bei48482_FM

Figure 11.17Sequence of neutron and proton energy levels according to the shell model (not to scale). The

numbers in the right-hand column correspond to the magic numbers expected on the basis of this sequence.

Without spin-orbit coupling With spin-orbit coupling

Nucleons

per level

2 j + 1

Nucleons

per

shell

Total

nucleons

4 s

5 d

6 g

7 i

4 p

5 f

6 h

3 s

4 d

5 g

3 p

4 f

2 s

3 d

2 p

1 s

8 j15/2

5 d3/2

4 s1/2

6 g7/2

7 i11/2

5 d5/2

6 g9/2

7 i13/2

4 p1/2

4 p3/2

5 f5/2

5 f7/2

6 h9/2

6 h11/2

3 s1/2

4 d3/2

4 d5/2

5 g7/2

5 g9/2

3 p1/2

4 f5/2

3 p3/2

4 f7/2

3 d3/2

2 s1/2

3 d5/2

2 p1/2

3 p3/2

1 s1/2

126

82

50

28

20

8

2

44

58 184

32

22

8

12

6

2

16

4

2

8

12

6

10

8 4 2 6 2 4 2

12

2

4

6

8

10

2

6

4

14

2

4

6

8

10

Energy

form a Jifor that particle of magnitude j(j 1 ). The various Jithen couple together

to form the total angular momentum J. The jjcoupling scheme holds for the great

majority of nuclei.

When an appropriate strength is assumed for the spin-orbit interaction, the energy

levels of either class of nucleon fall into the sequence shown in Fig. 11.17. The levels

410 Chapter Eleven

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