اثر رمسور-تاونسند با استفاده از اصل عدم قطعيت تعميم يافته با توان دوم تكانه

The Ramsauer-Townsend effect with generalized uncertainty principle withthe second order of momentum

در آزﻣﺎﯾﺶ رﻣﺴﻮر- ﺗﺎون ﺳﻨﺪ رﻓﺘﺎر ﺳﻄﺢ ﻣﻘﻄﻊ ﭘﺮاﮐﻨﺪﮔﯽ اﻟﮑﺘﺮونﻫﺎي ﮐﻢ اﻧﺮژي از اﺗﻢ ﻫﺎي ﮔﺎز ﻧﺎدر، ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮارﻣﯽﮔﯿﺮد. از ﻧﻘﻄﻪ ﻧﻈﺮ ﮐﻠﺎﺳﯿﮑﯽ، اﻧﺘﻈﺎر ﻣﯽرود ﮐﻪ اﺣﺘﻤﺎل ﭘﺮاﮐﻨﺪﮔﯽ ﺑﺮاﺑﺮ ﺑﺎ اﺣﺘﻤﺎل ﺗﺼﺎدم ﺑﯿﻦ ذرات اﻟﮑﺘﺮون ﺑﺎ ﮔﺎز ﺑﺎﺷﺪ. اﻣﺎ، ﻧﺘﺎﯾﺞ اﯾﻦ آزﻣﺎﯾﺶ ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ ﺳﻄﺢ ﻣﻘﻄﻊ ﭘﺮاﮐﻨﺪﮔﯽ ﺑﺮاي اﻧﺮژيﻫﺎي ﺧﺎﺻﯽ ﺻﻔﺮ اﺳﺖ و از اﯾﻦرو، ﮔﺬار ﺑﯿﺸﯿﻨﻪ ﻣﯽﺗﻮاﻧﺪ وﺟﻮد داﺷﺘﻪ ﺑﺎﺷﺪ. ﻃﻮل ﻣﻮج ﻫﺎي ﺗﺸﺪﯾﺪي ﮔﺬار ﺑﺎ ﺗﻮﺻﯿﻒ ﮐﻮاﻧﺘﻮﻣﯽ اﯾﻦ ﭘﺪﯾﺪه ﻗﺎﺑﻞ اﺳﺘﺨﺮاج ﻣﯽﺑﺎﺷﻨﺪ ﮐﻪ ﺗﻄﺎﺑﻖ ﺧﻮﺑﯽ ﻫﻢ ﺑﺎ ﻧﺘﺎﯾﺞ ﺗﺠﺮﺑﯽ دارﻧﺪ. از ﻃﺮﻓﯽ، ﺑﺎ ﻣﻌﺮﻓﯽ ﻃﻮل ﮐﻤﯿﻨﻪ، ﻃﺒﻖ ﻧﻈﺮﯾﻪﻫﺎي ﮐﻮاﻧﺘﻮم ﮔﺮاﻧﺸﯽ، اﺻﻞ ﻋﺪم ﻗﻄﻌﯿﺖ ﻣﻌﻤﻮل ﻫﺎﯾﺰﻧﯿﺮگ ﺑﺎﯾﺪ اﺻﻠﺎح ﺷﻮد ﮐﻪ ﺑﻪ اﺻﻞ ﻋﺪم ﻗﻄﻌﯿﺖ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﻣﻌﺮوف اﺳﺖ. ﺗﺼﺤﯿﺢ ﻃﻮل ﻣﻮج ﻫﺎي ﺗﺸﺪﯾﺪي در ﭼﺎرﭼﻮب اﺻﻞ ﻋﺪم ﻗﻄﻌﯿﺖ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﺑﺎ ﺗﻮان اول ﺗﮑﺎﻧﻪ ﻗﺒﻠﺎً ﻣﺤﺎﺳﺒﻪ ﺷﺪه اﻧﺪ. در اﯾﻦ ﻣﻘﺎﻟﻪ ﻣﺎ اﯾﻦ اﺛﺮ را ﺑﺎ اﺳﺘﻔﺎده از اﺻﻞ ﻋﺪم ﻗﻄﻌﯿﺖ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﺑﺎ ﺗﻮان دوم ﺗﮑﺎﻧﻪ ﺑﺮرﺳﯽ ﻣﯽ ﻧﻤﺎﯾﯿﻢ و ﺑﻪ ﻣﺤﺎﺳﺒﻪ ﺗﺼﺤﯿﺢ ﻃﻮل ﻣﻮج ﻫﺎي ﺗﺸﺪﯾﺪي در اﯾﻦ ﻧﻈﺮﯾﻪ ﻣﯽﭘﺮدازﯾﻢ.

in the Ramsauer-Townsend experiment, the scattering of the electron beam by atoms of the noble gas is studied. From the classical point of view, for the low energy beam, it is expected that the scattering amplitude is equal to the collision amplitude. However, the experimental results shows that the scattering amplitude vanishes for special energies and hence the transition amplitude can be maximum. Fortunately, the resonance wavelengths can be calculated via quantum mechanics andconfirms with the experimental results. The modifications of these resonance wavelengths also have been studied in the frame work of the generalized quantum mechanics with the Planck scale corrections of the first order of momentum. Here, we investigate the modified wavelengths via the generalized quantum mechanics with the second order of momentum.