Studies in Intermediate Coupling: the Energy States of¹³C and¹³N belonging to the Configuration 1p⁹

The nuclear shell-model and the theory of fractional parentage are used to derive theoretical formulae for certain observable features of nuclear energy levels that are not expected to be sensitive to the choice of the nucleon interaction potential. These features comprise: (i) the magnetic dipole transition strengths, (ii) the magnetic moments, (iii) the reduced widths for nucleon emission. Intermediate coupling, besides extreme L-S and extreme j-j coupling, is discussed, and the resulting formulae are applied to the low-lying odd-parity states of 13 C and 13 N in an attempt to explain all the relevant experimental data. It is found that the extreme coupling models give generally poor agreement of theory with experiment. On the other hand, all the data are consistent with an intermediate coupling model and quite a small range of values of the intermediate coupling parameter.