State dependence of shell-model reaction matrix elements

doi:10.1016/0375-9474(67)90790-7

Nuclear Physics A

Volume 103, Issue 1, 23 October 1967, Pages 71-96

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Abstract

Shell-model reaction matrix elements are calculated with a combination of the Moszkowski-Scott separation method and the reference-spectrum 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 short-range potential V_s and V_L the long-range potential. The contribution from G_s is then calculated with the reference-spectrum method, where the main criterion for choosing the separation distance is that G_s is best approximated by G_s^R, the reference-spectrum approximation of G_s. The second-order 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 state-dependent, which means that it has a dependence on binding energy, the local density and the centre-of-mass quantum number. The contributions from V_TL (Q/e) V_TL vary almost linearly with $ϱ^{23}$ , where ϱ is the local density. The reaction matrix elements so calculated have a fairly strong state-dependence 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. Shell-model applications have been made for nuclei ¹⁸O and ¹⁸F 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.

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^†: This work was supported in part by the U.S. Atomic Energy Commission and the Higgins Scientific Trust Fund. It made use of the Princeton Computer Facilities supported in part by the National Science Foundation Grant NSF-GP 579.

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State dependence of shell-model reaction matrix elements

Abstract

Nuclear Physics

Nuclear Physics

Phys. Lett.

Nuclear Physics

Nuclear Physics

Phys. Rev.

Nuclear Physics