State dependence of shellmodel reaction matrix elements
Abstract
Shellmodel reaction matrix elements are calculated with a combination of the MoszkowskiScott separation method and the referencespectrum method of Bethe, Brandow and Petschek. The reaction matrix G is expanded in terms of G_{s} and V_{L}, where G_{s} is the reaction matrix for the shortrange potential V_{s} and V_{L} the longrange potential. The contribution from G_{s} is then calculated with the referencespectrum method, where the main criterion for choosing the separation distance is that G_{s} is best approximated by G_{s}^{R}, the referencespectrum approximation of G_{s}. The secondorder tensor term V_{TL} ( Q/ e) V_{TL} is calculated with the closure approximation of Kuo and Brown, however the effective energy denominator is now statedependent, which means that it has a dependence on binding energy, the local density and the centreofmass quantum number. The contributions from V_{TL} ( Q/ e) V_{TL} vary almost linearly with ϱ ^{{2}/{3}}, where ϱ is the local density. The reaction matrix elements so calculated have a fairly strong statedependence which comes in predominantly through G_{s} and V_{TL} ( Q/ e) V_{TL}. The state dependence can be approximated quite accurately in a simple way, and thus the application to finite nuclei is convenient. Shellmodel applications have been made for nuclei ^{18}O and ^{18}F and we find that the matrix elements are generally weaker than those of Kuo and Brown, especially for those of T = 1, J = 0 ^{+} and T = 0, J = 1 ^{+}. This is desirable, because the Kuo and Brown matrix elements are often somewhat too strong.
 Publication:

Nuclear Physics A
 Pub Date:
 October 1967
 DOI:
 10.1016/03759474(67)907907
 Bibcode:
 1967NuPhA.103...71K