# Pairing matrix elements and pairing gaps with bare, effective, and induced interactions

## Abstract

The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential v{sub low-k}--designed so as to reproduce the low-energy observables avoiding the use of a repulsive core--is studied for a typical finite, superfluid nucleus ({sup 120}Sn). It is found that the matrix elements of v{sub low-k} follow closely those of v{sub Gogny} on a wide range of energy values around the Fermi energy e{sub F}, those associated with v{sub low-k} being less attractive. This result explains the fact that around e{sub F} the pairing gap {delta}{sub Gogny} associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective k mass m{sub k}{approx_equal}0.7 m) is a factor of about 2 larger than {delta}{sub low-k}, being in agreement with {delta}{sub exp}=1.4 MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction v{sub ind} peaked at e{sub F}. The interaction (v{sub low-k}+v{sub ind}) Z{sub {omega}} arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion ({omega}-mass and quasiparticle strength Z{sub {omega}}) associated with the particle-vibration coupling mechanism, leads to amore »

- Authors:

- Departamento de Fisica Aplicada III, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, E-41092 Sevilla (Spain)
- Dipartimento di Fisica, Universita degli Studi, via Celoria 16, I-20133 Milan (Italy)
- (Italy)
- (Denmark)
- Institut de Physique Nucleaire, 15 rue Georges Clemenceau, F-91406 Orsay Cedex (France)
- INFN Sezione di Milano, via Celoria 16, I-20133 Milan (Italy)
- Departament d'Estructura i Constituents de la Materia, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain)

- Publication Date:

- OSTI Identifier:
- 20699119

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevC.72.054314; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; COUPLING; ENERGY GAP; MATRIX ELEMENTS; MEV RANGE; NUCLEAR FORCES; NUCLEAR STRUCTURE; NUCLEON-NUCLEON POTENTIAL; NUCLEONS; PAIRING INTERACTIONS; RENORMALIZATION; SINGLE-PARTICLE MODEL; SUPERFLUIDITY; TIN 120; VIBRATIONAL STATES

### Citation Formats

```
Barranco, F., Bortignon, P.F., Colo, G., INFN Sezione di Milano, via Celoria 16, I-20133 Milan, Broglia, R.A., INFN Sezione di Milano, via Celoria 16, I-20133 Milan, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-20100 Copenhagen O, Schuck, P., Vigezzi, E., and Vinas, X..
```*Pairing matrix elements and pairing gaps with bare, effective, and induced interactions*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevC.72.054314.

```
Barranco, F., Bortignon, P.F., Colo, G., INFN Sezione di Milano, via Celoria 16, I-20133 Milan, Broglia, R.A., INFN Sezione di Milano, via Celoria 16, I-20133 Milan, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-20100 Copenhagen O, Schuck, P., Vigezzi, E., & Vinas, X..
```*Pairing matrix elements and pairing gaps with bare, effective, and induced interactions*. United States. doi:10.1103/PhysRevC.72.054314.

```
Barranco, F., Bortignon, P.F., Colo, G., INFN Sezione di Milano, via Celoria 16, I-20133 Milan, Broglia, R.A., INFN Sezione di Milano, via Celoria 16, I-20133 Milan, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-20100 Copenhagen O, Schuck, P., Vigezzi, E., and Vinas, X.. Tue .
"Pairing matrix elements and pairing gaps with bare, effective, and induced interactions". United States.
doi:10.1103/PhysRevC.72.054314.
```

```
@article{osti_20699119,
```

title = {Pairing matrix elements and pairing gaps with bare, effective, and induced interactions},

author = {Barranco, F. and Bortignon, P.F. and Colo, G. and INFN Sezione di Milano, via Celoria 16, I-20133 Milan and Broglia, R.A. and INFN Sezione di Milano, via Celoria 16, I-20133 Milan and Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-20100 Copenhagen O and Schuck, P. and Vigezzi, E. and Vinas, X.},

abstractNote = {The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential v{sub low-k}--designed so as to reproduce the low-energy observables avoiding the use of a repulsive core--is studied for a typical finite, superfluid nucleus ({sup 120}Sn). It is found that the matrix elements of v{sub low-k} follow closely those of v{sub Gogny} on a wide range of energy values around the Fermi energy e{sub F}, those associated with v{sub low-k} being less attractive. This result explains the fact that around e{sub F} the pairing gap {delta}{sub Gogny} associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective k mass m{sub k}{approx_equal}0.7 m) is a factor of about 2 larger than {delta}{sub low-k}, being in agreement with {delta}{sub exp}=1.4 MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction v{sub ind} peaked at e{sub F}. The interaction (v{sub low-k}+v{sub ind}) Z{sub {omega}} arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion ({omega}-mass and quasiparticle strength Z{sub {omega}}) associated with the particle-vibration coupling mechanism, leads to a value of the pairing gap at the Fermi energy {delta}{sub ren} that accounts for the experimental value. An important question that remains to be studied quantitatively is to what extent {delta}{sub Gogny}, which depends on average parameters, and {delta}{sub ren}, which explicitly depends on the parameters describing the (low-energy) nuclear structure, display or not a similar isotopic dependence and whether this dependence is borne out by the data.},

doi = {10.1103/PhysRevC.72.054314},

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

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}