Subatomic Physics

Question 1

Differential Cross Section

Answer 1

d sigma / d Omega =

N/jA

j is flux

A is area

Question 2

for elastic scattering in a 1/r potential

Answer 2

use conservation of angular momentum and the change in linear momentum (in one direction)

Question 3

Condition for a localised potential

Answer 3

V(r) = 0 for r>r₀

or

rV(r) -> 0 as r->infinity

Question 4

probability current

j=

Answer 4

-i hbar/m [phi* nabla phi - phi nabla phi*]

Question 5

Lippmann-Schwinger Equation

Answer 5

|psi> =

|phi> - V/(H₀ - E ± ie) |psi>

e is a small number

Question 6

What is the Born approximation?

Answer 6

If the perturbation due to the scattering is not too big, we can approximate

|psi> -> |phi>

= (the solution to the free particle)

Question 7

in the Born approximation, how are the scattering amplitude and the scattering potential related

Answer 7

scattering amplitude is the fourier transform of the scattering potential (with some constants)

Question 8

What pairs are not/allowed in the strong nuclear force?

What does this imply?

Answer 8

p-n allowed

n-n, p-p not allowed

this is because we can spin align n-p but not the others due to the pauli eclusion principal.

Hence the nuclear force must be very spin dependant.