## This content will become publicly available on September 12, 2020

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

## Abstract

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 $^3$$\textbf{H}$$ and $^4$$\textbf{He}$$ 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 $π$- 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 $^4$$\textbf{He}$$ rates obtained from bubble-chamber experiments (carried out over 50 years ago) prevent us from drawing any definite conclusions. No data exist for $^3$$\textbf{H}$$, but results are compared to those of a recent Faddeev calculation as a validation of the present GFMC method.

- Authors:

- INFN-TIFPA Trento Inst. of Fundamental Physics and Applications, Trento (Italy); Argonne National Lab. (ANL), Argonne, IL (United States). Physics Division
- Argonne National Lab. (ANL), Argonne, IL (United States). Physics Division; Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States). Theoretical Physics Dept.
- Old Dominion Univ., Norfolk, VA (United States). Dept. of Physics; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1566122

- Grant/Contract Number:
- AC02-06CH11357

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review C

- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 3; Journal ID: ISSN 2469-9985

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Lovato, A., Rocco, N., and Schiavilla, R. Muon capture in nuclei: An ab initio approach based on Green's function Monte Carlo methods. United States: N. p., 2019.
Web. doi:10.1103/PhysRevC.100.035502.
```

```
Lovato, A., Rocco, N., & Schiavilla, R. Muon capture in nuclei: An ab initio approach based on Green's function Monte Carlo methods. United States. doi:10.1103/PhysRevC.100.035502.
```

```
Lovato, A., Rocco, N., and Schiavilla, R. Thu .
"Muon capture in nuclei: An ab initio approach based on Green's function Monte Carlo methods". United States. doi:10.1103/PhysRevC.100.035502.
```

```
@article{osti_1566122,
```

title = {Muon capture in nuclei: An ab initio approach based on Green's function Monte Carlo methods},

author = {Lovato, A. and Rocco, N. and Schiavilla, R.},

abstractNote = {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 $^3$$\textbf{H}$ and $^4$$\textbf{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 $π$- 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 $^4$$\textbf{He}$ rates obtained from bubble-chamber experiments (carried out over 50 years ago) prevent us from drawing any definite conclusions. No data exist for $^3$$\textbf{H}$, but results are compared to those of a recent Faddeev calculation as a validation of the present GFMC method.},

doi = {10.1103/PhysRevC.100.035502},

journal = {Physical Review C},

number = 3,

volume = 100,

place = {United States},

year = {2019},

month = {9}

}