Application of the Bacher and Goudsmit Method to Nuclear Spectra

A method for the calculation of nuclear ${l}^{n}$ matrix elements in terms of those of ${l}^{n\ensuremath{-}1}$ is developed, assuming two-particle interactions. An example is the calculation of ${p}^{3}$ matrix elements as linear combinations of ${p}^{2}$ matrix elements. The coefficients in these linear combinations are tabulated. Application is made by calculating $_{3}\mathrm{Li}^{7}$ energies from $_{3}\mathrm{Li}^{6}$ energy data. A comparison of the calculated energies of $_{3}\mathrm{Li}^{7}$ with experiment leads to some restrictions on the nuclear potential. To perform the calculation it is necessary to fit the $_{3}\mathrm{Li}^{6}$ data; the results of the fit are presented. The existence of a $J=\frac{5}{{2}^{\ensuremath{-}}}$ energy level in $_{3}\mathrm{Li}^{7}$ at or near 6.53 Mev is also discussed.