Eigenvectors have been calculated for the $A=18,19,20,21,\mathrm{and}26$ nuclei in an $\mathrm{sd}$ shell basis. The decomposition of these states into their shell model components shows, in agreement with other recent work, that this distribution is not a single Gaussian. We find that the largest amplitudes are distributed approximately in a Gaussian fashion. Thus, many experimental measurements should be consistent with the Porter-Thomas predictions. We argue that the non-Gaussian form of the complete distribution can be simply related to the structure of the Hamiltonian.

NUCLEAR STRUCTURE ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$; calculated low-lying states with shell model. Examined amplitude distributions.

• Received 18 August 1980

DOI:https://doi.org/10.1103/PhysRevC.23.1259