The parity of a nucleus is even, or one, if its wave function stays
the same if the positive direction of all three Cartesian axes is
inverted. That replaces every
This section provides an overview of the ground-state spins of nuclei. It will be seen that the shell model does a pretty good job of predicting them.
For nuclei with both an even number of protons and an even number of neutrons, the odd-particle shell model predicts that the parity is even. This prediction is fully vindicated by the experimental data, figure 14.37. There are no known exceptions to this rule.
For nuclei with an odd mass number
The failures above
For odd-odd nuclei, the odd-particle shell model predicts that the parity is the product of those of the surrounding even-odd and odd-even nuclei. The results are shown in figure 14.40. Hits are green, failures red, and unable-to-tell black. Small grey signs are shell model values for the surrounding even-odd and odd-even nuclei. However actual even-odd and odd-even values were used in the prediction.
Failures for spherical nuclei indicate that sometimes the odd proton or neutron is in a different shell than in the corresponding odd-mass neighbors. A similar conclusion can be reached based on the spin data.
Note that the predictions also do a fairly good job in the regions in which the nuclei are not spherical. The reason is that the predictions make no assumptions about what sort of state, spherical or nonspherical, the odd nucleons are in. It merely assumes that they are in the same state as their neighbors.
Figure 14.41 shows a summary of the parity of all nuclei together. To identify the type of nucleus more easily, the even-even nuclei have been shown as green check marks. The odd-odd nuclei are found on the same vertical lines as the check marks. The even-odd nuclei are on the same horizontal lines as the check marks, and the odd-even ones on the same diagonal lines.
Parities that the shell model predicts correctly are in green, and those that it predicts incorrectly are in red. The parities were taken straight from section 14.12.2 with no tricks. Note that the shell model does get a large number of parities right straight off the bat. And much of the errors can be explained by promotion or nonspherical nuclei.
For parities in light green and light red, NUBASE 2003 expressed some reservation about the correct value. For parities shown as yellow crosses, no (unique) value was given.