Muon capture in nuclei: an ab initio approach based on quantum 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.Comment: 6 pages, 1 figur

Muon Capture in Nuclei: An \u3ci\u3eab initio\u3c/i\u3e Approach Based on Green\u27s Function Monte Carlo Methods

An ab initio Green’s function Monte Carlo (GFMC) method is introduced for calculating total rates of muon weak capture in light nuclei with mass number A ≤ 12. As a first application of the method, we perform a calculation of the rate in 3H and 4He 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 π-and ρ-meson exchange, and N-to-Δ 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 4He rates obtained from bubble-chamber experiments (carried out over 50 years ago) prevent us from drawing any definite conclusions. No data exist for 3H, but results are compared to those of a recent Faddeev calculation as a validation of the present GFMC method

Magnetic structure of few-nucleon systems at high momentum transfers in a χ\chiEFT approach

The five low-energy constants (LECs) in the electromagnetic current derived in chiral effective field theory ($\chi$EFT) up to one loop are determined by a simultaneous fit to the $A\,$=$\,2$--3 nuclei magnetic moments and to the deuteron magnetic form factor and threshold electrodisintegration at backward angles over a wide range of momentum transfers. The resulting parametrization then yields predictions for the $^3$He/$^3$H magnetic form factors in excellent accord with the experimental values for momentum transfers ranging up to $\approx 0.8$ GeV/c, beyond the expected regime of validity of the $\chi$EFT approach. The calculations are based on last-generation two-nucleon interactions including high orders in the chiral expansion and derived by Entem, Macheleidt, and Nosyk [Phys.\ Rev.\ C {\bf 96}, 024004 (2017)] and by Piarulli {\it et al.} [Phys.\ Rev.\ C {\bf 94}, 054007 (2016)], using different $\chi$EFT formulations. In the $A\,$=$\,3$ calculations, (chiral) three-nucleon interactions are also accounted for. The model dependence resulting from these different formulations of the interactions is found to be mild for momentum transfer below $\approx0.8$ GeV/c. An analysis of the convergence of the chiral expansion is also provided.Comment: 12 pages, 8 figure

Coulomb Sum Rule for \u3csup\u3e4\u3c/sup\u3eHE

We determine the Coulomb sum for 4He using the world data on 4He(e,e′) and compare the results to calculations based on realistic interactions and including two-body components in the nuclear charge operator. We find good agreement between theory and experiment when using free-nucleon form factors. The apparent reduction of the in-medium GEp implied by IA-interpretation of the L/T-ratios measured in 4He(e,e′p) and 4He(e→,e′p→) is not confirmed

Ab initio calculation of the electromagnetic and neutral-weak response functions of 4He and 12C

Precise measurement of neutrino oscillations, and hence the determination of their masses demands a quantitative understanding of neutrino-nucleus interactions. To this aim, two-body meson-exchange currents have to be accounted for along within realistic models of nuclear dynamics. We summarize our progresses towards the construction of a consistent framework, based on quantum Monte Carlo methods and on the spectral function approach, that can be exploited to accurately describe neutrino interactions with atomic nuclei over the broad kinematical region covered by neutrino experiments.Comment: 8 pages, 4 figure, Proceedings of the 21st International Conference on Few-Body Problems in Physics, Chicago, Illinois, US

Partial Muon Capture Rates in A = 3 and A = 6 Nuclei with Chiral Effective Field Theory

Searches for neutrinoless double-β 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-β decays take place at momentum transfers on the order of 100MeV /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 3He and 6Li nuclei using variational and Green\u27s 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

Comparative Study of \u3csup\u3e6\u3c/sup\u3eHe β-Decay Based on Different Similarity-Renormalization-Group Evolved Chiral Interactions

We report on a study of the Gamow-Teller matrix element contributing to ⁶Heβ decay with similarity renormalization group (SRG) versions of momentum- and configuration-space two-nucleon interactions. These interactions are derived from two different formulations of chiral effective field theory (χEFT)—without and with the explicit inclusion of Δ isobars. We consider evolution parameters ΛSRG in the range between 1.2 and 2.0 fm−1 and, for the Δ-less case, also the unevolved (bare) interaction. The axial current contains one- and two-body terms, consistently derived at tree level (no loops) in the two distinct χEFT formulations we have adopted here. The ⁶He and ⁶Li ground-state wave functions are obtained from hyperspherical-harmonics (HH) solutions of the nuclear many-body problem. In A = 6 systems, the HH method is limited at present to treat only two-body interactions and non-SRG evolved currents. Our results exhibit a significant dependence on ΛSRG of the contributions associated with two-body currents, suggesting that a consistent SRG-evolution of these is needed in order to obtain reliable estimates. We also show that the contributions from one-pion-exchange currents depend strongly on the model (chiral) interactions and on the momentum- or configuration-space cutoffs used to regularize them. These results might prove helpful in clarifying the origin of the sign difference recently found in no-core-shell-model and quantum Monte Carlo calculations of the ⁶He Gamow-Teller matrix element

Magnetic Structure and Radiative Captures of Few-Nucleon Systems: Status and Prospects

We review the main ingredients for an ab-initio study of few-nucleon reactions of astrophysical interest within the chiral effective field theory approach, with particular attention to radiative captures relevant for Big Bang Nucleosynthesis and stellar evolution. We conclude with an outlook for ongoing and future work

Local chiral potentials and the structure of light nuclei

We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M.\ Piarulli {\it et al.}, Phys.\ Rev.\ C {\bf 91}, 024003 (2015)], and use them in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of $^3$H, $^3$He, $^4$He, $^6$He, and $^6$Li nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with $\Delta$-isobars in the intermediate states up to order $Q^3$ ($Q$ denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order $Q^4$. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0--125 MeV or 0--200 MeV, and to the deuteron binding energy and $nn$ singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.Comment: 29 pages, 3 figure

Reply to Comment on \u27Quasielastic Lepton Scattering and b=Back-to-Back Nucleons in the Short-Time Approximation\u27

We briefly review the concept of scaling and how it occurs in quasielastic electron and neutrino scattering from nuclei, and then the particular approach to scaling in the short-time approximation. We show that, whereas two-nucleon currents do significantly enhance the transverse electromagnetic response, they do not spoil scaling, but, in fact, enhance it. We provide scaling results obtained in the short-time approximation that verify this claim. The enhanced scaling, although obtained empirically, is not “accidental”—as claimed in [O. Benhar, Phys. Rev. C 105, 049801 (2022)]—but rather reflects quasielastic kinematics and the dominant role played by pion-exchange interactions and currents in the quasielastic regime