# Large-scale exact diagonalizations reveal low-momentum scales of nuclei

## Abstract

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. In this paper, we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding $${10}^{10}$$ on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for $$^{6}\mathrm{Li}$$ in model spaces up to $${N}_{\mathrm{max}}=22$$ and to reveal the $$^{4}\mathrm{He}$$+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Finally, using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.

- Authors:

- Chalmers Univ. of Technology, Göteborg (Sweden). Dept. of Physics
- Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Physics Division

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); Swedish Foundation for International Cooperation in Research and Higher Education (STINT)

- OSTI Identifier:
- 1471876

- Alternate Identifier(s):
- OSTI ID: 1430150

- Grant/Contract Number:
- AC05-00OR22725; FG02-96ER40963; SC0008499; SC0018223; IG2012-5158

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review C

- Additional Journal Information:
- Journal Volume: 97; 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; few-body systems; nuclear many-body theory; nuclear structure & decays; ab initio calculations

### Citation Formats

```
Forssén, C., Carlsson, B. D., Johansson, H. T., Sääf, D., Bansal, A., Hagen, G., and Papenbrock, T..
```*Large-scale exact diagonalizations reveal low-momentum scales of nuclei*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.97.034328.

```
Forssén, C., Carlsson, B. D., Johansson, H. T., Sääf, D., Bansal, A., Hagen, G., & Papenbrock, T..
```*Large-scale exact diagonalizations reveal low-momentum scales of nuclei*. United States. doi:10.1103/PhysRevC.97.034328.

```
Forssén, C., Carlsson, B. D., Johansson, H. T., Sääf, D., Bansal, A., Hagen, G., and Papenbrock, T.. Wed .
"Large-scale exact diagonalizations reveal low-momentum scales of nuclei". United States.
doi:10.1103/PhysRevC.97.034328.
```

```
@article{osti_1471876,
```

title = {Large-scale exact diagonalizations reveal low-momentum scales of nuclei},

author = {Forssén, C. and Carlsson, B. D. and Johansson, H. T. and Sääf, D. and Bansal, A. and Hagen, G. and Papenbrock, T.},

abstractNote = {Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. In this paper, we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding ${10}^{10}$ on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for $^{6}\mathrm{Li}$ in model spaces up to ${N}_{\mathrm{max}}=22$ and to reveal the $^{4}\mathrm{He}$+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Finally, using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.},

doi = {10.1103/PhysRevC.97.034328},

journal = {Physical Review C},

number = 3,

volume = 97,

place = {United States},

year = {Wed Mar 28 00:00:00 EDT 2018},

month = {Wed Mar 28 00:00:00 EDT 2018}

}