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 $l^{n-1\mathrm{}}$ 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 $J=\frac{5}{2^{-}}$ energy level in ${}_3{}^{}{}_{}{}^{}\mathrm{Li}_{}^7{}_{}{}^{}$ at or near 6.53 Mev is also discussed.