Muon Capture on Light Nuclei

Abstract

This work investigates the muon capture reactions (2)H(mu (-), nu (mu) )nn and (3)He(mu (-), nu (mu) )(3)H and the contribution to their total capture rates arising from the axial two-body currents obtained imposing the partially-conserved-axial-current (PCAC) hypothesis. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v (18) two-nucleon potential, in combination with the Urbana IX three-nucleon potential in the case of A = 3. The weak current consists of vector and axial components derived in chiral effective field theory. The low-energy constant entering the vector (axial) component is determined by reproducting the isovector combination of the trinucleon magnetic moment (Gamow-Teller matrix element of tritium beta-decay). The total capture rates are 393.1(8) s(-1) for A = 2 and 1488(9) s(-1) for A = 3, where the uncertainties arise from the adopted fitting procedure

Theoretical studies of muon capture on light nuclei

“…These results are in good agreement with those of Refs. [9,10], as well as with experimental data, but not with those of Ref. [13], for which the discrepancy remains of the order of 4 − 9 %.…”

“…[13] differ from those of Refs. [9,10] by 7 − 10 %. Only very recently, the origin of this discrepancy has been understood, as it will discussed in the next section.…”

“…Note that just one year before the work of Refs. [9,10], an other calculation of Γ D was performed in Ref. [13] within the PMA, although the meson-exchange currents were of different origin.…”

“…In Refs. [9,10], reactions (1.1) and (1.2) are simultaneously studied within two different schemes: the "potential model approach" (PMA), also known as "standard nuclear physics approach", and the approach known as the "hybrid" chiral effective field theory (χEFT), often indicated with χEFT*. In PMA, Hamiltonians based on conventional two-nucleon (NN) and threenucleon (NNN) potentials are used to calculate the nuclear wave functions, and the weak transition operator includes, beyond the one-body contribution (the impulse approximation-IA) associated with the basic process p + µ − → n + ν µ , meson-exchange currents as well as currents arising from the excitation of ∆-isobar degrees of freedom [11].…”

Calculation of doublet capture rate for muon capture in deuterium within chiral effective field theory

“…Notice that in the calculations of [28] based on the Nijmegen I potential [30], the suppression of Λ 1/2 by ∼ 1 % was obtained for this current, whereas in Ref. [58] no effect has been found based on the nuclear wave functions generated by the Argonne v 18 potential [51]. For the EGM(205) version, the contribution of the short-range weak axial MECs,  A (EFT), is strongly enhanced as a consequence of the large value ofd R .…”