## Two-nucleon emission in neutrino and electron scattering from nuclei: The modified convolution approximation

## Abstract

In this paper, the theoretical formalism of inclusive lepton-nucleus scattering in the two-nucleon emission channel is discussed in the context of a simplified approach, the modified convolution approximation. This allows one to write the 2p2h responses of the relativistic Fermi gas as a folding integral of two 1p1h responses with the energies and momenta transferred to each nucleon. The idea behind this method is to introduce different average momenta for the two initial nucleons in the matrix elements of the two-body current, with the innovation that they depend on the transferred energies and momenta. This method treats exactly the two-body phase space kinematics, and reduces the formulae of the response functions from seven-dimensional integrals over momenta to much simpler three-dimensional ones. The applicability of the method is checked by comparing with the full results within a model of electroweak meson-exchange currents. Finally, the predictions are accurate enough, especially in the low-energy threshold region where the average momentum approximation works the best.

- Authors:

- Universidad de Granada (Spain)
- Università di Torino and INFN, Torino (Italy)
- Universidad de Sevill (Spain)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1511587

- Grant/Contract Number:
- FC02-94ER40818

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Annals of Physics

- Additional Journal Information:
- Journal Volume: 388; Journal Issue: C; Journal ID: ISSN 0003-4916

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; neutrino scattering; meson-exchange currents; 2p2h

### Citation Formats

```
Ruiz Simo, I., Amaro, J. E., Barbaro, M. B., Caballero, J. A., Megias, G. D., and Donnelly, T. W. Two-nucleon emission in neutrino and electron scattering from nuclei: The modified convolution approximation. United States: N. p., 2017.
Web. doi:10.1016/j.aop.2017.11.029.
```

```
Ruiz Simo, I., Amaro, J. E., Barbaro, M. B., Caballero, J. A., Megias, G. D., & Donnelly, T. W. Two-nucleon emission in neutrino and electron scattering from nuclei: The modified convolution approximation. United States. doi:10.1016/j.aop.2017.11.029.
```

```
Ruiz Simo, I., Amaro, J. E., Barbaro, M. B., Caballero, J. A., Megias, G. D., and Donnelly, T. W. Sat .
"Two-nucleon emission in neutrino and electron scattering from nuclei: The modified convolution approximation". United States. doi:10.1016/j.aop.2017.11.029. https://www.osti.gov/servlets/purl/1511587.
```

```
@article{osti_1511587,
```

title = {Two-nucleon emission in neutrino and electron scattering from nuclei: The modified convolution approximation},

author = {Ruiz Simo, I. and Amaro, J. E. and Barbaro, M. B. and Caballero, J. A. and Megias, G. D. and Donnelly, T. W.},

abstractNote = {In this paper, the theoretical formalism of inclusive lepton-nucleus scattering in the two-nucleon emission channel is discussed in the context of a simplified approach, the modified convolution approximation. This allows one to write the 2p2h responses of the relativistic Fermi gas as a folding integral of two 1p1h responses with the energies and momenta transferred to each nucleon. The idea behind this method is to introduce different average momenta for the two initial nucleons in the matrix elements of the two-body current, with the innovation that they depend on the transferred energies and momenta. This method treats exactly the two-body phase space kinematics, and reduces the formulae of the response functions from seven-dimensional integrals over momenta to much simpler three-dimensional ones. The applicability of the method is checked by comparing with the full results within a model of electroweak meson-exchange currents. Finally, the predictions are accurate enough, especially in the low-energy threshold region where the average momentum approximation works the best.},

doi = {10.1016/j.aop.2017.11.029},

journal = {Annals of Physics},

number = C,

volume = 388,

place = {United States},

year = {2017},

month = {12}

}