The elastic scattering of a charged particle of mass m off an atom can be approximated by the potential V(r)=\frac{\alpha }{r}{e}^{- r/R} where \alpha and R are positive constants. If the wave number of the incoming particle is k and the scattering angle is 2\theta, the differential cross-section in the Born approximation is

Scattering theory — CSIR Net PYQ (Question 9)

A Scattering theory previous-year question (PYQ) from Quantum Mechanics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 9 of 14 · 5.0 marks

The elastic scattering of a charged particle of mass

m

off an atom can be approximated by the potential

V (r) = \frac{α}{r} e^{- r / R}

where

α

and

R

are positive constants. If the wave number of the incoming particle is

k

and the scattering angle is

2 θ

, the differential cross-section in the Born approximation is

1 $\frac{m ^{2} α ^{2} R ^{4}}{4 ℏ ^{4} ( 1 + k ^{3} R ^{2} s in ^{2} θ )}$
2 $\frac{m ^{2} α ^{2} R ^{4}}{ℏ ^{4} ( 2 k ^{2} R ^{2} s in ^{2} θ ) ^{2}}$
3 $\frac{2 m ^{2} α ^{2} R ^{4}}{ℏ ^{4} ( 2 k ^{2} R ^{2} 2 s in ^{2} θ )}$
4 $\frac{4 m ^{2} α ^{2} R ^{4}}{ℏ ^{4} ( 1 + 4 k ^{2} R ^{2} s in ^{2} θ ) ^{2}}$

Correct answer: Option 4

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