1) On the basis of the extreme single particle shell model, the attached figure shows the shell structure obtained from a potential without (left) and with (right) spin-orbit interaction. For the following nuclei: i), ii) iii) iv) a) Use the figure to predict the ground state spins and parities of each nucleus. b) Use the predicted ground state spins and parities calculate the magnetic moment of each nucleus.

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1) On the basis of the extreme single particle shell model, the
attached figure shows the shell structure obtained from a
potential without (left) and with (right) spin-orbit interaction.
For the following nuclei:
i) ,
ii)
iii)
iv)
a) Use the figure to predict the ground state spins and parities
of each nucleus.
b) Use the predicted ground state spins and parities calculate
the magnetic moment of each nucleus.
Transcribed Image Text:1) On the basis of the extreme single particle shell model, the attached figure shows the shell structure obtained from a potential without (left) and with (right) spin-orbit interaction. For the following nuclei: i) , ii) iii) iv) a) Use the figure to predict the ground state spins and parities of each nucleus. b) Use the predicted ground state spins and parities calculate the magnetic moment of each nucleus.
2g7/2 (8)
3d2 (4)
2g (18)
4512 (2)
Зds2 (6)
lj (30)
lji5/2 (16)
liue (12)
138
138
2g9/2 (10)
126
Зр (6)
112
Зру2 (2)
li (26)
2fs/2 (6)
2f (14)
Зру2 (4)
lij32 (14)
2f72 (8)
Ih9/2 (10)
92
92
82
(2)
Ih (22)
3s
(12) מ1hj1
3s1/2 (2)
2d (10)
2d32 (4)
Ig7/2 (8)
58
58
2d52 (6)
1g (18)
50
2p
(6)
40
189/2 (10)
2p12 (2)
34
Ifs2 (6)
2p32 (4)
If (14)
28
If72 (8)
20
20
20
2s
(2)
Id32 (4)
ld (10)
(a2ו2s
1ds2 (6)
Тp (6)
Ip12 (2)
IP32 (4)
2
2
Is
(2)
1sı/2 (2)
Infinite
Woods-Saxon
Woods-Saxon plus
well
well
spin-orbit coupling
Sequences of bound single-particle states calculated for different forms of the
nuclear shell-model potential. The number of protons (and neutrons) allowed in each state is
indicated in parentheses and the numbers enclosed in circles indicate magic numbers corre-
sponding to closed shells.
Transcribed Image Text:2g7/2 (8) 3d2 (4) 2g (18) 4512 (2) Зds2 (6) lj (30) lji5/2 (16) liue (12) 138 138 2g9/2 (10) 126 Зр (6) 112 Зру2 (2) li (26) 2fs/2 (6) 2f (14) Зру2 (4) lij32 (14) 2f72 (8) Ih9/2 (10) 92 92 82 (2) Ih (22) 3s (12) מ1hj1 3s1/2 (2) 2d (10) 2d32 (4) Ig7/2 (8) 58 58 2d52 (6) 1g (18) 50 2p (6) 40 189/2 (10) 2p12 (2) 34 Ifs2 (6) 2p32 (4) If (14) 28 If72 (8) 20 20 20 2s (2) Id32 (4) ld (10) (a2ו2s 1ds2 (6) Тp (6) Ip12 (2) IP32 (4) 2 2 Is (2) 1sı/2 (2) Infinite Woods-Saxon Woods-Saxon plus well well spin-orbit coupling Sequences of bound single-particle states calculated for different forms of the nuclear shell-model potential. The number of protons (and neutrons) allowed in each state is indicated in parentheses and the numbers enclosed in circles indicate magic numbers corre- sponding to closed shells.
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