Muon capture rates in complex nuclei

Muon capture rates: Evaluation within the quasiparticle random phase approximation

“…As seen in the Table III the calculated capture rates using the small single-particle space are typically ≈20% smaller than those in the large single-particle space. Second, the bound muon wave function can be included in the factorized form, as the Z 4 eff factor, or without factorization. Again, we consider the variant without factorization preferable.…”

“…Using 2 μ g instead of 2 μ Z makes little difference as seen in Table II. Also, we tested that Z 4 eff is insensitive to variations of c rms . By changing it by 1% changes Z 4 eff also by approximately the same amount.…”

“…Also, we tested that Z 4 eff is insensitive to variations of c rms . By changing it by 1% changes Z 4 eff also by approximately the same amount. Replacing the Fermi distribution by the sharp surface nuclear charge distribution also changes Z 4 eff by only a small amount.…”

“…Note, that the experimental data are mostly for elements, not for individual isotopes. Thus, instead of using them directly, we use for comparison with calculations the so-called Goulard-Primakoff empirical formula [5] that describes sufficiently well the muon capture rate for all nuclei with given A and Z, μA GP (A, Z ) = Z 4 eff…”

“…has been studied in detail for a long time (see the classic reviews by Walecka [1], Mukhopadhyay [2], and Measday [3]). Experimental determination of the total muon capture rate is relatively straightforward, therefore it is known for many stable elements, sometimes even for the separated isotopes [4,5]. The nuclear response in this semileptonic weak process is governed by the momentum transfer of the order of muon mass.…”