Evidence for Three-Body Vector Forces in Light Nuclei

Abstract

The splittings of the $P$-doublet states of ${\mathrm{Li}}^{7}$ and ${\mathrm{N}}^{15}$, and the $D$-doublet states of ${\mathrm{O}}^{17}$, are calculated with phenomenological two-body vector forces of both Gaussian and Yukawa shapes with arbitrary ranges and exchange character. It is found to be impossible to fit the experimental data with a two-body force of fixed strength, in agreement with Pearse's calculations based on a relativistic two-body vector force. The splittings are then calculated with a phenomenological three-body vector force of the type expected to arise from higher order effects of the tensor force. The predicted ratio of the $P$ doublet splitting in ${\mathrm{N}}^{15}$ to that in ${\mathrm{Li}}^{7}$ is found to be quite insensitive to the range or shape of the three-body force, and in excellent agreement with experiment, provided that the exchange character of the force is not chosen close to the Serber mixture. The ${\mathrm{O}}^{17}$ $D$-doublet splitting, while somewhat more sensitive to the choice of range and exchange mixture, can also be fitted simultaneously, with a wide variety of three-body vector potentials. An attempt is then made to derive the parameters of the three-body vector force from the Gammel-Thaler tensor force parameters, but the resultant force has the wrong exchange character, and is also much too weak, to fit the experimental data. This is mainly due to the Serber-like exchange character of the Gammel-Thaler tensor force. A moderate increase in the strength or range of the odd-state tensor force would give a satisfactory three-body vector force. The splitting of the $^{3}D$ states of ${\mathrm{Li}}^{6}$ is also examined. Here one-, two-, and three-body vector forces all predict too small a splitting, when the strength of the interaction is normalized to the ${\mathrm{Li}}^{7}$ $P$-doublet splitting. For the three-body vector force, however, there exists the possibility that the strength parameter is greater for ${\mathrm{Li}}^{6}$ than for ${\mathrm{Li}}^{7}$, which would improve the fitting.