Muon capture revisited

The problem of inclusive muon capture in nuclei is studied by calculating the capture rate in asymmetric infinite nuclear matter and using the local density approximation to evaluate the capture rates in nuclei. It is shown that the method is rather reliable and allows one to improve on approximations used in the past. The need for a strong nuclear renormalization is shown, reducing the capture rates by about a factor two in medium and heavy nuclei. By using standard effective interactions in the spin-isospin channel one can account for this renormalization and one finds a remarkable overall agreement with the measured capture rates for a large list of nuclei through the periodic table.     

Muon catalyzed fusion in deuterium gas

We present the results of an experiment performed at PSI to investigate muon catalyzed fusion in pure deuterium gas of 5% density (LHD) at temperatures ranging from 28 K to 350 K. Using a new high pressure ionization chamber the reactions dd → n + ³He and dd → p+t were observed with 100% detection efficiency. The rates of dμd formation were measured with the absolute precision of 1% and the μd spin-flip rates with 0.5%. The temperature dependence of molecular formation and spin-flip rates display pronounced resonance structures. A preliminary fit based on the Vesman mechanism of resonant muonic molecule formation was carried out yielding a dd fusion rate of 3.5·10⁸ s^-1 and a hfs splitting energy of 24.3 meV, both in good agreement with the theory. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon capture on neutron-rich nuclei

Future facilities will allow the exploration of extremely neutron-rich nuclei far from the valley of stability. It is discussed that the strong-neutron excess results in changes in the collective excitations of such nuclei compared to conventional stable nuclei. We propose muon capture as an experimental tool to explore such changes. We will quantify our discussion by the calculation of the total and differential muon capture rates on selected calcium isotopes between ⁴⁰Ca and ⁶⁰Ca. Our calculations are based on the random phase approximation and agree nicely with the measured rates for ⁴⁰Ca and ⁴⁴Ca. Received: 6 April 2001 / Accepted: 14 May 2001     

Muon capture rates in Se and Cd isotopes

Energy and time spectra of γ rays following nuclear capture of negative muons in natural Se and Cd and isotopically enriched ⁷⁶Se and ¹⁰⁶Cd targets have been measured with HPGe detectors. Total muon lifetimes in Se and Cd isotopes and partial μ capture rates to excited levels of ⁷⁶As and ¹⁰⁶Ag are obtained. These results are necessary for calculation of nuclear matrix elements of the 2β decay of ⁷⁶Ge and ¹⁰⁶Cd respectively.     

Muon capture in oxides using the lifetime method

The relative capture rate has been measured for muons stopping in 22 oxides. The experimental method was to detect the decay electrons and to use the unique lifetime signature to determine which element captures the muon.     

Muon capture in atoms,crystals and molecules

The slowing down and capture of negative muons in solids is discussed on the basis of classical equations of motion where the energy dissipation is described in terms of frictional forces. Transport equations determining the energy distribution of the muons in the target are formulated and solved for various models. Using a statistical model of the atom it is shown that the muons are captured typically at energies of a few tens of electron volts, that the angular momentum distribution of the muons at capture is almost statistical, and that this distribution is not expected to be qualitatively changed by the subsequent cascade to the tightly bound orbits. In mixtures of atoms with atomic numbers Z₁ and Z₂ the capture ratio is to a good approximation proportional to the atomic concentration and, in the statistical model, proportional to $\text{(}\text{Z}{}_1\text{Z}{}_2\text{)}{}^{\mathrm{<mtext>7</mtext><mtext>6</mtext>}}$. Calculations are also performed with more accurate atomic models, and it is shown that capture ratios as well as angular momentum distributions are influenced by the ionicity of the atomic bonds and the atomic shell structure. No systematic study of these effects has been made but the few results obtained seem to be in reasonable agreement with experiments.     

Muon capture on the proton and deuteron

By measuring the lifetime of the negative muon in pure protium (¹H), the MuCap experiment determines the rate of muon capture on the proton, from which the proton’s pseudoscalar coupling g _p may be inferred. A precision of 15% for g _p has been published; this is a step along the way to a goal of 7%. This coupling can be calculated precisely from heavy baryon chiral perturbation theory and therefore permits a test of QCD’s chiral symmetry. Meanwhile, the MuSun experiment is in its final design stage; it will measure the rate of muon capture on the deuteron using a similar technique. This process can be related through pionless effective field theory and chiral perturbation theory to other two-nucleon reactions of astrophysical interest, including proton-proton fusion and deuteron breakup. for the MuCap [1] and MuSun [2] Collaborations     

Muon capture on nickel and tin isotopes

We calculate total and differential muon capture rates on nickel and tin isotopes ranging from the proton dripline to the neutron dripline. The total rates decrease as the neutron number increases due to the combined effect of gradual blocking of available final-state neutron levels and of decreased phase space. The ordering of single-particle levels determines when blocking becomes important. We show that the total capture rates thereby are sensitive to the evolution of nuclear structure along an isotope chain.Received: 28 January 2003, Revised: 7 March 2003, Published online: 4 June 2003PACS: 24.30.Cz Giant resonances - 23.40.-s Beta decay; double beta decay; electron and muon capture - 23.40.Hc Relation with nuclear matrix elements and nuclear structure     

Radiative capture of negative pions in deuterium

The transition rate for radiative capture of negative pions in deuterium is calculated with the Hamiltonian deduced from pion photoproduction data and with the transition amplitude obtained on the basis of the soft-pion theory. A large contribution to the physical amplitude from the intermediate states with the ρ-meson and nucleon-antinucleon pairs in the soft-pion approach brings both results into agreement within 5 %.     

Muon capture by He: the hyperfine effect

The hypertine effect for muon capture by ³He is calculated in a modified closure approximation as a function of g_p, the nucleon pseudoscalar form factor. It is found to be very sensitive to g_p.     

Physical applications of muon catalysis: Muon capture in hydrogen

Results of theoretical and experimental research on capture of negative muons in hydrogen are reported with an emphasis on the accompanying phenomenon of muon catalysis in hydrogen and subtleties of the experimental method. A conclusion is drawn that precise determination of the capture rate is important for refining the standard model.     

Molecular dynamics of two-dimensional gases with realistic potentials

Molecular dynamics calculations have mainly used hard-core interactions because of computational simplicity and increased speed. Algorithms for realistic intermolecular potentials have been used in studies of solids and liquids. By combining both techniques, an algorithm which can reasonably study dilute gases with realistic potentials has been achieved. The BoltzmannH-function is calculated for a hard-core and Lennard-Jones gas, and the latter is found to decrease more rapidly to equilibrium.Work supported in part by the National Science Foundation under Grant No. NSF-USDP GU-1598 and the U. S. Air Force Office of Scientific Research under Grant No. AF-AFOSR 1257-67.     

Muon capture in hydrogen: First MuCap results and future plans

We survey a new generation of high precision experiments on muon capture in hydrogen and on the positive muon lifetime, performed at the Paul Scherrer Institute (PSI). First results and plans for the future are presented.     

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.     

Muon capture by hydrogen and 3He

We present a new calculation of the capture rates, polarizations and asymmetry parameters of the final nucleus in the capture of muons by any $\text{spin}\text{-}\text{1}\text{2}\text{,}\text{isospin}\text{-}\text{1}\text{2}$ nucleus in the non-breakup channel. We treat nuclei as elementary particles and give explicitly the transition amplitude for any spin configuration. We apply our formulae to hydrogen and ³He, obtaining agreement with the experimental data.     

Towards a better understanding of O nuclear structure: Muon capture and radiative pion capture reactions

Muon capture and radiative pion capture reactions on ¹⁶O have been analysed with the aim to extract more information on the importance of higher components of the A = 16 nuclear ground and excited states. Good agreement with the experimental data for both reactions may be achieved if at least 2p2h components of the nuclear wave functions are taken into account. The positive parity excited states in ¹⁶N are shown to contribute 43 % to the radiative π⁻ capture but only ≈ 10 % to the muon capture rate.     

Muon transfer from ground state deuterium to helium nuclei and its temperature dependence

The energy and time distributions of the decay X-rays of excited, metastable, molecular (dμHe)*-resonances were measured. The comparison of the observed energy spectra with calculated ones suggests that decay from the rotational state J = 1 dominates at the investigated conditions. The muon transfer rates from ground state deuterium to the helium isotopes ³He and ⁴He at low temperatures were determined from the time distributions of these spectra. Additionally, the temperature dependence of the muon transfer rate was clearly established in deuterium / ⁴He mixtures. This revised version was published online in August 2006 with corrections to the Cover Date.     

μCR42β: Muon capture rates for double-beta decay

Gamma-rays following nuclear capture of negative muons in enriched ⁴⁸Ti, ⁷⁶Se, ¹⁰⁶Cd, as well as natural Se and Cd targets were measured. Time evolution of several gamma-lines allowed to deduce the total μ-capture rates in Ti, Se and Cd isotopes, which are compared to the Primakoff estimate. The data on the partial μ-capture rates will be used for more precise calculation of the 2β-NMEs of ⁴⁸Ca, ⁷⁶Se and ¹⁰⁶Cd. Presented by V. Egorov at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005. Partly supported by the Russian Foundation for Basic Research (grant 06-02-16587).     

Muon capture in Ar. The muon lifetime and yields of Cl isotopes

The time and energy spectra of γ rays, accompanying negative muon capture in a ⁴⁰Ar target, have been measured using Ge detectors. The results of measuring the muon lifetime in ⁴⁰Ar and yields of different Cl and S isotopes at μ capture are reported.