The Fine Structure of Nuclear Energy Levels on the Alpha-Model

Abstract

In studying the fine structure predictions of any proposed theory of nuclear forces it is important to know to what extent the results obtained are sensitive to the changes in the nuclear model employed in making the calculations. The present work is concerned with this. The splitting for ${\mathrm{He}}^{5}$, which should be very similar to that for ${\mathrm{Li}}^{5}$, is discussed on the alpha- and central field models. A deuteron group model for the alpha-particle is considered in addition to the simple alpha-group. ${\mathrm{Li}}^{7}$ is treated from the standpoint of the theory of "holes" and also on a modified alpha-particle model. The contribution of the exchange terms to the splitting in ${\mathrm{He}}^{5}$ is greater by a factor of the order of two or three on the alpha-model than on the central field model. The sign and magnitude of the total splitting are of about the same order on the two models. The deuteron group alpha-function gives essentially the same splitting as the ordinary alpha-function. So far as ordinary terms for ${\mathrm{Li}}^{7}$ are concerned, the spin-orbit interaction of a "hole" in a concentrated closed shell with a closed shell is the same, apart from a numerical factor, as the spin-orbit interaction of a single particle with a closed shell. The exchange terms for ${\mathrm{Li}}^{7}$ are approximately proportional to the degree of overlapping of the alpha- and triton groups. The exchange splitting has the same sign as the ordinary splitting. Energy splitting estimates on the alpha-model in which the exchange terms are neglected should give results reliable to an order of magnitude at least, as far as this model is concerned.