Effects of ground-state correlations on muon capture matrix elements

The muon capture matrix elements Mᵥ², Mₐ², and ${M_p}^2$ are calculated for ⁴He and ¹⁶O 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 ¹⁶O) 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 ¹⁶O are ${M_v}^{2\left(corr\right)}=0.82{M_a}^{2\left(corr\right)}=0.74{M_p}^{2\left(corr\right)}=0.58M^{2\left(osc\right)}$, while for ⁴He, ${M_v}^{2\left(corr\right)}=0.88{M_a}^{2\left(corr\right)}=0.78{M_p}^{2\left(corr\right)}=0.76M^{2\left(osc\right)}$. 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 ¹⁶O and ∼20% in ⁴He.NUCLEAR REACTIONS ⁴He, ¹⁶O, calculated total muon capture rate, closure and nuclear correlations.