Notation for nuclear energy states

Somewhat parallel to the labeling of atomic energy states, the labels of nuclear states are determined by their angular momenta. For single particle states you know that the spin part is S=1/2 and then the orbital angular momentum is used to determine a letter designation according to the spectroscopic notation. If L=2, then the state is represented by "d" and then the total angular momentum could be either L-S=3/2 or L+S=5/2. The two states would then be labeled:

与原子能态的标记方式有些相似，核态的标签由其角动量决定。对于单粒子态，你知道自旋部分是S=1/2，然后通过轨道角动量确定一个字母标记，根据光谱学记号。如果L=2，则该态用“d”表示，然后总角动量可能是L+S=3/2或L+S=5/2。这两个态则会被标记为：

The number n preceding the letter designation is analogous to the principal quantum number in the hydrogen atom in that it indicates the order of the energy states. But this number n is not subject to the same limitations as in the atomic case - it is just an indexing parameter. So the lowest energies with L=2 are labeled 1d (1d_3/2,1d_5/2), but there are higher levels with L=2 with would be labeled 2d_3/2,2d_5/2,3d_3/2,3d_5/2, etc.

字母标识前的数字n类似于氢原子中的主量子数，因为它表示能量态的顺序。但这个数字n并不像原子情况那样受限制——它只是一个索引参数。因此，最低的能量态（L=2）被标记为1d（1d 3/2，1d 5/2），但还有更高能级的L=2态，会被标记为2d 3/2，2d 5/2，3d 3/2，3d 5/2，等等。

For light nuclei it is presumed that the nucleons will fill levels according to the sequence of the shell model. Those nucleons in closed shells will be presumed not to contribute to the total nuclear spin, so the configuration of the nucleus will be indicated by the symbols for the nucleons outside closed shells. For example, ¹⁷O has one neutron outside a closed shell (Z=N=8= magic number) and its ground state would be designated (1d_5/2)¹.

对于轻核而言，假设核子将按照壳层模型的顺序填充能级。那些处于闭壳层中的核子将被认为不贡献总核自旋，因此核的配置将由闭壳层外的核子符号来表示。例如，17O有一个核子处于闭壳层外（Z=N=8=魔数），其基态将被表示为(1d 5/2) 1。

The parity of the nuclear state is also an important characteristic and often listed as a part of the notation for the state. By correlation with the single particle shell model, a value of L can be associated with a given odd nucleon, and the parity of the state is (-1)^L. For the ¹⁷O case, the associated L is 2 (d state), so the parity can be predicted to be even. For ¹⁵O, the odd neutron is in a p state (L=1) so the parity of that state is odd. The state of the ¹⁵O is sometimes written as 1p_1/2^- and that of ¹⁷O as 1d_5/2⁺ to indicate both the spin and parity of those nuclei in their ground states. The parity, like the nuclear spin, is taken to be a characteristic of the entire nucleus, but the parity would be even for closed shells so it is usually sufficient to consider the parity of the odd nucleon.

核态的宇称也是重要的特征之一，通常作为态的表示法的一部分列出。通过与单粒子壳层模型的关联，可以将一个给定的奇核子关联到一个L值，该态的宇称为(-1)^L。对于17O的情况，关联的L为2（d态），因此其宇称可预测为偶。对于15O，奇中子处于p态（L=1），因此该态的宇称为奇。15O的状态有时写作1p 1/2 -，而17O的状态则写作1d 5/2 +，以表示这些核在基态下的自旋和宇称。宇称，如同核自旋一样，被视为整个核的特征，但闭壳层的宇称为偶，因此通常只需考虑奇核子的宇称。