Partial Muon Capture Rates Research Articles

Partial muon capture rates in A=3 and A=6 nuclei with chiral effective field theory

Searches for neutrinoless double-$\ensuremath{\beta}$ decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless double-$\ensuremath{\beta}$ decays take place at momentum transfers on the order of $100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}/c$ and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate these currents. In this Letter, we present results of ab initio calculations of partial muon capture rates for $^{3}\mathrm{He}$ and $^{6}\mathrm{Li}$ nuclei using variational and Green's function Monte Carlo computational methods. We estimate the impact of the three-nucleon interactions, the cutoffs used to regularize two-nucleon $(2N)$ interactions, and the energy range of $2N$ scattering data used to fit these interactions.

Shell-model study of partial muon-capture rates in light nuclei

The nuclear shell model is used to study ordinary muon capture of light nuclei in the p, sd and p-sd shell-model spaces. Several well-established two-body interactions are applied to calculate the involved nuclear matrix elements and the emerging results are compared with each other. The resulting theoretical partial muon-capture rates are compared with experimental data and their stability against different model spaces and interactions studied. The effects of the induced-pseudoscalar strength, C p, on the capture rates is discussed. The relation between the allowed partial muon capture rates and the Gamow-Teller strength function is stressed.

A study of the partial muon capture rates [formula omitted

The muon capture reactions μ − + 6 Li → 6 He(g.s.) + ν μ and μ − + 6 Li → t + t ν μ are studied using the Fujii-Primakoff effective muon capture hamiltonian. For the 6Li and 6He ground states a fully antisymmetrised ( 3He + t) and (t + t) cluster-model wave function (including the shell-model variant) is used. The break-up channel is studied in the context of a plane-wave impulse approximation. The model dependence of the total rates, energy and angular distributions is studied. Good agreement is found with the experimental 6He(g.s.) transition rate. Large deviations from other theoretical estimates and from the only available experiment are observed in the case of the break-up reaction. The possibility of using the break-up reaction in an experiment to determine the muon neutrino mass is discussed.

Average polarization of 12B in polarized muon capture

A formula is given for the average polarization of the recoil nucleus in polarized muon capture in a spin zero nucleus. This formula includes the correction due to contributions from the excited states which are produced in the muon captures of the same parent nucleus, through γ-transitions. Average polarizations and partial muon capture rates are numerically obtained in the processes μ − + 12 C → 12 B(1 +, 2 +, 2 −, 1 −)+ ν μ . The nuclear wave functions adopted are of the Co Cohen-Kurath type for the postive parity states and of the most general configurations of 1 ħϵ excitations for the negative parity states. The average polarizations are, generally, less dependent on the nuclear structure than the partial muon capture rates. The experimental data on the average polarization of 12B given by the Louvain-Saclay-ETH group is analyzed with the correction from the excited states. This leads to (ɡ p − ɡ T )/ɡ A = 10.3 ± 2.7 for the form factors.

Partial muon capture rates in 12C from the generalized helm model

Partial capture rates in the reaction μ − + 12C → ν μ + 12B are calculated using the generalized Helm model. The results are in good agreement with the recent experiment data.

Muon capture rates on 16O leading to bound states of 16N

The partial muon capture rates on 16O leading to all four particle-stable states in 16N have been measured. The results obtained are compared to previous measurements and are also used to extract a value for the induced pseudoscalar coupling constant in muon capture.

Spectra of neutrons emitted after muon capture in 16O, 28Si, 32S and 40Ca

On the basis of the particle-hole model for the closed-(sub)shell nuclei 16O, 28Si, 32S and 40Ca, we present a calculation of the partial muon-capture rates to the T = 1 states of the model (which mainly represent the giant resonance), as well as of the spectra of neutrons emitted in the decay of these states to the ground and excited states of the corresponding daughter nuclei. Improved positions and empirical total widths for the resonant states have been used as obtained from photonuclear and electron scattering studies of the levels. The theoretical total muon-capture rates are in good agreement with measured rates. The calculated neutron spectra are compared to recently measured spectra following muon capture in 16O, 32S and 40Ca.

Muon-Capture and Photon-Absorption Calculations in a Configuration-Mixing Model forO16

The utility of multiparticle, multihole configuration mixing as a mechanism for resolving certain theoretical-experimental discrepancies for muon capture and photodisintegration on ${\mathrm{O}}^{16}$ is considered. An ${\mathrm{O}}^{16}$ ground state containing a two-particle, two-hole (2p-2h) component is assumed. The usual particle-hole odd-parity states are amended to contain three-particle, three-hole configuration admixtures consistent with the choice of the more complicated ground state. The results of the calculations indicate that the configuration-mixing model can appreciably lower the partial muon-capture rates to the lowest ${0}^{\ensuremath{-}}$, ${1}^{\ensuremath{-}}$, and ${2}^{\ensuremath{-}}$ states. Moreover, a shift in the energy distribution of the transition strength, obtained in the model calculations, lowers the capture rate and photodisintegration cross section in and below the giant-resonance region. However, correction terms, arising mainly from ${0}^{+}$ \ensuremath{\rightarrow} ${1}^{+}$ (2p-2h) allowed Gamow-Teller transitions, seem to preclude a lowering of the total capture rate.

Migdal's Theory of Nuclear Structure and Partial Muon Capture Rates inO16

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Migdal'S Theory of Nuclear Structure and Partial Muon Capture Rates inO16

The partial muon-capture rates in ${\mathrm{O}}^{16}$ leading to low-lying states in ${\mathrm{N}}^{16}$ are calculated in Migdal's theory of nuclear structure, with results that agree well with the available experiments for suitable values of ${C}_{P}=\frac{{m}_{\ensuremath{\mu}}{F}_{P}}{{F}_{A}}$. It is thus argued that the neglect of $G$-parity irregular terms was not the cause of previous apparent disagreement. The capture rates are in turn employed to examine the effect of the velocity-dependent terms in Migdal's effective amplitude.

A detector for the induced pseudoscalar coupling constant

The detection of partial muon capture rates in16O forms a sensitive detector for the induced pseudoscalar coupling constant. We here investigate the effects of nucleon velocity terms in the weak Hamiltonian and of realistic nuclear wave-functions. Their inclusion is essential for a correct treatment of the problem. In addition to the previously suggested detector level, we find that capture into the ground state of16N permits an almost complete elimination of nuclear physics by comparison to the β-decay rate.