Shell Model for the Positive-Parity States ofN15

Energy levels and wave functions arising from the configurations $s^4{p}^{10}s$, $s^4{p}^{10}d$, and $s^3{p}^{12}$ have been calculated using a central plus single-particle spin-orbit interaction. Correlations have been made between theory and experiment for a dozen identified positive parity levels in ${\mathrm{N}}^{15}$ (including the 5.31-Mev level). For the seven levels below 9 Mev this has been done mainly by considering ${\mathrm{N}}^{14}(d, p)l$ values and reduced widths. In order of increasing energy, the theoretical spin assignments for these levels are $\frac{5}{2}$, ½, $\frac{7}{2}$, $\frac{3}{2}$, $\frac{5}{2}$, ½, $\frac{3}{2}$ (the third and fifth could be interchanged); the wave functions derived for these levels give fair agreement for level positions and surprisingly good agreement for reduced widths. For the upper levels correlations are made by means of the experimental spin assignments. The general agreement here is poor; in particular, a state which has been invoked to explain thermal neutron capture and other neutron processes is not predicted, and the ${\mathrm{C}}^{15}$ $\beta$-decay lifetime is not properly given. In general, the wave functions indicate a small interaction between configurations but, apart from this, are not consistent with the idea that the inequivalent particle is effectively coupled to only one state for $A=14\mathrm{}$.