# Decoupling of spurious deeply bound states with the similarity renormalization group

## Abstract

The similarity renormalization group (SRG) is a continuous series of unitary transformations that can be implemented as a flow equation. When the relative kinetic energy (T{sub rel}) is used in the SRG generator, nuclear structure calculations have shown greatly improved convergence with basis size because of the decoupling of high-energy and low-energy physics. However this generator can sometimes be problematic. A test case is provided by a study of initial interactions from chiral effective field theories with large cutoffs, which can lead to spurious deeply bound states. We would like the SRG to decouple these from the physical shallow bound states. However, with T{sub rel} the high- and low-energy bound states are not decoupled in the usual sense. Replacing T{sub rel} by the momentum-space diagonal of the Hamiltonian (H{sub d}) in the SRG generator does produce decoupling, such that the shallow states are in the low-momentum region and the deeply bound states are at higher momentum. The flow toward universal low-momentum interactions is also restored.

- Authors:

- Department of Physics, Ohio State University, Columbus, Ohio 43210 (United States)

- Publication Date:

- OSTI Identifier:
- 21499468

- Resource Type:
- Journal Article

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

- Additional Journal Information:
- Journal Volume: 83; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevC.83.034005; (c) 2011 American Institute of Physics; Journal ID: ISSN 0556-2813

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CHIRALITY; COMPUTERIZED SIMULATION; CONVERGENCE; DECOUPLING; FIELD THEORIES; HAMILTONIANS; INTERACTIONS; KINETIC ENERGY; NUCLEAR STRUCTURE; RENORMALIZATION; TRANSFORMATIONS; ENERGY; MATHEMATICAL OPERATORS; PARTICLE PROPERTIES; QUANTUM OPERATORS; SIMULATION

### Citation Formats

```
Wendt, K. A., Furnstahl, R. J., and Perry, R. J..
```*Decoupling of spurious deeply bound states with the similarity renormalization group*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVC.83.034005.

```
Wendt, K. A., Furnstahl, R. J., & Perry, R. J..
```*Decoupling of spurious deeply bound states with the similarity renormalization group*. United States. doi:10.1103/PHYSREVC.83.034005.

```
Wendt, K. A., Furnstahl, R. J., and Perry, R. J.. Tue .
"Decoupling of spurious deeply bound states with the similarity renormalization group". United States. doi:10.1103/PHYSREVC.83.034005.
```

```
@article{osti_21499468,
```

title = {Decoupling of spurious deeply bound states with the similarity renormalization group},

author = {Wendt, K. A. and Furnstahl, R. J. and Perry, R. J.},

abstractNote = {The similarity renormalization group (SRG) is a continuous series of unitary transformations that can be implemented as a flow equation. When the relative kinetic energy (T{sub rel}) is used in the SRG generator, nuclear structure calculations have shown greatly improved convergence with basis size because of the decoupling of high-energy and low-energy physics. However this generator can sometimes be problematic. A test case is provided by a study of initial interactions from chiral effective field theories with large cutoffs, which can lead to spurious deeply bound states. We would like the SRG to decouple these from the physical shallow bound states. However, with T{sub rel} the high- and low-energy bound states are not decoupled in the usual sense. Replacing T{sub rel} by the momentum-space diagonal of the Hamiltonian (H{sub d}) in the SRG generator does produce decoupling, such that the shallow states are in the low-momentum region and the deeply bound states are at higher momentum. The flow toward universal low-momentum interactions is also restored.},

doi = {10.1103/PHYSREVC.83.034005},

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

issn = {0556-2813},

number = 3,

volume = 83,

place = {United States},

year = {2011},

month = {3}

}