Hyperfine Populations Prior to Muon Capture

It is shown that the 1S level hyperfine populations prior to muon capture will be statistical when either target or beam are unpolarised independent of the atomic level at which the hyperfine interaction becomes appreciable. This assertion holds in the absence of magnetic transitions during the cascade and is true because of minimal polarisation after atomic capture and selective feeding during the cascade.Comment: (revtex, 6 preprint pages, no figures

Three-Nucleon Electroweak Capture Reactions

Recent advances in the study of the p-d radiative and mu-3he weak capture processes are presented and discussed. The three-nucleon bound and scattering states are obtained using the correlated-hyperspherical-harmonics method, with realistic Hamiltonians consisting of the Argonne v14 or Argonne v18 two-nucleon and Tucson-Melbourne or Urbana IX three-nucleon interactions. The electromagnetic and weak transition operators include one- and two-body contributions. The theoretical accuracy achieved in these calculations allows for interesting comparisons with experimental data.Comment: 12 pages, 4 figures, invited talk at the CFIF Fall Workshop: Nuclear Dynamics, from Quarks to Nuclei, Lisbon, 31st of October - 1st of November 200

Nuclear muon capture by 3He: meson exchange currents for the triton channel

Exchange current corrections are calculated using currents found from the hard-pion model and AV14+3BF wavefunctions. Results are given for the rate and spin observables. Their sensitivity to g_P, the nucleon pseudoscalar form factor, is reported.Comment: 35 pages, uuencoded gz-compressed tar file 42 Kbyte

Final state interaction effects in mu-capture induced two-body decay of 3He

The mu-capture process on 3He leading to a neutron, a deuteron and a mu-neutrino in the final state is studied. Three-nucleon Faddeev wave functions for the initial 3He bound and the final neutron-deuteron scattering states are calculated using the BonnB and Paris nucleon-nucleon potentials. The nuclear weak current operator is restricted to impulse approximation. Large effects on the decay rates of the final state interaction are found. The comparison to recent experimental data shows that the inclusion of final state interactions drastically improves the description of the data.Comment: 14 pages, 6 eps figure

Muon capture by 3He nuclei followed by proton and deuteron production

The paper describes an experiment aimed at studying muon capture by ${}^{3}\mathrm{He}$ nuclei in pure ${}^{3}\mathrm{He}$ and $\mathrm{D}_2 + {}^{3}\mathrm{He}$ mixtures at various densities. Energy distributions of protons and deuterons produced via $\mu^-+{}^{3}\mathrm{He}\to p+n+n + \nu_{\mu }$ and $\mu^-+{}^{3} \mathrm{He} \to d+n + \nu_{\mu}$ are measured for the energy intervals $10 - 49$ MeV and $13 - 31$ MeV, respectively. Muon capture rates, $\lambda_\mathrm{cap}^p (\Delta E_p)$ and $\lambda_\mathrm{cap}^d (\Delta E_d)$ are obtained using two different analysis methods. The least--squares methods gives $\lambda_\mathrm{cap}^p = (36.7\pm 1.2) {s}^{- 1}$, $\lambda_\mathrm{cap}^d = (21.3 \pm 1.6) {s}^{- 1}$. The Bayes theorem gives $\lambda_\mathrm{cap}^p = (36.8 \pm 0.8) {s}^{- 1}$, $\lambda_\mathrm{cap}^d = (21.9 \pm 0.6) {s}^{- 1}$. The experimental differential capture rates, $d\lambda_\mathrm{cap}^p (E_p) / dE_p$ and $d\lambda_\mathrm{cap}^d (E_d) / dE_d$, are compared with theoretical calculations performed using the plane--wave impulse approximation (PWIA) with the realistic NN interaction Bonn B potential. Extrapolation to the full energy range yields total proton and deuteron capture rates in good agreement with former results.Comment: 17 pages, 13 figures, accepted for publication in PR

Quenching of Weak Interactions in Nucleon Matter

We have calculated the one-body Fermi and Gamow-Teller charge-current, and vector and axial-vector neutral-current nuclear matrix elements in nucleon matter at densities of 0.08, 0.16 and 0.24 fm$^{-3}$ and proton fractions ranging from 0.2 to 0.5. The correlated states for nucleon matter are obtained by operating on Fermi-gas states by a symmetrized product of pair correlation operators determined from variational calculations with the Argonne v18 and Urbana IX two- and three-nucleon interactions. The squares of the charge current matrix elements are found to be quenched by 20 to 25 % by the short-range correlations in nucleon matter. Most of the quenching is due to spin-isospin correlations induced by the pion exchange interactions which change the isospins and spins of the nucleons. A large part of it can be related to the probability for a spin up proton quasi-particle to be a bare spin up/down proton/neutron. We also calculate the matrix elements of the nuclear Hamiltonian in the same correlated basis. These provide relatively mild effective interactions which give the variational energies in the Hartree-Fock approximation. The calculated two-nucleon effective interaction describes the spin-isospin susceptibilities of nuclear and neutron matter fairly accurately. However $\geq$ 3-body terms are necessary to reproduce the compressibility. All presented results use the simple 2-body cluster approximation to calculate the correlated basis matrix elements.Comment: submitted to PR

The Axial-Vector Current in Nuclear Many-Body Physics

Weak-interaction currents are studied in a recently proposed effective field theory of the nuclear many-body problem. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar ($\sigma$) and vector ($\omega$) fields, and isovector vector ($\rho$) fields. The theory exhibits a nonlinear realization of $SU(2)_L \times SU(2)_R$ chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the axial-vector current and the strong-interaction dynamics, it satisfies the symmetries of the underlying theory of quantum chromodynamics, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. Moreover, it has recently been verified that for normal nuclear systems, it is possible to systematically expand the effective lagrangian in powers of the meson fields (and their derivatives) and to reliably truncate the expansion after the first few orders. Here it is shown that the expressions for the axial-vector current, evaluated through the first few orders in the field expansion, satisfy both PCAC and the Goldberger--Treiman relation, and it is verified that the corresponding vector and axial-vector charges satisfy the familiar chiral charge algebra. Explicit results are derived for the Lorentz-covariant, axial-vector, two-nucleon amplitudes, from which axial-vector meson-exchange currents can be deduced.Comment: 32 pages, REVTeX 4.0 with 12pt.rtx, aps.rtx, revsymb.sty, revtex4.cls, plus 14 figures; two sentences added in Summary; two references adde

Polarized photons in radiative muon capture

We discuss the measurement of polarized photons arising from radiative muon capture. The spectrum of left circularly polarized photons or equivalently the circular polarization of the photons emitted in radiative muon capture on hydrogen is quite sensitive to the strength of the induced pseudoscalar coupling constant $g_P$. A measurement of either of these quantities, although very difficult, might be sufficient to resolve the present puzzle resulting from the disagreement between the theoretical prediction for $g_P$ and the results of a recent experiment. This sensitivity results from the absence of left-handed radiation from the muon line and from the fact that the leading parts of the radiation from the hadronic lines, as determined from the chiral power counting rules of heavy-baryon chiral perturbation theory, all contain pion poles.Comment: 10 pages, 6 figure

Theoretical Study of the ^3He(mu^-,nu_mu)^3H Capture

The ^3He(mu^-,nu_mu)^3H weak capture is studied using correlated-hyperspherical-harmonics wave functions, obtained from realistic Hamiltonians consisting of the Argonne $v_{14}$ or Argonne $v_{18}$ two-nucleon, and Tucson-Melbourne or Urbana-IX three-nucleon interactions. The nuclear weak charge and current operators have vector and axial-vector components that include one- and two-body contributions. The strength of the leading two-body operator in the axial-vector current is adjusted to reproduce the Gamow-Teller matrix element in tritium $\beta$-decay. The calculated total capture rate is in excellent agreement with the most recent experimental determination $1496\pm 4$ sec$^{-1}$, when the PCAC value is adopted for the induced pseudo-scalar coupling constant $g_{PS}$. The predictions for the capture rate and angular correlation parameters $A_v$, $A_t$, and $A_\Delta$ are found to be only very weakly dependent on the model input Hamiltonian. The variation of these observables with $g_{PS}$ and the theoretical uncertainties deriving from the model-dependent procedure used to constrain the axial current are investigated.Comment: 16 pages, 1 figure, submitted to PR