺍﻟﺘﺸﻭﻩ‬ ‫ﻭﺍﻟﻌﻼﻗﺔ ﺍﻟﺘﻲ ﺘﺭﺒﻁ ﻤﻌﺎﻤل ﺍﻟﺘﺸﻭﻩ 2 ‪ β‬ﺒﺎﻟﻌﺯﻡ ﺭﺒﺎﻋﻲ ﺍﻟﻘﻁـﺏ ﺍﻟﻜﻬﺭﺒـﺎﺌﻲ ﺍﻟـﺫﺍﺘﻲ ‪ Qo‬ﻫـﻲ‬ ‫]3691 ,‪:[Krane , 1987], [Nemirovskii et al‬‬

‫= ‪Qo‬‬

‫3‬ ‫2‬ ‫) 2 ‪Rav Zβ 2 (1 + 0.16 β‬‬ ‫‪5π‬‬

‫)91-2(‬

‫ﺍﺫ ﺍﻥ 3 / 1‪ Rav = Ro A‬ﻴﻤﺜل ﻤﺘﻭﺴﻁ ﻨﺼﻑ ﻗﻁﺭ ﺍﻟﻨﻭﺍﺓ ﻭ )‪ ( Ro = 1.2 fm‬ﺍﻤﺎ ﻤﻌﺎﻤل ﺍﻟﺘـﺸﻭﻩ 2 ‪β‬‬

‫ﻓﻴﻌﻁﻰ ﺒﺎﻟﻌﻼﻗﺔ ﺍﻵﺘﻴﺔ‬

‫= 2‪β‬‬

‫⎞ ‪4 π ⎛ ∆R‬‬ ‫⎟‬ ‫⎜‬ ‫⎟ ‪3 5 ⎜ R av‬‬ ‫⎠‬ ‫⎝‬

‫)02-2(‬

‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫81‬

‫ﺍﺫ ‪ ∆R = b − a‬ﻭﻴﻤﺜل ‪ a‬ﺸﺒﻪ ﺍﻟﻤﺤـﻭﺭ ﺍﻟـﺼﻐﻴﺭ )‪ (Semi-minor axis‬ﻭ ‪ b‬ﻴﻤﺜـل ﺸـﺒﻪ‬ ‫ﺍﻟﻤﺤﻭﺭ ﺍﻟﻜﺒﻴﺭ )‪ (Semi-major axis‬ﻓﻲ ﺍﻟﻨﻭﺍﺓ ﺍﻟﻤﺸﻭﻫﺔ ﻜﻤﺎ ﻤﻭﻀـﺢ ﻓـﻲ ﺍﻟـﺸﻜل )3-2(‬ ‫]ﺨﻠﻴل , 6991[‬

‫‪Backbending Phenomenon‬‬

‫4-2 ﻅﺎﻫﺭﺓ ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫ﻫﻲ ﻋﻤﻠﻴﺔ ﺤﺩﻭﺙ ﺘﻐﻴﺭ ﻤﻔﺎﺠﺊ ﻓﻲ ﻗﻴﻤﺔ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻋﻨﺩ ﺯﺨﻭﻡ ﺯﺍﻭﻴـﺔ ﻋﺎﻟﻴـﺔ‬ ‫ﻨﺴﺒﻴﺎ , ﻓﻘﺩ ﻟﻭﺤﻅ ﺍﻥ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻭﺍﺓ ﻴﺯﺩﺍﺩ ﻓﺠﺄﺓ ﻋﻨﺩ ﺯﺨﻭﻡ ﺯﺍﻭﻴﺔ ﻤﻌﻴﻨﺔ ﻤﻤﺎ ﻴـﺅﺩﻱ‬ ‫ﹰ‬ ‫ﺒﺩﻭﺭﻩ ﺍﻟﻰ ﻫﺒﻭﻁ ﻓﻲ ﺍﻟﻁﺎﻗﺔ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﻟﻠﻨﻭﺍﺓ ﻋﻨﺩ ﺘﻠﻙ ﺍﻟﺯﺨﻭﻡ ﺍﻟﺯﺍﻭﻴﺔ ﻭﻫﺫﺍ ﻴﺅﺩﻱ ﺍﻟﻰ ﺤـﺩﻭﺙ‬ ‫ﺃﻨﺤﻨﺎﺀ ﺨﻠﻔﻲ ﻓﻲ ﻤﻨﺤﻨﻲ ﺍﻟﻁﺎﻗﺔ ﻤﻊ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ. ﻋﻨﺩ ﺭﺴﻡ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ‪ EJ‬ﻭ)1+‪ J(J‬ﻟﺤﺯﻤـﺔ‬ ‫ﺍﻟﻁﺎﻗﺎﺕ ﺍﻷﺩﻨﻰ ﻻﻴﻼﺤﻅ ﺍﻟﺘﻐﻴﺭ ﺍﻟﺤﺎﺼل ﻓﻲ ﺍﻟﻁﺎﻗﺔ ﺒﺸﻜل ﻭﺍﻀﺢ ﺍﻤﺎ ﻋﻨﺩ ﺭﺴﻡ ﺍﻟﻌﻼﻗـﺔ ﺒـﻴﻥ‬ ‫‪ 2ϑ‬ﻭﻤﺭﺒﻊ ﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ 2 ‪ h 2 ω‬ﻓـﺄﻥ ﺍﻟﺘﻐﻴـﺭ ﻓـﻲ ‪ ϑ‬ﻴﻅﻬـﺭ‬
‫2‪h‬‬

‫ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ‬

‫ﺒﻭﻀﻭﺡ ﻋﻠﻰ ﺸﻜل ﺍﻟﺤﺭﻑ ‪ Z‬ﺍﻟﻤﻘﻠﻭﺏ ﻜﻤﺎ ﻤﺒﻴﻥ ﻓﻲ ﺍﻟﺸﻜل )4-2( ﻭﻤﻥ ﻫﻨﺎ ﺠـﺎﺀﺕ ﺘـﺴﻤﻴﺔ‬ ‫ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ]1791, ‪. [Johnson et al‬‬

‫ﺸﻜل )4-2( ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ]0991 , ‪[Wonge‬‬
‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬ ‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫91‬

‫ﻭﻴﻤﻜﻥ ﺤﺴﺎﺏ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻤﻥ ﺨﻼل ﺍﻟﻔﺭﻕ ﻓﻲ ﺍﻟﻁﺎﻗﺔ ﺒﻴﻥ ﻤـﺴﺘﻭﻴﻴﻥ ﻓـﻲ ﺍﻟﺤﺯﻤـﺔ‬ ‫ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﻟﺤﺎﻻﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻻﺩﻨﻰ ﻤﻥ ﺍﻟﻤﻌﺎﺩﻟﺔ ]0991 , ‪[Wong‬‬
‫‪2ϑ‬‬ ‫2 − ‪4J‬‬ ‫2 − ‪4J‬‬ ‫=‬ ‫=‬ ‫2‬ ‫)2 − ‪E(J) − E(J‬‬ ‫‪Eγ‬‬ ‫‪h‬‬

‫)12-2(‬

‫ﻜﻤﺎ ﻴﻤﻜﻥ ﺤﺴﺎﺏ ﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻤﻥ ﺍﻻﻨﺘﻘﺎل ﻤﻥ ﻤﺴﺘﻭ ﺫﻱ ﺯﺨﻡ ﺯﺍﻭﻱ ‪ J‬ﺍﻟﻰ ﻤﺴﺘﻭ ﺍﺩﻨﻰ ﺫﻱ‬ ‫ٍ‬ ‫ٍ‬ ‫ﺯﺨﻡ ﺯﺍﻭﻱ )2-‪ (J‬ﻭﻷﻥ ﺍﻟﻁﺎﻗﺔ ﻟﻬﺎ ﻋﻼﻗﺔ ﺒـ )1+‪ J(J‬ﻓﺎﻨﻬﺎ ﺘﻨﺤـل ﺍﻟـﻰ )1-‪ (J-2)(J‬ﻋﻨـﺩ‬ ‫ﺍﻻﻨﺘﻘﺎل ﻤﻥ ﺍﻟﺤﺎﻟﺔ ‪ J‬ﺍﻟﻰ ﺍﻟﺤﺎﻟﺔ )2-‪ (J‬ﻜﻤﺎ ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ ]3791 , ‪[Sorensen‬‬
‫= ‪hω‬‬
‫)2 − ‪E ( J ) − E ( J‬‬ ‫)1 − ‪J ( J + 1) − ( J − 2)( J‬‬

‫=‬

‫‪Eγ‬‬ ‫)1 − ‪J ( J + 1) − ( J − 2)( J‬‬

‫)22-2(‬

‫ﻤﻥ ﺍﻟﺘﻔﺎﺴﻴﺭ ﺍﻟﻤﻭﻀﻭﻋﺔ ﻟﻅﺎﻫﺭﺓ ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺍﻥ ﺴﺒﺏ ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻴﻌﻭﺩ ﺍﻟﻰ‬ ‫ﺘﺄﺜﻴﺭ ﻗﻭﺓ ﻜﻭﺭﻴﻭﻟﺱ ﻋﻨﺩ ﺯﺨﻭﻡ ﺯﺍﻭﻴﺔ ﻋﺎﻟﻴﺔ ﻨﺴﺒﻴﺎ ﻋﻠﻰ ﺒﻌﺽ ﺍﻟﻨﻜﻠﻴﻭﻨﺎﺕ ﺍﻟﻭﺍﻗﻌﺔ ﻓﻲ ﺍﻟﻘﺸﺭﺍﺓ‬ ‫ﹰ‬ ‫ﺍﻟﺨﺎﺭﺠﻴﺔ ﻟﻠﻨﻭﺍﺓ ﻤﻤﺎ ﻴﺅﺩﻱ ﺍﻟﻰ ﻓﻙ ﺍﺭﺘﺒﺎﻁ )‪ (De-pairing‬ﺯﻭﺝ ﺍﻭ ﺍﻜﺜﺭ ﻤﻥ ﻫﺫﻩ ﺍﻟﻨﻜﻠﻴﻭﻨﺎﺕ ,‬ ‫ﺍﻥ ﻓﻙ ﺍﺭﺘﺒﺎﻁ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻴﺅﺩﻱ ﺍﻟﻰ ﻅﻬﻭﺭ ﺤﺯﻤﺔ ﺸﺒﻴﻬﻲ ﺍﻟﺠﺴﻴﻤﻴﻥ‬ ‫)‪ (Two-Quasiparticle-2qp‬ﻭﻫﺫﻩ ﺍﻟﺤﺯﻤﺔ ﺘﺴﻤﻰ )‪ (S-Band‬ﻭﺘﻨﺘﺞ ﻫﺫﻩ ﺍﻟﺤﺯﻤﺔ ﻋﻥ‬ ‫ﺍﻷﺼﻁﻔﺎﻑ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻟﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﺘﺠﺎﻩ ﺤﺭﻜﺔ ﺍﻟﻨﻭﺍﺓ ﻜﻤﺎ ﻤﻭﻀـﺢ ﻓﻲ ﺍﻟﺸـﻜل‬ ‫)5-2( ﺍﺫ ﻴﻜﻭﻥ ﺍﺘﺠﺎﻩ ﺯﺨﻤﻲ ﺍﻟﻨﻴﺘﺭﻭﻨﻴﻥ ﻓﻲ ﺍﻟﺒﺩﺍﻴﺔ ﻤﺘﻌﺎﻜﺴﻴﻥ ﻭﺒﺎﺘﺠﺎﻩ ﻋﻤﻭﺩﻱ ﻋﻠﻰ ﺯﺨﻡ ﺍﻟﻨﻭﺍﺓ‬ ‫ﻭﺒﻌﺩ ﻓﻙ ﺍﻷﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﻴﻥ ﻭﺒﺴﺒﺏ ﺩﻭﺭﺍﻥ ﺍﻟﻨﻭﺍﺓ ﻴﺘﺭﺍﺼﻑ ﺍﻟﻨﻴﺘﺭﻭﻨﻴﻥ ﺒﺄﺘﺠﺎﻩ ﺍﻟﻨﻭﺍﺓ‬ ‫ﻭﻴﺼﺒﺢ ﺍﻟﺯﺨﻡ ﺍﻟﻜﻠﻲ ﺒﺄﺘﺠﺎﻩ ﺯﺨﻡ ﺍﻟﻨﻭﺍﺓ , ﻭﺍﻥ ﻓﻙ ﺍﺭﺘﺒﺎﻁ ﺯﻭﺝ ﻤﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻓﻀﻼ ﻋﻥ ﺯﻭﺝ‬ ‫ﹰ‬ ‫ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻴﺅﺩﻱ ﺍﻟﻰ ﻅﻬﻭﺭ ﺤﺯﻤﺔ ﺍﺸﺒﺎﻩ ﺍﻟﺠﺴﻴﻤﺎﺕ ﺍﻷﺭﺒﻌﺔ )‪(Four-Quasiparticle-4qp‬‬ ‫ﻭﺘﻘﺎﻁﻊ ﻫﺫﻩ ﺍﻟﺤﺯﻡ ﻤﻊ ﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ ﻴﺴﺒﺏ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬ ‫‪، [Bengtsson‬‬ ‫‪and‬‬ ‫‪Frauendorf‬‬ ‫]9791,‬ ‫,‬ ‫‪[Stephens‬‬ ‫,‬ ‫]5791‬

‫]1991 , ‪.[Hara and Sun‬‬ ‫ﺍﺫﺍ ﻜﺎﻨﺕ ﺯﺍﻭﻴﺔ ﺍﻟﺘﻘﺎﻁﻊ ﻜﺒﻴﺭﺓ ﺒﻴﻥ ﺍﻟﺤﺯﻤﺔ ﺍﻟﻤﺜﺎﺭﺓ )‪ (S-band‬ﻭﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ‬ ‫)‪ (g-band‬ﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل )‪ (2-6a‬ﻓﺎﻥ ﺍﻟﺘﻔﺎﻋل ﺒﻴﻥ ﺍﻟﺤﺯﻤﺘﻴﻥ ﻋﻨﺩ ﻨﻘﻁﺔ ﺍﻟﺘﻘﺎﻁﻊ ﻴﻜﻭﻥ ﻀﻌﻴﻔﺎ‬ ‫ﹰ‬ ‫ﻭﻋﻨﺩﻫﺎ ﻴﻜﻭﻥ ﺘﻐﻴﺭ ﺍﻟﻁﺎﻗﺔ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﻤﻊ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻜﺒﻴﺭﺍ ﻭﻴﻜﻭﻥ ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻗﻭﻴﺎ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻭﻭﺍﻀﺤﺎ ﻭﺍﻟﺘﻐﻴﺭ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻤﻊ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻗﻭﻴﺎ ﻭﻤﻔﺎﺠﺌﺎ. ﺍﻤﺎ ﺍﺫﺍ ﻜﺎﻨﺕ ﺯﺍﻭﻴﺔ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﹰ‬
‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬ ‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫02‬

‫ﺍﻟﺘﻘﺎﻁﻊ ﺼﻐﻴﺭﺓ ﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل )‪ (2-6b‬ﻓﺄﻥ ﺍﻟﺘﻔﺎﻋل ﺒﻴﻥ ﺍﻟﺤﺯﻤﺘﻴﻥ ﻋﻨﺩ ﻨﻘﻁﺔ ﺍﻟﺘﻘﺎﻁﻊ ﻴﻜﻭﻥ‬ ‫ﻗﻭﻴﺎ ﻭﺍﻥ ﺘﻐﻴﺭ ﺍﻟﻁﺎﻗﺔ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﻤﻊ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻴﻜﻭﻥ ﻁﻔﻴﻔﺎ ﻭﺒﺫﻟﻙ ﻴﻜﻭﻥ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺼﻐﻴﺭﺍ ﻭﻴﻜﻭﻥ ﺘﻐﻴﺭ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻤﻊ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﺼﻐﻴﺭﺍ.‬ ‫ﹰ‬ ‫ﹰ‬

‫‪J‬‬

‫‪J‬‬

‫‪J‬‬ ‫‪J ω‬‬
‫‪ω‬‬

‫ﺍﻟﺸﻜل )5-2(: ﺘﺭﺍﺼﻑ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ‬

‫ﻭﺍﻟﺘﻔﺴﻴﺭ ﺍﻵﺨﺭ ﻟﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻫﻭ ﺍﻟﺘﺤﻭل ﺍﻟﻁﻭﺭﻱ ﻟﻠﻨﻭﺍﺓ ﻤﻥ ﺤﺎﻟﺔ ﺍﻟﻤﻴﻭﻋﺔ ﺍﻟﻔﺎﺌﻘﺔ‬ ‫)‪ (Super Fluid‬ﺍﻟﻰ ﺤﺎﻟﺔ ﺍﻟﻤﻴﻭﻋﺔ ﻏﻴﺭ ﺍﻟﻔﺎﺌﻘﺔ )‪ (Non-Super Fluid‬ﻭﺍﻟﻨﺎﺘﺞ ﻋﻥ ﺘﻐﻴﺭ‬ ‫ﺸﻜل ﺍﻟﻨﻭﺍﺓ ﻤﻥ ﺍﻟﺸﻜل ﺍﻟﺒﻴﻀﻭﻱ ﺍﻟﻤﺘﻁﺎﻭل ﺍﻟﻰ ﺍﻟﺒﻴﻀﻭﻱ ﺍﻟﻤﻔﻠﻁﺢ]1791, ‪, [Johnson et al‬‬ ‫]7791 , ‪[Lee et al‬‬

‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫12‬

‫‪E‬‬

‫‪g-band‬‬ ‫‪Yrast-band‬‬

‫‪E‬‬
‫‪g-band‬‬ ‫‪S-band‬‬

‫‪S-band‬‬ ‫‪Yrast-band‬‬

‫‪mixing‬‬ ‫‪area‬‬

‫‪mixing‬‬ ‫‪area‬‬

‫)‪ (b‬زاوﻳﺔ اﻟﺘﻘﺎﻃﻊ ﺻﻐﻴﺮة‬

‫‪J‬‬

‫)‪ (a‬زاوﻳﺔ اﻟﺘﻘﺎﻃﻊ آﺒﻴﺮة‬

‫‪J‬‬

‫ﺍﻟﺸﻜل )6-2(: ﺘﻘﺎﻁﻊ ﺤﺯﻤﺔ ﺍﻟﺤﺎﻟﺔ ﺍﻷﺭﻀﻴﺔ ﻤﻊ ﺍﻟﺤﺯﻤﺔ ﺍﻟﻤﺜﺎﺭﺓ )‪(S-band‬‬ ‫]1991, ‪[Hara and Sun‬‬

‫ﺨﺼﺎﺌﺹ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ‬

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ‬

‫ﺍﻟﺜﺎﻟﺚ‬

‫ﺍﻟﻔﺼﻞ‬

‫ﺍﻟﺒﻮﺯﻭﻧﺎﺕ ﺍﳌﺘﻔﺎﻋﻠﺔ‬

‫ﺍﳕﻮﺫﺝ‬

‫)1-‪(IBM‬‬

‫22‬

‫‪Interacting Bosone Model‬‬

‫3 ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫ﺍﻗﺘﺭﺡ ﺍﻟﺒﺎﺤﺜﺎﻥ ]4791,‪ [Arima and Iachello‬ﺃﻨﻤﻭﺫﺠﺎ ﺠﺩﻴﺩﺍ ﻟﺩﺭﺍﺴﺔ ﺍﻟﻨـﻭﺍﺓ ﺍﻁﻠﻘـﺎ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻋﻠﻴﻪ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ 1-‪، IBM‬ﺍﺫ ﻋﺩﺕ ﺍﻟﻨﻭﺍﺓ ﻤﻜﻭﻨﺔ ﻤﻥ ﻗﻠﺏ ﻫﺎﻤﺩ,ﺒﺄﻋﺩﺍﺩ ﺴﺤﺭﻴﺔ‬ ‫ﹰ‬ ‫ﻤﻥ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻭﻋﺩﺩ ﺁﺨﺭ ﻤﻥ ﺍﻟﻨﻜﻠﻴﻭﻨﺎﺕ ﺨﺎﺭﺝ ﺍﻟﻘﻠﺏ ﺘﺩﻋﻰ ﺒﻨﻜﻠﻴﻭﻨـﺎﺕ ﺍﻟﺘﻜـﺎﻓﺅ‬ ‫ﻭﻋﺩ ﻜل ﺯﻭﺝ ﻤﻥ ﻨﻜﻠﻴﻭﻨﺎﺕ ﺍﻟﺘﻜﺎﻓﺅ ﻫﺫﻩ ﺒﻭﺯﻭﻨﺎ ﺩﻭﻥ ﺍﻟﺘﻤﻴﻴﺯ ﻓﻲ ﻫﺫﺍ ﺍﻷﺼﺩﺍﺭ ﺍﻷﻭل ﻟﻸﻨﻤﻭﺫﺝ‬ ‫ﹰ‬ ‫‪‬‬ ‫1-‪ IBM‬ﺒﻴﻥ ﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ) ‪ (π‬ﻭﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ ) ‪, (ν‬ﻭﺍﻓﺘـﺭﺽ ﻓـﻲ ﻫـﺫﺍ‬ ‫ﺍﻷﻨﻤﻭﺫﺝ ﺍﻥ ﻫﻨﺎﻙ ﻨﻭﻋﻴﻥ ﻤﻥ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺒﻭﺯﻭﻨﺎﺕ ﺒﺯﺨﻡ ﺯﺍﻭﻱ )0=‪ (L‬ﺘﺩﻋﻰ ﺒﻭﺯﻭﻨـﺎﺕ )‪(s‬‬ ‫ﻭﺒﻭﺯﻭﻨﺎﺕ ﺒﺯﺨﻡ ﺯﺍﻭﻱ )2=‪ (L‬ﺘﺩﻋﻰ ﺒﻭﺯﻭﻨﺎﺕ )‪.(d‬ﻭﻴﺘﻡ ﺤﺴﺎﺏ ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ )ﺒﻭﺯﻭﻨـﺎﺕ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ‪ nπ‬ﻭﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ‪ ( nυ‬ﺒﻭﺼﻔﻬﺎ ﺍﺯﻭﺍﺝ ﺍﻟﺠﺴﻴﻤﺎﺕ ﺍﺒﺘﺩﺍﺀﺍ ﻤﻥ ﺍﻗﺭﺏ ﻗﺸﺭﺓ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻤﻐﻠﻘﺔ ﻭﺤﺘﻰ ﻤﻨﺘﺼﻑ ﺍﻟﻘﺸﺭﺓ ﺍﻟﺘﻲ ﺘﻠﻴﻬﺎ , ﺍﻤﺎ ﺍﺫﺍ ﻜﺎﻥ ﺍﻜﺜﺭ ﻤﻥ ﻨﺼﻑ ﺍﻟﻘﺸﺭﺓ ﻤﻤﺘﻠﺌﺎ ﻓـﺎﻥ ) ‪(nπ‬‬ ‫ﻭ ) ‪ (nυ‬ﺘﺅﺨﺫ ﻜﻌﺩﺩ ﺍﺯﻭﺍﺝ ﺍﻟﻔﺠﻭﺍﺕ ﺍﻟﻰ ﺍﻟﻘﺸﺭﺓ ﺍﻟﻤﻐﻠﻘﺔ ﺍﻟﺘﻲ ﺘﻠﻴﻬﺎ ﻭﺍﻥ ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻜﻠـﻲ‬

‫ﻜﻤﻴﺔ ﺜﺎﺒﺘﺔ ﻭﻤﺤﻔﻭﻅﺔ ﻟﻜل ﻨﻭﺍﺓ ‪N = n π + n υ‬‬ ‫]8791 , ‪[Casten and Warner , 1988] , [Iachello , 1980],[Scholten et al‬‬ ‫ﻭﻫﻨﺎﻙ ﺍﺼﺩﺍﺭﺍﺕ ﺍﺨﺭﻯ ﻤﻥ ﺍﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ )‪ (IBM‬ﺘﻌﺘﻤـﺩ ﻋﻠـﻰ ﺍﺯﻭﺍﺝ‬
‫ﺍﻟﻔﺭﻤﻴﻭﻨﺎﺕ ﺍﻟﻌﺎﺌﺩﺓ ﻟﻠﺒﻭﺯﻭﻨﺎﺕ ]3002,‪. [NSDD‬ﻓﺎﻻﺼﺩﺍﺭ ﺍﻻﻭل ﻭﻜﻤﺎ ﺫﻜﺭﻨﺎ 1-‪ IBM‬ﻴﻌﺘﻤﺩ‬ ‫ﻋﻠﻰ ﺍﻟﻨﻭﻉ ﺍﻟﻤﻨﻔﺭﺩ ﻤﻥ ﺍﺯﻭﺍﺝ ﺍﻟﻔﺭﻤﻴﻭﻨﺎﺕ,ﺃﻱ ﻻﻴﻤﻴﺯ ﺒﻴﻥ ﺍﻟﺒﺭﻭﺘﻭﻨـﺎﺕ ﻭﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ ﻭﻴﻌـﺩﻫﺎ‬ ‫‪‬‬ ‫‪‬‬ ‫ﻜﻨﻜﻠﻴﻭﻨﺎﺕ ﻤﺘﺸﺎﺒﻬﺔ, ﻓﻲ ﺤﻴﻥ ﻨﺠﺩ ﺍﻥ ﺍﻨﻤﻭﺫﺝ 2-‪ IBM‬ﻴﻤﻴﺯ ﺒـﻴﻥ ﺍﻟﺒﺭﻭﺘﻭﻨـﺎﺕ ﻭﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ‬ ‫‪‬‬

‫ﻭﻴﻌﺘﻤﺩ ﻋﻠﻰ ﺍﻟﺒﺭﻡ ﺍﻟﻤﺘﺴﺎﻭﻱ ﻟﻠﻨﻜﻠﻴﻭﻥ )1=‪ (T‬ﻭﻤﺭﻜﺒﺘﻪ ﺍﻟﺜﺎﻟﺜﺔ ﻟﺯﻭﺝ ﻨﻴﺘﺭﻭﻥ - ﻨﻴﺘـﺭﻭﻥ )‪(nn‬‬
‫ﻭﻴﻌﺘﻤﺩ ﻋﻠﻰ ﺍﻟﺘﻔﺎﻋل ﺒﻴﻥ ﺍﺯﻭﺍﺝ ‪ nn‬ﻭ‬

‫ﻫﻭ1-=‪.MT‬ﻭﻟﺯﻭﺝ ﺒﺭﻭﺘﻭﻥ-ﺒﺭﻭﺘﻭﻥ )‪MT=+1 (pp‬‬

‫‪ .pp‬ﺍﻤﺎ ﺍﻻﺼﺩﺍﺭﻴﻥ ﺍﻟﺠﺩﻴﺩﻴﻥ 3-‪ IBM‬ﻓﺎﻨﻪ ﻴﻌﺘﻤﺩ ﻋﻠﻰ ﺍﻟﺒﺭﻡ ﺍﻟﻤﺘﺴﺎﻭﻱ ﺍﻟﻜﺎﻤل )1=‪ (T‬ﻟﺠﻤﻴـﻊ‬ ‫ﺍﺯﻭﺍﺝ ﺍﻟﻔﺭﻤﻴﻭﻨﺎﺕ ﺍﺨﺫﺍ ﺒﻌﻴﻥ ﺍﻻﻋﺘﺒﺎﺭ ﺍﻟﺘﻔﺎﻋـل ﺒـﻴﻥ ﺍﺯﻭﺍﺝ ‪ nn‬ﺒﻘﻴﻤـﺔ 1-=‪ MT‬ﻭ ‪ np‬ﺒــ‬ ‫ﹰ‬ ‫0=‪ MT‬ﻭ ‪ pp‬ﺒـ 1+=‪ , MT‬ﻓﻴﻤﺎ ﻨﺠﺩ ﺍﻻﺼﺩﺍﺭ 4-‪ IBM‬ﻴﺎﺨﺫ ﺒﻌﻴﻥ ﺍﻻﻋﺘﺒﺎﺭ ﺍﻟﺒﺭﻡ ﺍﻟﻤﺘﺴﺎﻭﻱ‬ ‫ﺍﻟﻜﺎﻤل )1=‪ (T‬ﻭﻜﺫﻟﻙ )0=‪ (T‬ﻓﻬﻭ ﺍﺸﻤل ﻤﻥ ﺍﻻﺼﺩﺭﺍﺕ ﺍﻟﺴﺎﺒﻘﺔ ﺍﺫ ﻴﻌﺘﻤﺩ ﻋﻠﻰ ﺍﻟﺘﻔﺎﻋل ﺒـﻴﻥ‬

‫ﺍﺯﻭﺍﺝ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻭﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﺫﺍﺕ )1=‪ (S=0,T‬ﻭ )0=‪ . (S=1,T‬ﺍﻥ ﺍﻟﻨﻤﻭﺫﺠﻴﻥ 3-‪IBM‬‬
‫ﻭ 4-‪ IBM‬ﻴﺘﻀﻤﻨﺎﻥ ﺘﻔﺎﻋل ﺍﺯﻭﺍﺝ ‪ np‬ﻭﺍﻟﺫﻱ ﻻﻴﺅﺨﺫ ﺒﺎﻻﻋﺘﺒﺎﺭ ﻓـﻲ ﺍﻻﻨﻤـﻭﺫﺠﻴﻥ ﺍﻟـﺴﺎﺒﻘﻴﻥ‬ ‫1-‪ IBM‬ﻭ 2-‪,IBM‬ﻭﺍﻨﻬﻤﺎ ﻤﻬﻤﺎﻥ ﺠﺩﺍ ﻓﻲ ﺍﻟﺘﻁﺒﻴﻕ ﻟﻠﻨﻭﻯ ﺍﻟﺘﻲ ﻓﻴﻬﺎ ‪ N=Z‬ﻭ ‪ N~Z‬ﻭﺘﺒﻌﺎ ﻟﻬﺫﺍ‬ ‫ﹰ‬ ‫ﹰ‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫32‬

‫ﺍﻟﻭﺼﻑ ﻟﻸﻨﻤﻭﺫﺠﺎﺕ ﺍﻻﺭﺒﻌﺔ ﻓﺎﻥ 1-‪ IBM‬ﻫﻭ ﺍﻻﻨﺴﺏ ﻟﻸﺴﺘﺨﺩﺍﻡ ﻓﻲ ﺩﺭﺍﺴﺘﻨﺎ ﺍﻟﺤﺎﻟﻴﺔ ﻭﻴﻼﺌـﻡ‬ ‫ﺍﻟﻨﻭﻯ ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴﺔ.‬

‫‪Hamiltonian Operator‬‬

‫1-3 ﻤﺅﺜﺭ ﻫﺎﻤﻠﺘﻭﻥ‬

‫ـﺔ ]8791 ,‪،[Scholten et al‬‬ ‫ـﺔ ﺍﻵﺘﻴـ‬ ‫ـﻰ ـﺅﺜﺭ ـﺔ ـﺎﻤﻠﺘﻭﻥ ﺒﺎﻟﻌﻼﻗـ‬ ‫ﺩﺍﻟـ ﻫـ‬ ‫ﻴﻌﻁـ ﻤـ‬ ‫]9791 ,‪: [Iachello, 1980] ،[Arima and Iachello‬‬
‫‪N‬‬ ‫‪N‬‬

‫ˆ‬ ‫‪H = ∑ ε i + ∑ Vij‬‬
‫1= ‪i‬‬ ‫‪i< j‬‬

‫)1-3(‬

‫ﺍﺫ ﺍﻥ )‪ (ε‬ﻫﻲ ﻁﺎﻗﺔ ﺍﻟﺒﻭﺯﻭﻥ ﺍﻟﺫﺍﺘﻴﺔ ﻭ)‪ (N‬ﻫﻲ ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻭ )‪ (Vij‬ﻫﻲ ﻁﺎﻗﺔ ﺍﻟﺘﻔﺎﻋل ﺒﻴﻥ‬ ‫ﺍﻟﺒﻭﺯﻭﻨﺎﺕ )‪ i‬ﻭ‪(j‬‬ ‫ﻴﻤﻜــــﻥ ﺼــــﻴﺎﻏﺔ ﺍﻟﻤﻌﺎﺩﻟــــﺔ )1-3( ﺒﺎﺴــــﺘﻌﻤﺎل ﺼــــﻴﻐﺔ‬ ‫‪،[Iachello, 1980] (Multipole Expansion‬‬

‫ﺍﻟﻤﻤﺘـﺩ ﻤﺘﻌـﺩﺩ ﺍﻟﻘﻁﺒﻴـﺔ )‪Form‬‬

‫]8891 ,‪:[Greiner and Maruhn, 1996] ،[Casten and Warner‬‬

‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫4‪H = εn d + a o P.P + a1L.L + a 2 Q.Q + a 3T3 .T3 + a 4T4 .T‬‬

‫)2-3(‬

‫ﺇﺫ ﺍﻥ:‬

‫‪ε = εd − εs‬‬

‫)3-3(‬

‫ﻭﻟﻠﺴﻬﻭﻟﺔ ﺃﻋﺘﺒﺭ 0 = ‪ ε s‬ﻭﺒﺫﻟﻙ ﺘﻜﻭﻥ ﻁﺎﻗﺔ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻤﺴﺎﻭﻴﺔ ﻟﻁﺎﻗﺔ ﺒﻭﺯﻭﻨـﺎﺕ )‪(d‬‬
‫) ‪ ( ε = ε d‬ﻭﺍﻟﻤﻌﺎﻤﻼﺕ )‪ (a4, a3, a2, a1, ao‬ﺘﻤﺜل ﻗﻭﺓ ﺍﻟﺘﻔﺎﻋل ﺍﻻﺯﺩﻭﺍﺠﻲ ﻭﺍﻟﺯﺨﻡ ﺍﻟـﺯﺍﻭﻱ‬ ‫ﻭﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﻭﺜﻤﺎﻨﻲ ﺍﻟﻘﻁﺏ ﻭﺍﻟﻘﻁﺏ ﺍﻟﺴﺩﺍﺴﻲ ﻋﺸﺭ ﺒﻴﻥ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻋﻠﻰ ﺍﻟﺘﻭﺍﻟﻲ. ﻭﺘﻌﻁـﻰ‬ ‫ﻤﺅﺜﺭﺍﺕ ﺍﻟﻤﻌﺎﺩﻟﺔ )2-3( ﻜﻤﺎ ﻴﺄﺘﻲ: ]0891 ,‪:[Casten and Warner, 1988] ،[Iachello‬‬

‫ˆ‬ ‫) ‪ ( n d‬ﻤﺅﺜﺭ ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻤﻥ ﺍﻟﻨﻭﻉ ‪:d‬‬

‫ˆ‬ ‫~ ˆ‬ ‫ˆ‬ ‫] ‪n d = [d + . d‬‬
‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫)4-3(‬
‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫42‬

‫ˆ‬ ‫) ‪ ( P‬ﻤﺅﺜﺭ ﻁﺎﻗﺔ ﺍﻻﺯﺩﻭﺍﺝ )‪:(Pairing‬‬
‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫‪ˆ 1 ~ ~ 1 s s‬‬ ‫]~ . ~[ − ] ‪P = [ d . d‬‬ ‫2‬ ‫2‬
‫)5-3(‬

‫ˆ‬ ‫) ‪ ( L‬ﻤﺅﺜﺭ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ )‪:(Angular Momentum‬‬

‫~‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫)1(] ‪L = 10 [d + × d‬‬

‫)6-3(‬

‫ˆ‬ ‫) ‪ ( Q‬ﻤﺅﺜﺭ ﺍﻟﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ )‪:(Quadrupole‬‬

‫)2 ( ~ + ˆ 7‬ ‫~‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ ‪s‬‬ ‫] ‪[d × d‬‬ ‫− )2 (] ‪Q = [d + × ~ + s + × d‬‬ ‫2‬

‫)7-3(‬

‫ˆ‬ ‫) 3‪ ( T‬ﻤﺅﺜﺭ ﺍﻟﺜﻤﺎﻨﻲ ﺍﻟﻘﻁﺏ )‪:(Octapole‬‬

‫~‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫)3(] ‪T3 = [d + × d‬‬

‫)8-3(‬

‫ˆ‬ ‫) 4‪ ( T‬ﻤﺅﺜﺭ ﺍﻟﻘﻁﺏ ﺍﻟﺴﺩﺍﺴﻲ ﻋﺸﺭ )‪:(Hexadecapole‬‬
‫~‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫)4 (] ‪T4 = [d + × d‬‬
‫)9-3(‬

‫ﻭﻤﻥ ﺍﻟﺨﻭﺍﺹ ﺍﻷﺨﺭﻯ ﺍﻟﺘﻲ ﻴﻤﻜﻥ ﺤﺴﺎﺒﻬﺎ ﻓﻀﻼ ﻋﻥ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺒﺎﺴﺘﻌﻤﺎل ﻫـﺫﺍ‬ ‫ﹰ‬ ‫ﺍﻷﻨﻤ ـﻭﺫﺝ ﻫ ـﻲ ﻤﻌ ـﺩﻻﺕ ﺍﻻﻨﺘﻘ ـﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴ ـﺴﻴﺔ. ﺇﻥ ﺍﻟﻤ ـﺅﺜﺭ ﺭﺒ ـﺎﻋﻲ ﺍﻟﻘﻁﺒﻴ ـﺔ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫ـ‬ ‫,‪،[Iachello‬‬

‫‪1980] ،[Scholten‬‬

‫‪et‬‬

‫,‪al‬‬

‫)2‪ (E‬ﻴﻌﻁـــﻰ ﺒﺎﻟﻤﻌﺎﺩﻟـــﺔ ]8791‬
‫]8891 ,‪.[Casten and Warner‬‬

‫(‬ ‫)2 ‪TµE‬‬

‫)2 (‬ ‫)2 (‬ ‫ˆ‬ ‫ˆ‬ ‫⎤ ~ × + ‪⎡ d + × ~ + s + × ~ ⎤ + β ⎡d‬‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫‪s‬‬ ‫⎥‪d‬‬ ‫⎥‪d‬‬ ‫⎢ 2‪= α‬‬ ‫⎢2‬ ‫⎣‬ ‫‪⎦µ‬‬ ‫⎣‬ ‫‪⎦µ‬‬

‫)01-3(‬

‫ﺇﺫ ﺍﻥ ) 2 ‪ ( α‬ﻭ ) 2 ‪ ( β‬ﻤﻌﺎﻤﻼﺕ ﺘﺼﻑ ﺍﻟﺤﺩﻭﺩ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻓﻲ ﺍﻟﻤﺅﺜﺭ، ﻜﻤﺎ ﻴﻤﻜﻥ ﺤـﺴﺎﺏ ﻤﻌـﺩل‬

‫ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ ﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺒﻴﺔ ﺍﻟﻤﺨﺘﺯﻟﺔ ﻤﻥ ﺍﻟﻌﻼﻗﺔ ]0891 ,‪[Iachello‬‬
‫]7891 ,‪.[Arima and Iachello‬‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫52‬
‫2‬

‫1‬ ‫ˆ‬ ‫= ) ‪B( E 2; L i → L f‬‬ ‫‪L f T ( E 2) L i‬‬ ‫1 + ‪2L i‬‬

‫)11-3(‬

‫ﻋﻨﺎﺼﺭ ﺍﻟﻤﺼﻔﻭﻓﺔ ﺍﻟﺨﺎﺼﺔ ﺒﺎﻻﻨﺘﻘﺎل )2‪.(E‬‬

‫ˆ‬ ‫‪L f T ( E 2) L i‬‬

‫ﺍﺫ ﻴﻤﺜل‬

‫‪Dynamical Symmetries‬‬
‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫‪H IBM = ε s n s + ε d n d‬‬

‫2-3 ﺍﻟﺘﻨﺎﻅﺭﺍﺕ ﺍﻟﺤﺭﻜﻴﺔ‬

‫ﻴﻤﻜﻥ ﻜﺘﺎﺒﺔ ﺍﻟﻤﻌﺎﺩﻟﺔ )1-3( ﺒﺎﻟﺼﻴﻐﺔ ﺍﻻﺘﻴﺔ ]6991 ,‪:[Greiner and Maruhn‬‬

‫1‬ ‫~ ~‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫⎤ ‪2L + 1 C L ⎡[d + × d + ]L × [ d × d ]L‬‬ ‫∑ +‬ ‫⎢‬ ‫⎥‬ ‫⎣‬ ‫⎦‬ ‫2 4 ,2 ,0 = ‪L‬‬

‫0‬

‫⎤2 ~ ~ 2 + +ˆ 2 ~ ~ 2 +ˆ +ˆ ⎡ ~ 1‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫⎥ ] ‪V2 ⎢[d × d ] × [ d × s ] + [d × s ] × [ d × d‬‬ ‫+‬ ‫⎣ 2‬ ‫⎦‬ ‫ˆ ~1‬ ‫~ ~‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ ˆ‬ ‫‪s s‬‬ ‫⎤ 0] ‪+ Vo ⎡[d + × d + ]0 × [ ~ × ~ ]0 + [s + × s + ]0 × [ d × d‬‬ ‫⎥‬ ‫⎢ 2‬ ‫⎣‬ ‫⎦‬ ‫ˆ ~‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫⎤ 2] ~ × ‪+ U 2 ⎡[d + × s + ]2 × [ d‬‬ ‫⎥ ‪s‬‬ ‫⎢‬ ‫⎣‬ ‫⎦‬ ‫1‬ ‫ˆˆ‬ ‫‪ˆ ˆ ss‬‬ ‫)~ ~ + ‪+ U o (s + s‬‬ ‫2‬
‫0‬ ‫0‬

‫0‬

‫)21-3(‬

‫ﺍﺫ ﺍﻥ 0=‪ L‬ﻭ ‪ ε s‬ﻭ‪ ns‬ﻴﻤﺜﻼﻥ ﻁﺎﻗﺔ ﻭﻋﺩﺩ ﺒﻭﺯﻭﻨﺎﺕ ‪ s‬ﻭﺍﻥ ‪ ε d‬ﻭ‪ nd‬ﻴﻤﺜﻼﻥ ﻁﺎﻗﺔ ﻭﻋـﺩﺩ‬

‫ˆ ~‬ ‫ˆ‬ ‫ˆ ˆ‬ ‫ﺒﻭﺯﻭﻨﺎﺕ ‪ d‬ﻭﺍﻥ ) + ‪ ( d + , s‬ﻤﺅﺜﺭﺍ ﺍﻟﺘﻭﻟﻴﺩ )‪ (Creation Operators‬ﻭ ) ~ , ‪ ( d‬ﻫﻤﺎ ﻤﺅﺜﺭﺍ‬ ‫‪s‬‬
‫ﺍﻟﻔﻨﺎﺀ )‪ (Annihilation Operators‬ﻟﻠﺒﻭﺯﻭﻨﺎﺕ ﻭ )4 ,2 ,0 = ‪ CL(L‬ﻭ )2 ,0 = ‪ VL(L‬ﻭ‬ ‫)2 ,0 = ‪ UL(L‬ﺘﻤﺜل ﺘﻔﺎﻋل ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻤـﻊ ﺒﻌـﻀﻬﺎ ]9791 ,‪،[Arima and Iachello‬‬

‫]0891 ,‪[Iachello‬‬
‫ﻭﻋﻨﺩ ﺘﻁﺒﻴﻕ ﺍﻟﺤل ﺍﻟﺘﺤﻠﻴﻠﻲ ﻋﻠﻰ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ )1-‪ (IBM‬ﻴﺘﺒﻴﻥ ﺃﻥ ﻫﻨﺎﻙ‬ ‫ﺜﻼﺙ ﺤﺎﻻﺕ ﻓﻘﻁ ﻴﻤﻜﻥ ﺘﺤﻠﻴﻠﻬﺎ، ﺍﻥ ﻫﺫﻩ ﺍﻟﺤﺎﻻﺕ ﺍﻟـﺜﻼﺙ ﻤـﺼﻨﻔﺔ ﺒـﺜﻼﺙ ﺴﻼﺴـل ﺯﻤﺭﻴـﺔ‬ ‫)‪ (Group Chain‬ﺘﺒﺩﺃ ﺒﺎﻟﺯﻤﺭﺓ )6(‪ U‬ﻭﺘﻨﺘﻬﻲ ﺒﺯﻤﺭ ﻤﺨﺘﻠﻔﺔ ﺤﺴﺏ ﻨﻭﻉ ﺍﻟﺘﺤﺩﻴﺩ ﺍﻟﺫﻱ ﺘﻤﺘﻠﻜـﻪ‬
‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬ ‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫62‬

‫ـﻲ ]0891 ,‪،[Iachello‬‬ ‫ـﺔ ﻫــ‬ ‫ـﺩﺍﺕ ﻤﺨﺘﻠﻔــ‬ ‫ـﺔ ﺘﺤﺩﻴــ‬ ‫ـﺎﻙ ﺜﻼﺜــ‬ ‫ـﻭﺍﺓ ﻭﻫﻨــ‬ ‫ﺍﻟﻨــ‬

‫]7891 ,‪[Casten and Warner, 1988] ،[Arima and Iachello‬‬

‫‪Vibrational Limit‬‬

‫1-2-3 ﺍﻟﺘﺤﺩﻴﺩ ﺍﻻﻫﺘﺯﺍﺯﻱ‬

‫ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﺘﻜﻭﻥ ﻁﺎﻗﺔ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ) ‪ (ε‬ﺍﻜﺒﺭ ﺒﻜﺜﻴﺭ ﻤﻥ ﺠﻬﺩ ﺍﻟﺘﻔﺎﻋل ﺒﻴﻥ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ‬ ‫ﺃﻱ )‪ (ε >> V‬ﻴﺘﻤﺜل ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﺒﺎﻟﻤﺠﻤﻭﻋﺔ ﺍﻟﻔﺭﻋﻴﺔ )5(‪ SU‬ﻭﺍﻟﻘﻴﻤﺔ ﺍﻟﺫﺍﺘﻴﺔ ﻟﻠﻬﺎﻤﻠﺘﻭﻥ ﺘﻌﺭﻑ‬

‫ﺒـ ]5002 , ‪:[NSDD‬‬

‫)31-3( )1+ ‪E ( n d , ν,L )= ε n d + k1 n d (n d + 4) +k 4 ν(ν + 3) + k 5 L(L‬‬
‫ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﺘﻨﺤل ﺍﻟﺯﻤﺭﺓ ﺍﻟﻭﺤﺩﻭﻴﺔ )6(‪ U‬ﺍﻟﻰ ﺍﻟﺴﻠـﺴﻠﺔ , ]4891 , ‪[Dieoerink‬‬ ‫]7891 , ‪[Arima and Iachello‬‬
‫)2 (‪U (6) ⊃ SU (5) ⊃ O (5) ⊃ O (3) ⊃ O‬‬

‫)41-3(‬

‫]‪[N‬‬

‫‪nd‬‬

‫∆‪ν , n‬‬

‫‪L‬‬

‫‪ML‬‬

‫ﺍﺫ ﺍﻥ ) ‪ (n d , ν, n ∆ , L, M L‬ﻭﺍﻟﺘﻲ ﺘﻌﺭﻑ ﻜﻤﺎ ﻴﺄﺘﻲ ]7891 , ‪:[Arima and Iachello‬‬ ‫‪ nd‬ﻫﻲ ﻋﺩﺩ ﺒﻭﺯﻭﻨﺎﺕ ‪ d‬ﻭﺘﺄﺨﺫ ﺍﻟﻘﻴﻡ ﺍﻵﺘﻴﺔ :‬

‫.…,1-‪nd=N , N‬‬

‫)51-3(‬

‫ﻭ ‪ ν‬ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻤﻥ ﻨﻭﻉ ‪ d‬ﻏﻴﺭ ﺍﻟﻤﺭﺘﺒﻁﺔ ﺒﺯﺨﻡ ﺯﺍﻭﻱ ﺼﻔﺭﻱ ﻭﺘﺄﺨﺫ ﺍﻟﻘﻴﻡ :‬

‫)‪ν = n d , n d − 2,....1,0 (nd odd or even‬‬

‫)61-3(‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫72‬

‫ﺘﻤﺜل ﺜﻼﺜﻴﺎﺕ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ﺒﺯﺨﻡ ﺯﺍﻭﻱ ﺼﻔﺭﻱ ﻭ ‪ L‬ﻫﻭ ﺍﻟﺯﺨﻡ ﺍﻟـﺯﺍﻭﻱ ﻭ‬

‫∆‪n‬‬

‫ﻭ‬

‫‪ ML‬ﻫﻲ ﺍﻟﻤﺭﻜﺒﺔ ﺍﻟﺜﺎﻟﺜﺔ ﻟﻠﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ.‬ ‫ﻭﻴﺨﺘﺯل ﻫﺎﻤﻠﺘﻭﻥ ﻤﺘﻌﺩﺩ ﺍﻟﻘﻁﺒﻴﺔ ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﺇﻟﻰ ]8891 ,‪:[Casten and Warner‬‬

‫ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫4‪H ( I) = εn d + a1L.L + a 3T3 .T3 + a 4 T4 .T‬‬

‫)71-3(‬

‫ˆ ˆ‬ ‫ﻴﺘﺒﻴﻥ ﻤﻥ ﺍﻟﻤﻌﺎﺩﻟﺔ )71-3( ﺇﻥ ﺍﻟﻤﺅﺜﺭﻴﻥ ) ‪ ( Q , P‬ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )2-3( ﻏﻴﺭ ﻓﻌـﺎﻟﻴﻥ‬
‫ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ، ﻭﺍﻟﺸﻜل )1-3( ﻴﻤﺜل ﻁﻴﻔﺎ ﻨﻤﻭﺫﺠﻴﺎ ﻟﻠﺘﺤﺩﻴﺩ )5(‪.SU‬‬ ‫ﹰ‬ ‫ﻭﻤﺅﺜﺭ ﺍﻷﻨﺘﻘﺎل ﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﻴﻌﻁﻰ ﺒﺎﻟﻤﻌﺎﺩﻟـﺔ )01-3( ﻭﻴﺤﻘـﻕ‬

‫ﻗﻭﺍﻋﺩ ﺍﻻﺨﺘﻴﺎﺭ 1±,0 = ‪[Arima et al , 1977] ∆nd‬‬
‫ﺃﻤﺎ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﺨﺘﺯﻟﺔ ﻻﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎل ﺭﺒﺎﻋﻲ ﺍﻟﻘﻁﺒﻴﺔ ﺒﻴﻥ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﺤﺎﻟـﺔ ﺍﻷﺭﻀـﻴﺔ‬ ‫ﻓﺈﻨﻬﺎ ﺘﻌﻁﻰ ﺒـ ]8791 ,‪:[Arima and Iachello, 1987] ،[Scholten et al‬‬

‫1‬ ‫)‪B( E 2; L + 2 → L) = α 2 ( L + 2)(2 N − L‬‬ ‫2‬ ‫4‬

‫)81-3(‬

‫ﺍﻤﺎ ﻨﺴﺏ ﺍﻟﺘﻔﺭﻉ )‪ R (Branching Ratios‬ﻭ '‪ R‬ﻭ ''‪ R‬ﻟﻠﺘﺤﺩﻴـﺩ )5(‪ SU‬ﻓﺘﻌﻁـﻰ‬ ‫ﺒﺎﻟﻤﻌﺎﺩﻻﺕ ﺍﻵﺘﻴﺔ ]9791 ,‪:[Arima and Iachello, 1987] ،[Arima and Iachello‬‬
‫+‬ ‫+‬ ‫) 12 → 14;2 ‪B(E‬‬ ‫)1 − ‪( N‬‬ ‫2=‬ ‫2 → ∞ → ‪⎯N‬‬ ‫⎯⎯‬ ‫=‪R‬‬ ‫+‬ ‫+‬ ‫‪N‬‬ ‫) 10 → 12;2 ‪B(E‬‬ ‫+‬ ‫+‬ ‫) 12 → 2 2;2 ‪B(E‬‬ ‫)1 − ‪( N‬‬ ‫2=‬ ‫2 → ∞ → ‪⎯N‬‬ ‫⎯⎯‬ ‫= '‪R‬‬ ‫+‬ ‫+‬ ‫‪N‬‬ ‫) 10 → 12;2 ‪B(E‬‬

‫)91-3(‬

‫)02-3(‬

‫= ' '‪R‬‬

‫+‬ ‫) 12 → + 0;2 ‪B( E‬‬ ‫)1 − ‪( N‬‬ ‫2‬ ‫2=‬ ‫2 → ∞ → ‪⎯N‬‬ ‫⎯⎯‬ ‫+‬ ‫+‬ ‫‪N‬‬ ‫) 10 → 12;2 ‪B( E‬‬

‫)12-3(‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫واﻟﺰﺧﻢ اﻟﺰاوي ﻟﻜﻞ ﻣﺴﺘﻮ.‬ ‫ٍ‬
‫82‬

‫)∆‪(ν,n‬‬

‫اﻟﺸﻜﻞ )1-3(: اﻟﻄﻴﻒ اﻟﻨﻤﻮذﺟﻲ ﻟﻠﺘﺤﺪﻳﺪ )5(‪ SU‬ﻟـ )6=‪ (N‬ﻣﻊ ﻗﻴﻢ‬ ‫]7891,‪[Arima and Iachello‬‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫]‬

‫92‬

‫‪Rotational Limit‬‬

‫2-2-3ﺍﻟﺘﺤﺩﻴﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ‬

‫ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﺘﻜﻭﻥ ﻁﺎﻗﺔ ﺍﻟﺘﻔﺎﻋل ﺒﻴﻥ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻜﺒﺭ ﺒﻜﺜﻴـﺭ ﻤـﻥ ﻁﺎﻗـﺔ ﺍﻟﺒﻭﺯﻭﻨـﺎﺕ‬ ‫ـﺴﺔ ]0891 ,‪،[Iachello‬‬ ‫ـﺔ )6(‪ U‬ـﻰ ﺍﻟﺴﻠـ‬ ‫ﺍﻟـ‬ ‫ـﺭﺓ ﺍﻟﻭﺤﺩﻭﻴـ‬ ‫ـل ﺍﻟﺯﻤـ‬ ‫)‪ (V >> ε‬ﻭﺘﻨﺤـ‬ ‫]7891 ,‪:[Arima and Iachello‬‬

‫)2( ‪U (6) ⊃ SU (3) ⊃ O (3) ⊃ O‬‬

‫)22-3(‬

‫]‪[N‬‬

‫‪(λ , µ) K‬‬

‫‪L‬‬

‫‪ML‬‬

‫ﻫﻲ ﺍﻋﺩﺍﺩ ﻜﻤﻴﺔ ﻤﺨﺘﺯﻟﺔ ﺘـﺭﺘﺒﻁ ﺒــ ‪ N‬ﺒﺎﻟﻌﻼﻗـﺔ‬

‫ﺍﺫ ﺍﻥ ‪ N‬ﻫﻲ ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻭ )‪(λ , µ‬‬

‫]0891 ,‪:[Arima and Iachello, 1987] ، [Iachello‬‬
‫⎫‪⎧ (0, N) ⎫ ⎧N = even‬‬ ‫⎨⊕....⊕ ) 4 , 8 − ‪( λ , µ ) = ( 2N, 0 ) ⊕( 2N − 4, 2)⊕ ( 2N‬‬ ‫⎬‬ ‫⎨⎬‬ ‫⎭ ‪⎩ (2, N −1) ⎭ ⎩N = odd‬‬ ‫‪⎧ ( 0, N − 3)⎫ ⎧N − 3 = even‬‬ ‫⎫‬ ‫⎨⊕....⊕ ) 2 ,01−‪⊕(2N− 6, 0)⊕(2N‬‬ ‫⎨⎬‬ ‫⎬‬ ‫⎭ ‪⎩( 2, N − 4) ⎭ ⎩N − 3 = odd‬‬ ‫⎫‬ ‫‪⎧ (0, N − 6 ) ⎫ ⎧ N − 6 = even‬‬ ‫⎨⊕....⊕)2 ,61−‪⊕(2N−12, 0)⊕(2N‬‬ ‫⎬‬ ‫⎨⎬‬ ‫⎭ ‪⎩ ( 2, N − 7 )⎭ ⎩ N − 6 = odd‬‬ ‫)32-3(‬ ‫....⊕‬

‫ﻭﻴﺩﺨل ﺍﻟﻌﺩﺩ ﺍﻟﻜﻤﻲ )‪ (K‬ﺒﻴﻥ ﺍﻟﺯﻤﺭﺘﻴﻥ )3(‪ SU‬ﻭ )3(‪ O‬ﻷﻥ ﺍﻟﺘﺤﻠل ﻻﻴﻜﻭﻥ ﺘﺎﻤﺎ , ﻭ ‪ K‬ﻟـﻪ‬ ‫ﹰ‬ ‫ً‬ ‫ﻋﻼﻗﺔ ﺒﻤﺴﻘﻁ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ‪ L‬ﻋﻠﻰ ﻤﺤﻭﺭ ﺍﻟﺘﻜﻤﻴﻡ .‬

‫ﻭﻴﻌﻁﻰ ﺍﻟﻬﺎﻤﻠﺘﻭﻨﻴﻥ ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﺒـ ]6891 , ‪[Barfield et al‬‬

‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ ˆ‬ ‫‪H ( II) = a1L.L + a 2 Q.Q‬‬

‫)42-3(‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫03‬

‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫ﻴﺘﺒﻴﻥ ﻤﻥ ﺍﻟﻤﻌﺎﺩﻟﺔ )42-3( ﺇﻥ ﺍﻟﻤﺅﺜﺭﺍﺕ ) ‪ ε‬ﻭ ‪ P‬ﻭ 3‪ T‬ﻭ 4‪ ( T‬ﻏﻴﺭ ﻓﻌﺎﻟﺔ ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴـﺩ‬
‫ﻭﺍﻟﺸﻜل )2-3( ﻴﻤﺜل ﻁﻴﻔﺎ ﻨﻤﻭﺫﺠﻴﺎ ﻟﻠﺘﺤﺩﻴﺩ )3(‪.SU‬‬ ‫ﹰ‬

‫اﻟﺸﻜﻞ )2-3(: اﻟﻄﻴﻒ اﻟﻨﻤﻮذﺟﻲ ﻟﻠﺘﺤﺪﻳﺪ )3(‪ SU‬ﻟـ )6=‪ (N‬ﻣﻊ ﻗﻴﻢ )‪ (λ,µ‬واﻟﺰﺧﻢ اﻟﺰاوي ﻟﻜﻞ ﻣﺴﺘﻮ.‬ ‫ٍ‬ ‫]7891,‪[Arima and Iachello‬‬
‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫)2‬
‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫13‬

‫ﻭﺍﻟﻘﻴﻤﺔ ﺍﻟﺫﺍﺘﻴﺔ ﻟﻠﻤﻌﺎﺩﻟﺔ )42-3( ﺘﻌﻁﻰ ﺒـ ]5002 , ‪:[NSDD‬‬

‫)1+‪E (λ,µ,L)=K2 (λ 2 +µ2 +3 (λ+µ )+λ µ)+K5 L(L‬‬

‫)52-3(‬

‫− 1‪[Casten and Warner, 1988] K 5 =a‬‬

‫2‪a‬‬ ‫2‪3 a‬‬ ‫= 2‪ K‬ﻭ‬ ‫ﺍﺫ ﺍﻥ‬ ‫8‬ ‫2‬

‫ـﺔ ﺍﻵ ـﺔ‬ ‫ﺘﻴـ‬ ‫ـﻰ ﺒﺎﻟﻤﻌﺎﺩﻟـ‬ ‫ـﺎﺌﻲ ﻴﻌﻁـ‬ ‫ـﺏ ﺍﻟﻜﻬﺭﺒـ‬ ‫ﺇﻥ ـﺅﺜﺭ ﺍﻻﻨ ـﺎل ـﺎﻋﻲ ﺍﻟﻘﻁـ‬ ‫ﺘﻘـ ﺭﺒـ‬ ‫ﻤـ‬ ‫]8791 ,‪:[Casten and Warner, 1988] ،[Arima and Iachello‬‬
‫(‬ ‫)2 ‪TµE‬‬ ‫)2 (‬ ‫⎛⎡‬ ‫ˆ‬ ‫⎤ ˆ‬ ‫⎟‪ˆ ˆ d‬‬ ‫⎥⎞ ~ × + ‪ˆ + × ~ + s + × ~ ⎞ − 7 ⎛ d‬‬ ‫‪s‬‬ ‫‪= α 2 ⎢⎜ d‬‬ ‫⎟‪d‬‬ ‫ˆ⎜‬ ‫⎝ 2‬ ‫‪⎠µ‬‬ ‫⎥⎠‬ ‫⎝⎢‬ ‫⎣‬ ‫⎦‬

‫)62-3(..…‬

‫− = 2‪β‬‬

‫7‬ ‫2‪α‬‬ ‫2‬

‫ﺤﻴﺙ ﻋ ‪‬ﺕ‬ ‫ﺩ‬

‫ـﺏ ـﻴﻥ ـﺴﺘﻭﻴﺎﺕ‬ ‫ـﺎل ـﺎﻋﻲ ﺍﻟﻘﻁـ ﺒـ ﻤـ‬ ‫ـﺔ ﺍﻻﻨﺘﻘـ ﺭﺒـ‬ ‫ـﺔ ﻻﺤﺘﻤﺎﻟﻴـ‬ ‫ـﺔ ﺍﻟﻤﺨﺘﺯﻟـ‬ ‫ﺃﻤ ـﺎ ﺍﻟﻘﻴﻤـ‬ ‫ـ‬ ‫ـﻰ ]8791 ,‪،[Iachello, 1980] ،[Scholten et al‬‬ ‫ـﺎ ﺘﻌﻁـ‬ ‫ـﻴﺔ ﻓﺈﻨﻬـ‬ ‫ـﺔ ﺍﻷﺭﻀـ‬ ‫ﺍﻟﺤﺎﻟـ‬ ‫]7891 ,‪:[Arima and Iachello‬‬

‫2 ‪B(E 2; L + 2 → L) = α‬‬ ‫2‬

‫)1 + ‪3(L + 2)(L‬‬ ‫)3 + ‪(2 N − L)(2 N + L‬‬ ‫)5 + ‪4(2L + 3)(2L‬‬

‫)72-3(‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫23‬

‫ﺍﻤﺎ ﻨﺴﺏ ﺍﻟﺘﻔﺭﻉ ‪ R‬ﻭ '‪ R‬ﻭ ''‪ R‬ﻟﻬﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﺘﻌﻁﻰ ﺒﺎﻟﻤﻌﺎﺩﻻﺕ ﺍﻵﺘﻴـﺔ‬ ‫]9791 ,‪:[Arima and Iachello, 1987] ،[Arima and Iachello‬‬
‫+‬ ‫+‬ ‫)5 + ‪B(E 2;41 → 21 ) 10 ( N − 1)(2 N‬‬ ‫01‬ ‫→ ∞ → ‪⎯N‬‬ ‫⎯⎯‬ ‫=‬ ‫+‬ ‫+‬ ‫7‬ ‫)3 + ‪B(E 2;21 → 01 ) 7 N(2 N‬‬ ‫+‬ ‫+‬ ‫) 12 → 2 2;2 ‪B(E‬‬ ‫0=‬ ‫+‬ ‫+‬ ‫) 10 → 12;2 ‪B(E‬‬

‫=‪R‬‬ ‫= '‪R‬‬

‫)82-3(‬

‫)92-3(‬

‫+‬ ‫+‬ ‫) 12 → 2 0;2 ‪B(E‬‬ ‫0=‬ ‫= ' '‪R‬‬ ‫+‬ ‫+‬ ‫) 10 → 12;2 ‪B(E‬‬

‫)03-3(‬

‫)6(‪γ - Unstable Limit O‬‬

‫3-2-3 ﺍﻟﺘﺤﺩﻴﺩ ‪ γ‬ﻏﻴﺭ ﺍﻟﻤﺴﺘﻘﺭ )6(‪O‬‬
‫∧ ∧‬

‫ﺍﻟﺘﻔﺎﻋل ) ‪ ( P. P‬ﺍﻟﺤﺎﺼل ﺒﻴﻥ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻫﻭ ﺍﻟﺴﺎﺌﺩ ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﻨﺴﺒﺔ ﺍﻟـﻰ ﻁﺎﻗـﺔ‬ ‫ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ) ‪ , ( V > > ε‬ﺍﻥ ﺍﻟﺯﻤﺭﺓ ﺍﻟﻭﺤﺩﻭﻴﺔ )6(‪ U‬ﺘﻨﺤل ﺍﻟﻰ ﺍﻟﺴﻠـﺴﻠﺔ ]0891 ,‪،[Iachello‬‬ ‫]7891 ,‪:[Arima and Iachello‬‬

‫)2( ‪U(6 ) ⊃ O (6) ⊃ O (5) ⊃ O (3) ⊃ O‬‬

‫)13-3(‬

‫]‪[N‬‬

‫‪σ‬‬

‫‪τ‬‬

‫∆‪ν‬‬

‫‪L‬‬

‫‪ML‬‬

‫ﻫﻲ ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻏﻴﺭ ﺍﻟﻤﺭﺘﺒﻁﺔ ﺒﺯﺨﻡ ﺯﺍﻭﻱ ﺼﻔﺭﻱ ﻭﺘﺄﺨﺫ ﺍﻟﻘﻴﻡ‬

‫‪σ‬‬

‫ﺍﺫ ﺍﻥ‬

‫]0891 , ‪:[Casten and Warner , 1988] , [Iachello‬‬

‫) ‪σ = N , N− 2 ,...., 0 or 1 ( N=even or odd‬‬

‫)23-3(‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫33‬

‫‪ τ‬ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻤﻥ ﻨﻭﻉ ‪ d‬ﻏﻴﺭ ﺍﻟﻤﺭﺘﺒﻁﺔ ﺒﺯﺨﻡ ﺯﺍﻭﻱ ﺼﻔﺭﻱ ﻭﺘﺄﺨﺫ ﺍﻟﻘﻴﻡ‬

‫]9791 , ‪:[Arima and Iachollo‬‬
‫0 , 1, ..... , 1 − ‪τ = σ , σ‬‬

‫)33-3(‬

‫ﺍﻥ ﺍﻟﺨﻁﻭﺓ ﺒﻴﻥ ﺍﻟﺯﻤﺭﺘﻴﻥ )5(‪ O‬ﻭ )3(‪ O‬ﻻﺘﻨﺤل ﺒﺎﻟﻜﺎﻤل ﻭﻟﻬﺫﺍ ﻴﺘﻡ ﺇﺩﺨﺎل ﺍﻟﻌﺩﺩ ﺍﻟﻜﻤـﻲ‬ ‫∆ ‪ ν‬ﺍﻟﺫﻱ ﻴﻤﺜل ﺜﻼﺜﻴﺎﺕ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ﺒﺯﺨﻡ ﺯﺍﻭﻱ ﺼﻔﺭﻱ ﻹﻜﻤﺎل ﺘﺤﻠل ﻫـﺫﻩ ﺍﻟﺤﺎﻟـﺔ ,‬ ‫ﻭﺘﺠﺯﺃ ‪ τ‬ﺇﻟﻰ :‬

‫‪τ = 3ν ∆ + λ‬‬

‫)43-3(‬

‫ﺇﺫ‬
‫...., 2 ,1, 0 = ∆ ‪ν‬‬ ‫‪nd‬‬ ‫3‬

‫)53-3(‬

‫ﺍﻤﺎ ‪ L‬ﻓﺘﺭﺘﺒﻁ ﺒـ ‪ λ‬ﺒﺎﻟﻌﻼﻗﺔ‬

‫‪L = 2λ , 2λ − 2 , ....., λ + 1, λ‬‬

‫)63-3(‬

‫ﻭﺍﻟﻘﻴﻤﺔ )1 − ‪ ( 2λ‬ﻏﻴﺭ ﻤﺴﻤﻭﺤﺔ ]7891 ,‪[Casten and Warner‬‬
‫ﺍﻥ ﺩﺍﻟﺔ ﻫﺎﻤﻠﺘﻭﻥ ﻟﻬﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﺘﻌﻁﻰ ﺒـ ]8891 ,‪:[Casten and Warner‬‬

‫ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫3‪H ( III) = a 0 P.P + a1L.L + a 3T3 .T‬‬

‫)73-3(‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫43‬

‫ﻭﺘﻌﻁﻰ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺒﺎﻟﻌﻼﻗﺔ ]5002 , ‪:[NSDD‬‬

‫)83-3( )1+‪E(σ,τ , L)=K 3 [ N(N+4) −σ (σ+4) ] +K4τ (τ +3) +K 5 L(L‬‬
‫ﺍﺫ ‪ K3=ao‬ﻭ 3/3‪ K4=a‬ﻭ 01/3‪[Casten and Warner, 1988] K5=a1+a‬‬ ‫ﻭﻟﺤﺯﻤﺔ ﺍﻟﺯﺨﻭﻡ ﺫﺍﺕ ﺍﻟﻁﺎﻗﺎﺕ ﺍﻟﺩﻨﻴﺎ ﻓﺄﻥ ‪ N = σ‬ﻭﺒﺫﻟﻙ ﺘﺼﺒﺢ ﺍﻟﻤﻌﺎﺩﻟﺔ )83-3(‬

‫)1+‪E(τ , L)=K4τ (τ +3) +K 5 L(L‬‬

‫)93-3(‬

‫ˆ ˆ‬ ‫ˆ‬ ‫ﻤﻥ ﺍﻟﻤﻌﺎﺩﻟﺔ )73-3( ﻴﺘﺒﻴﻥ ﺇﻥ ﺍﻟﻤﺅﺜﺭﺍﺕ ) ‪ ε‬ﻭ ‪ Q‬ﻭ 4‪ ( T‬ﻏﻴﺭ ﻓﻌﺎﻟﺔ ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ‬
‫ﻭﺍﻟﻁﻴﻑ ﺍﻟﻨﻤﻭﺫﺠﻲ ﻓﻲ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ﻤﺒﻴﻥ ﻓﻲ ﺍﻟﺸﻜل )3-3(‬

‫(ˆ‬ ‫ﺃﻤــــﺎ ﺍﻟﻤــــﺅﺜﺭ ) )2 ‪ ( TµE‬ﻓــــﻲ ﻫــــﺫﺍ ﺍﻟﺘﺤﺩﻴــــﺩ ﻓﺎﻨــــﻪ‬
‫]9791 ,‪،[Iachello, 1980] ،[Arima and Iachello‬‬ ‫ﻴﻜﺘــﺏ ﻜﻤــﺎ ﻴــﺄﺘﻲ‬ ‫]8891 ,‪:[Casten and Warner‬‬

‫~‬ ‫ˆ‬ ‫ˆ‬ ‫ˆ‬ ‫(ˆ‬ ‫⎤ ‪TµE 2) = α 2 ⎡d + × ~ + s + × d‬‬ ‫ˆ ‪s‬‬ ‫⎢‬ ‫⎥‬ ‫⎣‬ ‫‪⎦µ‬‬

‫)2 (‬

‫)04-3(‬
‫ﺍﺫ ﺃﻥ:‬

‫0 = 2‪β‬‬

‫)14-3(‬

‫ـﺔ‬ ‫ـﺎﻻﺕ ﺭﺒﺎﻋﻴـــ‬ ‫ـﺔ ﺍﻻﻨﺘﻘـــ‬ ‫ـﺔ ﻻﺤﺘﻤﺎﻟﻴـــ‬ ‫ـﺔ ﺍﻟﻤﺨﺘﺯﻟـــ‬ ‫ـﺭﻑ ﺍﻟﻘﻴﻤـــ‬ ‫ﻭﺘﻌـــ‬ ‫ـﺔ ]9791 ,‪،[Iachello, 1980] ،[Arima and Iachello‬‬ ‫ـﺔ ﺒﺎﻟﻌﻼﻗــ‬ ‫ﺍﻟﻘﻁﺒﻴــ‬ ‫]7891 ,‪:[Arima and Iachello‬‬

‫2 ‪B(E 2; L + 2 → L) = α‬‬ ‫2‬
‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫1 )2 + ‪(L‬‬ ‫)8 + ‪(2 N − L)(2 N + L‬‬ ‫4 )5 + ‪2(L‬‬

‫)24-3(‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫53‬

‫ﻭﻟﻠﺤﺎﻟﺔ 0=‪L‬‬

‫1‬ ‫+‬ ‫+‬ ‫)4 + ‪B( E 2;21 → 01 ) = α 2 N( N‬‬ ‫2‬ ‫5‬

‫)34-3(‬

‫ﺍﻤﺎ ﻟﻠﺤﺎﻟﺔ 2=‪ L‬ﻓﺄﻥ‬

‫2‬ ‫+‬ ‫+‬ ‫)5 + ‪B E2;41 →21 =α 2 ( N −1)(N‬‬ ‫2‬ ‫7‬

‫(‬

‫)‬

‫)44-3(‬

‫ـﺎﺩﻻﺕ ﺍﻵ ـﺔ‬ ‫ﺘﻴـ‬ ‫ـﺩ ﺒﺎﻟﻤﻌـ‬ ‫ـﺭﻉ ‪ R‬ﻭ '‪ R‬ﻭ ''‪ R‬ـﺫﺍ ﺍﻟﺘﺤﺩﻴـ‬ ‫ﻟﻬـ‬ ‫ـﻰ ـﺴﺏ ﺍﻟﺘﻔـ‬ ‫ﻭﺘﻌﻁـ ﻨـ‬ ‫]9791 ,‪:[Arima and Iachello, 1987] ،[Arima and Iachello‬‬
‫+‬ ‫+‬ ‫)5 + ‪B(E 2;41 → 21 ) 10 ( N − 1)( N‬‬ ‫01‬ ‫=‬ ‫→ ∞→‪⎯N‬‬ ‫⎯⎯‬ ‫+‬ ‫+‬ ‫7‬ ‫)4 + ‪B(E 2;21 → 01 ) 7 N( N‬‬

‫=‪R‬‬

‫)54-3(‬

‫+‬ ‫)5 + ‪B( E 2;2 + → 21 ) 10 ( N − 1)( N‬‬ ‫01‬ ‫2‬ ‫= '‪R‬‬ ‫=‬ ‫→ ∞ → ‪⎯N‬‬ ‫⎯⎯‬ ‫+‬ ‫+‬ ‫7‬ ‫)4 + ‪B( E 2;21 → 01 ) 7 N ( N‬‬

‫)64-3(‬

‫= ' '‪R‬‬

‫+‬ ‫+‬ ‫) 12 → 2 0;2 ‪B(E‬‬ ‫0=‬ ‫+‬ ‫+‬ ‫) 10 → 12;2 ‪B(E‬‬

‫)74-3(‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫واﻟﺰﺧﻢ اﻟﺰاوي ﻟﻜﻞ ﻣﺴﺘﻮ.‬ ‫ٍ‬

‫)∆‪(σ,ν‬‬

‫اﻟﺸﻜﻞ )3-3(: اﻟﻄﻴﻒ اﻟﻨﻤﻮذﺟﻲ ﻟﻠﺘﺤﺪﻳﺪ )6(‪ O‬ﻟـ )6=‪ (N‬ﻣﻊ ﻗﻴﻢ‬ ‫]7891,‪[Arima and Iachello‬‬

‫63‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫73‬

‫3-3 ﺍﻟﻤﻨﺎﻁﻕ ﺍﻻﻨﺘﻘﺎﻟﻴﺔ ﻓﻲ ﺃﻨﻤﻭﺫﺝ 1-‪IBM‬‬ ‫1-‪Transition Regions in IBM‬‬
‫ﺍﻥ ﺍﻟﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ ﺍﻟﺘﻲ ﺘﻡ ﺸﺭﺤﻬﺎ ﻓﻲ ﺍﻟﻔﻘﺭﺓ )2-3( ﻤﻔﻴـﺩﺓ ﻓﻴﻤـﺎ ﻴﺨـﺹ ﺍﻟﻨـﻭﻯ‬ ‫ﺍﻟﺨﺎﻟﺼﺔ , ﻭﻟﻜﻥ ﻤﻌﻅﻡ ﺍﻟﻨﻭﻯ ﺘﺒﺘﻌﺩ ﺒﺨﻭﺍﺼﻬﺎ ﻋﻥ ﺍﻟﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ ﻟﺘﻘﻊ ﺒﻴﻥ ﺨﻭﺍﺹ ﺘﺤﺩﻴـﺩﻴﻥ‬ ‫ﺃﻭ ﺜﻼﺜﺔ ﻟﺘﻜـﻭﻥ ﻤﻨـﺎﻁﻕ ﺍﻨﺘﻘﺎﻟﻴـﺔ ]0891 ,‪،[Arima and Iachello, 1987] ،[Iachello‬‬ ‫ـﻴﺢ ـﺫﻩ ـﺎﻁﻕ ﺒﻤﺜﻠ ـﺙ ـﺎﻅﺭ‬ ‫ـ ﻤﺘﻨـ‬ ‫]8891 ,‪ .[Casten and Warner‬ﻴﻤﻜ ـﻥ ﺘﻭﻀـ ﻫـ ﺍﻟﻤﻨـ‬ ‫ـ‬ ‫)ﻤﺜﻠﺙ ‪ (Casten‬ﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل )4-3( ﺇﺫ ﺘﻤﺜل ﺍﻟﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ ﺍﻟﺨﺎﻟـﺼﺔ ﺭﺅﻭﺱ ﺍﻟﻤﺜﻠـﺙ،‬ ‫ﻭﺘﻤﺜل ﺃﻀﻼﻉ ﺍﻟﻤﺜﻠﺙ ﺍﻟﺤﺎﻻﺕ ﺍﻻﻨﺘﻘﺎﻟﻴﺔ ﺒﻴﻥ ﻜل ﺘﺤﺩﻴﺩﻴﻥ ﻭﺍﻟﻤﻭﻗﻊ ﻋﻠﻰ ﺃﻱ ﻀﻠﻊ ﻴﺤـﺩﺩ ﺘﺒﻌـﺎ‬ ‫ﻟﻠﻨﺴﺒﺔ ﺒﻴﻥ ﺍﻟﻤﺅﺜﺭﺍﺕ ﺍﻟﺘﻲ ﺘﺼﻑ ﻜل ﺘﺤﺩﻴﺩ. ﻭﺍﻟﻤﺴﺎﻓﺔ ﺒﻴﻥ ﺍﻷﻀﻼﻉ ﺍﻟﺜﻼﺜﺔ ﺘﻤﺜل ﻜـل ﺍﻟﺤﻠـﻭل‬ ‫ﺍﻟﻤﻤﻜﻨﺔ ﻟﺩﺍﻟﺔ ﻫﺎﻤﻠﺘﻭﻥ. ﻭﻴﻼﺤﻅ ﻜـﺫﻟﻙ ﻗـﻴﻡ ﻨـﺴﺏ ﺍﻟﺘﻔـﺭﻉ )‪ R‬ﻭ '‪ R‬ﻭ ''‪ R‬ﻭ '''‪ (R‬ﻟﻠﻐﺎﻴـﺔ‬ ‫∞ → ‪ N‬ﺍﻟﺨﺎﺼﺔ ﺒﻜل ﺘﺤﺩﻴﺩ ﻋﻠﻰ ﻜل ﺭﺃﺱ ﻤﻥ ﺭﺅﻭﺱ ﺍﻟﻤﺜﻠﺙ ﻭﺍﻟﻤﻌﺎﻤل ﺍﻟﻤﻬﻡ ﻟﻜل ﺘﺤﺩﻴﺩ،‬ ‫ﻋﻠﻤﺎ ﺃﻥ:‬
‫+‬ ‫) 10 → + 2;2 ‪B(E‬‬ ‫2‬ ‫= ' ' '‪R‬‬ ‫+‬ ‫+‬ ‫) 12 → 2 2;2 ‪B(E‬‬

‫)84-3(‬

‫ﺍﻨﺘﻘﺎﻟﻴﺔ‬

‫ﺍﻫﺘﺯﺍﺯﻴﺔ‬

‫ﺩﻭﺭﺍﻨﻴﺔ‬

‫ﺍﻟﺸﻜل )4-3(: ﻤﺜﻠﺙ ‪ Casten‬ﻴﺒﻴﻥ ﺍﻟﻤﻨﺎﻁﻕ ﺍﻻﻨﺘﻘﺎﻟﻴﺔ ﺒﻴﻥ ﺍﻟﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ‬

‫]7891 ,‪[Arima and Iachello‬‬
‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬ ‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫83‬

‫ﻭﻴﻤﻜﻥ ﺘﺼﻨﻴﻑ ﺍﻟﻨﻭﻯ ﻋﻠﻰ ﺃﺭﺒﻌﺔ ﺃﺼﻨﺎﻑ:‬

‫‪Class A‬‬

‫1-3-3 ﺍﻟﺼﻨﻑ ‪A‬‬

‫ﺍﻟﻨﻭﻯ ﻓﻲ ﻫﺫﺍ ﺍﻟﺼﻨﻑ ﺘﻤﺘﻠﻙ ﺼﻔﺎﺕ ﺍﻨﺘﻘﺎﻟﻴﺔ ﺒﻴﻥ ﺍﻟﺘﺤﺩﻴﺩﻴﻥ ﺍﻻﻫﺘﺯﺍﺯﻱ )‪ (I‬ﻭ ﺍﻟﺩﻭﺭﺍﻨﻲ‬ ‫)‪ (II‬ﻭﻴﺄﺨﺫ ﻫـﺎﻤﻠﺘﻭﻨﻴﻥ ﺍﻟـﺼﻴﻐﺔ ]0891 ,‪،[Arima and Iachello, 1987] ،[Iachello‬‬ ‫]8891 ,‪:[Casten and Warner‬‬

‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫‪H ( I + II) = εn d + a1L.L + a 2Q.Q‬‬

‫)94-3(‬

‫ﺨﻭﺍﺹ ﺍﻟﻨﻭﻯ ﻓﻲ ﻫﺫﺍ ﺍﻟﺼﻨﻑ ﺘﻌﺘﻤﺩ ﻋﻠﻰ ﺍﻟﻨﺴﺒﺔ )2‪ (ε / a‬ﻓﻌﻨﺩﻤﺎ ﺘﻜﻭﻥ ﻫـﺫﻩ ﺍﻟﻨـﺴﺒﺔ‬ ‫ﻜﺒﻴﺭﺓ ﻓﺎﻥ ﺍﻟﺨﻭﺍﺹ ﺘﻘﺘﺭﺏ ﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ )5(‪ SU‬ﻭﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﻫﺫﻩ ﺍﻟﻨﺴﺒﺔ ﺼـﻐﻴﺭﺓ ﻓـﺎﻟﺨﻭﺍﺹ‬ ‫ﺘﻘﺘﺭﺏ ﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ )3(‪.SU‬‬

‫‪Class B‬‬

‫2-3-3 ﺍﻟﺼﻨﻑ ‪B‬‬

‫ﻓﻲ ﻫﺫﺍ ﺍﻟﺼﻨﻑ ﺘﻜﻭﻥ ﺨﺼﺎﺌﺹ ﺍﻟﻨﻭﺍﺓ ﺍﻨﺘﻘﺎﻟﻴﺔ ﺒﻴﻥ ﺍﻟﺘﺤﺩﻴـﺩﻴﻥ )‪ (II‬ﻭ )‪ (III‬ﻭﺘﻌﻁـﻰ‬ ‫ﺒﺎﻟـ‬ ‫ﺩﺍﻟـ ﻫـ‬ ‫ـﺔ ـﺎﻤﻠﺘﻭﻥ ـﺼﻴﻐﺔ ]9791 ,‪،[Iachello, 1980] ،[Arima and Iachello‬‬ ‫]7891 ,‪:[Arima and Iachello‬‬

‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫‪H ( II + III) = a o P.P + a1L.L + a 2Q.Q‬‬

‫)05-3(‬

‫ﻭﺘﻌﺘﻤﺩ ﺨﻭﺍﺹ ﺍﻟﻨﻭﻯ ﻓﻲ ﻫﺫﺍ ﺍﻟﺼﻨﻑ ﻋﻠﻰ ﺍﻟﻨﺴﺒﺔ )2‪ (a0 / a‬ﻓﻌﻨﺩﻤﺎ ﺘﻜﻭﻥ ﻫﺫﻩ ﺍﻟﻨﺴﺒﺔ‬ ‫ﻜﺒﻴﺭﺓ ﻓﺎﻥ ﺍﻟﺨﻭﺍﺹ ﺴﺘﻜﻭﻥ ﺍﻗﺭﺏ ﻟﻠﺘﺤﺩﻴﺩ )6(‪ O‬ﻭﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﺼﻐﻴﺭﺓ ﻓﺎﻥ ﺍﻟﺨﻭﺍﺹ ﺴـﺘﻜﻭﻥ‬ ‫ﺍﻗﺭﺏ ﻟﻠﺘﺤﺩﻴﺩ )3(‪.SU‬‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫93‬

‫‪Class C‬‬

‫3-3-3 ﺍﻟﺼﻨﻑ ‪C‬‬

‫ﻓﻲ ﻫﺫﺍ ﺍﻟﺼﻨﻑ ﺘﻜﻭﻥ ﺨﺼﺎﺌﺹ ﺍﻟﻨـﻭﺍﺓ ﺒـﻴﻥ ﺍﻟﺘﺤﺩﻴـﺩﻴﻥ )‪ (I‬ﻭ )‪ (III‬ﻭﺍﻟﻬـﺎﻤﻠﺘﻭﻨﻴﻥ‬ ‫ﺍﻟﻤﻨﺎﺴﺏ ﻴﻌﻁﻰ ﺒـ ]7891 ,‪:[Casten and Warner, 1988] ،[Arima and Iachello‬‬

‫ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫‪H ( I+ III) = εn d + a o P.P + a 1L.L + a 3T.T‬‬

‫)15-3(‬

‫ﻭﺘﻌﺘﻤﺩ ﺨﻭﺍﺹ ﺍﻟﻨﻭﻯ ﻓﻲ ﻫﺫﺍ ﺍﻟﺼﻨﻑ ﻋﻠﻰ ﺍﻟﻨﺴﺒﺔ )0‪ (ε / a‬ﻓﻌﻨﺩﻤﺎ ﺘﻜﻭﻥ ﺍﻟﻨﺴﺒﺔ ﻜﺒﻴﺭﺓ‬ ‫ﻓﺈﻥ ﻫﺫﺍ ﻴﻌﻨﻲ ﺃﻥ ﺍﻟﻨﻭﺍﺓ ﻗﺭﻴﺒﺔ ﻓﻲ ﺨﻭﺍﺼﻬﺎ ﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ )5(‪ SU‬ﻭﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﺼـﻐﻴﺭﺓ ﻓﺈﻨـﻪ‬ ‫ﻴﻌﻨﻲ ﺃﻥ ﺍﻟﻨﻭﺍﺓ ﻗﺭﻴﺒﺔ ﻓﻲ ﺨﻭﺍﺼﻬﺎ ﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ )6(‪.O‬‬

‫‪Class D‬‬

‫4-3-3 ﺍﻟﺼﻨﻑ ‪D‬‬
‫ﻭﺍﻟﻬﺎﻤﻠﺘﻭﻨﻴﻥ ﻟﻪ ]7891 ,‪:[Iachello, 1980] ،[Arima and Iachello‬‬

‫ﺍﻟﻨﻭﻯ ﻓﻲ ﻫﺫﺍ ﺍﻟﺼﻨﻑ ﺘﻤﺘﻠﻙ ﺨﻭﺍﺼﺎ ﻤﺘﻭﺴـﻁﺔ ﺒـﻴﻥ ﺍﻟﺘﺤﺩﻴـﺩﺍﺕ )‪ (I‬ﻭ )‪ (II‬ﻭ )‪(III‬‬ ‫ﹰ‬

‫ˆ ˆ‬ ‫ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ ˆ‬ ‫ˆ‬ ‫4 ‪H ( I + II + III) = εn d + a o P.P + a1L.L + a 2 Q.Q + a 3T 3 .T 3 + a 4 T 4 .T‬‬

‫)25-3(‬

‫أﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ‬

‫اﻟﻔﺼﻞ اﻟﺜﺎﻟﺚ‬

‫ﺍﻟﻔﺼﻞ‬ ‫ﺍﻟﺮﺍﺑﻊ‬

‫ﺍﳊﺴﺎﺑﺎﺕ ﻭﺍﻟﻨﺘﺎﺋﺞ‬

‫04‬

‫ﺍﺴﺘﺨﺩﻡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ 1-‪ IBM‬ﺍﻟﺘﺤﺩﻴـﺩ ﻜﺎﻤـﺎ ﻏﻴـﺭ ﺍﻟﻤـﺴﺘﻘﺭ )6(‪O‬‬ ‫ﻭﺍﻟﺘﺄﻜﺩ ﻤﻥ ﻭﻗﻭﻋﻬﺎ ﻀﻤﻥ ﺍﻟﺘﺤﺩﻴـﺩ )6(‪O‬‬
‫621-021‬

‫ﻭﺫﻟﻙ ﺒﻌﺩ ﺍﻟﺘﻌﺭﻑ ﻋﻠﻰ ﺨﻭﺍﺹ ﺍﻟﻨﻅﺎﺌﺭ ‪Xe‬‬ ‫]8891 , ‪[Casten and Warner‬‬

‫ـﺎﺌﺭ ـﻥ ﺍﻟﻌﻼﻗــﺔ‬ ‫ﻤـ‬ ‫ـﺎﺕ ـﺫﻩ ﺍﻟﻨﻅـ‬ ‫ﻟﻬـ‬ ‫ـﺭﺓ )1-4( . ـﺩ ـﺴﺏ ـﺩﺩ ﺍﻟﺒﻭﺯﻭﻨـ‬ ‫ﻋـ‬ ‫ﻟﻘـ ﺤـ‬ ‫ﺍﻟﻔﻘـ‬

‫‪N = nπ + nν‬‬

‫)1-4(‬

‫ﺍﺫ ﺍﻥ ‪ N‬ﺘﻤﺜل ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻜﻠﻴﺔ ﻭ ‪ nπ‬ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻜﻭﻨﺔ ﻤـﻥ ﺍﺯﻭﺍﺝ ﺒﺭﻭﺘﻭﻨـﺎﺕ‬ ‫ﺍﻟﺘﻜﺎﻓﺅ ﻭ ‪ nν‬ﺘﻤﺜل ﻋﺩﺩ ﺒﻭﺯﻭﻨﺎﺕ ﻨﻴﺘﺭﻭﻨﺎﺕ ﺍﻟﺘﻜﺎﻓﺅ , ﻭﻷﻥ ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ﺘﻤﺘﻠﻙ 45 ﺒﺭﻭﺘﻭﻨﺎ‬ ‫ﹰ‬ ‫ﺃﻱ ﺍﻥ ﻫﻨﺎﻙ 4 ﺒﺭﻭﺘﻭﻨﺎﺕ ﺘﻜﺎﻓﺅ ﺨﺎﺭﺝ ﺍﻟﻐﻼﻑ ﺍﻟﻤﻐﻠﻕ 05 ﻭﻫﺫﺍ ﻴﻭﻟﺩ 2 ﺒﻭﺯﻭﻥ ﻟﻜـل ﻨﻅﻴـﺭ‬ ‫ﻭﻫﺫﻴﻥ ﺍﻟﺒﻭﺯﻭﻨﻴﻥ ﺘﻭﻟﺩﺍ ﻤﻥ ﺍﺯﻭﺍﺝ ﺍﻟﺠﺴﻴﻤﺎﺕ )ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ( . ﺍﻤﺎ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻨﻅـﺎﺌﺭ‬ ‫ﺘﺎﺭﻜﺔ ﻤﻥ 61 ﻓﺠﻭﺓ‬
‫621‬ ‫621‬

‫ﺍﻟﻰ 27 ﻨﻴﺘﺭﻭﻨﺎ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫ﹰ‬
‫621‬ ‫021‬

‫021‬

‫ﹰ‬ ‫ﺍﻟﻤﺩﺭﻭﺴﺔ ﻓﻬﻲ 66 ﻨﻴﺘﺭﻭﻨﺎ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬
‫021‬

‫ﻭﻜل ﺯﻭﺝ ﻤﻥ ﻫﺫﻩ ﺍﻟﻔﺠـﻭﺍﺕ ﺘـﺸﻜل ﺒﻭﺯﻭﻨـﺎ‬ ‫ﹰ‬ ‫, ﻤﻊ‬ ‫ﻭ 5 ﺒﻭﺯﻭﻨﺎﺕ ﻨﻴﺘﺭﻭﻨﻴﺔ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﺍﻟﻰ 01 ﻓﺠﻭﺍﺕ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬
‫021‬

‫ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﻓﻴﻜﻭﻥ ﻫﻨﺎﻙ 8 ﺒﻭﺯﻭﻨﺎﺕ ﻨﻴﺘﺭﻭﻨﻴﺔ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫ﻤﻼﺤﻅﺔ ﺍﻥ ﺍﻟﻨﻅﻴﺭ ‪Xe‬‬ ‫ﺒﻭﺯﻭﻨﺎﺕ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﻟﻪ 61 ﺠﺴﻴﻤﺎ ﻨﻴﺘﺭﻭﻨﻴﺎ ﺨﺎﺭﺝ ﺍﻟﻐـﻼﻑ ﺍﻟﻤﻐﻠـﻕ 05 ﻭ 61 ﻓﺠـﻭﺓ‬ ‫ﹰ‬ ‫ﹰ‬
‫621‬

‫ﻨﻴﺘﺭﻭﻨﻴﺔ ﻟﻠﻭﺼﻭل ﺍﻟﻰ ﺍﻟﻐﻼﻑ 28 ﺍﻟﻤﻐﻠﻕ ﻓﻴﻜﻭﻥ ﻤﺠﻤﻭﻉ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻜﻠﻴﺔ ﻟﻜل ﻨﻅﻴﺭ ﻤـﻥ 01‬ ‫.‬ ‫ﺍﻟﻰ 7 ﺒﻭﺯﻭﻨﺎﺕ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬
‫021‬

‫‪Energy Levels‬‬

‫1-4 ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ‬

‫ﻴﻤﻜﻥ ﺍﻟﺘﻌﺭﻑ ﻋﻠﻰ ﺨﻭﺍﺹ ﻭﻤﻭﺍﻗﻊ ﺍﻟﻨﻅﺎﺌﺭ ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴـﺔ ﻤـﻥ ﺨـﻼل ﺍﻟﻌﺩﻴـﺩ ﻤـﻥ‬ ‫ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﺍﻟﻤﺘﻭﺍﻓﺭﺓ ﻋﻥ ﻜل ﻨﻅﻴﺭ.ﻭﻤﻥ ﻫﺫﻩ ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﻤﻭﺍﻗﻊ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻟﻨﺴﺒﺔ ﺒﻴﻥ ﻗﻴﻡ‬ ‫ﻁﺎﻗﺎﺕ ﻫﺫﻩ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﻭﻤﻥ ﺨﻼل ﺍﻟﺘﻌﺭﻑ ﻋﻠﻰ ﻤﻭﻗﻊ ﻁﺎﻗﺔ ﺍﻟﻤﺴﺘﻭﻱ +2 ,ﻭﺍﻟﻨﺴﺒﺔ ﺒـﻴﻥ ﻁﺎﻗـﺔ‬ ‫= ‪ R‬ﻴﺘﻀﺢ ﺍﻥ ﺍﻟﻨﻅﺎﺌﺭ ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴﺔ ﺘﻘﻊ ﻀﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ )6(‪ O‬ﺍﺫ‬
‫+‬ ‫14 ‪E‬‬ ‫+‬ ‫12 ‪E‬‬ ‫+‬ ‫+‬ ‫ﺍﻟﻤﺴﺘﻭﻴﻴﻥ 14 ﺍﻟﻰ 12‬

‫ﺍﻥ 5.2=‪ R‬ﻟﻬﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ ]8891 ,‪ [Casten and Warner‬ﻭﺍﻟﺠﺩﻭل )1-4( ﻴﺒﻴﻥ ﻫﺫﻩ ﺍﻟﻘﻴﻡ .‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫14‬

‫ﺍﻟﺠﺩﻭل: )1-4( ﻗﻴﻡ 12 ‪ E‬ﻭ 14 ‪ E‬ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﺴﺒﺔ ﺒﻴﻨﻬﻤﺎ ﻟﻜل ﻨﻅﻴﺭ‬ ‫‪Isotopes‬‬
‫021‬ ‫221‬ ‫421‬ ‫621‬

‫)‪E 21 (keV‬‬

‫)‪E 41 (keV‬‬

‫=‪R‬‬

‫14‪E‬‬ ‫12‪E‬‬

‫‪Xe‬‬ ‫‪Xe‬‬ ‫‪Xe‬‬ ‫‪Xe‬‬

‫16.223‬ ‫82.133‬ ‫41.453‬ ‫136.883‬

‫61.697‬ ‫35.828‬ ‫30.978‬ ‫249‬

‫764.2‬ ‫5.2‬ ‫284.2‬ ‫324.2‬

‫ﺒﻌﺩ ﺍﻟﺘﻌﺭﻑ ﻋﻠﻰ ﺨﺼﺎﺌﺹ ﺍﻟﻨﻅﺎﺌﺭ ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴﺔ ﻁﺒﻘﺕ ﻤﻌﺎﺩﻟﺔ ﺍﻟﺘﺤﺩﻴـﺩ )6(‪, O‬ﻭﻫـﻲ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ )93-3( ﻟﺤﺴﺎﺏ ﻗﻴﻡ ﺍﻟﻤﻌﺎﻤﻠﻴﻥ 4‪ K‬ﻭ 5‪ . K‬ﻭﻷﻥ ﺍﻷﻫﺘﻤﺎﻡ ﻓﻲ ﻫﺫﻩ ﺍﻟﺩﺭﺍﺴـﺔ ﻴﻨـﺼﺏ‬ ‫ﻋﻠﻰ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻷﺩﻨﻰ )‪ (Yrast Levels‬ﺍﻟﻤﺘﺸﻜﻠﺔ ﻤﻥ ﺤـﺯﻤﺘﻴﻥ ﻤﺨﺘﻠﻔﺘـﻴﻥ , ﺍﻟﺤﺯﻤـﺔ‬ ‫ﺍﻷﺭﻀﻴﺔ )‪ (g-band‬ﻭﺍﻟﺤﺯﻤﺔ ﺍﻟﻤﺜﺎﺭﺓ ﺤﺯﻤﺔ ‪ . (S-band) S‬ﺘﻡ ﺤﺴﺎﺏ ﻗﻴﻡ ﺍﻟﻤﻌـﺎﻤﻠﻴﻥ 4‪ K‬ﻭ‬ ‫5‪ K‬ﻤﺭﺘﻴﻥ , ﻤﺭﺓ ﻟﻠﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﻭﺍﺨﺭﻯ ﻟﻠﺤﺯﻤﺔ ‪ . S‬ﻭﺍﻟﺠﺩﻭل )2-4( ﻴﻭﻀﺢ ﻫـﺫﻩ ﺍﻟﻘـﻴﻡ‬ ‫ﻓﻀﻼ ﻋﻥ ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻟﻜل ﻨﻅﻴﺭ.‬ ‫ﹰ‬
‫621-021‬

‫ﺍﻟﺠﺩﻭل )2-4(: ﻋﺩﺩ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﻭﻗﻴﻡ ﻜل ﻤﻥ 4‪ K‬ﻭ 5‪ K‬ﻟﻠﺤﺯﻤﺘﻴﻥ ‪ g‬ﻭ ‪ S‬ﻟﻠﻨﻅﺎﺌﺭ ‪Xe‬‬ ‫‪Number‬‬ ‫‪g-band‬‬ ‫)‪K4(keV‬‬ ‫552.19‬ ‫800.19‬ ‫209.59‬ ‫23.411‬ ‫)‪K5(keV‬‬ ‫860.7-‬ ‫4854.5-‬ ‫3119.4-‬ ‫344.11-‬ ‫‪S-band‬‬ ‫)‪K4(keV‬‬ ‫34.481‬ ‫17.061‬ ‫89.402‬ ‫84.502‬ ‫)‪K5(keV‬‬ ‫542.04-‬ ‫838.13-‬ ‫207.54-‬ ‫722.64-‬

‫‪Isotopes‬‬

‫‪of‬‬ ‫‪Bosones‬‬ ‫01‬ ‫9‬ ‫8‬ ‫7‬

‫021‬ ‫221‬ ‫421‬ ‫621‬

‫‪Xe‬‬ ‫‪Xe‬‬ ‫‪Xe‬‬ ‫‪Xe‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫24‬

‫ﺒﻌﺩ ﺤﺴﺎﺏ ﻗﻴﻡ ﺍﻟﻤﻌﺎﻤﻠﻴﻥ 4‪ K‬ﻭ 5‪ K‬ﺤﺴﺒﺕ ﻗﻴﻡ ﻁﺎﻗﺎﺕ ﺍﻟﺤﺯﻤﺘﻴﻥ ‪ g‬ﻭ ‪ S‬ﻭﺫﻟﻙ ﺒﺒﻨـﺎﺀ‬ ‫ﺒﺭﻨﺎﻤﺞ ٍ ﺒﻠﻐﺔ 7-‪ MATLAB‬ﺴﻤﻲ )‪ (Yraste-Code‬ﻭﻤﻥ ﺜﻡ ﺤﺴﺎﺏ ﻁﺎﻗﺎﺕ ﻫـﺫﻩ ﺍﻟﺤﺯﻤـﺔ‬ ‫ﻟﻜل ﻨﻅﻴﺭ. ﻭﺘﻡ ﺤﺴﺎﺏ ﻨﺴﺒﺔ ﺍﻟﺨﻁﺄ ﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻟﻜل ﻤـﺴﺘﻭ ﻋﻠـﻰ ﻭﻓـﻕ‬ ‫ٍ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬
‫= )%( ∆‬ ‫. ‪EExp. − ECal‬‬ ‫.‪E Exp‬‬ ‫001 ×‬

‫)2-4(‬

‫ﻭﺍﻟﺠﺩﺍﻭل )3-4( ﺍﻟﻰ )6-4( ﺘﺒﻴﻥ ﻗﻴﻡ ﺍﻟﻁﺎﻗﺎﺕ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﻌﻤﻠﻴﺔ ﺒﻭﺤـﺩﺍﺕ )‪ (keV‬ﻭﻨـﺴﺒﺔ‬ ‫ﺍﻟﺯﻭﺠﻴﺔ - ﺍﻟﺯﻭﺠﻴﺔ .‬
‫621-021‬

‫ﺍﻟﺨﻁﺄ ﻟﻠﻨﻅﺎﺌﺭ ‪Xe‬‬

‫ﻭﺒﻌﺩ ﺤﺴﺎﺏ ﻗﻴﻡ ﺍﻟﻁﺎﻗﺎﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻟﻜل ﻨﻅﻴﺭ ﺭﺴﻤﺕ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻷﺩﻨﻰ ﻟﻜل ﺯﺨـﻡ‬ ‫ﺯﺍﻭﻱ ﻭﻫﺫﺍ ﻤﻭﻀﺢ ﻓﻲ ﺍﻟﺸﻜل )1-4( , ﻭﻤﻥ ﺜﻡ ﺘﺤﺩﻴﺩ ﺒﻌﺽ ﺍﻟﺨﻭﺍﺹ ﻟﻬﺫﻩ ﺍﻟﻨﻅﺎﺌﺭ . ﻓﺎﻟـﺸﻜل‬ ‫)2-4( ﻴﺒﻴﻥ ﻤﻭﺍﻗﻊ ﻁﺎﻗﺎﺕ ﺍﻟﻤﺴﺘﻭﻱ +12 ﻟﻜل ﻨﻅﻴﺭ ﻤﻘﺎﺭﻨﺔ ﺒﺎﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ .‬ ‫ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻟﻜل ﻨﻅﻴﺭ ﻤﻘﺎﺭﻨﺔ ﺒﻤﻭﺍﻗﻊ ﻫـﺫﻩ ﺍﻟﻨـﺴﺏ‬
‫+‬ ‫14 ‪E‬‬ ‫ﻭﺍﻟﺸﻜل )3-4( ﻴﺒﻥ ﺍﻟﻨﺴﺒﺔ‬ ‫+‬ ‫12 ‪E‬‬

‫ﻟﻠﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ ﻓﻲ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ ﺍﻟﺘﺤﺩﻴﺩ )5(‪ SU‬ﻭﺍﻟﺘﺤﺩﻴﺩ )3(‪ SU‬ﻭﺍﻟﺘﺤﺩﻴـﺩ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻤﺤﺴﻭﺒﺔ ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻤﻘﺎﺭﻨﺔ ﺒﻤﻭﺍﻗﻊ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻤﺤﺴﻭﺒﺔ ﻤﻊ ﻋﺩﺩ‬
‫+‬ ‫16 ‪E‬‬ ‫)6(‪ O‬ﻭﺍﻟﺸﻜل )4-4( ﻴﺒﻴﻥ ﺍﻟﻨﺴﺒﺔ‬ ‫+‬ ‫12 ‪E‬‬

‫+‬ ‫18 ‪E‬‬ ‫ﻫﺫﻩ ﺍﻟﻨﺴﺏ ﻟﻠﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ ﺍﻤﺎ ﺍﻟﺸﻜل )5-4( ﻓﻴﺒﻴﻥ ﺍﻟﻨﺴﺒﺔ‬ ‫+‬ ‫12 ‪E‬‬

‫ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻟﻜل ﻨﻅﻴﺭ ﻤﻘﺎﺭﻨﺔ ﺒﻤﻭﺍﻗﻊ ﻫﺫﻩ ﺍﻟﻨﺴﺏ ﻟﻠﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ ﺍﻴﻀﺎ . ﺭﺴﻤﺕ ﺍﻟﻌﻼﻗﺔ ﺒـﻴﻥ‬ ‫ﹰ‬ ‫ﺍﻟﻁﺎﻗﺎﺕ ﺍﻷﺩﻨﻰ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﻌﻤﻠﻴﺔ ‪ EJ‬ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻜل ﻨﻅﻴﺭ ﻭﺍﻷﺸﻜﺎل ﻤﻥ )6-4( ﺍﻟـﻰ‬ ‫)9-4( ﺘﻭﻀﺢ ﺫﻟﻙ .‬ ‫ﻭﺤﻴﺙ ﺍﻥ ﺍﻟﺩﺭﺍﺴﺔ ﺍﻟﺤﺎﻟﻴﺔ ﺍﻫﺘﻤﺕ ﺒﺤﺎﻻﺕ ﺍﻟﻁﺎﻗﺎﺕ ﺍﻟﺩﻨﻴﺎ ﺍﻟﻨﺎﺘﺠﺔ ﻋﻥ ﺘﻘﺎﻁﻊ ﺍﻟﺤﺯﻤﺘﻴﻥ ‪g‬‬ ‫ﻭ ‪ S‬ﻓﻤﻥ ﺍﻟﻤﺘﻭﻗﻊ ﻅﻬﻭﺭ ﺍﻨﺤﻨﺎﺀ ﺨﻠﻔﻲ ﻋﻨﺩ ﻁﺎﻗﺎﺕ ﻫﺫﻩ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﻓـﻲ ﻨﻘﻁـﺔ ﺍﻟﺘﻘـﺎﻁﻊ ﺒـﻴﻥ‬ ‫ﺒﻴﻥ ﻜل ﻤﺴﺘﻭﻴﻴﻥ ﻤﺘﺘـﺎﻟﻴﻥ ﻭﺤـﺴﺎﺏ‬
‫‪2ϑ‬‬ ‫2‪h‬‬

‫ﺍﻟﺤﺯﻤﺘﻴﻥ ﻟﺫﺍ ﺘﻡ ﺤﺴﺎﺏ ﻁﺎﻗﺎﺕ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ‪Eγ‬‬

‫ﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ‪ hω‬ﺒﺄﺴﺘﺨﺩﺍﻡ ﺍﻟﻤﻌﺎﺩﻟﺔ )22-2( ﻭﻜﺫﻟﻙ ﺤﺴﺎﺏ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟـﺫﺍﺘﻲ‬

‫ﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﻟﻤﻌﺎﺩﻟﺔ )12-2( ﻟﻤﺎ ﻟﻬﺫﻩ ﺍﻟﻤﻌﺎﻟﻡ ﻤﻥ ﺍﻫﻤﻴﺔ ﻓﻲ ﺘﺤﺩﻴﺩ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ﻤـﺴﺘﻭﻴﺎﺕ‬
‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬ ‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫34‬

‫ﺍﻟﻁﺎﻗﺔ ﻋﻨﺩ ﻨﻘﻁﺔ ﺍﻟﺘﻘﺎﻁﻊ ﺒﻴﻥ ﺍﻟﺤﺯﻤﺘﻴﻥ ‪ g‬ﻭ ‪ S‬ﻭﺍﻟﺠﺩﺍﻭل ﻤﻥ )7-4( ﺍﻟﻰ )01-4( ﺘﺒـﻴﻥ ﻫـﺫﻩ‬ ‫ﻋﻠﻰ ﺍﻟﺘﻭﺍﻟﻲ .‬ ‫‪ 2ϑ‬ﺩﺍﻟﺔ ﻟـ ‪ J‬ﺒﻭﺤﺩﺍﺕ ‪ h‬ﺍﻟﻤﺤـﺴﻭﺏ ﻤـﻥ‬
‫2‪h‬‬
‫621‬

‫ﺍﻟﻰ ‪Xe‬‬

‫021‬

‫ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻟﻠﻨﻅﺎﺌﺭ ﻤﻥ ‪Xe‬‬

‫ﺘﻡ ﺭﺴﻡ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ‬

‫ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﻟﺸﻜل )01-4( ﻴﺒﻴﻥ ﻫﺫﻩ ﺍﻟﻌﻼﻗﺔ ﻟﻠﻨﻅﺎﺌﺭ ﻗﻴـﺩ‬ ‫ﺍﻟﺩﺭﺍﺴﺔ . ﺍﻤﺎ ﺍﻟﺸﻜل )11-4( ﻓﻴﺒﻴﻥ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ‪ J‬ﻭ ‪ hω‬ﺍﻟﻤﺤﺴﻭﺒﺔ ﻤـﻥ ﻗـﻴﻡ‬ ‫ﺍﻟﻁﺎﻗﺎﺕ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻤﺤﺴﻭﺒﺔ ﻓﻲ ﻫﺫﻩ ﺍﻟﺭﺴﺎﻟﺔ ﻟﻠﻨﻅﺎﺌﺭ ﺍﻟﻤﺩﺭﻭﺴﺔ, ﻭﻤﻨﻬﺎ ﻴﺘـﻀﺢ ﺘﻐﻴـﺭ ﺍﻟﺘـﺭﺩﺩ‬ ‫ﺍﻟﺩﻭﺭﺍﻨﻲ ﻋﻨﺩ ﻨﻘﻁﺔ ﺍﻟﺘﻘﺎﻁﻊ . ﻭﺍﻟﺸﻜل )21-4( ﻴﺒﻴﻥ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻁﺎﻗﺔ ﺍﻻﻨﺘﻘﺎل ‪ Eγ‬ﺍﻟﻤﺤـﺴﻭﺒﺔ‬ ‫ﻭﺍﻟﻌﻤﻠﻴﺔ ﺩﺍﻟﺔ ﻟـ ‪ J‬ﺒﻭﺤﺩﺍﺕ ‪ , h‬ﺍﻤﺎ ﺍﻟﺸﻜل )31-4( ﻓﻴﺒﻴﻥ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻋﺯﻡ ﺍﻟﻘـﺼﻭﺭ ﺍﻟـﺫﺍﺘﻲ‬ ‫ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻟﻠﻨﻅﺎﺌﺭ ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴﺔ .‬

‫2-4 ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺍﻟﻤﺨﺘﺯﻟﺔ )2‪B(E‬‬
‫ﺘﻌﺩ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﺎﻤﻴﺔ ﻭﺍﺤﺘﻤﺎﻟﻴﺎﺘﻬﺎ ﺒﻴﻥ ﻤﺨﺘﻠﻑ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻤﻥ ﺍﻟﻤﻌﺎﻟﻡ ﺍﻟﻤﻬﻤـﺔ ﻓـﻲ‬ ‫ﺩﺭﺍﺴﺔ ﺍﻟﺨﻭﺍﺹ ﺍﻟﻨﻭﻭﻴﺔ ﻷﻱ ﻨﻅﻴﺭ,ﻟﺫﺍ ﺍﻭﻟﻲ ﺍﻷﻫﺘﻤﺎﻡ ﻓﻲ ﻫﺫﻩ ﺍﻟﺭﺴﺎﻟﺔ ﺍﻟﻰ ﺤﺴﺎﺏ ﻫـﺫﻩ ﺍﻟﺩﺍﻟـﺔ‬ ‫َ‬ ‫ﻷﻨﺘﻘﺎﻻﺕ ﻤﺨﺘﻠﻔﺔ ﺒﻴﻥ ﻤﺴﺘﻭﻴﺎﺕ ﻤﺘﻌﺩﺩﺓ ﻟﻜل ﻨﻅﻴﺭ ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴﺔ ﻭﻤﻘﺎﺭﻨﺘﻬـﺎ ﺒﺎﻟﻨﺘـﺎﺌﺞ ﺍﻟﻌﻤﻠﻴـﺔ .‬ ‫ﺍﻋﺘﻤﺩﺕ ﻓﻲ ﻫﺫﻩ ﺍﻟﺭﺴﺎﻟﺔ ﻁﺭﻴﻘﺘﻴﻥ ﻟﻠﺤﺴﺎﺏ , ﺤﻴﺙ ﺘﻡ ﺍﻷﻋﺘﻤﺎﺩ ﻓﻲ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻻﻭﻟﻰ ﻋﻠﻰ ﺍﻟﻘـﻴﻡ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ ﺍﻟﻤﺘﻭﻓﺭﺓ ﻟﻁﺎﻗﺎﺕ ﻜﺎﻤﺎ ﻟﻸﻨﺘﻘﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻭﻋﻠﻰ ﺍﻟﻌﻤﺭ ﺍﻟﻨﺼﻔﻲ ﻷﻨﺘﻘﺎل ﻜﺎﻤﺎ ﺒﺄﺴـﺘﺨﺩﺍﻡ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ )61-2( , ﺍﺫ ﺘﻡ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﻟﺘﺤﻭل ﺍﻟﺩﺍﺨﻠﻲ ‪ α‬ﺒﺒﻨﺎﺀ ﺒﺭﻨﺎﻤﺞ ٍ ﺒﻠﻐﺔ7-‪MATLAB‬‬ ‫ﻟﻌﻤل ﺍﺴﺘﻜﻤﺎل ﻟﻠﻘﻴﻡ ﺍﻟﺒﻴﻨﻴﺔ )‪ (Interpolation‬ﻏﻴﺭ ﺍﻟﻤﺘﻭﻓﺭﺓ ﻋﻤﻠﻴﺎ ﻤﻥ ﺨﻼل ﺍﻟﻘـﻴﻡ ﺍﻟﻤﺘـﻭﻓﺭﺓ‬ ‫ﹰ‬ ‫ﻟﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ﺫﺍﺕ ﺍﻟﻌﺩﺩ ﺍﻟﺫﺭﻱ 45=‪ . Z‬ﺍﺩﺨﻠـﺕ ﺍﻟﻤﻌﻠﻭﻤـﺎﺕ ﺍﻟﻤﺘـﻭﺍﻓﺭﺓ ﻟﻁﺎﻗـﺎﺕ ﻜﺎﻤـﺎ‬ ‫ﻟﻼﻨﺘﻘﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻭﺍﻟﻌﻤﺭ ﺍﻟﻨﺼﻔﻲ ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )61-2( ﻟﺤﺴﺎﺏ ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘـﺎل ﺍﻟﺭﺒﺎﻋﻴـﺔ‬ ‫ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻲ ﺍﻟﻤﺨﺘﺯﻟﺔ ﺒﻭﺤﺩﺍﺕ 2‪ e2b‬ﻭﻤﻥ ﺜﻡ ﻁﺒﻘﺕ ﺍﻟﻤﻌﺎﺩﻟﺔ )71-2( ﻟﻠﺘﺤﻭﻴل ﺍﻟﻰ ﻭﺤﺩﺍﺕ‬ ‫ﻭﺍﻴﺴﻜﻭﻑ .ﻭﺍﻟﺠﺩﺍﻭل ﻤﻥ )11-4( ﺍﻟﻰ )31-4( ﺘﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤـﺴﻭﺒﺔ ﺒﻭﺤـﺩﺍﺕ ﻭﺍﻴـﺴﻜﻭﻑ‬ ‫.‬
‫421-021‬

‫ﻭﻭﺤﺩﺍﺕ 2‪ e2b‬ﻤﻘﺎﺭﻨﺔ ﻤﻊ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻟﻠﻨﻅﺎﺌﺭ ‪Xe‬‬

‫ﻭﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﺜﺎﻨﻴﺔ ﺍﻋﺘﻤﺩﺕ ﻋﻠﻰ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ 1-‪ IBM‬ﺍﻟﺘﺤﺩﻴﺩ ﻜﺎﻤﺎ ﻏﻴـﺭ‬ ‫ﺍﻟﻤﺴﺘﻘﺭ )6(‪ O‬ﻟﺤﺴﺎﺏ )2‪ B(E‬ﻤﺭﺓ ﺜﺎﻨﻴﺔ ﻭﻤﻘﺎﺭﻨﺘﻬﺎ ﻤﻊ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ , ﻓﻘـﺩ ﺤـﺴﺒﺕ )2‪B(E‬‬ ‫ﻟﻠﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ‪ g-band‬ﻓﻘﻁ ﻭﺫﻟﻙ ﺒﺎﺩﺨﺎل ﺍﻟﻤﻌﺎﻤل 22 ‪ α‬ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )24-3( ﺍﻟﺫﻱ ﺘﻡ ﺤﺴﺎﺒﻪ‬
‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬ ‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫44‬
‫+‬ ‫+‬ ‫ﺒﺘﻌﻭﻴﺽ ﻗﻴﻤﺔ )2‪ B(E‬ﺍﻟﻌﻤﻠﻴﺔ ﻟﻸﻨﺘﻘﺎل ﻤﻥ 12 ﺍﻟﻰ 10 ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )34-3( ﻭﺘﻌﺩﻴل ﻗﻴﻤﺔ 22 ‪α‬‬

‫ﺍﻟﻤﺤﺴﻭﺒﺔ ﻷﻋﻁﺎﺀ ﺍﻓﻀل ﺘﻁﺎﺒﻕ ﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻟـ )2‪ B(E‬ﻤﻊ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﺍﻟﻤﺘـﻭﺍﻓﺭﺓ .‬ ‫ﺍﻟﺠﺩﻭل )41-4( ﻴﻌﻁﻲ ﻗﻴﻡ 22 ‪ α‬ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﺠﺩﺍﻭل )51-4( ﻭ )61-4( ﻭ )71-4( ﺘﻌﻁﻲ ﻗﻴﻡ‬ ‫)2‪ B(E‬ﺍﻟﻤﺤﺴﻭﺒﺔ ﺒﻭﺤﺩﺍﺕ 2‪ e2b‬ﻤﻘﺎﺭﻨﺔ ﺒﺎﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﺍﻟﻤﺘﻭﻓﺭﺓ ﻟﻠﻨﻅﺎﺌﺭ ‪. 120-124Xe‬ﺍﻤﺎ ﻓﻴﻤـﺎ‬ ‫ﻓﺘﻭﺠﺩ ﻗﻴﻤﺔ ﻋﻤﻠﻴﺔ ﻭﺍﺤﺩﺓ ﻟﻪ ﻟﻼﻨﺘﻘﺎل ﻤﻥ +12 ﺍﻟﻰ +10 ﻟﺫﻟﻙ ﻟـﻡ ﺘﺤـﺴﺏ‬
‫621‬

‫ﻴﺨﺹ ﺍﻟﻨﻅﻴﺭ ‪Xe‬‬

‫)2‪ B(E‬ﺒﺄﻱ ﻤﻥ ﺍﻟﻁﺭﻴﻘﺘﻴﻥ ﺍﻟـﺴﺎﺒﻘﺘﻴﻥ . ﺍﻟـﺸﻜل )41-4( ﻴﺒـﻴﻥ ﺍﻟﻨـﺴﺏ ﺒـﻴﻥ ﺍﻻﻨﺘﻘـﺎﻻﺕ‬ ‫ﺍﺫ ﺭﺴﻤﺕ‬
‫421-021‬

‫. ﻟﻠﻨﻅﺎﺌﺭ ‪Xe‬‬

‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫) 16 → 18;2 ‪B ( E‬‬ ‫) 14 → 16;2 ‪B( E‬‬ ‫) 12 → 14;2 ‪B ( E‬‬ ‫,‬ ‫,‬ ‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫) 10 → 12;2 ‪B ( E‬‬ ‫) 10 → 12;2 ‪B( E‬‬ ‫) 10 → 12;2 ‪B( E‬‬

‫ﺍﻟﻨﺴﺏ ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻟﻠﺤﺎﻻﺕ ﺍﻟﺜﻼﺙ )5(‪ SU‬ﻭ )3(‪ SU‬ﻭ )6(‪ O‬ﻭﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﻌﻤﻠﻴﺔ ﻟﻘﻴﻡ‬ ‫)2‪ B(E‬ﻟﻼﻨﺘﻘﺎﻻﺕ ﺍﻟﻤﺫﻜﻭﺭﺓ ﺴﺎﺒﻘﺎ.‬ ‫ﹰ‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫54‬
‫021‬

‫ﺍﻟﺠﺩﻭل )3-4( :ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫‪Jπ‬‬
‫+‬ ‫10‬ ‫+‬ ‫12‬ ‫+‬ ‫14‬ ‫+‬ ‫16‬ ‫+‬ ‫18‬ ‫+‬ ‫101‬

‫*‬

‫)‪Eexp (keV‬‬ ‫0‬ ‫16.223‬ ‫61.697‬ ‫3.7931‬ ‫2.9902‬ ‫7.2782‬ ‫5.6763‬ ‫9.8544‬ ‫3.2325‬ ‫1506‬ ‫4.5596‬ ‫1.5597‬ ‫1.1509‬

‫)‪Ecal (keV‬‬ ‫0‬ ‫16.223‬ ‫91.177‬ ‫7.5431‬ ‫2.6402‬ ‫7.2782‬ ‫2.1863‬ ‫9.8544‬ ‫5.3825‬ ‫1.5516‬ ‫5.3707‬ ‫8.8308‬ ‫1.1509‬

‫)%( ∆‬
‫0‬ ‫0‬ ‫41.3‬ ‫07.3‬ ‫05.2‬ ‫0‬ ‫31.0-‬ ‫0‬ ‫89.0-‬ ‫27.1-‬ ‫07.1-‬ ‫50.1-‬ ‫0‬

‫+‬ ‫121‬

‫+‬ ‫141‬

‫+‬ ‫161‬

‫+‬ ‫181‬ ‫+‬ ‫102‬ ‫+‬ ‫122‬ ‫+‬ ‫142‬

‫]2002 , ‪* Ref: [Kitao et al‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫64‬
‫221‬

‫ﺍﻟﺠﺩﻭل )4-4( :ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫)‪Ecal (keV‬‬ ‫0‬ ‫82.133‬ ‫19.008‬ ‫9.8041‬ ‫2.5512‬ ‫9.9303‬ ‫8.1173‬ ‫9.3654‬ ‫8.2845‬ ‫4.8646‬ ‫7.0257‬ ‫7.9368‬

‫‪Jπ‬‬
‫+‬ ‫10‬ ‫+‬ ‫12‬

‫*‬

‫)‪Eexp (keV‬‬ ‫0‬ ‫82.133‬ ‫35.828‬ ‫1.7641‬ ‫7.7122‬ ‫9.9303‬ ‫1.0283‬ ‫9.3654‬ ‫7045‬ ‫1.0736‬ ‫1.3547‬ ‫7.9368‬

‫)%( ∆‬
‫0‬ ‫0‬ ‫33.3‬ ‫79.3‬ ‫28.2‬ ‫0‬ ‫48.2‬ ‫0‬ ‫04.1-‬ ‫45.1-‬ ‫09.0-‬ ‫0‬

‫+‬ ‫14‬

‫+‬ ‫16‬

‫+‬ ‫18‬

‫+‬ ‫101‬

‫+‬ ‫121‬

‫+‬ ‫141‬

‫+‬ ‫161‬

‫+‬ ‫181‬

‫+‬ ‫102‬ ‫+‬ ‫122‬

‫]7002 ,‪* Ref: [Tamura‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫74‬
‫421‬

‫ﺍﻟﺠﺩﻭل )5-4( :ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫)‪Ecal (keV‬‬ ‫0‬ ‫41.453‬ ‫97.068‬ ‫0251‬ ‫6.1332‬ ‫1.2713‬ ‫6.9393‬ ‫5.1574‬ ‫7.7065‬ ‫2.8056‬ ‫1.3547‬

‫‪Jπ‬‬
‫+‬ ‫10‬

‫*‬

‫)‪Eexp (keV‬‬ ‫0‬ ‫41.453‬ ‫30.978‬ ‫8.8451‬ ‫6.1332‬ ‫1.2713‬ ‫9.3883‬ ‫4.3164‬ ‫6645‬ ‫1.9346‬ ‫1.3547‬

‫)%( ∆‬
‫0‬ ‫0‬ ‫70.2‬ ‫68.1‬ ‫0‬ ‫0‬ ‫34.1-‬ ‫00.3-‬ ‫06.2-‬ ‫70.1-‬ ‫0‬

‫+‬ ‫12‬

‫+‬ ‫14‬

‫+‬ ‫16‬

‫+‬ ‫18‬

‫+‬ ‫101‬

‫+‬ ‫121‬

‫+‬ ‫141‬

‫+‬ ‫161‬

‫+‬ ‫181‬

‫+‬ ‫102‬

‫]7991 , ‪* Ref: [Iimura et al‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫84‬
‫621‬

‫ﺍﻟﺠﺩﻭل )6-4( :ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫‪Jπ‬‬
‫+‬ ‫10‬

‫*‬

‫)‪Eexp (keV‬‬ ‫0‬ ‫36.883‬ ‫249‬ ‫5361‬ ‫7.5342‬ ‫1.4133‬ ‫6.4883‬ ‫4.9164‬ ‫6.8055‬

‫)‪Ecal (keV‬‬ ‫0‬ ‫36.883‬ ‫63.419‬ ‫2.7751‬ ‫1.7732‬ ‫1.4133‬ ‫6.4883‬ ‫6764‬ ‫6.8055‬

‫)%( ∆‬
‫0‬ ‫0‬ ‫49.2‬ ‫45.3‬ ‫04.2‬ ‫0‬ ‫0‬ ‫22.1-‬ ‫0.‬

‫+‬ ‫12‬

‫+‬ ‫14‬

‫+‬ ‫16‬

‫+‬ ‫18‬

‫+‬ ‫101‬

‫+‬ ‫121‬

‫+‬ ‫141‬

‫+‬ ‫161‬

‫]2002 , ‪* Ref: [Katakura and Kitao‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫94‬
‫021‬

‫ﺍﻟﺠﺩﻭل )7-4(: ﻁﺎﻗﺎﺕ ﺍﻻﻨﺘﻘﺎل ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬
‫*‬

‫‪J →J‬‬
‫‪π‬‬ ‫‪i‬‬

‫‪π‬‬ ‫‪f‬‬

‫‪Experimental‬‬
‫)‪E γ (keV) hω (keV‬‬

‫‪Calculated‬‬
‫)‪hω (keV‬‬

‫)‪2ϑ/h 2 (keV) −1 E γ (keV‬‬

‫1− )‪2ϑ/h 2 (keV‬‬

‫+‬ ‫+‬ ‫10 → 12‬

‫65.223‬ ‫44.374‬ ‫2.106‬ ‫68.107‬ ‫5.377‬ ‫8.308‬ ‫4.287‬ ‫6.377‬ ‫7.818‬ ‫4.409‬ ‫7.999‬ ‫6901‬

‫86.131‬ ‫70.432‬ ‫13.992‬ ‫41.053‬ ‫12.683‬ ‫85.104‬ ‫39.093‬ ‫6.683‬ ‫81.904‬ ‫50.254‬ ‫17.994‬ ‫88.745‬

‫106810.0‬ ‫175920.0‬ ‫395630.0‬ ‫447240.0‬ ‫721940.0‬ ‫822750.0‬ ‫810960.0‬ ‫541080.0‬ ‫105580.0‬ ‫542680.0‬ ‫620680.0‬ ‫667580.0‬

‫16.223‬ ‫85.844‬ ‫45.475‬ ‫15.007‬ ‫74.628‬ ‫15.808‬ ‫17.777‬ ‫26.428‬ ‫35.178‬ ‫44.819‬ ‫43.569‬ ‫3.2101‬

‫7.131‬ ‫87.122‬ ‫40.682‬ ‫64.943‬ ‫66.214‬ ‫78.304‬ ‫95.883‬ ‫90.214‬ ‫95.534‬ ‫70.954‬ ‫45.284‬ ‫10.605‬

‫895810.0‬ ‫12130.0‬ ‫292830.0‬ ‫628240.0‬ ‫979540.0‬ ‫598650.0‬ ‫434960.0‬ ‫681570.0‬ ‫913080.0‬ ‫729480.0‬ ‫780980.0‬ ‫268290.0‬

‫+‬ ‫+‬ ‫1 2 → 14‬

‫+‬ ‫+‬ ‫1 4 → 16‬

‫+‬ ‫+‬ ‫16 → 18‬

‫+‬ ‫+‬ ‫18 → 101‬

‫+‬ ‫+‬ ‫101 → 121‬

‫+‬ ‫+‬ ‫121 → 141‬

‫+‬ ‫+‬ ‫141 → 161‬

‫+‬ ‫+‬ ‫102 → 181‬

‫+‬ ‫+‬ ‫181 → 102‬

‫+‬ ‫+‬ ‫102 → 122‬

‫+‬ ‫+‬ ‫122 → 142‬

‫]2002 , ‪* Ref: [Kitao et al‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫05‬
‫221‬

‫ﺍﻟﺠﺩﻭل )8-4(: ﻁﺎﻗﺎﺕ ﺍﻻﻨﺘﻘﺎل ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫‪Experimental‬‬
‫)‪E γ (keV‬‬
‫*‬

‫‪J →J‬‬
‫‪π‬‬ ‫‪i‬‬

‫‪π‬‬ ‫‪f‬‬

‫‪Calculated‬‬
‫)‪E γ (keV‬‬
‫1− )‪hω (keV) 2ϑ/h 2 (keV‬‬

‫)‪hω (keV‬‬

‫1− )‪2ϑ/h 2 (keV‬‬

‫+‬ ‫+‬ ‫1 0 → 12‬

‫62.133‬ ‫2.794‬ ‫5.836‬ ‫7.057‬ ‫2.228‬ ‫2.087‬ ‫7.347‬ ‫348‬ ‫1.369‬ ‫9.2801‬ ‫4.6811‬

‫42.531‬ ‫28.542‬ ‫88.713‬ ‫5.473‬ ‫25.014‬ ‫37.983‬ ‫95.173‬ ‫82.124‬ ‫53.184‬ ‫72.145‬ ‫40.395‬

‫311810.0‬ ‫851820.0‬ ‫654430.0‬ ‫369930.0‬ ‫712640.0‬ ‫959850.0‬ ‫16270.0‬ ‫745370.0‬ ‫286270.0‬ ‫920270.0‬ ‫884270.0‬

‫82.133‬ ‫36.964‬ ‫89.706‬ ‫23.647‬ ‫76.488‬ ‫78.176‬ ‫51.258‬ ‫78.819‬ ‫95.589‬ ‫3.2501‬ ‫9111‬

‫42.531‬ ‫81.232‬ ‫96.203‬ ‫23.273‬ ‫27.144‬ ‫26.533‬ ‫87.524‬ ‫91.954‬ ‫95.294‬ ‫89.525‬ ‫63.955‬

‫211810.0‬ ‫118920.0‬ ‫681630.0‬ ‫791040.0‬ ‫459240.0‬ ‫564860.0‬ ‫963360.0‬ ‫474760.0‬ ‫320170.0‬ ‫321470.0‬ ‫258670.0‬

‫+‬ ‫+‬ ‫1 2 → 14‬

‫+‬ ‫+‬ ‫14 → 16‬

‫+‬ ‫+‬ ‫16 → 18‬

‫+‬ ‫+‬ ‫18 → 101‬

‫+‬ ‫+‬ ‫101 → 121‬

‫+‬ ‫+‬ ‫121 → 141‬

‫+‬ ‫+‬ ‫141 → 161‬

‫+‬ ‫+‬ ‫102 → 181‬

‫+‬ ‫+‬ ‫181 → 102‬

‫+‬ ‫+‬ ‫102 → 122‬

‫]7002 ,‪* Ref: [Tamura‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫15‬
‫421‬

‫ﺍﻟﺠﺩﻭل )9-4( : ﻁﺎﻗﺎﺕ ﺍﻻﻨﺘﻘﺎل ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫‪Experimental‬‬
‫)‪E γ (keV‬‬
‫*‬

‫‪Jiπ →Jfπ‬‬

‫‪Calculated‬‬
‫)‪E γ (keV‬‬

‫1− )‪hω (keV) 2ϑ/h 2 (keV‬‬

‫1− )‪hω (keV) 2ϑ/h 2 (keV‬‬

‫+‬ ‫+‬ ‫1 0 → 12‬

‫31.453‬ ‫39.425‬ ‫87.966‬ ‫28.287‬ ‫94.048‬ ‫18.117‬ ‫84.927‬ ‫95.258‬ ‫1.479‬ ‫4101‬

‫75.441‬ ‫35.952‬ ‫64.333‬ ‫25.093‬ ‫66.914‬ ‫75.553‬ ‫94.463‬ ‫70.624‬ ‫58.684‬ ‫38.605‬

‫349610.0‬ ‫76620.0‬ ‫748230.0‬ ‫323830.0‬ ‫212540.0‬ ‫426460.0‬ ‫520470.0‬ ‫27270.0‬ ‫168170.0‬ ‫329670.0‬

‫41.453‬ ‫56.605‬ ‫71.956‬ ‫86.118‬ ‫5.048‬ ‫94.767‬ ‫48.118‬ ‫91.658‬ ‫45.009‬ ‫9.449‬

‫85.441‬ ‫94.052‬ ‫71.823‬ ‫29.404‬ ‫66.914‬ ‫83.383‬ ‫46.504‬ ‫78.724‬ ‫90.054‬ ‫92.274‬

‫249610.0‬ ‫236720.0‬ ‫573330.0‬ ‫69630.0‬ ‫112540.0‬ ‫639950.0‬ ‫615660.0‬ ‫414270.0‬ ‫137770.0‬ ‫945280.0‬

‫+‬ ‫+‬ ‫1 2 → 14‬

‫+‬ ‫+‬ ‫14 → 16‬

‫+‬ ‫+‬ ‫16 → 18‬

‫+‬ ‫+‬ ‫18 → 101‬

‫+‬ ‫+‬ ‫101 → 121‬

‫+‬ ‫+‬ ‫121 → 141‬

‫+‬ ‫+‬ ‫141 → 161‬

‫+‬ ‫+‬ ‫102 → 181‬

‫+‬ ‫+‬ ‫181 → 102‬

‫]7991 , ‪* Ref: [Iimura et al‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫25‬
‫621‬

‫ﺍﻟﺠﺩﻭل )01-4( :ﻁﺎﻗﺎﺕ ﺍﻻﻨﺘﻘﺎل ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫*‪Experimental‬‬ ‫‪Calculated‬‬

‫‪Jiπ →Jfπ‬‬
‫)‪E γ (keV‬‬

‫)‪hω (keV‬‬

‫1− )‪2ϑ/h 2 (keV‬‬

‫)‪Eγ (keV‬‬

‫1− )‪hω (keV) 2ϑ/h 2 (keV‬‬

‫+‬ ‫+‬ ‫1 0 → 12‬

‫36.883‬ ‫83.355‬ ‫39.296‬ ‫58.008‬ ‫34.878‬

‫66.851‬ ‫95.372‬ ‫89.443‬ ‫25.993‬ ‫6.834‬

‫934510.0‬ ‫992520.0‬ ‫947130.0‬ ‫64730.0‬ ‫952340.0‬

‫36.883‬ ‫37.525‬ ‫38.266‬ ‫39.997‬ ‫30.739‬

‫66.851‬ ‫29.952‬ ‫99.923‬ ‫60.993‬ ‫68.764‬

‫934510.0‬ ‫36620.0‬ ‫191330.0‬ ‫305730.0‬ ‫455040.0‬

‫+‬ ‫+‬ ‫1 2 → 14‬

‫+‬ ‫+‬ ‫14 → 16‬

‫+‬ ‫+‬ ‫16 → 18‬

‫+‬ ‫+‬ ‫18 → 101‬

‫+‬ ‫+‬ ‫101 → 121‬

‫4.075‬

‫39.482‬

‫546080.0‬

‫34.075‬

‫49.482‬

‫146080.0‬

‫+‬ ‫+‬ ‫121 → 141‬

‫88.437‬ ‫1.988‬

‫91.763‬ ‫23.444‬

‫184370.0‬ ‫337960.0‬

‫44.197‬ ‫95.238‬

‫54.593‬ ‫80.614‬

‫32860.0‬ ‫764470.0‬

‫+‬ ‫+‬ ‫141 → 161‬

‫]2002 , ‪* Ref: [Katakura and Kitao‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫021‬

‫ﺍﻟﺠﺩﻭل )11-4(:ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ ﻋﻤﺭ ﺍﻟﻨﺼﻑ 2/1‪ T‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫‪T‬‬ ‫)‪1/2(exp‬‬ ‫)‪(ps‬‬
‫)‪E γ (keV‬‬

‫‪α+tot‬‬
‫911330.0‬ ‫474010.0‬ ‫9515500.0‬ ‫5117300.0‬ ‫4429200.0‬ ‫3176200.0‬ ‫101‬ ‫711‬ ‫811‬ ‫79‬ ‫29‬ ‫38‬

‫+‬ ‫+‬ ‫10 → 12‬

‫‪exp‬‬ ‫11.99‬ ‫12.711‬ ‫95.911‬ ‫45.89‬ ‫93.39‬ ‫37.38‬

‫*‬

‫7.54‬ ‫8.5‬ ‫37.1‬ ‫79.0‬ ‫36.0‬ ‫85.0‬ ‫96.0‬ ‫84.0‬ ‫62.0‬ ‫21.0‬ ‫90.0‬ ‫8.308‬ ‫4.287‬ ‫6.377‬ ‫7.818‬ ‫4.409‬ ‫7.999‬ ‫5.377‬ ‫68.107‬ ‫2.106‬ ‫44.374‬

‫65.223‬

‫7453.0‬ ‫9014.0‬ ‫4414.0‬ ‫6043.0‬ ‫1323.0‬ ‫5192.0‬

‫70843.0‬

‫+‬ ‫+‬ ‫12 → 14‬ ‫+‬ ‫+‬ ‫14 → 16‬ ‫+‬ ‫+‬ ‫16 → 18‬ ‫+‬ ‫+‬ ‫18 → 101‬ ‫+‬ ‫+‬ ‫101 → 121‬ ‫+‬ ‫+‬ ‫121 → 141‬ ‫+‬ ‫+‬ ‫141 → 161‬ ‫+‬ ‫+‬ ‫102 → 181‬ ‫+‬ ‫+‬ ‫181 → 102‬ ‫+‬ ‫+‬ ‫102 → 122‬

‫46114.0‬

‫24.0‬

‫70643.0‬

‫99723.0‬

‫60492.0‬ ‫648200.0‬ ‫5329200.0‬ ‫4955200.0‬ ‫3530200.0‬ ‫1136100.0‬ ‫08‬ ‫021‬ ‫071‬ ‫022‬ ‫081‬ ‫45.08‬ ‫5.221‬ ‫24.071‬ ‫85.422‬ ‫35.181‬ ‫9082.0‬ ‫4124.0‬ ‫0795.0‬ ‫6277.0‬ ‫1236.0‬

‫68282.0‬

‫22034.0‬

‫15895.0‬

‫27887.0‬

‫35736.0‬ ‫]2002 , ‪+ Ref:[Rosel et al ,1978] , * Ref:[Kitao et al‬‬

‫35‬

‫ﺍﻟﺤﺴﺎﺒﺎﺕ ﻭﺍﻟﻨﺘﺎﺌﺞ‬

‫ﺍﻟﻔﺼل ﺍﻟﺭﺍﺒﻊ‬

‫‪J →J‬‬
‫‪π‬‬ ‫‪i‬‬ ‫‪π‬‬ ‫‪f‬‬

‫‪B(E2) W.u‬‬ ‫*‬ ‫‪cal‬‬ ‫‪exp‬‬

‫2‪B(E2) e2b‬‬ ‫‪cal‬‬

‫221‬

‫ﺍﻟﺠﺩﻭل )21-4(:ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ ﻋﻤﺭ ﺍﻟﻨﺼﻑ 2/1‪ T‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬
‫‪α tot‬‬

‫‪Jiπ →Jfπ‬‬
‫‪T‬‬ ‫)‪1/2(exp‬‬ ‫)‪(ps‬‬
‫)‪E γ (keV‬‬

‫‪B(E2) W.u‬‬ ‫‪exp‬‬
‫*‬

‫2‪B(E2) e2b‬‬ ‫‪calc‬‬ ‫19.87‬ ‫‪exp‬‬
‫*‬

‫‪calc‬‬ ‫40082.0‬

‫+‬ ‫+‬ ‫10 → 12‬

‫3.94‬

‫62.133‬

‫7030.0‬

‫87‬

‫13382.0‬

‫+‬ ‫+‬ ‫12 → 14‬

‫5.4‬

‫2.794‬

‫810.0‬
‫+‬

‫411‬

‫8.411‬

‫92904.0‬

‫61214.0‬

‫+‬ ‫+‬ ‫14 → 16‬

‫4.1‬

‫5.836‬

‫3027400.0‬

‫011‬
‫+‬

‫50.701‬

‫39493.0‬

‫43483.0‬

‫+‬ ‫+‬ ‫16 → 18‬

‫8.0‬

‫7.057‬

‫5241300.0‬

‫08‬
‫+‬

‫25.38‬

‫22782.0‬

‫68992.0‬

‫+‬ ‫+‬ ‫18 → 101‬

‫43.0‬

‫2.228‬

‫2435200.0‬

‫021‬

‫47.421‬

‫38034.0‬

‫58744.0‬

‫]7002 , ‪+ Ref:[Rosel et al, 1978 ] , * Ref: [Tamura‬‬ ‫45‬

‫ﺍﻟﺤﺴﺎﺒﺎﺕ ﻭﺍﻟﻨﺘﺎﺌﺞ‬

‫ﺍﻟﻔﺼل ﺍﻟﺭﺍﺒﻊ‬

‫421‬

‫ﺍﻟﺠﺩﻭل )31-4(:ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ ﻋﻤﺭ ﺍﻟﻨﺼﻑ 2/1‪ T‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫‪T‬‬ ‫)‪1/2(exp‬‬ ‫)‪(ps‬‬
‫)‪E (keV‬‬
‫‪γ‬‬

‫‪Jiπ →Jfπ‬‬
‫‪α tot‬‬

‫‪B(E2) W.u‬‬ ‫‪exp‬‬ ‫28‬
‫+‬ ‫+‬ ‫+‬ ‫*‬

‫2‪B(E2) e2b‬‬ ‫‪calc‬‬ ‫30.38‬ ‫‪exp‬‬
‫*‬

‫‪calc‬‬ ‫58003.0‬

‫+‬ ‫+‬ ‫10 → 12‬

‫33‬ ‫5.3‬ ‫9.0‬ ‫0.1‬ ‫5.1‬ ‫8.2‬ ‫28.287‬ ‫94.048‬ ‫18.117‬ ‫87.966‬ ‫39.425‬ ‫8348700.0‬

‫31.453‬

‫8420.0‬

‫1892.0‬ ‫011‬ ‫031‬ ‫25‬ ‫42.111‬ ‫83.821‬ ‫50.35‬ ‫85304.0‬ ‫69674.0‬ ‫87091.0‬

‫+‬ ‫+‬ ‫1 2 → 14‬

‫83993.0‬

‫+‬ ‫+‬ ‫14 → 16‬

‫3771400.0‬

‫19064.0‬

‫+‬ ‫+‬ ‫16 → 18‬

‫4248200.0‬ ‫804200.0‬

‫64091.0‬
‫+‬ ‫+‬

‫+‬ ‫+‬ ‫18 → 101‬

‫42‬ ‫9285300.0‬ ‫03‬

‫97.42‬ ‫54.03‬

‫450880.0‬ ‫70011.0‬

‫200980.0‬

‫]7991 , ‪+ Ref:[Rosel et al, 1978 ] , * Ref: [Iimura et al‬‬

‫55‬

‫ﺍﻟﺤﺴﺎﺒﺎﺕ ﻭﺍﻟﻨﺘﺎﺌﺞ‬

‫+‬ ‫+‬ ‫101 → 121‬

‫23901.0‬

‫ﺍﻟﻔﺼل ﺍﻟﺭﺍﺒﻊ‬

‫65‬
‫421-021‬

‫ﺍﻟﺠﺩﻭل: )41-4(: ﻗﻴﻡ 22 ‪ α‬ﻟﻨﻅﺎﺌﺭ ‪Xe‬‬
‫2‬ ‫2 ‪α 2 e 2b‬‬

‫‪Isotopes‬‬
‫021‬

‫‪Xe‬‬ ‫‪Xe‬‬ ‫‪Xe‬‬

‫75900.0‬ ‫69110.0‬ ‫66510.0‬

‫221‬

‫421‬

‫021‬

‫ﺍﻟﺠﺩﻭل )51-4( : ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ 1-‪ IBM‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫2‪B(E2) e2 b‬‬ ‫)‪Ei (keV‬‬ ‫‪Transition‬‬
‫)‪E γ (keV‬‬

‫‪Exp‬‬ ‫16.223‬ ‫61.697‬ ‫3.7931‬ ‫2.9902‬ ‫7.2782‬
‫+‬ ‫+‬ ‫10 → 12‬

‫*‬

‫)1-‪Cal(IBM‬‬

‫65.223‬ ‫44.374‬ ‫2.106‬ ‫68.107‬ ‫5.377‬

‫17453.0‬ ‫9014.0‬ ‫24414.0‬ ‫66043.0‬ ‫5523.0‬

‫9762.0‬ ‫1963.0‬ ‫2804.0‬ ‫144.0‬ ‫4793.0‬

‫+‬ ‫+‬ ‫12 → 14‬

‫+‬ ‫+‬ ‫14 → 16‬

‫+‬ ‫+‬ ‫16 → 18‬

‫+‬ ‫+‬ ‫18 → 101‬

‫]2002 , ‪* Ref: [Kitao et al‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫75‬
‫221‬

‫ﺍﻟﺠﺩﻭل )61-4( :ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ 1-‪ IBM‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫2‪B(E2) e2 b‬‬ ‫)‪Ei (keV‬‬ ‫‪Transition‬‬
‫)‪E γ (keV‬‬

‫*‪Exp‬‬
‫+‬ ‫+‬ ‫10 → 12‬

‫)1-‪Cal(IBM‬‬

‫82.133‬

‫62.133‬

‫0082.0‬

‫8972.0‬

‫35.828‬

‫+‬ ‫+‬ ‫12 → 14‬

‫2.794‬

‫3904.0‬

‫7283.0‬

‫1.7641‬

‫+‬ ‫+‬ ‫14 → 16‬

‫5.836‬

‫9493.0‬

‫6814.0‬

‫7.7122‬

‫+‬ ‫+‬ ‫16 → 18‬

‫7.057‬

‫2782.0‬

‫4714.0‬

‫9.9303‬

‫+‬ ‫+‬ ‫18 → 101‬

‫2.228‬

‫6424.0‬

‫9093.0‬

‫]7002 ,‪* Ref: [Tamura‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫85‬
‫421‬

‫ﺍﻟﺠﺩﻭل )71-4( :ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ )2‪ B(E‬ﺒﺎﺴﺘﺨﺩﺍﻡ 1-‪ IBM‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫2‪B(E2) e2 b‬‬ ‫)‪Ei (keV‬‬ ‫‪Transition‬‬
‫)‪E γ (keV‬‬

‫*‪Exp‬‬

‫)1-‪Cal(IBM‬‬

‫41.453‬

‫+‬ ‫+‬ ‫10 → 1 2‬

‫31.453‬

‫58003.0‬

‫6003.0‬

‫30.978‬

‫+‬ ‫+‬ ‫12 → 1 4‬

‫39.425‬

‫85304.0‬

‫1704.0‬

‫8.8451‬

‫+‬ ‫+‬ ‫1 4 → 16‬

‫87.966‬

‫69674.0‬

‫4834.0‬

‫6.1332‬

‫+‬ ‫+‬ ‫16 → 18‬

‫28.287‬

‫87091.0‬

‫7241.0‬

‫]7991 , ‪* Ref: [Iimura et al‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫95‬

‫)‪E(keV‬‬ ‫)‪E(keV‬‬

‫‪exp‬‬
‫021‬

‫‪calc‬‬ ‫‪Xe‬‬

‫‪exp‬‬
‫221‬

‫‪calc‬‬ ‫‪Xe‬‬

‫)‪E(keV‬‬

‫)‪E(keV‬‬

‫‪exp‬‬
‫421‬

‫‪calc‬‬ ‫‪Xe‬‬

‫‪exp‬‬
‫621‬

‫‪calc‬‬ ‫‪Xe‬‬

‫ﺍﻟﺸﻜل )1-4(: ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﻟﺤﺯﻤﺔ ‪Yrast‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫06‬

‫621-021‬

‫ﺍﻟﺸﻜل )2-4(: ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻁﺎﻗﺔ ﺍﻟﻤﺴﺘﻭﻱ ) +12( ‪ E‬ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻟﻠﻨﻅﺎﺌﺭ‪Xe‬‬

‫+‬ ‫+‬ ‫ﺍﻟﺸﻜل )3-4(: ﺘﻐﻴﺭ ﻗﻴﻡ ﻨﺴﺒﺔ ﺍﻟﻁﺎﻗﺔ ) 12(‪ E(41 ) / E‬ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻨﻤﻭﺫﺠﻴﺔ‬

‫ﻟﻜل ﺘﺤﺩﻴﺩ ]8891 ,‪.[Casten and Warner‬‬
‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬ ‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫16‬

‫ﺍﻟﺸﻜل )4-4(: ﺘﻐﻴﺭ ﻗﻴﻡ ﻨﺴﺒﺔ ﺍﻟﻁﺎﻗﺔ ) +12( ‪ E (61+ ) / E‬ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻟﻜل‬ ‫ﺘﺤﺩﻴﺩ ]8891 ,‪.[Casten and Warner‬‬

‫ﺍﻟﺸﻜل )5-4(: ﺘﻐﻴﺭ ﻗﻴﻡ ﻨﺴﺒﺔ ﺍﻟﻁﺎﻗﺔ ) +12( ‪ E (81+ ) / E‬ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻟﻜل‬ ‫ﺘﺤﺩﻴﺩ ]8891 ,‪.[Casten and Warner‬‬
‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬ ‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫26‬

‫021‬

‫ﺍﻟﺸﻜل )6-4(: ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫221‬

‫ﺍﻟﺸﻜل )7-4(: ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫36‬

‫421‬

‫ﺍﻟﺸﻜل )8-4(: ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫621‬

‫ﺍﻟﺸﻜل )9-4(: ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻨﻅﺭﻴﺔ ﺩﺍﻟﺔ ﻟـ )1+‪ J(J‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫46‬

‫ﺍﻟﺸﻜل )01-4(: ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻭﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫56‬

‫ﺍﻟﺸﻜل )11-4(: ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫66‬

‫ﺍﻟﺸﻜل )21-4(: ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻁﺎﻗﺔ ﺍﻻﻨﺘﻘﺎل ‪ Eγ‬ﻭﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫76‬

‫ﺍﻟﺸﻜل )31-4(: ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫86‬

‫ﻭﺍﻟﻘﻴﻡ‬

‫421-021‬

‫ﺍﻟﺸﻜل )41-4(: ﺘﻐﻴﺭ ﻗﻴﻡ ‪ R‬ﻷﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎل ﻤﻊ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻟﻨﻅﺎﺌﺭ ‪Xe‬‬ ‫ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻟﻜل ﺘﺤﺩﻴﺩ]7891 , ‪[Arima and Iachello‬‬

‫اﻟﺤﺴﺎﺑﺎت واﻟﻨﺘﺎﺋﺞ‬

‫اﻟﻔﺼﻞ اﻟﺮاﺑﻊ‬

‫ﺍﳋﺎﻣﺲ‬

‫ﺍﻟﻔﺼﻞ‬

‫ﻭﺍﻻﺳﺘﻨﺘﺎﺟﺎﺕ ﻭﺍﳌﻘﱰﺣﺎﺕ‬

‫ﺍﳌﻨﺎﻗﺸﺔ‬

‫96‬

‫1-5 ﻤﻘﺩﻤﺔ‬
‫ﺘﺘﻜﻭﻥ ﻨﻭﺍﺓ ﺫﺭﺓ ﺍﻟﺯﻴﻨﻭﻥ ‪ Xe‬ﻤﻥ 45 ﺒﺭﻭﺘﻭﻨﺎ ﺘﻤﻸ ﺍﻟﻐﻼﻑ ﺍﻟﺭﺌﻴﺴﻲ ﺍﻟﺨﺎﻤﺱ ﺒــ 05‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﺒﺭﻭﺘﻭﻨﺎ ﺘﺎﺭﻜﺔ 4 ﺒﺭﻭﺘﻭﻨﺎﺕ ﻓﻲ ﺍﻟﻐﻼﻑ ﺍﻟﺴﺎﺩﺱ ﻭﻋﺎﺩﺓ ﺘﻜﻭﻥ ﻓﻲ ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ 2/7‪ 1g‬ﺍﻟـﺫﻱ‬ ‫ﻴﺘﺴﻊ ﺍﻟﻰ 8 ﻨﻜﻠﻴﻭﻨﺎﺕ )ﻫﻨﺎ ﺒﺭﻭﺘﻭﻨﺎﺕ( . ﺍﻥ ﻭﺠﻭﺩ 4 ﺒﺭﻭﺘﻭﻨﺎﺕ ﺨﺎﺭﺝ ﺍﻟﻐﻼﻑ ﺍﻟﻤﻐﻠﻕ ﺍﻟﺨﺎﻤﺱ‬ ‫ﻴﺠﻌل ﺍﻟﻨﻭﺍﺓ ﻗﺭﻴﺒﺔ ﻤﻥ ﺨﻭﺍﺹ ﺍﻟﻨﻭﻯ ﺍﻟﻜﺭﻭﻴﺔ ﺍﻻﻫﺘﺯﺍﺯﻴﺔ )5(‪. SU‬‬ ‫ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴﺔ ﻓﻬﻲ ﺘﺨﺘﻠﻑ ﻓﻲ ﺨﻭﺍﺼﻬﺎ ﻋﻥ ﺨﻭﺍﺹ ﺍﻟﻨـﻭﻯ‬ ‫,‬
‫621‬ ‫621-021‬

‫ﺍﻤﺎ ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ‪Xe‬‬

‫ﺍﻟﻰ 27 ﻨﻴﺘﺭﻭﻨﺎ ﻟﻠﻨﻅﻴـﺭ ‪Xe‬‬ ‫ﹰ‬

‫021‬

‫ﺍﻷﻫﺘﺯﺍﺯﻴﺔ ﻭﺫﻟﻙ ﻷﺤﺘﻭﺍﺌﻬﺎ ﻋﻠﻰ 66 ﻨﻴﺘﺭﻭﻨﺎ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫ﹰ‬

‫ﺍﻥ ﺍﻟﻌﺩﺩ 66 ﻴﻘﻊ ﻓﻲ ﻤﻨﺘﺼﻑ ﺍﻟﻐﻼﻑ ﺍﻟﺴﺎﺩﺱ , ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ 2/3‪ 2d‬ﻤﺎﻟﺌﺎ ﺍﻟﻐﻼﻓﻴﻥ ﺍﻟﺜﺎﻨﻭﻴﻴﻥ‬ ‫ﹰ‬ ‫2/7‪ 1g‬ﻭ 2/5‪ 2d‬ﻓﻀﻼ ﻋﻥ ﻨﻴﺘﺭﻭﻨﻴﻥ ﻓﻲ ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ 2/3‪ 2d‬ﺍﻟﺫﻱ ﻴﻤﺘﻠﻙ 61 ﻤﻭﻗﻌﺎ ﻤﻥ ﺍﺼل‬ ‫ﹰ‬ ‫ﹰ‬ ‫23 ﻤﻭﻗﻌﺎ ﻓﻲ ﺍﻟﻐﻼﻑ ﺍﻟﺴﺎﺩﺱ , ﻓﻴﻜﻭﻥ ﻫﺫﺍ ﺍﻟﻨﻅﻴﺭ ﻓﻲ ﻤﻨﺘﺼﻑ ﺍﻟﻤﺴﺎﻓﺔ ﺒﻴﻥ ﺍﻟﻐﻼﻑ ﺍﻟﺨـﺎﻤﺱ‬ ‫ﹰ‬ ‫ﺴـﻴﻤﺘﻠﻙ‬
‫021‬

‫ﹰ‬ ‫ﻭﺍﻟﻐﻼﻑ ﺍﻟﺴﺎﺩﺱ ﺠﺎﻋﻼ ﻤﻥ ﺍﻟﻨﻭﺍﺓ ﺫﺍﺕ ﺨﻭﺍﺹ ﺩﻭﺭﺍﻨﻴﺔ . ﻭﻋﻠﻴـﻪ ﻓـﺎﻟﻨﻅﻴﺭ ‪Xe‬‬

‫ﺨﻭﺍﺼﺎ ﺍﻫﺘﺯﺍﺯﻴﺔ ﺒﺘﺄﺜﻴﺭ ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻟﻭﺤﺩﻫﺎ ﻭﺨﻭﺍﺼﺎ ﺩﻭﺭﺍﻨﻴﺔ ﺒﺘﺄﺜﻴﺭ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻟﻭﺤﺩﻫﺎ ﻭﻴﻜﻭﻥ‬ ‫ﹰ‬ ‫ﹰ‬ ‫ﻫﺫﺍ ﺍﻟﻨﻅﻴﺭ ﻤﺎﻟﻜﺎ ﻟﺨﻭﺍﺹ ﺍﺨﺭﻯ ﻏﻴﺭ ﺍﻻﻫﺘﺯﺍﺯﻴﺔ ﻭﻏﻴﺭ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﻋﻨـﺩ ﺍﺨـﺫ ﺘـﺄﺜﻴﺭ ﺠﻤﻴـﻊ‬ ‫ﹰ‬ ‫ﺍﻟﻨﻜﻠﻴﻭﻨﺎﺕ )ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ( . ﻭﻤﻥ ﺼﻔﺎﺕ ﻫﺫﺍ ﺍﻟﻨﻅﻴﺭ ﺍﻤﺘﻼﻜﻪ ﻟـ 61 ﺠـﺴﻴﻤﺎ ﻭ 61‬ ‫ﹰ‬
‫621‬ ‫421‬ ‫221‬

‫ﻭ ‪Xe‬‬

‫ﻭ ‪Xe‬‬

‫ﻓﺠﻭﺓ ﻓﻲ ﺍﻟﻐﻼﻑ ﺍﻟﺴﺎﺩﺱ . ﺍﻤﺎﺒﻘﻴﺔ ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ﺍﻟﻤﺩﺭﻭﺴﺔ ﺤﺎﻟﻴﺎ ‪Xe‬‬ ‫ﹰ‬
‫421‬

‫ﻓﺎﻨﻬﺎ ﺘﻤﺘﻠﻙ ﻋﺩﺩﺍ ﻤﻥ ﺍﻟﻔﺠﻭﺍﺕ ﺍﻗل ﻤﻥ ﻋﺩﺩ ﺍﻟﺠﺴﻴﻤﺎﺕ ﻓﻲ ﺍﻟﻐﻼﻑ ﺍﻟﺴﺎﺩﺱ ﺤﻴﺙ ﻴﻜـﻭﻥ ﻋـﺩﺩ‬ ‫ﹰ‬ ‫ﻓﻴﻤﺘﻠـﻙ 01‬
‫621‬

‫21 ﻓﺠﻭﺓ ﺍﻤﺎ ﺍﻟﻨﻅﻴـﺭ ‪Xe‬‬ ‫.‬
‫021‬

‫41 ﻓﺠﻭﺓ ﻭﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫221‬

‫ﺍﻟﻔﺠﻭﺍﺕ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﻓﺠﻭﺍﺕ ﻭﻫﻲ ﺠﻤﻴﻌﻬﺎ ﻗﺭﻴﺒﺔ ﺒﺨﻭﺍﺼﻬﺎ ﻤﻥ ﺨﻭﺍﺹ ﺍﻟﻨﻅﻴﺭ ‪Xe‬‬

‫ﻭﻟﺘﺤﺩﻴﺩ ﺨﻭﺍﺹ ﺍﻟﻨﻅﺎﺌﺭ ﺍﻟﻤﺩﺭﻭﺴﺔ ﺘﻡ ﺍﻷﻋﺘﻤﺎﺩ,ﻓﻀﻼ ﻋﻥ ﻤﺎﺫﻜﺭ,ﻋﻠﻰ ﺍﻟﻨﺴﺒﺔ ﺒـﻴﻥ ﻁﺎﻗـﺔ‬ ‫ﹰ‬ ‫ﺍﻟﻤﺴﺘﻭﻱ +14 ﺍﻟﻰ ﻁﺎﻗﺔ ﺍﻟﻤﺴﺘﻭﻱ +12 ﺤﻴﺙ ﻜﺎﻨﺕ ﻫﺫﻩ ﺍﻟﻨﺴﺒﺔ ﻭﻟﺠﻤﻴﻊ ﻨﻅﺎﺌﺭ ﺍﻟﺯﻴﻨﻭﻥ ﺍﻟﻤﺩﺭﻭﺴﺔ‬ ‫ﻭﺍﻟﺠﺩﻭل )1-4( ﻴﺒﻴﻥ ﻗـﻴﻡ ﻫـﺫﻩ ﺍﻟﻨـﺴﺏ ﻟﻠﻨﻅـﺎﺌﺭ‬
‫221‬

‫ﻗﺭﻴﺒﺔ ﻤﻥ 5.2 ﻭﻫﻲ 5.2 ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﺍﻟﻤﺩﺭﻭﺴ ـﺔ ﻤﻤ ـﺎ ﻴﺠﻌﻠﻬ ـﺎ ﻗﺭﻴﺒ ـﺔ ﻤ ـﻥ ﺨ ـﻭﺍﺹ ﺍﻟﺘﺤﺩﻴ ـﺩ ﻜﺎﻤ ـﺎ ﻏﻴ ـﺭ ﺍﻟﻤ ـﺴﺘﻘﺭ )6(‪O‬‬ ‫ـ‬ ‫ـ ـ‬ ‫ـ‬ ‫ـ ـ ـ‬ ‫ـ‬ ‫ـ ـ‬ ‫]7002 , ‪ , [Pan and Feng‬ﻜﺫﻟﻙ ﻓﺎﻥ ﻤﻭﻗﻊ ﻁﺎﻗﺔ ﺍﻟﻤﺴﺘﻭﻱ +12 ﻟﻠﻨﻅﺎﺌﺭ ﺍﻟﻤﺩﺭﻭﺴـﺔ ﻓـﻭﻕ‬ ‫‪ 300keV‬ﻭﺍﻗل ﻤﻥ ‪ 500keV‬ﻴﺩﻋﻡ ﻓﻜﺭﺓ ﻭﻗﻭﻉ ﻫﺫﻩ ﺍﻟﻨﻅﺎﺌﺭ ﻀﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ )6(‪ O‬ﻭﺍﻷﺸـﻜﺎل‬ ‫ﻭﻴﺘﻀﺢ ﺍﻥ ﻫﺫﻩ ﺍﻟﻨﻅﺎﺌﺭ‬
‫+‬ ‫+‬ ‫+‬ ‫) 18( ‪E‬‬ ‫) 16 ( ‪E‬‬ ‫) 14 ( ‪E‬‬ ‫)2-4( ﺍﻟﻰ )5-4( ﺘﺒﻴﻥ ﻨﺴﺏ ﺍﻟﻁﺎﻗﺎﺕ.‬ ‫ﻭ‬ ‫ﻭ‬ ‫+‬ ‫+‬ ‫+‬ ‫) 12 ( ‪E‬‬ ‫) 12 ( ‪E‬‬ ‫) 12 ( ‪E‬‬

‫ﻗﺭﻴﺒﺔ ﺠﺩﺍ ﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ )6(‪. O‬‬ ‫ﹰ‬
‫اﻟﻤﻨﺎﻗﺸﺔ واﻷﺳﺘﻨﺘﺎﺟﺎت واﻟﻤﻘﺘﺮﺣﺎت‬ ‫اﻟﻔﺼﻞ اﻟﺨﺎﻣﺲ‬

‫07‬

‫2-5 ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ‬
‫ﺒﻌﺩ ﺍﻟﺘﻌﺭﻑ ﻋﻠﻰ ﺨﻭﺍﺹ ﻭﺘﺤﺩﻴﺩ ﻫﺫﻩ ﺍﻟﻨﻅﺎﺌﺭ ﺍﺴﺘﺨﺩﻤﺕ ﺍﻟﻤﻌﺎﺩﻟـﺔ )93-3( ﻟﻬـﺫﺍ ﺍﻟﺘﺤﺩﻴـﺩ‬ ‫ﻟﺤﺴﺎﺏ ﻗﻴﻤﺔ ﺍﻟﻤﻌﺎﻤﻠﻴﻥ 4‪ K‬ﻭ 5‪ K‬ﻭﺫﻟﻙ ﺒﺤل ﻫﺫﻩ ﺍﻟﻤﻌﺎﺩﻟﺔ ﺁﻨﻴﺎ , ﻭﺤﻴﺙ ﺍﻥ ﺍﻷﻫﺘﻤﺎﻡ ﻓﻲ ﻫـﺫﻩ‬ ‫ﺍﻟﺭﺴﺎﻟﺔ ﻴﻨﺼﺏ ﻋﻠﻰ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻷﺩﻨﻰ )‪ (Yrast Levels‬ﺍﻟﻤﺘﻜﻭﻨﺔ ﻤﻥ ﺘﻘﺎﻁﻊ ﺍﻟﺤـﺯﻤﺘﻴﻥ‬ ‫ﺍﻷﺭﻀﻴﺔ )‪ (g-band‬ﻭﺍﻟﺤﺯﻤﺔ ‪ (S-band) S‬ﻓﻘﺩ ﻜﺎﻥ ﻤﻥ ﺍﻻﻓﻀل ﺤﺴﺎﺏ ﻗﻴﻤﺔ ﺍﻟﻤﻌﺎﻤﻠﻴﻥ 4‪K‬‬ ‫ﻭ 5‪ K‬ﻤﺭﺘﻴﻥ , ﻤﺭﺓ ﻟﻠﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﻭﺍﺨﺭﻯ ﻟﻠﺤﺯﻤﺔ ‪ S‬ﻭﺍﻟﺠﺩﻭل )2-4( ﻴﺒﻴﻥ ﻫﺫﻩ ﺍﻟﻘﻴﻡ.ﻓﻘـﺩ‬ ‫ﺍﺩﺨﻠﺕ ﻗﻴﻤﺔ ﻫﺫﻴﻥ ﺍﻟﻤﻌﺎﻤﻠﻴﻥ ﻓﻲ ﺍﻟﻤﻌﺎﺩﻟﺔ )93-3( ﻤﺭﺘﻴﻥ ﻤﺭﺓ ﻟﺤﺴﺎﺏ ﻗـﻴﻡ ﻤـﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗـﺔ‬ ‫ﻟﻠﺤﺯﻤﺔ ‪ g‬ﻭﺍﻷﺨﺭﻯ ﻟﺤﺴﺎﺏ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﺤﺯﻤﺔ ‪ . S‬ﻭﺍﻟﺠﺩﺍﻭل )3-4( ﺍﻟﻰ )6-4( ﺘﺒـﻴﻥ‬ ‫ﻤﻊ ﻨﺴﺏ ﺍﻟﺨﻁﺄ ﻤﻘﺎﺭﻨﺔ ﺒﺎﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴـﺔ.ﻭﻴﺘـﻀﺢ‬
‫621-021‬

‫ﻗﻴﻡ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻷﺩﻨﻰ ﻟﻨﻅﺎﺌﺭ ‪Xe‬‬
‫221‬

‫ﻤﻥ ﻫﺫﻩ ﺍﻟﺠﺩﺍﻭل ﺍﻥ ﺍﻋﻠﻰ ﻨﺴﺒﺔ ﺨﻁﺄ ﻜﺎﻨﺕ %07.3 ﻟﻠﻤﺴﺘﻭﻱ +16 ﻟﻠﻨﻅﻴﺭ ‪ ,120Xe‬ﺍﻤﺎ ﺍﻟﻨﻅﻴـﺭ‬ ‫ﻓﻜﺎﻨﺕ ﺍﻋﻠﻰ ﻨﺴﺒﺔ ﺨﻁﺄ ﻟﻠﻤﺴﺘﻭﻱ +16 ﻜﺫﻟﻙ ﻭﻫﻲ %79.3 ﻭﺍﻋﻠﻰ ﻨﺴﺒﺔ ﺨﻁﺄ ﻓﻲ ﺤﺴﺎﺏ‬
‫621‬

‫‪Xe‬‬

‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﻴﺭ ‪ 124Xe‬ﻜﺎﻨﺕ %3 ﻟﻠﻤـﺴﺘﻭﻱ +141 ﻭﻫـﻲ %45.3 ﻟﻠﻨﻅﻴـﺭ ‪Xe‬‬

‫ﻭﻟﻠﻤﺴﺘﻭﻱ ﻨﻔﺴﻪ +16 ﻭﻨﺴﺏ ﺍﻟﺨﻁﺄ ﻫﺫﻩ ﻗﻠﻴﻠﺔ ﻭﺘﺸﻴﺭﺍﻟﻰ ﻤﺩﻯ ﻨﺠﺎﺡ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﻤﻘﺘﺭﺤﺔ ﻓﻲ ﻫـﺫﻩ‬ ‫ﺍﻟﺭﺴﺎﻟﺔ ﻓﻲ ﺤﺴﺎﺏ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻷﺩﻨﻰ.ﻭﺍﻟﺸﻜل )1-4( ﻴﺒﻴﻥ ﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﺍﻟﻘـﻴﻡ ﺍﻟﻤﺤـﺴﻭﺒﺔ‬ ‫ﺠﻤﻴﻌﻬﺎ ﺍﺫ ﻴﺘﻀﺢ ﺍﻟﺘﻭﺍﻓﻕ ﺍﻟﺠﻴﺩ ﺒـﻴﻥ ﺍﻟﻘـﻴﻡ‬
‫621-021‬

‫ﻭﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﻨﻅﺎﺌﺭ ‪Xe‬‬ ‫ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ.‬

‫ﻭﻷﻥ ﺍﻷﻫﺘﻤﺎﻡ ﻓﻲ ﻫﺫﻩ ﺍﻟﺭﺴﺎﻟﺔ ﻴﻨﺼﺏ ﻋﻠﻰ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺍﻟﺤﺎﺼل ﻓﻲ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗـﺔ‬
‫ﻋﻨﺩ ﻨﻘﻁﺔ ﺍﻟﺘﻘﺎﻁﻊ ﺒﻴﻥ ﺍﻟﺤﺯﻤﺘﻴﻥ ‪ g‬ﻭ ‪ S‬ﻓﻜﺎﻥ ﻤﻥ ﺍﻟﻀﺭﻭﺭﻱ ﺤﺴﺎﺏ ﻗﻴﻡ ﻁﺎﻗﺎﺕ ﺍﻷﻨﺘﻘـﺎل ‪Eγ‬‬

‫ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ‪ hω‬ﻓﻀﻼ ﻋﻥ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻟﻜل ﺍﻨﺘﻘﺎل ﻟﻜـل ﻨﻅﻴـﺭ , ﻭﺍﻟﺠـﺩﺍﻭل‬ ‫ﹰ‬ ‫)7-4( ﺍﻟﻰ )01-4( ﺘﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻟﻬﺫﻩ ﺍﻟﻤﻌﻠﻤـﺎﺕ ﻭﻤـﻥ ﺘﻔﺤـﺹ ﻫـﺫﻩ‬ ‫ﺍﻟﺠﺩﺍﻭل ﻴﺘﻀﺢ ﻤﺩﻯ ﺘﻘﺎﺭﺏ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻤﻊ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻤﻤﺎ ﻴﺅﻜﺩ ﺼﺤﺔ ﺍﻷﺴـﻠﻭﺏ ﺍﻟﻤﺘﺒـﻊ‬ ‫ﻓﻲ ﺤﺴﺎﺒﺎﺕ ﻫﺫﻩ ﺍﻟﻤﻌﻠﻤﺎﺕ ﻟﻬﺫﻩ ﺍﻟﻨﻅﺎﺌﺭ ﻓﻲ ﻫﺫﻩ ﺍﻟﺩﺭﺍﺴﺔ.‬ ‫ﺭﺴﻤﺕ ﺍﻷﺸﻜﺎل )6-4( ﺍﻟﻰ )9-4( ﻟﺘﻭﻀﺢ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺤﺎﺼل ﻓﻲ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻟﻌﻤﻠﻴـﺔ‬ ‫ﻭﺍﻟﻤﺤﺴﻭﺒﺔ ﺩﺍﻟﺔ ﻟـ )1+‪.J(J‬ﻭﻴﺘﻀﺢ ﻤﻥ ﻫﺫﻩ ﺍﻷﺸﻜﺎل ﺍﻻﺘﻔﺎﻕ ﺍﻟﺘﺎﻡ ﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﻘـﻴﻡ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ ﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺘﻁﺎﺒﻕ ﻤﻭﻗﻊ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻟﺠﻤﻴﻊ ﺍﻟﻨﻅﺎﺌﺭ ﻋﻨﺩ ﻗﻴﻤـﺔ 01=‪ J‬ﻋـﺩﺍ‬ ‫ﻭﺍﻗﻠﻬﺎ ﻟﻠﻨﻅﻴﺭ‬ ‫ﻭﺍﻜﺒـﺭ‬
‫021‬ ‫621‬

‫ﺍﺫ ﻅﻬﺭ ﺍﻷﻨﺤﻨﺎﺀ ﻋﻨﺩ 8=‪, J‬ﻭﺍﻥ ﺍﺒﺭﺯ ﺍﻨﺤﻨﺎﺀ ﺤﺼل ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫421‬

‫ﺍﻟﻨﻅﻴﺭ‪Xe‬‬
‫021‬

‫ﻭﻴﻌﻭﺩ ﻫﺫﺍ ﺍﻟﻰ ﺯﺍﻭﻴﺔ ﺍﻟﺘﻘﺎﻁﻊ ﺒﻴﻥ ﺍﻟﺤﺯﻤﺘﻴﻥ ‪ g‬ﻭ ‪ S‬ﻓﻬﻲ ﺍﻗل ﻟﻠﻨﻅﻴـﺭ ‪Xe‬‬

‫‪Xe‬‬

‫اﻟﻤﻨﺎﻗﺸﺔ واﻷﺳﺘﻨﺘﺎﺟﺎت واﻟﻤﻘﺘﺮﺣﺎت‬

‫اﻟﻔﺼﻞ اﻟﺨﺎﻣﺲ‬

‫17‬

‫ﺍﻻﺸﻜﺎل )1-5 ﺍﻟﻰ 2-5( ﻭﻴﻌﻭﺩ ﻫﺫﺍ ﺍﻟﻰ ﺯﻴﺎﺩﺓ ﻋﺩﺩ ﺍﻟﺠﺴﻴﻤﺎﺕ ﻋـﻥ ﻤﻨﺘـﺼﻑ‬

‫621‬

‫ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﺍﻟﻤﺴﺎﻓﺔ ﻓﻲ ﺍﻟﻐﻼﻑ ﺍﻟﺴﺎﺩﺱ ﻭﻨﻘﺼﺎﻥ ﻋﺩﺩ ﺍﻟﻔﺠﻭﺍﺕ ﻓﻲ ﺍﻟﻐﻼﻑ ﻨﻔﺴﻪ , ﻭﻷﻥ ﻤﻨﺘﺼﻑ ﺍﻟﻤـﺴﺎﻓﺔ‬ ‫ﺘﻌﻁﻲ ﺼﻔﺎﺕ ﻗﺭﻴﺒﺔ ﻤﻥ ﺼﻔﺎﺕ ﺍﻟﻐﻼﻑ ﺍﻟﻤﻐﻠﻕ ﻟﺫﺍ ﻴﺘﻭﻗﻊ ﺍﻥ ﺯﻴﺎﺩﺓ ﻋﺩﺩ ﺍﻟﺠﺴﻴﻤﺎﺕ ﻋﻨﺩ ﺍﻟﻐﻼﻑ‬ ‫2/7‪) 1g‬ﺒﺎﻟﻌﺩﺩ 46 ( ﺘﺴﺒﺏ ﺯﻴﺎﺩﺓ ﻓﻲ ﺯﺍﻭﻴﺔ ﺍﻟﺘﻘﺎﻁﻊ ﺒﻴﻥ ﺍﻟﺤﺯﻤﺘﻴﻥ ﻜﻠﻤﺎ ﺯﺍﺩ ﻋـﺩﺩ ﺍﻟﺠـﺴﻴﻤﺎﺕ‬ ‫ﻋﻥ ﺒﻘﻴـﺔ‬
‫421‬

‫ﻋﻥ )46( ﻟﺯﻴﺎﺩﺓ ﺘﻔﺎﻋﻠﻬﺎ ﻤﻊ ﺒﻌﺽ ﺍﻤﺎ ﺴﺒﺏ ﺍﺨﺘﻼﻑ ﻤﻭﻗﻊ ﺍﻷﻨﺤﻨﺎﺀ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﺍﻟﻨﻅﺎﺌﺭ ﻓﻨﻘﺘﺭﺡ ﺍﻥ ﺴﺒﺏ ﺫﻟﻙ ﻫﻭ ﺍﻤﺘﻼﺀ ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ 2/1‪ 3S‬ﺘﻤﺎﻤﺎ ﺒﺎﻟﻨﻴﺘﺭﻭﻨـﺎﺕ ﻓـﻲ ﻫـﺫﺍ‬ ‫ﹰ‬ ‫ﺍﻟﻨﻅﻴﺭ ﻤﻤﺎ ﻴﺘﻁﻠﺏ ﻁﺎﻗﺔ ﺍﻜﺒﺭ ﻟﻜﺴﺭ ﺘﺭﺍﺒﻁﻬﻤﺎ ﻤﻤﺎ ﻴﺴﺒﺏ ﺤﺼﻭل ﻨﻘﺼﺎﻥ ﻓـﻲ ﻗﻴﻤـﺔ ﺍﻟﻁﺎﻗـﺔ‬ ‫ﻟﻠﻤﺴﺘﻭﻱ ﻋﻨﺩ ﺍﻟﻤﺴﺘﻭﻱ +18 ﻗﺒل ﺍﻟﻤﺴﺘﻭﻱ +101 ﻜﺒﻘﻴﺔ ﺍﻟﻨﻅﺎﺌﺭ.ﻭﻫﻨﺎﻙ ﺩﺭﺍﺴﺎﺕ ﺍﻜﺩﺕ ﻭﺠﻭﺩ ﺸﺒﻪ‬ ‫ﺍﻟﻘﺸﺭﺓ ﺫﺍﺕ ﺍﻟﻌﺩﺩ )46( ]9891,‪. [Mheemeed et al‬‬ ‫‪ 2ϑ‬ﺩﺍﻟﺔ ﻟـ ‪ J‬ﻭﻴﺘﻀﺢ ﻤـﻥ‬
‫2‪h‬‬

‫ﺍﻤﺎ ﺍﻟﺸﻜل )01-4( ﻴﺒﻴﻥ ﺘﻐﻴﺭ ﻗﻴﻤﺔ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ‬

‫ﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻷﺭﺒﻌﺔ ﻓﻲ ﻫﺫﺍ ﺍﻟﺸﻜل ﺯﻴﺎﺩﺓ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻋﻨﺩ ﺍﻟﻤﺴﺘﻭﻱ +101 ﺒﻨـﺴﺒﺔ ﺍﻜﺒـﺭ‬ ‫ﻋﻠـﻰ‬
‫421‬

‫ﻤﻥ ﺍﻟﺯﻴﺎﺩﺍﺕ ﺍﻟﺤﺎﺼﻠﺔ ﻓﻲ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﺴﺎﺒﻘﺔ ﻟﻪ ﻟﻠﻨﻅﺎﺌﺭ ﺠﻤﻴﻌﻬﺎ ﺒﻤﻀﻨﻬﺎ ﺍﻟﻨﻅﻴﺭ ‪Xe‬‬

‫ﺍﻟﺭﻏﻡ ﻤﻥ ﺍﻥ ﺍﻻﻨﺤﻨﺎﺀ ﻓﻲ ﻫﺫﺍ ﺍﻟﻨﻅﻴﺭ ﻅﻬﺭ ﻋﻨﺩ ﺍﻟﻤﺴﺘﻭﻱ +18 ﻭﻫﺫﺍ ﻨـﺎﺘﺞ ﻋـﻥ ﺍﻥ ﺍﻟﺯﻴـﺎﺩﺓ‬ ‫ﺍﻟﺤﺎﺼﻠﺔ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻋﻨﺩ ﺍﻟﻤﺴﺘﻭﻱ +101 ﺍﻜﺒﺭ ﻤﻥ ﺍﻟﺯﻴﺎﺩﺓ ﺍﻟﺤﺎﺼﻠﺔ ﻋﻨﺩ ﺍﻟﻤـﺴﺘﻭﻱ‬ ‫+18 ﻤﻘﺎﺭﻨﺔ ﺒﺎﻟﻤﺴﺘﻭﻴﻴﻥ ﺍﻟﻠﺫﻴﻥ ﻴﺴﺒﻘﺎﻨﻬﻤﺎ ﻭﻟﻜﻥ ﺍﻟﺯﻴﺎﺩﺓ ﺍﺒﺘﺩﺍﺀ ﻗﺩ ﺤﺼﻠﺕ ﻋﻨـﺩ +18 ﻓﻴﻤـﺎ ﻴﺨـﺹ‬ ‫‪‬‬ ‫ﻭﺍﻷﻗـل‬
‫621‬ ‫421‬

‫ﻭﺍﻥ ﻫﺫﻩ ﺍﻟﺯﻴﺎﺩﺓ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﺘﻜﻭﻥ ﺍﻷﻜﺒﺭ ﻟﻠﻨﻅﻴـﺭ ‪Xe‬‬

‫ﺍﻟﻨﻅﻴﺭ‪Xe‬‬

‫ﻭﻟﻠﺴﺒﺏ ﺍﻟﻤﺫﻜﻭﺭ ﻨﻔﺴﻪ, ﻭﻻﺒﺘﻌﺎﺩ ﺍﻟﻨﻭﺍﺓ ﻋﻥ ﺍﻟﻐﻼﻑ ﺍﻟﻤﻐﻠﻕ ﺍﻟﺨـﺎﻤﺱ. ﻜﻤـﺎ ﺍﻥ‬

‫021‬

‫ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﺯﻴﺎﺩﺓ ﻋﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻴﺴﺒﺏ ﺍﺴﺘﻁﺎﻟﺔ ﻓﻲ ﺸﻜل ﺍﻟﻨﻭﺍﺓ ﻤﻤﺎ ﻴﺴﺒﺏ ﺯﻴﺎﺩﺓ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟـﺫﺍﺘﻲ‬ ‫ﻟﻬﺎ ]6002 , ‪. [Singo‬‬ ‫ﺍﻟﺭﺴﻭﻤﺎﺕ ﻓﻲ ﺍﻟﺸﻜل )11-4( ﺘﻭﻀﺢ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﺯﺨﻡ ﺍﻟﺯﺍﻭﻱ ‪ J‬ﺩﺍﻟﺔ ﻟﻠﺘﺭﺩﺩ ﺍﻟـﺩﻭﺭﺍﻨﻲ‬ ‫‪ hω‬ﻭﻴﺘﻀﺢ ﻤﻥ ﻫﺫﻩ ﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻥ ﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻴﺯﺩﺍﺩ ﺒﺯﻴﺎﺩﺓ ‪ J‬ﻭﺴﺒﺏ ﺫﻟـﻙ ﻫـﻭ ﻜـﺴﺭ‬ ‫ﺘﺭﺍﺒﻁ ﺯﻭﺝ ﻤﻥ ﺍﻟﻨﻜﻠﻴﻭﻨﺎﺕ ﻓﻲ ﻤﺴﺘﻭﻱ ﻤﻌﻴﻥ ﻭﻤﻐﺎﺩﺭﺘﻬﻤﺎ ﺍﻟﻰ ﻤﺴﺘﻭﻴﺎﺕ ﺍﺨﺭﻯ ﻤﺴﺒﺒﺔ ﺍﻷﺨﺘﻼﻑ‬ ‫ﻓﻲ ﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻟﻠﻨﻭﺍﺓ ]0991 , ‪ . [Wong‬ﻭﺍﻟﺸﻜل )21-4( ﻴﻭﻀﺢ ﺍﻟﻌﻼﻗﺔ ﺒـﻴﻥ ﻁﺎﻗـﺔ‬ ‫ﺍﻷﻨﺘﻘﺎل ‪ Eγ‬ﺩﺍﻟﺔ ﻟـ ‪ J‬ﻭﻴﺘﻀﺢ ﻜﺫﻟﻙ ﺯﻴﺎﺩﺓ ﻓﻲ ﻁﺎﻗﺔ ﺍﻷﻨﺘﻘﺎل ﺒﺯﻴﺎﺩﺓ ‪ J‬ﺍﻟﻰ ﺍﻟﻘﻴﻤﺔ 01=‪ J‬ﻭﻤـﻥ‬ ‫ﺜﻡ ﺤﺼﻭل ﻨﻘﺼﺎﻥ ﻓﻲ ﻁﺎﻗﺔ ﺍﻷﻨﺘﻘﺎل ﺒﻌﺩ 01=‪ J‬ﻭﻟﻼﺴﺒﺎﺏ ﺍﻟﻤﺫﻜﻭﺭﺓ ﻨﻔﺴﻬﺎ ﺴﺎﺒﻘﺎ ﻋﻠﻰ ﺍﻟـﺭﻏﻡ‬ ‫ﹰ‬ ‫ﺒﺴﺒﺏ ﺤﺩﻭﺙ ﺍﻷﻨﺤﻨﺎﺀ‬
‫421‬

‫ﻤﻥ ﺍﻥ ﺸﻜل ﺍﻟﻤﻨﺤﻨﻲ ﺒﻴﻥ ﺍﻟﻤﺴﺘﻭﻴﻴﻥ +18 ﻭ +101 ﻗﺩ ﺘﻐﻴﺭ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫ﻋﻨﺩ ﺍﻟﻤﺴﺘﻭﻱ +18 ﻟﻬﺫﺍ ﺍﻟﻨﻅﻴﺭ ﻜﻤﺎ ﺫﻜﺭ . ﺍﻤﺎ ﺍﻟﺸﻜل )31-4( ﻓﻴﺒﻴﻥ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻋﺯﻡ ﺍﻟﻘـﺼﻭﺭ‬
‫اﻟﻤﻨﺎﻗﺸﺔ واﻷﺳﺘﻨﺘﺎﺟﺎت واﻟﻤﻘﺘﺮﺣﺎت‬ ‫اﻟﻔﺼﻞ اﻟﺨﺎﻣﺲ‬

‫27‬

‫‪ 2ϑ‬ﻭﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ‪ hω‬ﺍﺫ ﻴﺘﻀﺢ ﻤﻥ ﻫﺫﻩ ﺍﻷﺸﻜﺎل ﺍﻟﻨﻘﺼﺎﻥ ﺍﻟﻤﻔﺎﺠﺊ ﻓﻲ ﺍﻟﺘـﺭﺩﺩ‬

‫2‪h‬‬

‫ﺍﻟﺫﺍﺘﻲ‬

‫ﺍﻟﺩﻭﺭﺍﻨﻲ ﻴﺭﺍﻓﻘﻪ ﺯﻴﺎﺩﺓ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻭﺫﻟﻙ ﺒﺴﺒﺏ ﻨﻘﺼﺎﻥ ﻁﺎﻗﺔ ﺍﻷﻨﺘﻘﺎل ﻋﻨـﺩ ﻗﻴﻤـﺔ‬
‫‪2ϑ‬‬ ‫2‪h‬‬

‫ﻋﺎﻟﻴﺔ ﻨﺴﺒﻴﺎ 21=‪ J‬ﻤﺴﺒﺒﺔ ﺍﻟﻨﻘﺼﺎﻥ ﻓﻲ ﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ )ﺍﻟﻤﻌﺎﺩﻟﺔ 22-2( ﻭﺍﻟﺯﻴﺎﺩﺓ ﻓـﻲ‬ ‫ﹰ‬ ‫ﹰ‬

‫)ﺍﻟﻤﻌﺎﺩﻟﺔ 12-2( ﻭﻟﻼﺴﺒﺎﺏ ﺍﻟﻤﺫﻜﻭﺭﺓ ﻨﻔﺴﻬﺎ . ﻭﻴﺘﻀﺢ ﻜﺫﻟﻙ ﻤﻥ ﻫﺫﺍ ﺍﻟﺸﻜل ﺤﺩﻭﺙ ﺍﻨﻜﻤﺎﺵ ﻓﻲ‬ ‫ﻗﺒل ﺍﻟﻤﻭﻗﻊ ﺍﻟﺤﺎﺼل ﻓﻴﻪ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻓﻲ ‪ hω‬ﻟﻠـﺴﺒﺏ ﺍﻟـﺴﺎﺒﻕ‬
‫421‬

‫ﺯﻴﺎﺩﺓ ‪ hω‬ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬ ‫ﻨﻔﺴﻪ.‬

‫3-5 ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺍﻟﻤﺨﺘﺯﻟﺔ‬
‫ﺘﻌﺘﺒﺭ ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎﻻﺕ ﺍﻟﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻴـﺔ ﺍﻟﻤﺨﺘﺯﻟـﺔ )2‪ B(E‬ﺒـﻴﻥ ﻤﺨﺘﻠـﻑ‬ ‫ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﻤﻥ ﺍﻟﻤﻌﺎﻟﻡ ﺍﻟﻤﻬﻤﺔ ﻓﻲ ﺍﻟﺘﺭﻜﻴﺏ ﺍﻟﻨﻭﻭﻱ ﻟﻠﻨﻭﻯ ﺍﻟﺯﻭﺠﻴﺔ – ﺍﻟﺯﻭﺠﻴﺔ ﻟﻌﻼﻗﺔ ﻫﺫﺍ ﺍﻟﻤﻌﻠﻡ‬ ‫ﺒﺸﻜل ﺍﻟﻨﻭﺍﺓ ﻜﻤﺎ ﺍﻥ ﺍﻟﻨﺴﺏ ﺒﻴﻥ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺘﻌﻁﻲ ﻤﻔﻬﻭﻤﺎ ﻋﻥ ﺨﻭﺍﺹ ﺍﻟﻨﻭﺍﺓ ﻭﻤﻭﻗﻌﻬـﺎ ﻀـﻤﻥ‬ ‫ﹰ‬ ‫ﺍﻟﺘﺤﺩﻴﺩﺍﺕ ﺍﻟﺜﻼﺜﺔ )5(‪ SU‬ﻭ )3(‪ SU‬ﻭ )6(‪ O‬ﻟﻬﺫﺍ ﺘﻡ ﺤﺴﺎﺏ )2‪ B(E‬ﻟﻸﻨﺘﻘﺎل ﺒـﻴﻥ ﻤﺨﺘﻠـﻑ‬ ‫ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﻭﺒﻁﺭﻴﻘﺘﻴﻥ ﻤﺨﺘﻠﻔﺘﻴﻥ . ﺍﻋﺘﻤﺩﺕ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﺍﻟﻤﺘﻭﺍﻓﺭﺓ ﻟﻁﺎﻗـﺎﺕ ﺍﻻﻨﺘﻘـﺎل ﻭﺍﻟﻌﻤـﺭ‬ ‫ﺍﻟﻨﺼﻔﻲ ﻟﺤﺴﺎﺏ )2‪ B(E‬ﻭﺫﻟﻙ ﺒﺎﻟﻭﺤﺩﺘﻴﻥ 2‪ e2b‬ﻭﻭﺤﺩﺓ ﺍﻟﻭﺍﻴﺴﻜﻭﻑ ‪ W.u‬ﻭﺍﻟﺠـﺩﺍﻭل )11-4(‬ ‫ﻭ)21-4( ﻭ )31-4( ﺘﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﺒﺎﻟﻭﺤﺩﺘﻴﻥ 2‪ e2b‬ﻭ ‪ W.u‬ﻤﻘﺎﺭﻨﺔ ﻤﻊ ﺍﻟﻘـﻴﻡ ﺍﻟﻌﻤﻠﻴـﺔ‬ ‫ﻓﻠﻡ ﻴﺘﻡ ﺤﺴﺎﺏ ﺍﻻﻨﺘﻘﺎﻻﺕ ﻓﻴﻪ ﻟﻌﺩﻡ ﺘـﻭﻓﺭ‬
‫621‬ ‫421‬ ‫221‬ ‫021‬

‫ﺍﻤﺎ ﺍﻟﻨﻅﻴﺭ ‪Xe‬‬

‫ﻭ‪Xe‬‬

‫ﻭ‪Xe‬‬

‫ﻟﻠﻨﻅﺎﺌﺭ ‪Xe‬‬

‫ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻟﻠﻌﻤﺭ ﺍﻟﻨﺼﻔﻲ ﻟﻸﻨﺘﻘﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻟﻠﻨﻅﻴﺭ . ﻭﻴﺘﻀﺢ ﻤﻥ ﻫﺫﻩ ﺍﻟﺠﺩﺍﻭل ﻤﺩﻯ ﺍﻟﺘﻘﺎﺭﺏ‬ ‫ﺒﻴﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻭﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻭﻫﺫﺍ ﻴﺸﻴﺭ ﺍﻟﻰ ﺼﺤﺔ ﺍﺴﻠﻭﺏ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﻟﺘﺤﻭل ﺍﻟـﺩﺍﺨﻠﻲ‬ ‫ﺍﻟﻀﺭﻭﺭﻱ ﻓﻲ ﺤﺴﺎﺏ )2‪ B(E‬ﺍﺫ ﺘﻡ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﻟﺘﺤـﻭل ﺍﻟـﺩﺍﺨﻠﻲ ﺒﻁﺭﻴﻘـﺔ ﺍﻷﺴـﺘﻜﻤﺎل‬ ‫)‪ (Interpolation‬ﻭﺒﻨﺎﺀ ﺒﺭﻨﺎﻤﺞ ﻟﻬﺫﺍ ﺍﻟﻐﺭﺽ .‬ ‫ﻭﺘﻡ ﺤﺴﺎﺏ )2‪ B(E‬ﻟﻸﻨﺘﻘﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﺒﻴﻥ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺍﻷﺩﻨﻰ ﻓﻲ ﺍﻟﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ‬ ‫ﻓﻲ ﺍﻟﺘﺤﺩﻴﺩ )6(‪ O‬ﻓﻘﺩ ﺘﻡ ﺤﺴﺎﺏ )2‪ B(E‬ﻟﻸﻨﺘﻘـﺎﻻﺕ ﻀـﻤﻥ‬ ‫ﺤﻴﺙ ﺘﻡ ﺤﺴﺎﺏ )2‪ B(E‬ﻟﻐﺎﻴـﺔ‬
‫421‬ ‫621-021‬

‫ﻓﻘﻁ ﻭﻟﻭﻗﻭﻉ ﺍﻟﻨﻅﺎﺌﺭ ‪Xe‬‬

‫ﺍﻟﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ ﺒﺄﺴﺘﺨﺩﺍﻡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ ﺍﻟﺘﺤﺩﻴﺩ ﻜﺎﻤـﺎ ﻏﻴـﺭ ﺍﻟﻤـﺴﺘﻘﺭ )6(‪O‬‬ ‫ﻭﻟﻸﻨﺘﻘﺎﻻﺕ ﻤﻥ +10 → +12 ﺍﻟﻰ +18 → +101 ﻋﺩﺍ ﺍﻟﻨﻅﻴﺭ ‪Xe‬‬

‫ﺍﻷﻨﺘﻘﺎل +16 → +18 ﻀﻤﻥ ﺍﻟﺤﺯﻤﺔ ﺍﻷﺭﻀﻴﺔ )‪ (g-band‬ﻭﺫﻟﻙ ﻟﻭﻗـﻭﻉ ﺍﻟﻤـﺴﺘﻭﻱ +101 ﻟﻬـﺫﺍ‬ ‫ﺍﻟﻨﻅﻴﺭ ﻀﻤﻥ ﺍﻟﺤﺯﻤﺔ ‪. S‬ﺘﻡ ﺍﻷﻋﺘﻤﺎﺩ ﻋﻠﻰ ﺍﻟﻤﻌﺎﺩﻟﺔ )34-3( ﺍﻟﺘﺤﺩﻴﺩ ﻜﺎﻤﺎ ﻏﻴﺭ ﺍﻟﻤـﺴﺘﻘﺭ )6(‪O‬‬
‫اﻟﻤﻨﺎﻗﺸﺔ واﻷﺳﺘﻨﺘﺎﺟﺎت واﻟﻤﻘﺘﺮﺣﺎت‬ ‫اﻟﻔﺼﻞ اﻟﺨﺎﻣﺲ‬

‫37‬

‫ﻟﺤﺴﺎﺏ ﻗﻴﻡ ﺍﻟﻤﻌﺎﻤل 22 ‪ α‬ﺒﺎﻷﻋﺘﻤﺎﺩ ﻋﻠﻰ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﺍﻟﻤﺘﻭﻓﺭﺓ ﻟﻸﻨﺘﻘﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻀﻤﻥ ﺍﻟﺤﺯﻤﺔ‬ ‫ﺍﻷﺭﻀﻴﺔ , ﻭﻟﻘﺩ ﺍﻋﺘﻤﺩﺕ ﺍﻓﻀل ﻗﻴﻤﺔ ﻟﻬﺫﺍ ﺍﻟﻤﻌﻠﻡ 22 ‪ . α‬ﻭﺍﻟﺠﺩﻭل )41-4( ﻴﺒﻴﻥ ﻗﻴﻤﺔ ﻫﺫﺍ ﺍﻟﻤﻌﻠـﻡ‬ ‫.ﺒﻌﺩ ﺤﺴﺎﺏ ﻭﺍﻋﺘﻤﺎﺩ ﺍﻓﻀل ﻗﻴﻤﺔ ﻟـ 22 ‪ α‬ﺘﻡ ﺤﺴﺎﺏ ﺍﺤﺘﻤﺎﻟﻴﺔ‬
‫421‬ ‫021‬

‫ﺍﻟﻰ ‪Xe‬‬

‫ﻟﻠﻨﻅﺎﺌﺭ ﺍﻟﺜﻼﺜﺔ ‪Xe‬‬
‫021‬

‫ﺍﻷﻨﺘﻘﺎل ﺭﺒﺎﻋﻴﺔ ﺍﻟﻘﻁﺏ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺍﻟﻤﺨﺘﺯﻟﺔ )2‪ B(E‬ﻟﻸﻨﺘﻘﺎل ﻓﻲ ﺍﻟﺤﺯﻤـﺔ ﺍﻷﺭﻀـﻴﺔ ﻟﻠﻨﻅـﺎﺌﺭ‬ ‫ﻭﺍﻟﺠﺩﺍﻭل )51-4( ﻭ )61-4( ﻭ )71-4( ﺘﺒﻴﻥ ﻫﺫﻩ ﺍﻟﻘـﻴﻡ ﺒﻭﺤـﺩﺍﺕ‬
‫421‬

‫,‪Xe ,122Xe‬‬

‫‪Xe‬‬

‫2‪ e2b‬ﻤﻘﺎﺭﻨﺔ ﻤﻊ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻭﻜﺎﻨﺕ ﺍﻟﻨﺘﺎﺌﺞ ﺠﻴﺩﺓ ﻭﻻﺴﻴﻤﺎ ﻋﻨﺩ ﻤﺭﺍﺠﻌﺔ ﺍﻟﻤﻨﺸﻭﺭﺍﺕ ﺍﻟﺴﺎﺒﻘﺔ ﻓﻲ‬ ‫ﺤﺴﺎﺏ )2‪ B(E‬ﺒﺎﻷﻋﺘﻤﺎﺩ ﻋﻠﻰ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ ﻟﻨـﻭﻯ ﺍﺨـﺭﻯ ]ﻨـﻭﺭﻱ ,5002[‬ ‫,]ﻤﺼﻁﻔﻰ , 5002[ ,]ﻴﻭﺴﻑ,5002[. ﻭﻋﻨﺩ ﺭﺴﻡ ﺍﻟﻌﻼﻗﺔ ﺒـﻴﻥ ﻋـﺩﺩ ﺍﻟﻨﻴﺘﺭﻭﻨـﺎﺕ ﻟﻠﻨﻅـﺎﺌﺭ‬ ‫,‬
‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫) 14 → 16;2 ‪B( E‬‬ ‫) 12 → 14;2 ‪B ( E‬‬ ‫,‬ ‫ـﺎﻻﺕ‬ ‫ـﺴﺏ ـﻴﻥ ﺍﻻﻨﺘﻘــ‬ ‫ﺒــ‬ ‫ـﺔ ﻭﺍﻟﻨــ‬ ‫ﺍﻟﻤﺩﺭﻭﺴــ‬ ‫+‬ ‫+‬ ‫+‬ ‫+‬ ‫) 10 → 12;2 ‪B( E‬‬ ‫) 10 → 12;2 ‪B ( E‬‬ ‫+‬ ‫+‬ ‫) 16 → 18;2 ‪B( E‬‬ ‫+‬ ‫+‬ ‫) 10 → 12;2 ‪B( E‬‬

‫ﻭﻤﻥ ﺍﻟﺸﻜل )41-4( ﻴﺘﻀﺢ ﺘﻭﺍﻓﻕ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻭ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻟﻬﺫﻩ ﺍﻟﻨﺴﺏ ﻤﻊ‬

‫ﺍﻟﻘﻴﻡ ﺍﻟﻨﻤﻭﺫﺠﻴﺔ ﻀﻤﻥ ﺍﻟﺘﺤﺩﻴﺩ )6(‪. O‬‬

‫اﻟﺸﻜﻞ )1-5(:زاوﻳﺔ اﻟﺘﻘﺎﻃﻊ ﺑﻴﻦ اﻟﺤﺰﻣﺔ اﻻرﺿﻴﺔ ‪g‬‬ ‫021‬ ‫واﻟﺤﺰﻣﺔ اﻟﻤﺜﺎرة ‪ S‬ﻟﻠﻨﻈﻴﺮ ‪Xe‬‬

‫اﻟﻤﻨﺎﻗﺸﺔ واﻷﺳﺘﻨﺘﺎﺟﺎت واﻟﻤﻘﺘﺮﺣﺎت‬

‫اﻟﻔﺼﻞ اﻟﺨﺎﻣﺲ‬

‫47‬

‫اﻟﺸﻜﻞ )2-5(:زاوﻳﺔ اﻟﺘﻘﺎﻃﻊ ﺑﻴﻦ اﻟﺤﺰﻣﺔ اﻻرﺿﻴﺔ ‪ g‬واﻟﺤﺰﻣﺔ‬ ‫221‬ ‫اﻟﻤﺜﺎرة ‪ S‬ﻟﻠﻨﻈﻴﺮ ‪Xe‬‬

‫اﻟﺸﻜﻞ )3-5(:زاوﻳﺔ اﻟﺘﻘﺎﻃﻊ ﺑﻴﻦ اﻟﺤﺰﻣﺔ اﻻرﺿﻴﺔ ‪g‬‬ ‫421‬ ‫واﻟﺤﺰﻣﺔ اﻟﻤﺜﺎرة ‪ S‬ﻟﻠﻨﻈﻴﺮ ‪Xe‬‬

‫اﻟﻤﻨﺎﻗﺸﺔ واﻷﺳﺘﻨﺘﺎﺟﺎت واﻟﻤﻘﺘﺮﺣﺎت‬

‫اﻟﻔﺼﻞ اﻟﺨﺎﻣﺲ‬

‫57‬

‫اﻟﺸﻜﻞ )4-5(:زاوﻳﺔ اﻟﺘﻘﺎﻃﻊ ﺑﻴﻦ اﻟﺤﺰﻣﺔ اﻻرﺿﻴﺔ ‪g‬‬ ‫621‬ ‫واﻟﺤﺰﻣﺔ اﻟﻤﺜﺎرة ‪ S‬ﻟﻠﻨﻈﻴﺮ ‪Xe‬‬

‫4-5 ﺍﻻﺴﺘﻨﺘﺎﺠﺎﺕ‬
‫1. ﻨﺠﺎﺡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ )6(‪ IBM-1,O‬ﻓﻲ ﺘﺤﺩﻴﺩ ﺍﻻﻨﺤﻨـﺎﺀ ﺍﻟﺨﻠﻔـﻲ ﻓـﻲ‬ ‫ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﺒﺘﻭﺍﻓﻕ ﺠﻴﺩ ﻤﻊ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ ﻤﻤﺎ ﻴﺩل ﻋﻠﻰ ﺼـﺤﺔ ﺍﺴـﻠﻭﺏ ﺤـﺴﺎﺏ‬ ‫ﻤﻌﻠﻤﺎﺕ ﻜل ﺤﺯﻤﺔ ﻋﻠﻰ ﺤﺩﻯ .‬ ‫2. ﻨﺠﺎﺡ ﺍﻟﺒﺭﻨﺎﻤﺞ ﺍﻟﺫﻱ ﺘﻡ ﺍﻋﺩﺍﺩﻩ ﻓﻲ ﻫﺫﻩ ﺍﻟﺩﺭﺍﺴﺔ ﺒﻠﻐﺔ 7-‪ MATLAB‬ﻭﺍﻟـﺫﻱ ﺃﺴـﻤﻴﻨﺎﻩ‬ ‫ﹰ‬ ‫‪ Yrast-Code‬ﺒﺩﻴﻼ ﻋﻥ ﺍﻟﺒﺭﻨﺎﻤﺞ ﺍﻟﺠﺎﻫﺯ ‪ PHINT‬ﺒﻠﻐﺔ ﻓﻭﺭﺘﺭﺍﻥ 77 ,ﻭﺍﻟﺫﻱ ﺘﻡ ﻓﻴﻪ‬ ‫ﺤﺴﺎﺏ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﻠﺤﺯﻤﺔ ‪ Yrast‬ﻭﻟﻠﺘﺤﺩﻴﺩ )6(‪. O‬‬ ‫ﻀـﻤﻥ ﺍﻟﺘﺤﺩﻴـﺩ‬
‫621-021‬

‫) +18, +16, +14 = +1 ‪ ( J‬ﻭﻗﻭﻉ ﺍﻟﻨﻅﺎﺌﺭ ‪Xe‬‬

‫+ ‪EJ‬‬
‫1‬

‫+2 ‪E‬‬
‫1‬

‫3. ﺍﻅﻬﺭﺕ ﺍﻟﻨﺴﺏ‬

‫)6(‪ O‬ﻭﻜﺎﻨﺕ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺤﺴﻭﺒﺔ ﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻟﺤﺯﻤـﺔ ‪ Yrast‬ﻤﺘﻭﺍﻓﻘـﺔ ﻤـﻊ ﺍﻟﻘـﻴﻡ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ.‬ ‫4. ﺘﺎﺜﻴﺭ ﻤﻭﻗﻊ ﻨﻜﻠﻴﻭﻨﺎﺕ ﺍﻟﺘﻜﺎﻓﺅ ﻭﺍﻤﺘﻼﺀ ﺍﻟﻐﻼﻑ ﺍﻟﺜﺎﻨﻭﻱ ﺒﺎﻟﻨﻴﺘﺭﻭﻨﺎﺕ ﻴـﺴﺒﺏ ﺘﻐﻴـﺭﺍ ﻓـﻲ‬ ‫ﹰ‬ ‫ﻤﻭﻗﻊ ﺍﻻﻨﺤﻨﺎﺀﺍﻟﺨﻠﻔﻲ ﻜﻤﺎ ﻟﻭﺤﻅ ﻓﻲ ﺍﻟﻨﻅﻴﺭ ‪.124Xe‬‬ ‫5. ﺯﻴﺎﺩﺓ ﺍﻟﺘﻐﻴﺭ ﻓﻲ ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﺒﺯﻴﺎﺩﺓ ﺍﻟﻌﺩﺩ ﺍﻟﻜﺘﻠﻲ ﻟﻠﻨﻅﺎﺌﺭ ﺍﻟﻤﺩﺭﻭﺴﺔ ﺤﻴﺙ ﻟﻭﺤﻅ ﺍﻥ‬ ‫ﺍﻟﺯﻴﺎﺩﺓ ﻓﻲ ﻋﺯﻡ ﺍﻟﻘﺼﻭﺭ ﺍﻟﺫﺍﺘﻲ ﻭﺍﻟﻨﻘﺼﺎﻥ ﻓﻲ ﺍﻟﺘﺭﺩﺩ ﺍﻟﺩﻭﺭﺍﻨﻲ ﻭﻁﺎﻗﺔ ﺍﻻﻨﺘﻘـﺎل ﺍﻜﺒـﺭ‬ ‫ﺍﻻﺸﻜﺎل )01-4 ﺍﻟﻰ 31-4(.‬
‫اﻟﻤﻨﺎﻗﺸﺔ واﻷﺳﺘﻨﺘﺎﺟﺎت واﻟﻤﻘﺘﺮﺣﺎت‬
‫021‬

‫ﻭﺍﻗﻠﻬﺎ ﻟﻠﻨﻅﻴﺭ ‪Xe‬‬

‫621‬

‫ﻤﺎﻟﻭﺤﻅ ﻓﻲ ﺍﻟﻨﻅﻴﺭ ‪Xe‬‬
‫اﻟﻔﺼﻞ اﻟﺨﺎﻣﺲ‬

‫67‬

‫5-5 ﺍﻟﻤﻘﺘﺭﺤﺎﺕ‬
‫1. ﺍﺴﺘﺨﺩﺍﻡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠـﺔ ﻟﻠﻨـﻭﻯ ﻀـﻤﻥ ﺍﻟﺘﺤﺩﻴـﺩﻴﻥ )5(‪ SU‬ﻭ)3(‪SU‬‬ ‫ﻭﺍﻟﺤﺎﻟﺔ ﺍﻷﻨﺘﻘﺎﻟﻴﺔ ﺒﻴﻨﻬﻤﺎ ﻓﻲ ﻭﺼﻑ ﻅﺎﻫﺭﺓ ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻭﻤﻌﺭﻓﺔ ﻤﺩﻯ ﺍﻟﻨﺠﺎﺡ ﺍﻟـﺫﻱ‬ ‫ﻴﺤﻘﻕ ﻀﻤﻥ ﻫﺫﺍ ﺍﻟﺘﺤﺩﻴﺩ .‬ ‫2. ﺩﺭﺍﺴﺔ ﺍﻟﺘﻐﻴﺭ ﻓﻲ ﺍﻟﺨﻭﺍﺹ ﺍﻟﻨﻭﻭﻴﺔ ﻋﻨﺩ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻌﺎﻟﻴﺔ ﺒﺎﻻﻋﺘﻤـﺎﺩ ﻋﻠـﻰ ﺃﻨﻤـﻭﺫﺝ‬ ‫( ﻭﺩﺭﺍﺴﺔ ﻤﺩﻯ ﻨﺠﺎﺡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ ﻓﻲ ﺘﺤﺩﻴـﺩ ﺘﻠـﻙ‬
‫‪Eγ‬‬ ‫‪J‬‬

‫‪) E-Gos‬‬ ‫ﺍﻟﺨﻭﺍﺹ.‬

‫3. ﺩﺭﺍﺴﺔ ﺍﻤﻜﺎﻨﻴﺔ ﺘﺤﺴﻴﻥ ﺍﻟﻤﻌﺎﺩﻻﺕ ﺍﻟﻤﺴﺘﺨﺩﻤﺔ ﻓﻲ ﺤﺴﺎﺏ ﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻷﻨﺘﻘﺎﻻﺕ ﺍﻟﻤﺨﺘﺯﻟـﺔ‬ ‫ﻀﻤﻥ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ ﻟﻐﺭﺽ ﺘﺤﺴﻴﻥ ﺍﻟﻨﺘﺎﺌﺞ ﻭﺘﻭﺍﻓﻘﻬﺎ ﻤﻊ ﺍﻟﻘﻴﻡ ﺍﻟﻌﻤﻠﻴﺔ .‬ ‫4. ﺩﺭﺍﺴﺔ ﻅﺎﻫﺭﺓ ﺍﻷﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻟﻌﺩﺩ ﻤﻥ ﺍﻟﻨﻅﺎﺌﺭ ﺒﺄﺴﺘﺨﺩﺍﻡ ﺃﻨﻤﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ‬ ‫2-‪ IBM‬ﻭﻤﻘﺎﺭﻨﺘﻬﺎ ﻤﻊ ﺃﻨﻤﻭﺫﺝ 1-‪ IBM‬ﻜﺫﻟﻙ ﺍﺴﺘﺨﺩﺍﻡ 3-‪ IBM‬ﻭ 4-‪ IBM‬ﻟﻌﺩﺩ ﻤﻥ‬ ‫ﺍﻟﻨﻅﺎﺌﺭ ‪ N=Z‬ﻭﺩﺭﺍﺴﺔ ﻁﺎﻗﺎﺕ ﺍﻟﺭﺒﻁ ﻟﻬﺎ.‬

‫اﻟﻤﻨﺎﻗﺸﺔ واﻷﺳﺘﻨﺘﺎﺟﺎت واﻟﻤﻘﺘﺮﺣﺎت‬

‫اﻟﻔﺼﻞ اﻟﺨﺎﻣﺲ‬

‫ﺍﳌﺼﺎﺩﺭ‬

‫77‬

‫ﺍﻟﻤﺼﺎﺩﺭ ﺍﻟﻌﺭﺒﻴﺔ‬

‫ﺇﻨﻜﺎ، ﺘﺭﺠﻤﺔ: ﻋﺯﻭﺯ، ﻋﺎﺼﻡ ﻋﺒﺩﺍﻟﻜﺭﻴﻡ)3891( "ﻤﻘﺩﻤﺔ ﻓﻲ ﺍﻟﻔﻴﺯﻴﺎﺀ ﺍﻟﻨﻭﻭﻴـﺔ"، ﻤﻁـﺎﺒﻊ‬ ‫ﻤﺩﻴﺭﻴﺔ ﺩﺍﺭ ﺍﻟﻜﺘﺏ ﻟﻠﻁﺒﺎﻋﺔ ﻭﺍﻟﻨﺸﺭ، ﺠﺎﻤﻌﺔ ﺍﻟﻤﻭﺼل.‬ ‫ﺨﻠﻴل، ﻤﻨﻴﺏ ﻋﺎﺩل )6991(، "ﺍﻟﻔﻴﺯﻴﺎﺀ ﺍﻟﻨﻭﻭﻴﺔ"، ﺩﺍﺭ ﺍﻟﻜﺘﺏ ﻟﻠﻁﺒﺎﻋﺔ ﻭﺍﻟﻨﺸﺭ، ﺍﻟﻤﻭﺼل.‬ ‫ﻋﺒﺩﺍﻟﺭﺤﻤﻥ، ﺨﺎﻟﺩ ﺍﻤﻴﻥ ﻤﺤﻤﺩ )4002( "ﺘﻁﻭﻴﺭ ﺍﻨﻤـﻭﺫﺝ ﻅـﻭﺍﻫﺭﻱ ﻟﻤـﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗـﺔ‬ ‫ﻭﻅﺎﻫﺭﺓ ﺍﻻﻨﺤﻨﺎﺀ ﺍﻟﺨﻠﻔﻲ ﻟﻌﺩﺩ ﻤﻥ ﺍﻟﻨﻭﻯ ﺍﻟﺩﻭﺭﺍﻨﻴﺔ ﺍﻟﺯﻭﺠﻴـﺔ – ﺍﻟﺯﻭﺠﻴـﺔ"، ﺍﻁﺭﻭﺤـﺔ‬ ‫ﺩﻜﺘﻭﺭﺍﻩ ﻓﻠﺴﻔﺔ ﻓﻲ ﺍﻟﻔﻴﺯﻴﺎﺀ ﺍﻟﻨﻭﻭﻴﺔ، ﻜﻠﻴﺔ ﺍﻟﻌﻠﻭﻡ، ﺠﺎﻤﻌﺔ ﺍﻟﻤﻭﺼل.‬ ‫ﻤﺼﻁﻔﻰ، ﻤﺤﻤﺩ ﺍﺒﺭﺍﻫﻴﻡ ﻤﺤﻤﺩ )5002( "ﺩﺭﺍﺴﺔ ﺨـﺼﺎﺌﺹ ﺍﻟﺘﺭﻜﻴـﺏ ﺍﻟﻨـﻭﻭﻱ ﻟﻨﻅـﺎﺌﺭ‬ ‫"، ﺭﺴﺎﻟﺔ ﻤﺎﺠﺴﺘﻴﺭ، ﻜﻠﻴﺔ ﺍﻟﺘﺭﺒﻴﺔ، ﺠﺎﻤﻌﺔ ﺍﻟﻤﻭﺼل.‬
‫491-881‬

‫ﺍﻻﻭﺯﻭﻤﻴﻭﻡ ‪Os‬‬

‫ﻴﻭﺴﻑ، ﻤﻌﺘﺼﻡ ﻤﺤﻤﻭﺩ )5002( "ﺍﺴﺘﺨﺩﺍﻡ ﺍﻨﻤـﻭﺫﺝ ﺍﻟﺒﻭﺯﻭﻨـﺎﺕ ﺍﻟﻤﺘﻔﺎﻋﻠـﺔ )1-‪(IBM‬‬ ‫ﻟﺤﺴﺎﺏ ﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻁﺎﻗﺔ ﻭﺍﺤﺘﻤﺎﻟﻴﺔ ﺍﻻﻨﺘﻘﺎﻻﺕ ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ ﺍﻟﻤﺨﺘﺯﻟﺔ ﻟﻌـﺩﺩ ﻤـﻥ ﻨﻅـﺎﺌﺭ‬ ‫"، ﺭﺴﺎﻟﺔ ﻤﺎﺠﺴﺘﻴﺭ، ﻜﻠﻴﺔ ﺍﻟﺘﺭﺒﻴﺔ، ﺠﺎﻤﻌﺔ ﺍﻟﻤﻭﺼل.‬
‫891-291‬

‫‪Pt‬‬

‫ﻨﻭﺭﻱ، ﺴﻭﺯﺍﻥ ﺸﻜﺭ )5002( "ﺩﺭﺍﺴﺔ ﻨﻅﺭﻴـﺔ ﻟﻠﺘﺭﻜﻴـﺏ ﺍﻟﻨـﻭﻭﻱ ﻟﻨﻅـﺎﺌﺭ ﺍﻟﻨـﺩﻤﻴﻭﻡ‬ ‫ﺍﻟﺯﻭﺠﻴﺔ - ﺍﻟﺯﻭﺠﻴﺔ"، ﺭﺴﺎﻟﺔ ﻤﺎﺠﺴﺘﻴﺭ، ﻜﻠﻴﺔ ﺍﻟﺘﺭﺒﻴﺔ، ﺠﺎﻤﻌﺔ ﺍﻟﻤﻭﺼل.‬
‫051-441‬

‫‪Nd‬‬

78

‫ﺍﻟﻤﺼﺎﺩﺭ ﺍﻻﺠﻨﺒﻴﺔ‬

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‫ﺍﳌﻠﺤﻖ‬

85

(1)‫اﻟﻤﻠﺤﻖ‬ ‫اﻟﺒﺮﻧﺎﻣﺞ اﻟﻤﺴﺘﺨﺪم ﻓﻲ هﺬﻩ اﻟﺪراﺳﺔ‬ Yrast-Code
%This Program to Calculate and Plot the Energy Levels,Energy Transition, %Moment of Inertia and Rotation Frequency % Xe126 %This Loop to Calculate Energy Levels for Ground Band clc format short g p1g=2; p2g=10; pp1g=p1g*(p1g+1); pp2g=p2g*(p2g+1); t1g=p1g/2*(p1g/2+3); t2g=p2g/2*(p2g/2+3); ag=[t1g pp1g;t2g pp2g ]; bg=[388.631 ;3314.14 ]; xg=inv(ag)*bg; k4g=xg(1); k5g=xg(2); Jg=2:2:10; Tg=Jg./2; Ecg=k4g*Tg.*(Tg+3)+k5g*Jg.*(Jg+1); Eeg=[0 388.631 942 1634.98 2435.71 3314.14]; %This Loop to Calculate Energy Levels for S Band p1s=12; p2s=16; pp1s=p1s*(p1s+1); pp2s=p2s*(p2s+1); t1s=p1s/2*(p1s/2+3); t2s=p2s/2*(p2s/2+3); as=[t1s pp1s;t2s pp2s ]; bs=[3884.57;5508.6]; xs=inv(as)*bs; k4s=xs(1); k5s=xs(2); Js=12:2:16; Ts=Js./2; Ecs=k4s*Ts.*(Ts+3)+k5s*Js.*(Js+1); Ees=[3884.57 4619.45 5508.6 ];

86 %This Loop to Calculate and Plot the Energy Levels,Energy Transition, %Moment of Inertia and Rotation Frequency for Yrast Energy Levels Ec=[0 Ecg Ecs]; Ee=[ Eeg Ees]; JJ=[0 Jg Js]; XX=2:2:16; Eedd=[388.633 553.38 692.93 800.85 878.43 570.4 734.88 889.1]; Ecdd=diff(Ec); x1=sqrt(XX.*(XX+1)); x2=sqrt((XX-2).*(XX-1)); Ihe=(4*XX-2)./Eedd; Ihc=(4*XX-2)./Ecdd; hwe=Eedd./(x1-x2); hwc=Ecdd./(x1-x2); R=((Ee - Ec)./Ee)*100; disp([hwe' hwc' Ihe' Ihc']) disp([JJ' Ee' Ec' R']) figure(1),subplot(2,1,1),plot(hwe,Ihe,'ko-',hwc,Ihc,'k-*') xlabel('hw (keV)'), ylabel('2\vartheta/ h^2 (keV)^-1') legend('exp','calc.') subplot(2,1,2),plot(XX,Eedd,'ko-',XX,Ecdd,'k-*') xlabel('J'), ylabel('E_\gamma (keV)') legend('exp','calc') figure(2),subplot(2,1,1),plot(hwe,XX,'ko-',hwc,XX,'k-*') xlabel('hw (keV)'), ylabel('J(h)') legend('exp','calc') subplot(2,1,2),plot(XX,Ihe,'ko-',XX,Ihc,'k-*') xlabel('J(h)'), ylabel('2\vartheta/h^2 (keV) ^-1') legend('exp','calc') figure(3),plot(JJ.*(JJ+1),Ee,'ko-',JJ.*(JJ+1),Ec,'k*-') xlabel('J(J+1)'),ylabel('E(keV)') legend('exp','calc') j=JJ; [r d]=size(j); X=[1 1.2];X1=[1.3 1.5];% this control by legth of line for i=1:d de=[Ee(i) Ee(i)]; de1=[Ec(i) Ec(i)]; hold on; figure(4), plot(X,de,'k',X1,de1,'k') end gtext('0^+');gtext('2^+');gtext('4^+');gtext('6^+');gtext('8^+');gtext('10^+') gtext('12^+');gtext('14^+');gtext('16^+') gtext('0^+');gtext('2^+');gtext('4^+');gtext('6^+');gtext('8^+');gtext('10^+') gtext('12^+');gtext('14^+');gtext('16^+')

Abstract
The intracting boson model (IBM-1) γ -unstable O(6) limit has been used to calculate the yrast energy levels for even – even
120-126

Xe isotopes. A new approach

has been used to calculate the parameters of the O(6) limit K4 and K5 through calculating them for twice; one for the ground band (g-band) and the other for the excited band (S-band) instead of calculating them onces for the both states. After then the calculated parameters K4 and K5 are introduced in the equation of the O(6) limit to calculate the yrast energy levels which inturn showed a good a agreement with that of experimental ones. Consequently, the backbending in the energy levels is identified from the calculated energy levels and is compared with that produced from the experimental ones which showed good agreement with them. Nevertheless ,anew simulation of IBM-1 model named yrast-code is introduced by us through using a MATLAB-7 program is likely used to identify the parameters of the O(6) limit and to calculate the energy levels of the isotopes instead of using the ordinary program "PHINT" which is used to use in previous studies by the others. The electrical quadrapole transition probablity B(E2) has been calculated by two methods. The first one depended on the experimental half life of the transition (T1/2), the transition energy (Eγ) between two particular follwing states and the internal conversion factor (α) which is calculated by interpolation method using a specified program for this purpose. The results showed a good agreement with that experimental ones. The second method for calculating B(E2) depended on the equation corresponded to the O(6) limit of IBM-1 model and the results, in general were in good agreement with the experimental ones and also with that calculated by the first method. Moreover , the study also investigated the effect of the neutron excess on the energy levels and on the branching ratios:
+ + + + + + B ( E 2;41 → 21 ) B ( E 2;61 → 41 ) B ( E 2;81 → 61 ) , , . + + + + + + B ( E 2;21 → 01 ) B ( E 2;21 → 01 ) B( E 2;21 → 01 )

The

importance of these calculations latent in determining the according to the O(6)

120-126

Xe isotope positions

,SU(3) and SU(5) limits which indicated that the studied

isotopes is lying within the

γ - unstable O(6) limit.

Computer New Simulation of the Interacting Boson Model (IBM-1) to study the Backbending in Even – Even 120-126Xe Isotopes

A Thesis Submitted By

Mushtaq Abd Da,od Al-Jubbori

To The Council of the College of Education University of Mosul In Partial Fulfillment of the Requirements for the Degree of Master of Science in Physics

Supervised by

Imad M.Ahmed
Assistant Professor
2008 A.D. 1429 A.H.

University of Mosul
College of Education

Computer New Simulation of the Interacting Boson Model (IBM-1) to study the Backbending in Even – Even 120-126Xe Isotopes

Mushtaq Abd Da,od Al-Jabbori

Master of Science Physics

Supervised by

Imad M.Ahmed
Assistant Professor

2008 A.D

1429 A.H