Muon Capture Rates Research Articles

Nuclear many-body effects on particle emission following muon capture on Si28 and Ca40

Background: Muon captures on nuclei have provided us with plenty of knowledge of nuclear properties. Recently, this reaction attracts attention in electronics, because charged particle emissions following muon capture on silicon become to trigger non-negligible soft errors in memory devices.Purpose: To date, there is no theoretical framework based on the nuclear structure that describes a muon capture reaction followed by particle emissions comprehensively. The purpose of this work is to develop a new method that considers the nuclear many-body correlation for the accurate understanding of the soft errors in memory devices.Method: We combined the second Tamm-Dancoff approximation that is used to estimate muon capture rates with the two-component exciton model, the model describing particle emission from the pre-equilibrium state. For particle evaporation from the compound state, the Hauser-Feshbach statistical models were applied. We chose $^{28}\mathrm{Si}$ and $^{40}\mathrm{Ca}$ to check the performance of the framework.Result: We paid attention to the muon capture rates, the particle emission spectra, and the multiplicities that have a close interrelation with each other. We found that the nuclear many-body correlations including two-particle two-hole excitations is a key to explaining them simultaneously.Conclusion: The present study showed that the combination of the microscopic approach of muon capture and the two-component exciton model of particle emission is an effective tool to describe particle emission following the muon captures, giving the nuclear structure information additionally. For a finer understanding of particle emission following muon capture and a validation of the present framework, further experimental studies on particle emission spectra are highly expected.

Muon capture on deuteron using local chiral potentials

The muon capture reaction μ− + d → n + n + νμ in the doublet hyperfine state is studied using nuclear potentials and consistent currents derived in the chiral effective field theory, which are local and expressed in coordinate space (the so-called Norfolk models). Only the largest contribution due to the 1S0nn scattering state is considered. Particular attention is given to the estimate of theoretical uncertainty, for which four sources have been identified: 1) the model dependence, 2) the chiral-order convergence for the weak nuclear current, 3) the uncertainty in the single-nucleon axial form factor, and 4) the numerical technique adopted to solve the bound and scattering A = 2 systems. This last source of uncertainty has turned out to be essentially negligible. For the 1S0 doublet muon capture rate ΓD(S01), we obtain ΓD(S01)=255.8(0.6)(4.4)(2.9) s−1, where the three errors come from the first three sources of uncertainty. The value for ΓD(S01) obtained within this local chiral framework is compared with previous calculations and found in very good agreement.

Total Capture Rate of Negative Muons in 24Mg

Total Capture Rate of Negative Muons in 24Mg

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.

Search for Muon-to-Electron Conversion with the COMET Experiment

Charged Lepton Flavor Violation is expected to be one of the most powerful tools to reveal physics beyond the Standard Model. The COMET experiment aims to search for the neutrinoless coherent transition of a muon into an electron in the field of a nucleus. Muon-to-electron conversion has never been observed, and can be, and would be, clear evidence of new physics if discovered. The experimental sensitivity of this process, defined as the ratio of the muon-to-electron conversion rate to the total muon capture rate, is expected to be significantly improved by a factor of 100 to 10,000 in the coming decade. The COMET experiment will take place at J-PARC with single event sensitivities of the orders of 10−15 and 10−17 in Phase-I and Phase-II, respectively. The ambitious goal of the COMET experiment is achieved by realizing a high-quality pulsed beam and an unprecedentedly powerful muon source together with an excellent detector apparatus that can tolerate a severe radiation environment. The construction of a new beam line, superconducting magnets, detectors and electronics is in progress towards the forthcoming Phase-I experiment. We present the experimental methods, sensitivity and backgrounds along with recent status and prospects.

Machine-learning-based inversion of nuclear responses

A microscopic description of the interaction of atomic nuclei with external electroweak probes is required for elucidating aspects of short-range nuclear dynamics and for the correct interpretation of neutrino oscillation experiments. Nuclear quantum Monte Carlo methods infer the nuclear electroweak response functions from their Laplace transforms. Inverting the Laplace transform is a notoriously ill-posed problem; and Bayesian techniques, such as maximum entropy, are typically used to reconstruct the original response functions in the quasielastic region. In this work, we present a physics-informed artificial neural network architecture suitable for approximating the inverse of the Laplace transform. Utilizing simulated, albeit realistic, electromagnetic response functions, we show that this physics-informed artificial neural network outperforms maximum entropy in both the low-energy transfer and the quasielastic regions, thereby allowing for robust calculations of electron scattering and neutrino scattering on nuclei and inclusive muon capture rates.

Exploiting Dirac equations solution for exact integral calculations in processes of muonic atoms

Precise muon wave functions are calculated by solving the Dirac equations within a method based on modern neural networks and stochastic optimization techniques. The reduced radial wave functions (up and bottom) of a bound muon in muonic atoms are then given as linear combinations of the well behaved sigmoid functions. As concrete applications, the known muonnucleus overlap integrals, which determine the structure and evolution of muonic atoms (twobody quantum systems bound together due to the fundamental electromagnetic interactions), may accurately be calculated. In this work, the muon-nucleus integrals for a set of nuclei including the 28Si and 64Zn entering the ordinary muon capture rates are exactly obtained through numerical integrations using Gauss integration algorithms.

Theoretical study of Nb isotope productions by muon capture reaction on Mo100

The isotope $ {}^{99} \rm{Mo} $, the generator of $ {}^{99m} \rm{Tc} $ used for diagnostic imaging, is supplied by extracting from fission fragments of highly enriched uranium in reactors. However, a reactor-free production method of $ {}^{99} \rm{Mo} $ is searched over the world from the point of view of nuclear proliferation. Recently, $ {}^{99} \rm{Mo} $ production through a muon capture reaction was proposed and it was found that about $ 50 \, \% $ of $ {}^{100} \rm{Mo} $ turned into $ {}^{99} \rm{Mo} $ through $ {}^{100} \rm{Mo} \left( \mu^-, n \right) $ reaction [arXiv:1908.08166]. However, the detailed physical process of the muon capture reaction is not completely understood. We, therefore, study the muon capture reaction of $ ^{100} \rm{Mo} $ by a theoretical approach. We used the proton-neutron QRPA to calculate the muon capture rate. The muon wave function is calculated with considering the electronic distribution of the atom and the nuclear charge distribution. The particle evaporation process from the daughter nucleus is calculated by a statistical model. From the model calculation, about $ 38 \, \% $ of $ {}^{100} \rm{Mo} $ is converted to $ {}^{99} \rm{Mo} $ through the muon capture reaction, which is in a reasonable agreement with the experimental data. It is revealed that negative parity states, especially $ 1^- $ state, play an important role in $ {}^{100} \rm{Mo} \left( \mu^-, n \right) {}^{99} \rm{Nb} $. The feasibility of $ {}^{99} \rm{Mo} $ production by the muon capture reaction is also discussed. Isotope production by the muon capture reaction strongly depends on the nuclear structure.

Muon capture rates: Evaluation within the quasiparticle random phase approximation

The Quasiparticle Random Phase Approximation (QRPA) is used in evaluation of the total muon capture ratesfor the final nuclei participating in double-beta decay. Several variants of the method are used, depending on the size of the single particle model space used, or treatment of the initial bound muon wave function. The resulting capture rates are all reasonably close to each other. In particular, the variant that appears to be most realistic, results in rates in good agreement with the experimental values. There is no necessity for an empirical quenching of the axial current coupling constant $g_A$. Its standard value $g_A$ = 1.27 seems to be adequate.

Systematic study of the muon-nucleus overlap integrals for various processes in muonic atoms

As it is known, the bound muon of a muonic atom can participate in many electroweak processes as the allowed channels of the ordinary ^""-capture by the atomic nucleus, μ~ •+- (A, Z) -» (A,Z — l) + νβ, and the muon decay in orbit, μ~ -» e~ + υμ ·+- ve, as well as the exotic channels of the muon-to-electron, μ~ + (A, Z) —> (.A, Z)* + e~, and muon-to-positron, μ~ + (A, Ζ) -» (A, Ζ — 2) + e+, conversions. The latter reactions have not been seen by experiments up to now, but they are predicted by various extensions of the standard model (they violate the flavor and/or lepton quantum numbers). For all the above muonic processes, the muon-nucleus overlap integrals are necessary in order to calculate the relevant rates. These integrals can be evaluated if, in addition to the nuclear states, the wave function of the bound muon (also that of the outgoinglepton) are known. In the present work, we perform precise calculations of the muon (and electron/positron) wave functions for both the Schrödinger and Dirac equations. We use modern neural network techniques to overcome the difficulties arising from the finite size of the nucléon and nuclear Coulomb potential. As some applications, the obtained muonnucleus integrals for various muonic atoms are going to be used for evaluating exclusive muon-capture rates and muon to electron/positron conversion branching ratios.

Detailed calculations for muon capture rates within the quasi-particle RPA

Detailed calculations for bound muon capture in complex nuclei are performed by employing the quasi particle random phase approximation (QRPA). The required bound muon wavefunctions for the large and the small components of the Dirac muon wavefunctions are obtained by using the genetic algorithm approach. We ob- tained contributions for 2p muon orbit; that is to say wavefunctions for atomic ex- cited state of the muonic atoms in nucleus 28Si. As a byproduct the above method give the corresponding energies to these wavefunctions which are compared with those of other methods. Our goal is to use the method developed recently by Laganke, Zinner and Vogel and our advantageous numerical approach to obtain state by state calculations of the muon capture rates within the QRPA.

Nuclear muon capture rates by using relativistic muon wavefunctions

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Muon capture in nuclei: An ab initio approach based on Green's function Monte Carlo methods

An ab initio quantum Monte Carlo method is introduced for calculating total rates of muon weak capture in light nuclei with mass number $A \leq 12$. As a first application of the method, we perform a calculation of the rate in $^4$He in a dynamical framework based on realistic two- and three-nucleon interactions and realistic nuclear charge-changing weak currents. The currents include one- and two-body terms induced by $\pi$- and $\rho$-meson exchange, and $N$-to-$\Delta$ excitation, and are constrained to reproduce the empirical value of the Gamow-Teller matrix element in tritium. We investigate the sensitivity of theoretical predictions to current parametrizations of the nucleon axial and induced pseudoscalar form factors as well as to two-body contributions in the weak currents. The large uncertainties in the measured values obtained from bubble-chamber experiments (carried out over 50 years ago) prevent us from drawing any definite conclusions.

Muon-capture strength functions in intermediate nuclei of 0νββ decays

Capture rates of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of current experimental interest are computed. The corresponding OMC (capture-rate) strength functions have been analyzed in terms of multipole decompositions. The computed low-energy OMC-rate distribution to $^{76}\mathrm{As}$ is compared with the available data of Zinatulina et al. [Phys. Rev. C 99, 024327 (2019)]. The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The participant nuclear wave functions are obtained in extended no-core single-particle model spaces using the spherical version of proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. The Hamiltonian parameters are taken from our earlier work [Jokiniemi et al., Phys. Rev. C 98, 024608 (2018)], except for $A=82$ nuclei for which the parameters were determined in this work. Both the OMC and $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decays involve momentum exchanges of the order of 100 MeV and thus future measurements of the OMC strength functions for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ daughter nuclei help trace the in-medium renormalization of the weak axial couplings with the aim to improve the accuracy of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements.

Effect of Siegert's theorem on low-energy neutrino-nucleus interactions

We examine the importance of conserving the vector current in calculating low-energy neutrino-nucleus interactions by implicitly invoking Siegert's Theorem in describing the vector transverse electric current. We find that at low neutrino energies (E? <50 MeV), Siegert's Theorem can change neutrino cross sections for normal-parity non-spin-flip excitations by about a factor of two.The same is true of muon capture rates. At higher neutrino energies the effect of Siegert's Theorem diminishes, and by about 100 MeV the effect is very small.

Value of the Axial-Vector Coupling Strength in β and ββ Decays: A Review

In this review the quenching of the weak axial-vector coupling strength, $g_{\rm A}$, is discussed in nuclear $\beta$ and double-$\beta$ decays. On one hand, the nuclear-medium and nuclear many-body effects are separated, and on the other hand the quenching is discussed from the points of view of different many-body methods and different $\beta$-decay and double-$\beta$-decay processes. Both the historical background and the present status are reviewed and contrasted against each other. The theoretical considerations are tied to performed and planned measurements, and possible new measurements are urged, whenever relevant and doable. Relation of the quenching problem to the measurements of charge-exchange reactions and muon-capture rates is pointed out.

Detailed description of exclusive muon capture rates using realistic two-body forces

Starting from state-by-state calculations of exclusive rates of the ordinary muon capture (OMC), we evaluated total muon-capture rates for a set of light- and medium-weight nuclear isotopes. We employed a version of the proton-neutron quasi-particle random phase approximation (pn-QRPA, for short) which uses as realistic nuclear forces the Bonn C-D one boson exchange potential. Special attention was paid on the percentage contribution to the total muon-capture rate of specific low-spin multipolarities resulting by summing over the corresponding multipole transitions. The nuclear method used offers the possibility of estimating separately the individual contributions to the total and partial rates of the polar-vector and axial-vector components of the weak interaction Hamiltonian for each accessible final state of the daughter nucleus. One of our main goals is to provide a reliable description of the charge changing transitions matrix elements entering the description of other similar semileptonic nuclear processes like the charged-current neutrino-nucleus reactions, the electron capture on nuclei, the single \b{eta}-decay mode, etc., which play important role in currently interesting laboratory and astrophysical applications like the neutrino-detection through lepton- nucleus interaction probes, and neutrino-nucleosynthesis. Such results can be also be useful in various ongoing muon-capture experiments at PSI, Fermilab, JPARC and RCNP.

MuSun: muon capture on the deuteron

The goal of the MuSun experiment at PSI is to measure the rate of muon capture on the deuteron with a precision of 1.5%. This rate will be used to fix the low-energy constant that describes the two-nucleon weak axial current in Chiral perturbation theory. It will therefore calibrate evaluations of solar proton-proton fusion and neutrino-deuteron scattering(SNO experiment). MuSun forms part of the systematic program to achieve a new level of precision in confronting the theories of weak interactions, QCD and few body physics. MuSun inherits some of the well developed techniques and apparatus from a successful measurement of the rate for muon capture on the proton, the MuCap experiment, also performed at PSI. As in MuCap, MuSun uses a TPC as an active target. To optimize the molecular kinetics, its ultra-pure deuterium gas is kept at 31K. The status of the hardware and details of the data analysis for a high statistics run taken in 2013 will be presented.

MuSun: muon capture on the deuteron

The goal of the MuSun experiment at PSI is to measure the rate of muon capture on the deuteron with a precision of 1.5%. This rate will be used to fix the low-energy constant that describes the two-nucleon weak axial current in Chiral perturbation theory. It will therefore calibrate evaluations of solar proton-proton fusion and neutrino-deuteron scattering(SNO experiment). MuSun forms part of the systematic program to achieve a new level of precision in confronting the theories of weak interactions, QCD and few body physics. MuSun inherits some of the well developed techniques and apparatus from a successful measurement of the rate for muon capture on the proton, the MuCap experiment, also performed at PSI. As in MuCap, MuSun uses a TPC as an active target. To optimize the molecular kinetics, its ultra-pure deuterium gas is kept at 31K. The status of the hardware and details of the data analysis for a high statistics run taken in 2013 will be presented.

Muon capture on the deuteron and the neutron-neutron scattering length

We study the capture rate in the doublet hyperfine initial state for the muon capture reaction $\mu^- + \,^2{\rm H} \rightarrow \nu_\mu + n + n$ ($\Gamma^D$) and the total capture rate for the reaction $ \mu^- + \,^3{\rm He} \rightarrow \nu_\mu + \,^3{\rm H}$ ($\Gamma_0$). We investigate whether $\Gamma^D$ and $\Gamma_0$ could be sensitive to the $nn$ $S$-wave scattering length ($a_{nn}$). To this aim, we consider nuclear potentials and weak currents derived within $\chi$EFT. We employ the N3LO chiral potential with cutoff $\Lambda$=500 MeV, but the low-energy constant (LEC) determining $a_{nn}$ is varied so as to obtain $a_{nn}$=-18.95 (the present empirical value), -16.0, -22.0, and +18.22 fm. The last value leads to a $nn$ bound state with a binding energy of 139 keV. The LECs $c_D$ and $c_E$, present in the three-nucleon potential and axial-vector current, are fitted to reproduce the $A=3$ binding energies and the triton Gamow-Teller matrix element. The capture rate $\Gamma^D$ is found to be 399(3) s$^{-1}$ for $a_{nn}$=-18.95 and -16.0 fm; and 400(3) s$^{-1}$ for $a_{nn}$=-22.0 fm. For $a_{nn}$=+18.22 fm, we obtain 275(3) s$^{-1}$ (135(3) s$^{-1}$), when the final $nn$ system is unbound (bound). The rate $\Gamma_0$ is found to be 1494(15), 1491(16), 1488(18), and 1475(16) s$^{-1}$ for $a_{nn}$=-18.95, -16.0, -22.0, and +18.22 fm, respectively. The theoretical uncertainties are due to the fitting procedure and radiative corrections. Our results seem to exclude the possibility of constraining a negative $a_{nn}$ with an uncertainty of less than $\sim \pm$ 3 fm through an accurate determination of the muon capture rates, but the uncertainty on the present empirical value will not complicate the interpretation of the (forth-coming) experimental results for $\Gamma^D$. Finally, a comparison with the already available experimental data discourages the possibility of a bound $nn$ state.