5. Nucleon- Nucleon Potential, Shell Structure Flashcards
1
Q
How do we obtain the shell model for atoms?
A
Solve the SE for a single electron in the EM potential of a nucleus
2
Q
What is the solution for the shell model?
A
- Set of discrete energy levels, numbered by n
- For each n, have l = …n-1 degenerate E levels
- For each l, have m_l = -l … l
- For each n, l, m_l we have two states with opposite electron spin
3
Q
What is the behaviour of the nucleon-nucleon potential?
A
- Short ranged on order of nucleus size
- Stronger than EM repulsion of p’s but repulsive at small separations
- Charge symmetric and independent (pp) = (nn) = (pn)
4
Q
Why does SoC imply m_l and m_s are not good quantum numbers?
A
They are not eigenstates of the orbital momentum and spin operators J = L + S
5
Q
What is the expectation value for < l s > ?
A
h bar^2 / 2 [ j(j+1) - l(l+1) - s(s+1) ]
= h_bar ^2 l/2 if j = l+1/2
= h_bar ^2 (-l+1)/2 if j = l - 1/2
6
Q
How does SoC affect the energy levels?
A
It breaks the degeneracy e.g. 1p -> 1p_1/2 1p_3/2
7
Q
How many degenerate energy states are there at each energy level?
A
2j + 1
