Fermi Gas Model

1. Let’s move on to the 2nd
nuclear model…
“Fermi-Gas Model”

2. 2.2The Fermi-Gas Model
•Let’s see this video….
•https://www.youtube.com/watch?v=emSekijh7XI&list=PLN2lYn64UF7N69l
WRl8VSKys9ktrl4rxw

3. • Fermi momentum, pF
;
pF
= (2MEF
)1/2
• Where M = mass of nucleon
Within volume,V
• Density of states factor (the no. of
states with momentum between p and
p + dp);
where
, R0
= 1.21 fm
State
• Assuming the depth of both wells are same and
N=Z,

4. • For heavy nuclei, N > Z
• Fermi level equal – neutron well deeper
• Protons less tightly bound in nuclei
• Dependence of binding energy to surplus of
neutrons;
1. Average kinetic energy per nucleon , <Ekin
>
2. Evaluating the integrals
3. Consider N and Z, total Ekin
;
4. When the excess of neutron is considered,
Fermi level
Volume term
Correction
due to N ≠ Z

5. 2.3The Shell Model
•Analogous model - electron shell
in an atom.
•Give more detailed explanation
than Fermi-gas model.

6. Shell structure of atoms
• ΔEbe
of electron – Coulomb potential of nucleus and
other electrons.
• Atomic energy levels = Principal quantum number, n
Energy degenerate levels

7. • Any value of l - (2l + 1) sub-states with
different magnetic quantum number, ml
.
• Each states - electrons with different spin,
corresponding to spin-projection quantum
number, ms
= ±1/2
• Hence, we can relate n with nd
;
Same energy
Degenerate energy states, nd

8. Atomic magic number
• The proton number, Z of any atom with closed shell and closed subshell structure.
• Electrons are paired off; all states are full – no valence electron available.
• Atoms chemically inert.

10. Nuclear magic numbers
• Values of Z and N – nuclear binding particularly
strong.
• Nuclei with both N and Z listed above – doubly
magic – greater stability.
• E.g Helium nucleus a.k.a α-particle.
• Atomic magic number;
• Atomic magic number ≠ Nuclear magic
number
• Due to different quantum numbers of
nucleus.

11. What is the differences?
• In nucleus;
l = not restricted
= 0,1,2,3,4…..
• Total angular momentum, j
• j = l + ms
; ms
= ±1/2
= ½, 3/2, 5/2, 7/2……
• Determine the no. of protons/neutrons
that can occupy a certain state.
j No.of protons/neutrons
½ 2
3/2 4
5/2 6
7/2 8
j = x/2, No. of proton/neutrons = x + 1

12. Nuclear energy levels
l Orbital
0 S
1 P
2 D
3 F
4 G
5 H
• Written in the form of nlj
• Example : 1P3/2
• Configuration of real nuclide
• Represent by notation (nlj
)k
• k = Maximum no. of
protons/neutrons.

13. Exercises
•