4. SEMF and Fermi Gas Model

Question 1

What is the liquid gas model?

Answer 1

Nucleon densities inside the nucleus are ~ constant
- BE is prop. to # nucleons
So the interior density is roughly constant, and the latent heat of vapourization is prop. to mass

Question 2

What three corrections are implemented into the liquid gas model?

Answer 2

1. Nucleons only feel the force of neighbouring nucleons so add -a1 A (VOLUME)
2. Surface nucleons have fewer neighbours so add a2 A^2/3 (SURFACE)
3. Coulomb repulsion so add a3 Z(Z-1) / A^1/3 (COULOMB)
   First 3 terms of the SEMF

Question 3

Describe how we view the nucleus with reference to the Fermi gas model

Answer 3

• View nucleus as a Fermi gas where it occupies the lowest energy state upto the Fermi energy
• Fermi momentum p_F = (2M E_F)^1/2
• Square quantum well

Question 4

What is the density of states for a nucleus with reference to the Fermi gas model?

Answer 4

DoS - Number of states with a momentum between p and p + dp

Question 5

Describe the p and n numbers for the following nuclei:
even-even
even-odd
odd-odd

Answer 5

N, Z even
N even, Z odd or vv
N, Z odd

Question 6

How successfully does SEMF work?

Answer 6

Works well to predict masses of heavier nuclei, but misses some details
- Not well for low A values i.e. small nuclei