Nuclear & Particle Physics - Selection Rules

An energy-level diagram of the n = 1 and n = 2 levels of atomic hydrogen (including the effect of spin-orbit coupling and relativity) is shown in the figure. Three transitions are labeled A, B, and C. Which of the transitions will be possible electric-dipole transition?

A. B only
B. C only
C. A and C only
D. B and C only
E. A, B, and C

(GR0177 #84)

Solution:

Selection rules:

1.	Principal quantum number	:	∆n = anything
2.	Orbital angular momentum	:	∆l = ±1
3.	Magnetic quantum number	:	∆ml = 0, ±1
4.	Spin	:	∆s = 0
5.	Total angular momentum	:	∆j = 0, ±1, but j = 0 ↛j = 0

Transition A:  
l = 0 to l = 0 → ∆l = 0 → NOT ALLOWED

Transition B:
l = 1 to l = 0 → ∆l = −1 → ALLOWED
j = 3/2 to j = 1/2 → ∆j = −1 → ALLOWED

Transition C:
 j = 1/2 to j = 1/2 → ∆j = 0 → ALLOWED

Answer: D