Effects of ground-state correlations on muon capture matrix elements

R. J. McCarthy; G. E. Walker

doi:10.1103/PhysRevC.11.383

Abstract

The muon capture matrix elements ${M_{v}}^{2}$ , ${M_{a}}^{2}$ , and ${M_{p}}^{2}$ are calculated for ${}^{4}{He}$ and ${}^{16}O$ using the closure approximation and utilizing the linked cluster expansion to introduce correlations in the nuclear target wave functions. An important set of diagrams is summed by replacing uncorrelated wave functions with Bethe-Goldstone wave functions. However, we also find it necessary to include diagrams insuring that the pair number operator is unchanged and (for ${}^{16}O$ ) particle-hole diagrams to account for the fact that oscillator orbitals rather than Hartree-Fock orbitals are used for the uncorrelated basis. Typical results for ${}^{16}O$ are ${M_{v}}^{2 (corr)} = 0.82 {M_{a}}^{2 (corr)} = 0.74 {M_{p}}^{2 (corr)} = 0.58 M^{2 (osc)}$ , while for ${}^{4}{He}$ , ${M_{v}}^{2 (corr)} = 0.88 {M_{a}}^{2 (corr)} = 0.78 {M_{p}}^{2 (corr)} = 0.76 M^{2 (osc)}$ . The bulk of the effects arise from correlations induced by the tensor component of the nucleon-nucleon interaction. We find that including correlations reduces the predicted total capture rate by ∼30% in ${}^{16}O$ and ∼20% in ${}^{4}{He}$ .

NUCLEAR REACTIONS ${}^{4}{He}$ , ${}^{16}O$ , calculated total muon capture rate, closure and nuclear correlations.

Received 1 July 1974

DOI:https://doi.org/10.1103/PhysRevC.11.383

Physical Review C

covering nuclear physics