Fermi Gas Model

Fermi Gas Model

1. Let’s move on to the 2
nd

nuclear model…
“Fermi-Gas Model”

2. 2.2 The Fermi-Gas Model
•Let’s see this video….






•https://www.youtube.com/watch?v=emSekijh7XI&list=PLN2lYn64UF7N69l
WRl8VSKys9ktrl4rxw

3. •Fermi momentum, p
F
;
p
F
= (2ME
F
)
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
, R
0
= 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 , <E
kin
>


2.Evaluating the integrals


3.Consider N and Z, total E
kin
;




4.When the excess of neutron is considered,
Fermi level
Volume term
Correction
due to N ≠ Z

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

6. Shell structure of atoms
•ΔE
be
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, m
l
.

•Each states - electrons with different spin,
corresponding to spin-projection quantum
number, m
s
= ±1/2




•Hence, we can relate n with n
d
;
Same energy
Degenerate energy states, n
d

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 + m
s
; m
s
= ±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 nl
j
•Example : 1P
3/2

•Configuration of real nuclide
•Represent by notation (nl
j
)
k

•k = Maximum no. of
protons/neutrons.

13. Exercises
•