# Corrections to nucleon capture cross sections computed in truncated Hilbert spaces

## Abstract

Nucleon capture cross sections enter various astrophysical processes. Here, the measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are sensitive to the long-distance asymptotics of the wave functions. A theoretical foundation for estimating and correcting errors introduced in capture cross sections due to Hilbert space truncation has so far been lacking. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and they also open the way for the use of *ab initio* many-body wave functions represented in finite Hilbert spaces in precision calculations of nucleon capture on heavier nuclei.

- Authors:

- Univ. of Tennessee, Knoxville, TN (United States)
- Chalmers Univ. of Technology, Goteborg (Sweden)
- Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1460244

- Alternate Identifier(s):
- OSTI ID: 1345439

- Grant/Contract Number:
- AC05-00OR22725; FG02-96ER40963; SC0008499

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review C

- Additional Journal Information:
- Journal Volume: 95; 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

```
Acharya, B., Ekstrom, Andreas, Odell, Daniel M., Papenbrock, Thomas F., and Platter, Lucas J.
```*Corrections to nucleon capture cross sections computed in truncated Hilbert spaces*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevC.95.031301.

```
Acharya, B., Ekstrom, Andreas, Odell, Daniel M., Papenbrock, Thomas F., & Platter, Lucas J.
```*Corrections to nucleon capture cross sections computed in truncated Hilbert spaces*. United States. doi:10.1103/PhysRevC.95.031301.

```
Acharya, B., Ekstrom, Andreas, Odell, Daniel M., Papenbrock, Thomas F., and Platter, Lucas J. Wed .
"Corrections to nucleon capture cross sections computed in truncated Hilbert spaces". United States.
doi:10.1103/PhysRevC.95.031301. https://www.osti.gov/servlets/purl/1460244.
```

```
@article{osti_1460244,
```

title = {Corrections to nucleon capture cross sections computed in truncated Hilbert spaces},

author = {Acharya, B. and Ekstrom, Andreas and Odell, Daniel M. and Papenbrock, Thomas F. and Platter, Lucas J.},

abstractNote = {Nucleon capture cross sections enter various astrophysical processes. Here, the measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are sensitive to the long-distance asymptotics of the wave functions. A theoretical foundation for estimating and correcting errors introduced in capture cross sections due to Hilbert space truncation has so far been lacking. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and they also open the way for the use of ab initio many-body wave functions represented in finite Hilbert spaces in precision calculations of nucleon capture on heavier nuclei.},

doi = {10.1103/PhysRevC.95.031301},

journal = {Physical Review C},

number = 3,

volume = 95,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}