General properties of the residual interaction as measured near closed shells

Abstract

Residual interaction matrix elements for shell model calculations in a specified configuration space are unique to the extent that the nuclear interaction can be represented as a sum of two‐body interactions. Many diagonal matrix elements have been obtained from two‐nucleon multiplets near closed shells. The limited purity of such multiplets was taken into consideration by weighting the observed fractions of the two‐nucleon configurations by their spectroscopic strengths and by using the resulting energy centroids. The occasional simultaneous knowledge of empirical particle‐particle and particle‐hole multiplets for the same configuration permits estimates of the uncertainty of the extraction procedure and indicates that diagonal matrix elements are often known to better than 10% or 100 keV, whichever is larger. Evidence is increasing that matrix elements for spaces of a major shell (or larger) have remarkable regularities along the lines initially pointed out by Schiffer. A significant but smooth A dependence has been found. The available matrix elements primarily depend on T and A and the parity of the multiplet. They depend in a general way on the coupling of j1 and j2, but not noticeably on the major quantum numbers 1 and n. These systematic features are also found in the matrix elements of Kuo and Brown and in some short range model forces (MDSI), although agreement of experiment with these theoretically derived matrix elements varies. The empirical data suggest that scaling of known matrix elements with A−0.75 may be used to predict residual matrix elements for regions away from closed shells or in other major shells.