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DOUBLET SPLITTING IN THE NUCLEAR 1P-SHELL DUE TO A SPIN-ORBIT INTERACTION
Abstract
The second order contribution of a two-body spin- orbit interaction to the doublet splitting in N15 and He5 nuclei has been estimated. Initially an estimate was obtained by replacing the energy denominators in the Schrödinger perturbation formula for the second order energy shift by a single denominator. This permitted the use of closure and the resulting expression contains only ground state matrix elements. Appropriate choice of the single denominator yields a rigorous bound on the exact second order splitting. For a short range force, the two-body terms so obtained seemed unreasonably large. For this reason a second estimate was made by adding the three- and four-body terms calculated by the single energy denominator method to the exact two-body terms, computed with the Bolsterli-Feenberg technique. The exact two-body terms, while reduced from those of the first estimate, are still strikingly large.The potential parameters used in making the above estimates were, in each case, chosen in two ways. One was to require that the potential resemble, as closely as possible, the Gammel-Thaler phenomenological spin-orbit potential. The other was to require that the splitting obtained by first order perturbation theory be equal to the experimental splitting. With the potentials deter- mined in each fashion both estimates of the second order contribution to the splitting were larger than and oppo- site in sign to the first order result. The conclusion is drawn that it is unwarranted to attempt to account for the role which the two-body spin-orbit interaction plays in the doublet splitting by a perturbation expansion.
Subject Area
Nuclear physics
Recommended Citation
FRASER, WILLIAM AVON, "DOUBLET SPLITTING IN THE NUCLEAR 1P-SHELL DUE TO A SPIN-ORBIT INTERACTION" (1964). ETD collection for University of Nebraska-Lincoln. AAI6408876.
https://digitalcommons.unl.edu/dissertations/AAI6408876