Question

The system consists of two atoms located at the position (0,0,0) and (0,0,d). The electron has a momentum P. hk directed along . Consider the wavefunction before scattering be a plane wave. Each atom has an amplitude of isotropic scattering f. Find an angular dependence of the scattering amplitude for these two particles

Answer 1

atoms Eborated as Iva2) be the potential b/w two, particles . write to reduced mass system like in hydrozen atom wel can system) bekare scattering be al The system consists of two atmy Everet position (o, e o) and to end) The elest a p₂ = tk momentum com has î directed a along Consider the wave function before scatte a plane mare Ceach atom has an amplit of isotropic scathering of find an angular dependence of the scattain amplitude for here te particles g ²4 (3) tv (r) 418) = E 4(6) - 24 Lab Frame where r = 1 n - u= mm2 I (2-weis) lood) Salute P = tk 1(0,0,0) - Here we will deal with Auantum Mechanical discreption blu true particle having scattering amplitude f be mass m, & m, respectively, interaction is time independent them wars function for two particles is i Etth a long consider so range vlado enn me , becomes (97+ ko? Join (m) zo م ( قوله : (رورا | Er bo total energy le 4 , 2) be the solution of time independent Schrodings equation in where K² = 2uE ħ2 a behane as a free interaction. So it can be plane more in lä) = A e particle before described by i) = E tu, dan L 200 m2 COO - (2)

a Scattered wave dA= r2d2 assoria Forn & Ain S where with zation to in wave rectas the incident particle constant i A is normali- - Homs cattered ача Lwane target 1 ikler-9 den cose of isotopic scattering the sun incident wame is spherically symmetic hanin - helm e Along (0,0) detection ked E 6) = A floop © fig. 2 there we have to find this fce, o = 2() is scattered mane So here all are using result of - Green's function - given and floo) by is scattering amplitude, R in mare vector associated with (n,r) = -1 e ne scattered mane o be angle b/w Kol Thus tatal wave is superpositan of These two waves her & & & are along 2- axis la) - Puls) + dar How rewriting ear ③ is as (02+) 4 (52) = 24V() 46 ) - 0 tfl2,) now using Green's Identity will con write- Af either - K2

Everyone Evergnon floa) le ها ها (اوا اولا :-u 20M? expansion Sinonial ñ ñ ker /1-2 , 2012 kr - kr. ill Ysta =ker - Kha (he here we have obtained scattering amplitude in terms of a A exponential team which are directly related to angular frequency * Vllasal) Ko-Ka - Honce angular amplitude is dependence of ginen by scattering en 17 - This wing 4 4 6 Thon i ke im enn ② w in pol (n) 4/91) da Hle) ** 440,9% is 60