Muon Capture and Nuclear Structure

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We have studied the fundamental muon-nucleon interaction from the muon capture in gaseous and molecular hydrogen and the nuclear structure problem upon the knowledge of the former from muon captures in C^<12> and O^<16>. The phenomenological V-A theory of leptonic interactions is adopted for the fundamental process μ^-+p→n+ν_μ. The behavior of the form factors is determined under the assumptions of 1) conserved vector current, 2) isotriplet vector current, 3) partially conserved axial vector current, 4) definite G-parity for the current, and 5) muon-electron universality. Calculated muon capture rates are in agreement with the recent data on gaseous hydrogen, and also with the data on molecular hydrogen if the molecular factor 2γ=1.00 is accepted. The muon capture rate is calculated for the reaction μ^-+C^<12>→B^<12> (ground state)+ν_μ, with general p-shell wave functions which were obtained by considering the dynamical properties in the A=12 system. The experimental ft value of the beta decay of B^<12>, which in all previous theories is used to normalize the muon capture rate, has not been adopted in this analysis. An excellent fit to the experimental data for the capture rate as well as for the ft value has been obtained with the B^<12> wave function proposed by Kurath to explain the magnetic moment of B^<12> and a C^<12> wave function introduced here. The oscillator strength parameter is chosen to be b=1.64 fm; this is in conformity with the elastic and most of the inelastic electron scattering data. The muon capture rates are also calculated for the reactions μ^-+O^<16>→N^<16>(0^-, 1^-, 2^-)+ν_μ, with the RPA and Tamm-Dancoff models. The calculated capture rates agree well with experimental date,if 1) C_p/C__A=5~14 and the Gillet wave functions are adopted in the reaction 0^+→0^-, 2) a configuration mixing is taken into account in the reaction 0^+→1^-, and 3) a normalization by the experimental bate decay rate of N^<16> is introduced in the reaction 0^+→2^-.
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Muon Capture and Nuclear Structure

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