The Fine Structure of the Nuclear Ground Level ofLi7

Calculations of the fine structure of the ground level of the ${\mathrm{Li}}^7$ nucleus are made with the object of throwing light on the form of the interaction energy between pairs of nuclear particles. The requirements of relativistic covariance do not determine the spin-orbit interactions uniquely. Adjustable parameters, which are essentially coefficients of invariant additions to the Hamiltonian, are not fixed by considerations of covariance. The calculations reported show how, with approximate assumptions about the wave function, these parameters should be chosen in order to obtain agreement with the observed fine structure. A general rule simplifying the calculation of the spin-orbit interaction with a closed shell is developed for interactions between pairs of particles. The results are sensitive to the wave function used. The assumption of approximate symmetry of the nuclear Hamiltonian leads to an approximately symmetric coordinate function which is a linear combination of ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^1{}_{}{}^{}D$ states of the two neutrons in the $p$ shell. For this function relatively large values of the adjustable parameters (∼3) are needed. If, however, the ${}_{}{}^1{}_{}{}^{}S$ state is supposed to be the predominant one, values of the parameters ∼1 suffice. Present evidence favors the symmetric function and, therefore, the larger values of the parameters. These values do not correspond, even approximately, to the picture of a nuclear particle moving in a scalar field. An additional interaction having the transformation properties of an electromagnetic field is needed to obtain them. The sensitivity of the fine structure to perturbations suggests caution regarding the quantitative side of the calculations. Only qualitative significance can be attached to them.