Radiative Muon Capture and the Induced Pseudoscalar Coupling in Nuclei

Abstract

The experimental attempts to exploit the sensitivity of the radiative muon capture (RMC) reaction[1] $$ {\mu^{ - }}N\left( {A,Z} \right) \to N * \left( {A,Z - 1} \right){\nu_{\mu }}\gamma $$ to the induced pseudoscalar coupling g P until now are limited to the two nuclear targets 16 O[2] and 40 Ca [2,3,4]. The observables are the photon energy spectrum above a cutoff energy of 57 MeV, below which the muon decay electron induced bremsstrahlung prohibits the measurement, and the muon spin photon angular correlation. The latter quantity has only been measured with poor statistical accuracy for 40 Ca[3,5,6]. The data are scarce because the low rate (the radiative branch above 57 MeV contributes only 2 * 10-5 to the total muon absorption rate in 40 Ca), the modest resolution attainable for medium energy photons and the high background environment of fast neutrons severely trouble the measurement. But even this limited amount of data has lead to surprising results, when compared to theoretical calculations [7,8,9], which proceed in the impulse approximation with a Hamiltonian derived from the elementary μ - p → nν μ γ reaction and a nuclear response function, adapted to describe the results of other medium energy weak or electromagnetic processes. The interpretation of the integrated photon yield and the photon spectrum in terms of the pseudoscalar coupling yields g P = (4.5±1.5)g A for 40 Ca[4] and g P exceeding 12g A for 16 O [1,2,9].