# Quantum Monte Carlo formalism for dynamical pions and nucleons

## Abstract

In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schrodinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, a Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- National Science Foundation (NSF); USDOE Office of Science - Office of Nuclear Physics

- OSTI Identifier:
- 1595682

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. C, Nuclear Physics

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 3

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Madeira, Lucas, Lovato, Alessandro, Pederiva, Francesco, and Schmidt, Kevin E.
```*Quantum Monte Carlo formalism for dynamical pions and nucleons*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.98.034005.

```
Madeira, Lucas, Lovato, Alessandro, Pederiva, Francesco, & Schmidt, Kevin E.
```*Quantum Monte Carlo formalism for dynamical pions and nucleons*. United States. doi:10.1103/PhysRevC.98.034005.

```
Madeira, Lucas, Lovato, Alessandro, Pederiva, Francesco, and Schmidt, Kevin E. Thu .
"Quantum Monte Carlo formalism for dynamical pions and nucleons". United States. doi:10.1103/PhysRevC.98.034005.
```

```
@article{osti_1595682,
```

title = {Quantum Monte Carlo formalism for dynamical pions and nucleons},

author = {Madeira, Lucas and Lovato, Alessandro and Pederiva, Francesco and Schmidt, Kevin E.},

abstractNote = {In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schrodinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, a Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.},

doi = {10.1103/PhysRevC.98.034005},

journal = {Physical Review. C, Nuclear Physics},

number = 3,

volume = 98,

place = {United States},

year = {2018},

month = {9}

}

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