A Precision Measurement of Nuclear Muon Capture on 3He

The muon capture rate in the reaction mu- 3He -> nu + 3H has been measured at PSI using a modular high pressure ionization chamber. The rate corresponding to statistical hyperfine population of the mu-3He atom is (1496.0 +- 4.0) s^-1. This result confirms the PCAC prediction for the pseudoscalar form factors of the 3He-3H system and the nucleon.Comment: 13 pages, 6 PostScript figure

Resonant Formation of dμtd\mu t Molecules in Deuterium: An Atomic Beam Measurement of Muon Catalyzed dt Fusion

Resonant formation of $d\mu t$ molecules in collisions of muonic tritium ($\mu t$) on D$_2$ was investigated using a beam of $\mu t$ atoms, demonstrating a new direct approach in muon catalyzed fusion studies. Strong epithermal resonances in $d\mu t$ formation were directly revealed for the first time. From the time-of-flight analysis of $2036\pm 116$ $dt$ fusion events, a formation rate consistent with $0.73\pm (0.16)_{meas} \pm (0.09)_{model}$ times the theoretical prediction was obtained. For the largest peak at a resonance energy of $0.423 \pm 0.037$ eV, this corresponds to a rate of $(7.1 \pm 1.8) \times 10^9$ s$^{-1}$, more than an order of magnitude larger than those at low energies.Comment: To appear in Phys. Rev. Let

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

X-ray emission during the muonic cascade in hydrogen

We report our investigations of X rays emitted during the muonic cascade in hydrogen employing charge coupled devices as X-ray detectors. The density dependence of the relative X-ray yields for the muonic hydrogen lines (K_alpha, K_beta, K_gamma) has been measured at densities between 0.00115 and 0.97 of liquid hydrogen density. In this density region collisional processes dominate the cascade down to low energy levels. A comparison with recent calculations is given in order to demonstrate the influence of Coulomb deexcitation.Comment: 5 pages, Tex, 4 figures, submitted to Physical Review Letter

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

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

Induced pseudoscalar coupling of the proton weak interaction

The induced pseudoscalar coupling $g_p$ is the least well known of the weak coupling constants of the proton's charged--current interaction. Its size is dictated by chiral symmetry arguments, and its measurement represents an important test of quantum chromodynamics at low energies. During the past decade a large body of new data relevant to the coupling $g_p$ has been accumulated. This data includes measurements of radiative and non radiative muon capture on targets ranging from hydrogen and few--nucleon systems to complex nuclei. Herein the authors review the theoretical underpinnings of $g_p$, the experimental studies of $g_p$, and the procedures and uncertainties in extracting the coupling from data. Current puzzles are highlighted and future opportunities are discussed.Comment: 58 pages, Latex, Revtex4, prepared for Reviews of Modern Physic

Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble

We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x) \sim \phi(x)/x^{1 + \alpha}, where \alpha > 0 is the Pareto index and $\phi(x)$ is the cut-off function. We consider two forms of \phi(x): a bounded function \phi(x) = 1 for L \leq x \leq H, and zero otherwise, and a smooth exponential function \phi(x) = \exp(-L/x - x/H). In both cases \Psi(x) has moments of arbitrary order. We show that, for \alpha > 1, P(\omega) always has a unimodal form and is peaked at \omega = 1/2, so that most probably x_1 \approx x_2. For 0 < \alpha < 1 we observe a more complicated behavior which depends on the value of \delta = L/H. In particular, for \delta < \delta_c - a certain threshold value - P(\omega) has a three-modal (for a bounded \phi(x)) and a bimodal M-shape (for an exponential \phi(x)) form which signifies that in such ensembles the wealths x_1 and x_2 are disproportionately different.Comment: 9 pages, 8 figures, to appear in Physica

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