核壳层模型，一个利用泡利不相容原理的结构来描述的原子核的能量级别的一个模型，外文名叫做Nuclear shell model，提出时间是在1949年，提出者是迈耶夫人和简森。
变形的谐振子近似模型
考虑一个三维谐振子。这给出在第一、二层的核壳层(“l”是角量子数)
我们可以想像自己建立一个原子核，并开始对它加入质子和中子。质子和中子必会从能量较低的能级开始填入，因此，头两个质子先填入第0能级，下6个质子则填第一能级，依此类推。
在三维谐振子中，每个能级可填入的核子数量如为 ( n + 1 ) ( n + 2 ) 2 {\displaystyle {(n+1)(n+2) \over 2}} ，由于自旋的简并性是加倍 ( n + 1 ) ( n + 2 ) {\displaystyle (n+1)(n+2)}
因此
对所有的整数k，给出了以下的幻数2,8,20,40,70,112...
前六个能级是
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.
自旋核轨域
level 0 ( n =0): 2 states ( j = ⁄ 2 ). 奇数对
level 1 ( n =1): 2 states ( j = ⁄ 2 ) + 4 states ( j = ⁄ 2 ) = 6. 偶数对
level 2 ( n =2): 2 states ( j = ⁄ 2 ) + 4 states ( j = ⁄ 2 ) + 6 states ( j = ⁄ 2 ) = 12. 奇数对
level 3 ( n =3): 2 states ( j = ⁄ 2 ) + 4 states ( j = ⁄ 2 ) + 6 states ( j = ⁄ 2 ) + 8 states ( j = ⁄ 2 ) = 20. 偶数对
level 4 ( n =4): 2 states ( j = ⁄ 2 ) + 4 states ( j = ⁄ 2 ) + 6 states ( j = ⁄ 2 ) + 8 states ( j = ⁄ 2 ) + 10 states ( j = ⁄ 2 ) = 30. 奇数对
level 5 ( n =5): 2 states ( j = ⁄ 2 ) + 4 states ( j = ⁄ 2 ) + 6 states ( j = ⁄ 2 ) + 8 states ( j = ⁄ 2 ) + 10 states ( j = ⁄ 2 ) + 12 states ( j = ⁄ 2 ) = 42. 偶数对
核轨域
核壳层与预测的幻数
核轨域能级交错的情形
参考文献
Talmi, Igal; de-Shalit, A.Nuclear Shell Theory. Academic Press, (reprinted by Dover Publications). 1963. ISBN 0-486-43933-X.
Talmi, Igal.Simple Models of Complex Nuclei: The Shell Model and the Interacting Boson Model. Harwood Academic Publishers. 1993. ISBN 3-7186-0551-1.
