# Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables

## Abstract

The traditional approach to nuclear physics encodes phase shift information in a nucleon-nucleon (NN) potential, producing a nucleon-level interaction that captures the sub-GeV consequences of QCD. A further reduction to the nuclear scale is needed to produce an effective interaction for soft Hilbert spaces, such as those employed in the shell model. Here we describe an alternative construction of the effective interaction that is simple and quite precise, proceeding from the QCD scale directly to the nuclear scale. This eliminates the need for constructing and renormalizing the high-momentum NN potential. Instead, continuum phase shifts and mixing angles are used directly at the nuclear scale. The method exploits the analytic continuity in energy of HOBET (Harmonic-Oscillator-Based Effective Theory) to connect bound states to continuum solutions at specific energies. The procedure is systematic, cutoff independent, and convergent, yielding keV accuracy at NNLO or N^{3}LO, depending on the channel. Lepage plots are provided.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)

- OSTI Identifier:
- 1559062

- Alternate Identifier(s):
- OSTI ID: 1580933

- Grant/Contract Number:
- SC00046548; AC02-05CH11231; KB0301052; SC0015376

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 797 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Effective theory; Nucleon-nucleon interaction; Phase shifts

## Citation Formats

```
McElvain, K. S., and Haxton, W. C. Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables. Netherlands: N. p., 2019.
Web. doi:10.1016/j.physletb.2019.134880.
```

```
McElvain, K. S., & Haxton, W. C. Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables. Netherlands. https://doi.org/10.1016/j.physletb.2019.134880
```

```
McElvain, K. S., and Haxton, W. C. Tue .
"Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables". Netherlands. https://doi.org/10.1016/j.physletb.2019.134880.
```

```
@article{osti_1559062,
```

title = {Nuclear physics without high-momentum potentials: Constructing the nuclear effective interaction directly from scattering observables},

author = {McElvain, K. S. and Haxton, W. C.},

abstractNote = {The traditional approach to nuclear physics encodes phase shift information in a nucleon-nucleon (NN) potential, producing a nucleon-level interaction that captures the sub-GeV consequences of QCD. A further reduction to the nuclear scale is needed to produce an effective interaction for soft Hilbert spaces, such as those employed in the shell model. Here we describe an alternative construction of the effective interaction that is simple and quite precise, proceeding from the QCD scale directly to the nuclear scale. This eliminates the need for constructing and renormalizing the high-momentum NN potential. Instead, continuum phase shifts and mixing angles are used directly at the nuclear scale. The method exploits the analytic continuity in energy of HOBET (Harmonic-Oscillator-Based Effective Theory) to connect bound states to continuum solutions at specific energies. The procedure is systematic, cutoff independent, and convergent, yielding keV accuracy at NNLO or N3LO, depending on the channel. Lepage plots are provided.},

doi = {10.1016/j.physletb.2019.134880},

journal = {Physics Letters B},

number = C,

volume = 797,

place = {Netherlands},

year = {2019},

month = {10}

}

https://doi.org/10.1016/j.physletb.2019.134880

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
Nucleon-nucleon effective field theory without pions

journal, July 1999

- Chen, Jiunn-Wei; Rupak, Gautam; Savage, Martin J.
- Nuclear Physics A, Vol. 653, Issue 4

##
Sur la détermination des premiers états d'un système de fermions dans le cas dégénéré

journal, September 1958

- Bloch, Claude; Horowitz, Jules
- Nuclear Physics, Vol. 8

##
Variational calculations using low-momentum potentials with smooth cutoffs

journal, August 2006

- Bogner, S. K.; Furnstahl, R. J.
- Physics Letters B, Vol. 639, Issue 3-4

##
Form of the effective interaction in harmonic-oscillator-based effective theory

journal, March 2008

- Haxton, W. C.
- Physical Review C, Vol. 77, Issue 3

##
Accurate nucleon-nucleon potential with charge-independence breaking

journal, January 1995

- Wiringa, R. B.; Stoks, V. G. J.; Schiavilla, R.
- Physical Review C, Vol. 51, Issue 1

##
Is nuclear matter perturbative with low-momentum interactions?

journal, December 2005

- Bogner, S. K.; Schwenk, A.; Furnstahl, R. J.
- Nuclear Physics A, Vol. 763

##
The effective interaction of two nucleons in the s-d shell

journal, April 1980

- Lee, S. Y.; Suzuki, K.
- Physics Letters B, Vol. 91, Issue 2

##
Linked-Cluster Expansions for the Nuclear Many-Body Problem

journal, October 1967

- Brandow, Baird H.
- Reviews of Modern Physics, Vol. 39, Issue 4

##
Morphing the Shell Model into an Effective Theory

journal, June 2000

- Haxton, W. C.; Song, C. -L.
- Physical Review Letters, Vol. 84, Issue 24

##
Variational calculations of nuclei with low-momentum potentials

journal, January 2006

- Bogner, S. K.; Furnstahl, R. J.
- Physics Letters B, Vol. 632, Issue 4

##
Perturbative Effective Theory in an Oscillator Basis?

journal, October 2002

- Haxton, W. C.; Luu, T.
- Physical Review Letters, Vol. 89, Issue 18

##
Higher-order terms and the apparent non-convergence of the perturbation expansion for the effective interaction in finite nuclei

journal, June 1970

- Barrett, Bruce R.; Kirson, Michael W.
- Nuclear Physics A, Vol. 148, Issue 1

##
Recent developments in no-core shell-model calculations

journal, May 2009

- Navrátil, Petr; Quaglioni, Sofia; Stetcu, Ionel
- Journal of Physics G: Nuclear and Particle Physics, Vol. 36, Issue 8

##
Spin–orbit force from lattice QCD

journal, July 2014

- Murano, K.; Ishii, N.; Aoki, S.
- Physics Letters B, Vol. 735

##
Q UANTUM M ONTE C ARLO C ALCULATIONS OF L IGHT N UCLEI

journal, December 2001

- Pieper, Steven C.; Wiringa, R. B.
- Annual Review of Nuclear and Particle Science, Vol. 51, Issue 1

##
Projection operator formalisms and the nuclear shell model

journal, October 2005

- Jennings, B. K.
- Europhysics Letters (EPL), Vol. 72, Issue 2

##
Renormalization of Hamiltonians

journal, December 1993

- Głazek, Stanisław D.; Wilson, Kenneth G.
- Physical Review D, Vol. 48, Issue 12

##
Coupled-cluster computations of atomic nuclei

journal, September 2014

- Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M.
- Reports on Progress in Physics, Vol. 77, Issue 9

##
Effective interactions for the three-body problem

journal, July 2004

- Luu, T. C.; Bogner, S.; Haxton, W. C.
- Physical Review C, Vol. 70, Issue 1

##
Structure of finite nuclei and the free nucleon-nucleon interaction

journal, September 1966

- Kuo, T. T. S.; Brown, G. E.
- Nuclear Physics, Vol. 85, Issue 1

##
Third-order perturbation calculations in nuclear matter for realistic potentials

journal, November 1976

- Côté, Jean; Rouben, B.; De Tourreil, R.
- Nuclear Physics A, Vol. 273, Issue 2

##
Large-basis ** ***ab initio* no-core shell model and its application to ${}^{12}\mathbf{C}$

journal, October 2000

*ab initio*

- Navrátil, P.; Vary, J. P.; Barrett, B. R.
- Physical Review C, Vol. 62, Issue 5

##
Nucleon-nucleon scattering parameters in the limit of SU(3) flavor symmetry

journal, August 2013

- Beane, S. R.; Chang, E.; Cohen, S. D.
- Physical Review C, Vol. 88, Issue 2

##
Chiral potential renormalized in harmonic-oscillator space

journal, December 2016

- Yang, C. -J.
- Physical Review C, Vol. 94, Issue 6

##
Convergence of the Born series with low-momentum interactions

journal, July 2006

- Bogner, S. K.; Furnstahl, R. J.; Ramanan, S.
- Nuclear Physics A, Vol. 773, Issue 3-4

##
Computation of spectroscopic factors with the coupled-cluster method

journal, July 2010

- Jensen, Ø.; Hagen, G.; Papenbrock, T.
- Physical Review C, Vol. 82, Issue 1

##
Chiral effective field theory and nuclear forces

journal, June 2011

- Machleidt, R.; Entem, D. R.
- Physics Reports, Vol. 503, Issue 1

##
Similarity renormalization group for nucleon-nucleon interactions

journal, June 2007

- Bogner, S. K.; Furnstahl, R. J.; Perry, R. J.
- Physical Review C, Vol. 75, Issue 6

##
No-core shell model in an effective-field-theory framework

journal, September 2007

- Stetcu, I.; Barrett, B. R.; van Kolck, U.
- Physics Letters B, Vol. 653, Issue 2-4

##
Modern theory of nuclear forces

journal, December 2009

- Epelbaum, E.; Hammer, H. -W.; Meißner, Ulf-G.
- Reviews of Modern Physics, Vol. 81, Issue 4

##
Low-momentum interaction in few-nucleon systems

journal, December 2004

- Nogga, Andreas; Bogner, Scott K.; Schwenk, Achim
- Physical Review C, Vol. 70, Issue 6

##
Diffuse Surface Optical Model for Nucleon-Nuclei Scattering

journal, July 1954

- Woods, Roger D.; Saxon, David S.
- Physical Review, Vol. 95, Issue 2

##
Convergent Theory for Effective Interaction in Nuclei

journal, December 1980

- Suzuki, K.; Lee, S. Y.
- Progress of Theoretical Physics, Vol. 64, Issue 6

##
Coupled-cluster approach to nuclear physics

journal, May 2004

- Dean, D. J.; Hjorth-Jensen, M.
- Physical Review C, Vol. 69, Issue 5

##
Perturbative renormalization group for Hamiltonians

journal, April 1994

- Glazek, Stanislaw D.; Wilson, Kenneth G.
- Physical Review D, Vol. 49, Issue 8

##
Two-nucleon higher partial-wave scattering from lattice QCD

journal, February 2017

- Berkowitz, Evan; Kurth, Thorsten; Nicholson, Amy
- Physics Letters B, Vol. 765

##
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei

journal, March 2016

- Hergert, H.; Bogner, S. K.; Morris, T. D.
- Physics Reports, Vol. 621

##
Three-nucleon forces from chiral effective field theory

journal, December 2002

- Epelbaum, E.; Nogga, A.; Glöckle, W.
- Physical Review C, Vol. 66, Issue 6

##
Perturbation theory for the effective interaction in nuclei

journal, April 1973

- Schucan, Thomas H.; Weidenmüller, Hans A.
- Annals of Physics, Vol. 76, Issue 2

##
Decoupling in the similarity renormalization group for nucleon-nucleon forces

journal, July 2008

- Jurgenson, E. D.; Bogner, S. K.; Furnstahl, R. J.
- Physical Review C, Vol. 78, Issue 1

##
The canonical nuclear many-body problem as an effective theory

journal, July 2001

- Haxton, W. C.; Luu, T.
- Nuclear Physics A, Vol. 690, Issue 1-3

##
The effective interaction in nuclei and its perturbation expansion: An algebraic approach

journal, September 1972

- Schucan, T. H.; Weidenmüller, H. A.
- Annals of Physics, Vol. 73, Issue 1

##
High-precision, charge-dependent Bonn nucleon-nucleon potential

journal, January 2001

- Machleidt, R.
- Physical Review C, Vol. 63, Issue 2

##
Neutron-Proton Scattering with Spin-Orbit Coupling. I. General Expressions

journal, May 1952

- Blatt, John M.; Biedenharn, L. C.
- Physical Review, Vol. 86, Issue 3

##
Pion-less effective field theory for atomic nuclei and lattice nuclei

journal, November 2018

- Bansal, A.; Binder, S.; Ekström, A.
- Physical Review C, Vol. 98, Issue 5

##
Off-Shell Effects in Nuclear Matter

journal, February 1971

- Haftel, Michael I.; Tabakin, Frank
- Physical Review C, Vol. 3, Issue 2

##
Family of Hermitian low-momentum nucleon interactions with phase shift equivalence

journal, March 2004

- Holt, Jason D.; Kuo, T. T. S.; Brown, G. E.
- Physical Review C, Vol. 69, Issue 3

##
Two Pion versus σ-Meson Exchange Potentials

journal, January 2015

- Oshima, Sachiko; Fujita, Takehisa; Kanda, Naohiro
- Journal of Modern Physics, Vol. 06, Issue 07