Chapter 8
Nuclear Physics – II
8.1 Basic Concepts and Formulae
Nuclear models
Fermi gas model
Total kinetic energy of all protons
E Z =
3
5
Z E Z (max); E Z (max) =
K
2
2M
Z
A
2
3
(8.1)
Total energy of all neutrons.
E N =
3
5
N E N (max); E N (max) =
K
2
2M
N
A
2
3
(8.2)
where K =
r 0
9π
4
1
3
(8.3)
Shell model Magic Numbers: 2, 8, 20, 28, 50, 82, 126. Table 8.1 shows the shell
number (Λ) occupation number (N s ) and the Number of neutrons and protons in
various shells (ΣN s ) under the spin – orbit coupling scheme.
Table 8.1
Λ
N s
ΣN s
5
N
Λ = 44
126
4
N
Λ = 32
82
3
N
Λ = 22
50
3
2 ( Λ + 1) = 8
2 8
2
N Λ = 12
20
1
N Λ = 6
8
0
N Λ = 2
2
427
Nuclear Physics – II
8.1 Basic Concepts and Formulae
Nuclear models
Fermi gas model
Total kinetic energy of all protons
E Z =
3
5
Z E Z (max); E Z (max) =
K
2
2M
Z
A
2
3
(8.1)
Total energy of all neutrons.
E N =
3
5
N E N (max); E N (max) =
K
2
2M
N
A
2
3
(8.2)
where K =
r 0
9π
4
1
3
(8.3)
Shell model Magic Numbers: 2, 8, 20, 28, 50, 82, 126. Table 8.1 shows the shell
number (Λ) occupation number (N s ) and the Number of neutrons and protons in
various shells (ΣN s ) under the spin – orbit coupling scheme.
Table 8.1
Λ
N s
ΣN s
5
N
Λ = 44
126
4
N
Λ = 32
82
3
N
Λ = 22
50
3
2 ( Λ + 1) = 8
2 8
2
N Λ = 12
20
1
N Λ = 6
8
0
N Λ = 2
2
427