核殼層模型，一個利用泡利不相容原理的結構來描述的原子核的能量級別的一個模型，外文名叫做Nuclear shell model，提出時間是在1949年，提出者是邁耶夫人和簡森。
變形的諧振子近似模型
考慮一個三維諧振子。這給出在第一、二層的核殼層(“l”是角量子數)
我們可以想像自己建立一個原子核，並開始對它加入質子和中子。質子和中子必會從能量較低的能級開始填入，因此，頭兩個質子先填入第0能級，下6個質子則填第一能級，依此類推。
在三維諧振子中，每個能級可填入的核子數量如爲 ( n + 1 ) ( n + 2 ) 2 {displaystyle {(n+1)(n+2) over 2}} ，由於自旋的簡併性是加倍 ( n + 1 ) ( n + 2 ) {displaystyle (n+1)(n+2)}
因此
對所有的整數k，給出了以下的幻數2,8,20,40,70,112...
前六個能級是
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.
自旋核軌域
level 0 ( n =0): 2 states ( j = ⁄ 2 ). 奇數對
level 1 ( n =1): 2 states ( j = ⁄ 2 ) + 4 states ( j = ⁄ 2 ) = 6. 偶數對
level 2 ( n =2): 2 states ( j = ⁄ 2 ) + 4 states ( j = ⁄ 2 ) + 6 states ( j = ⁄ 2 ) = 12. 奇數對
level 3 ( n =3): 2 states ( j = ⁄ 2 ) + 4 states ( j = ⁄ 2 ) + 6 states ( j = ⁄ 2 ) + 8 states ( j = ⁄ 2 ) = 20. 偶數對
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. 奇數對
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. 偶數對
核軌域
核殼層與預測的幻數
核軌域能級交錯的情形
參考文獻
Talmi, Igal; de-Shalit, ear Shell Theory. Academic Press, (reprinted by Dover Publications). 1963. ISBN 0-486-43933-X.
Talmi, le Models of Complex Nuclei: The Shell Model and the Interacting Boson Model. Harwood Academic Publishers. 1993. ISBN 3-7186-0551-1.
