Measurement of the breakup channels in nuclear muon capture by3He and4He

The rates of the breakup reactions _B(³He) and _B(⁴He) in nuclear muon capture by³He and⁴He have been measured. The measurements were performed on the muon beam of PSI with a multi-anode high-pressure ionization chamber filled with isotopically pure³He or⁴He at 120 bar. The chamber was used as a target and detector for both the incoming muons and for the charged reaction products (tritons, deuterons and protons) of the breakup reactions _B(³He) and _B(⁴He). Our statistics, about 5 × 10⁵ of breakup events, provides a possibility to improve the precision of evaluated rates. The preliminary results: _B(³He)=720 ± 70 s^–1, _B(⁴He)=415 ± 40 s^–1 are compared to theoretical predictions and to previous experiments.     

Negative muon capture in3He

We compute the partial capture rate of negative muons in³He by following the analysis of Peterson to include the relativistic corrections and the exchange effects, for various values of theg _p /g _A ratio. We also calculate the total capture rate. The ground state of³He is assumed to be spherical. The radial dependence of the ground state wave function is taken to be (a) one parameter Irving function, (b) a modified three-parameter Irving function and (c) a function having ‘soft-core’, whose parameters have been fixed in a variational calculation of the binding energy of the triton using a non-local momentum-dependent potential involvingp ² terms. The calculated values of the capture rates are compared with the experimental data to find a value for theg _p /g _A ratio.     

Meson exchange currents for nuclear muon capture by3He leading to the triton final state

We have calculated exchange corrections for nuclear muon capture by³He using the hard-pion model and realistic nuclear wavefunctions. These currents modify the vector and axial part of the weak nuclear current. In their absence the rate is found to be about 12% smaller than experiment. Our aim is to test the hard-pion model by making a realistic estimate of the theoretical uncertainty and comparing the calculated rate with its experimental value. Results for the rate and spin observables will be presented at the symposium. The recent precise measurement of the rate (see the contributions of A.A. Vorobyov and W. Prymas in these proceedings) allows the most stringent test of exchange currents for muon capture to date.Supported by the Sir James Knott Fellowship.Supported by grants nos. 202/94/0370 (GA CR) and 148410 (GA ASC CR).     

Measurement of the heavy neutrino admixture upper limit from muon capture by3He

The triton energy spectrum of the muon capture reaction µ³Het+_µ where µ³He is the ground state of muonic³He, has been measured by means of a high-pressure ionization chamber in order to investigate a possible heavyv admixture into the µ flavor with high sensitivity. The upper limit of the µ-heavy v_i mixing matrix element squared was obtained to be U_µi²10^–3 for heavy neutrino masses in the range of 25 E_0V75 MeV.     

Angular correlation for nuclear muon capture

Formulae for the capture rates, gamma-neutrino correlations, and angular distributions of recoil in muon capture processes J_i J_f by an unpolarized nucleus for J_i ≦ 3 and J_f ≦ 5/2, with and without change of parity of nuclear levels, are given explicitely in terms of the multipole amplitudes. Relation of helicity amplitudes for muonic atom decay to the multipole amplitudes and to amplitudes introduced by other authors is presented. The derivation is based on kinematics only, and the formulae are strictly valid for the muon capture by any nuclei. The formulae are convenient for model calculations of partial transitions with realistic nuclear and muon wave functions and for the phenomenological analysis of a weak interaction.     

Spin-isospin excitations and nuclear muon capture

Muon capture rates in complex nuclei are calculated on basis microscopic models of nuclear structure. The calculation results are consistent with experimental values, unsuppressed spin-isospin transitions, and in contrast to the data obtained from the cross sections for nuclear charge-exchange (p, n) and (n, p) reactions.     

Effect of correlations on nuclear muon capture

The process μ⁻+¹²C→¹²B+v _μ is studied using the modified Hartree Fock wavefunction obtained with the unitary-model-operator-approach starting from the realistic hardcore nucleon-nucleon interaction, with the aim of testing the wavefunctions and obtaining a numerical value for the induced pseudoscalar coupling constant (g _P ). These observables, namely, the partial capture rate to the¹²B(1⁺; g.s), its recoil nuclear polarisation and the total capture rate, which exhaust the available experimental data in the above process have been calculated and compared with the other theoretical and experimental results. As far as the partial capture rate is concerned the use of the unitary-model operator approach wave functions for¹²C withb=2.09 fm and Cohen-Kurath wave function for¹²B(1⁺; g.s) reduces the pure shell model capture rate by about 30%. The effect of strong configuration mixing in the ground state of¹²C in taken into account by introducing a scale factor ξ similar to the ‘amplitude reduction factor’ of Donnelly and Walecka. With this ξ the agreement with the experiment both for the partial capture rate and the beta decay ‘ft’ value is found to be satisfactory. The¹²B(1⁺; g.s) recoil polarisation is found to be insensitive to the use of the unitary-model-operator-approach wave functions. When compared with the experimental data, we obtaing _P =(14.9±1.9)g _A . The total capture rate is found to be sensitive to the use of the unitary-modeloperator-approach wave functions which contain the effect of nucleon-nucleon short range correlations and we obtain a satisfactory agreement with the experiment for¹⁶O and¹²C, thereby revealing the importance of the effect of such correlations in the total capture rate studies.     

Effects of kinematical constraints in nuclear muon capture

Muon capture is discussed in the framework of linear response theory. This approach allows a general discussion of the role played by kinematical constraints in determining which features of nuclear dynamics are actually probed in the capture event. It is argued that the muon momentum spread can increase the capture rate at large energy transfer.     

Neutrino mass effect on the nuclear muon capture

Multipole expansion of the partial transition amplitude in the nuclear muon capture with massive lefthanded Dirac neutrino has been derived. The multipole amplitudes for the partial nuclear transitions are given as the explicit functions of the neutrino mass parameter. As an example, the capture rate, the recoil asymmetry and the neutrino polarization are investigated in terms of these multipole amplitudes. The transversal neutrino polarization provides a connection between theT-violation and the neutrino mass: ifT-odd component in the neutrino polarization is observed, then neutrino must be a massive particle. It turns out that in the capture rate and recoil polarization, the effects due to very small neutrino mass can be proportional to the square ratio of the neutrino mass to its momentum, while the neutrino transversal polarization is proportional to this ratio only. Under the recent limits on the muon neutrino mass, the observable effects inthe partial transition may be below the order of ?10^?3.     

Time reversal test in the nuclear muon capture

Possible effects of breaking CP-symmetry are looked for in the muon capture by a linearly polarized target nucleus. With this aim the recoil polarization in the partial transitions \(0\xrightarrow{{\mu ^ - }}I,1/2\xrightarrow{{\mu ^ - }}J\) and \(1\xrightarrow{{\mu ^ - }}I\) is investigated in a nuclear model independent way. It is shown that the hyperfine structure of the muonic atom significantly influences theT-odd correlations in the recoil polarization formula, and the expectation for theT- odd signal in case of the linearly polarized target is higher by one order of magnitude. We obtain the complete set of theT-odd observables which could enter the polarization formula. As an example, within the impulse approximation for the weak interaction hamiltonian, we analyse the nonstandard, CP-breaking extension of the Fermi theory using complex Fujii-Primakoff form factorG _V e^iφ .     

A new measurement of muon capture in liquid deuterium

The lifetime technique has been used for the first time to measure the muon capture rate in ultra-pure liquid deuterium. The result: _c ^D=470±29 s^–1, is to be interpreted as the capture rate in thed Doublet spin state.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Chiral effective field theory predictions for muon capture on deuteron and {3}He

The muon-capture reactions {2}H(μ{-},ν{μ})nn and {3}He(μ{-},ν{μ}){3}H are studied with nuclear potentials and charge-changing weak currents, derived in chiral effective field theory. The low-energy constants (LECs) c{D} and c{E}, present in the three-nucleon potential and (c{D}) axial-vector current, are constrained to reproduce the A=3 binding energies and the triton Gamow-Teller matrix element. The muon-capture rates on deuteron and {3}He are predicted to be 399±3 sec{-1} and 1494±21 sec{-1}, respectively. The spread accounts for the cutoff sensitivity, as well as uncertainties in the LECs and electroweak radiative corrections. By comparing the calculated and precisely measured rates on {3}He, a value for the induced pseudoscalar form factor is obtained in good agreement with the chiral perturbation theory prediction.     

The nuclear excitations and particle emission following muon capture

The nuclear muon capture process is studied as an excitation of the analogues of various harmonics of the multipole giant resonance. The excitation energy distribution is calculated with the use of the hydrodynamical model of the nucleus. The following particle emission cascade (including precompound states) is considered and the obtained particle spectra as well as yields of various residual nuclei are in a fair agreement with the existing experimental data.     

Precision measurement of the rate of nuclear muon capture in the muonic hydrogen atom and the determination of the pseudoscalar form factor of the nucleon

The rate Λ _S of nuclear muon capture by a proton from the hyperfine singlet ground state of the µp atom has been measured using a new experimental method based on a time-projection chamber operating in an ultrapure hydrogen gas at a pressure of 10 atm. The capture rate has been determined from the difference between the measured lifetime of the negative muon in hydrogen and the world average lifetime of the positive muon. The analysis of 10% of the collected statistics (2 × 10¹⁰) of µe decays yields the muon capture rate Λ _S = 725.0 ± 17.4 s^?1, from which the pseudoscalar form factor of the nucleon, g _P (q _c ² = ?0.88m _µ ² ) = 7.3 ± 1.1, is determined. The further analysis of the collected experimental data should improve the precision of this measurement by a factor of 3.     

A measurement of the muon capture rate in liquid deuterium by the lifetime technique

The lifetime technique has been used to measure the muon capture rate in ultra pure liquid deuterium in conditions where the μd spin state is known. The experimental method avoids the earlier difficulties due to the fusion neutrons. The following result has been obtained for the capture rate in the μd doublet total spin state: λ_c^D = 470 ± 29 s⁻¹.     

Neutron-neutron interaction and muon capture by deutron

The reaction μ⁻ + d → 2n + v_μ is studied in the non-relativistic approximation using the Primakoff weak interaction Hamiltonian including relativistic corrections. The neutron-neutron interaction is treated (a) by the Om?es-Muskhelishvili equation, (b) in a potential model, (c) using the Bethe-Longmire procedure. Influence of D-state admixture in deutron upon the transition rates and neutron spectrum is investigated.     

Gamma-rays following muon capture

The energy and intensity of γ-rays following capture of muons by Si, Ti, Mn, Fe, Co, Ni, Y, Ag and Au were measured with a Ge(Li) detector. In most cases it was possible to identify the final nucleus from the energy of the γ-ray observed. In general, this showed that one or more neutrons were emitted in the initial stages of de-excitation. In the case of capture by Fe and Ni the evidence pointed to a mode of de-excitation by the emission of a proton and a neutron and in Ti by γ-rays alone. In these measurements it was possible to account for as much as 60% of the muons captured in Co, less in the other elements, and only 15 % in Si.     

Precision measurement of the muon momentum in pion decay at rest

A new series of precision measurements of the muon momentum p_μ⁺ in the decay π→μ⁺v_μ at rest have been made using a magnetic spectrometer. The result is p_μ⁺=(29.79139 ± 0.00083) MeV/c. The consequences of this value for the rest masses of the muon neutrino and of the charged pion are discussed.     

Symmetry tests within the Standard Model and beyond from nuclear muon capture

Precision measurements in nuclear muon capture on the proton and ³He allow for tests of the Standard Model for the strong and electroweak interactions, complementary to those achieved in high energy experiments. The present situation and future prospects are reviewed, emphasizing where renewed efforts could prove to be rewarding in exploring ever further beyond the confines of the Standard Model. This revised version was published online in August 2006 with corrections to the Cover Date.