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Title: 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 » 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.« less

Authors:
 [1]; ;  [2];  [3];  [2];  [3];  [4];  [5];  [6];  [7]
  1. Departamento de Fisica Aplicada III, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, E-41092 Sevilla (Spain)
  2. Dipartimento di Fisica, Universita degli Studi, via Celoria 16, I-20133 Milan (Italy)
  3. (Italy)
  4. (Denmark)
  5. Institut de Physique Nucleaire, 15 rue Georges Clemenceau, F-91406 Orsay Cedex (France)
  6. INFN Sezione di Milano, via Celoria 16, I-20133 Milan (Italy)
  7. 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}
}