# 核殼層模型

## 變形的諧振子近似模型

level n l ml ms
0 0 0 12
12
1 1 1 12
12
0 12
12
−1 12
12

${\sum_{n=0}}^k (n+1)(n+2) = {(k+1)(k+2)(k+3)\over 3}$

• level 0: 2 states (l = 0) = 2.
• level 1: 6 states (l = 1) = 6.
• level 2: 2 states (l = 0) + 10 states (l = 2) = 12.
• level 3: 6 states (l = 1) + 14 states (l = 3) = 20.
• level 4: 2 states (l = 0) + 10 states (l = 2) + 18 states (l = 4) = 30.
• level 5: 6 states (l = 1) + 14 states (l = 3) + 22 states (l = 5) = 42.

## 自旋核軌域

• level 0 (n=0): 2 states (j = 12). 奇數對
• level 1 (n=1): 2 states (j = 12) + 4 states (j = 32) = 6. 偶數對
• level 2 (n=2): 2 states (j = 12) + 4 states (j = 32) + 6 states (j = 52) = 12. 奇數對
• level 3 (n=3): 2 states (j = 12) + 4 states (j = 32) + 6 states (j = 52) + 8 states (j = 72) = 20. 偶數對
• level 4 (n=4): 2 states (j = 12) + 4 states (j = 32) + 6 states (j = 52) + 8 states (j = 72) + 10 states (j = 92) = 30. 奇數對
• level 5 (n=5): 2 states (j = 12) + 4 states (j = 32) + 6 states (j = 52) + 8 states (j = 72) + 10 states (j = 92) + 12 states (j = 112) = 42. 偶數對

## 參考文獻

1. Talmi, Igal; de-Shalit, A. Nuclear Shell Theory. Academic Press, (reprinted by Dover Publications). 1963. ISBN 0-486-43933-X.
2. Talmi, Igal. Simple Models of Complex Nuclei: The Shell Model and the Interacting Boson Model. Harwood Academic Publishers. 1993. ISBN 3-7186-0551-1.
1. ^ Nuclear Shell Model
2. ^ Ozawa, A.; Kobayashi, T.; Suzuki, T.; Yoshida, K.; Tanihata, I. New Magic Number, N=16, near the Neutron Drip Line. Physical Review Letters. 2000, 84 (24): 5493. Bibcode:2000PhRvL..84.5493O. doi:10.1103/PhysRevLett.84.5493. PMID 10990977.
1. Igal Talmi. On single nucleon wave functions. RIKEN Nishina Center. Nov. 24 2010.
2. Internet streaming broadcasting both on WM and QT at (at 64 kbit/s, 256 kbit/s, 1 Mbit/s ) and DVD ISO (NTSC and PAL) delivery are now available at RIKEN Nishina Center.