Pairing matrix elements and pairing gaps with bare, effective, and induced interactions
Abstract
The dependence on the singleparticle states of the pairing matrix elements of the Gogny force and of the bare lowmomentum nucleonnucleon potential v{sub lowk}designed so as to reproduce the lowenergy observables avoiding the use of a repulsive coreis studied for a typical finite, superfluid nucleus ({sup 120}Sn). It is found that the matrix elements of v{sub lowk} 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 lowk} 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 singleparticle 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 lowk}, being in agreement with {delta}{sub exp}=1.4 MeV. The exchange of lowlying collective surface vibrations among pairs of nucleons moving in timereversal states gives rise to an induced pairing interaction v{sub ind} peaked at e{sub F}. The interaction (v{sub lowk}+v{sub ind}) Z{sub {omega}} arising from the renormalization of the bare nucleonnucleon potential and of the singleparticle motion ({omega}mass and quasiparticle strength Z{sub {omega}}) associated with the particlevibration coupling mechanism, leads to amore »
 Authors:
 Departamento de Fisica Aplicada III, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, E41092 Sevilla (Spain)
 Dipartimento di Fisica, Universita degli Studi, via Celoria 16, I20133 Milan (Italy)
 (Italy)
 (Denmark)
 Institut de Physique Nucleaire, 15 rue Georges Clemenceau, F91406 Orsay Cedex (France)
 INFN Sezione di Milano, via Celoria 16, I20133 Milan (Italy)
 Departament d'Estructura i Constituents de la Materia, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E08028 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; NUCLEONNUCLEON POTENTIAL; NUCLEONS; PAIRING INTERACTIONS; RENORMALIZATION; SINGLEPARTICLE MODEL; SUPERFLUIDITY; TIN 120; VIBRATIONAL STATES
Citation Formats
Barranco, F., Bortignon, P.F., Colo, G., INFN Sezione di Milano, via Celoria 16, I20133 Milan, Broglia, R.A., INFN Sezione di Milano, via Celoria 16, I20133 Milan, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK20100 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, I20133 Milan, Broglia, R.A., INFN Sezione di Milano, via Celoria 16, I20133 Milan, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK20100 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, I20133 Milan, Broglia, R.A., INFN Sezione di Milano, via Celoria 16, I20133 Milan, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK20100 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, I20133 Milan and Broglia, R.A. and INFN Sezione di Milano, via Celoria 16, I20133 Milan and Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK20100 Copenhagen O and Schuck, P. and Vigezzi, E. and Vinas, X.},
abstractNote = {The dependence on the singleparticle states of the pairing matrix elements of the Gogny force and of the bare lowmomentum nucleonnucleon potential v{sub lowk}designed so as to reproduce the lowenergy observables avoiding the use of a repulsive coreis studied for a typical finite, superfluid nucleus ({sup 120}Sn). It is found that the matrix elements of v{sub lowk} 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 lowk} 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 singleparticle 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 lowk}, being in agreement with {delta}{sub exp}=1.4 MeV. The exchange of lowlying collective surface vibrations among pairs of nucleons moving in timereversal states gives rise to an induced pairing interaction v{sub ind} peaked at e{sub F}. The interaction (v{sub lowk}+v{sub ind}) Z{sub {omega}} arising from the renormalization of the bare nucleonnucleon potential and of the singleparticle motion ({omega}mass and quasiparticle strength Z{sub {omega}}) associated with the particlevibration 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 (lowenergy) 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}
}

The bare nucleonnucleon interaction is essential for the production of pair correlations in nuclei, but an important contribution also arises from the induced interaction resulting from the exchange of collective vibrations between nucleons moving in time reversal states close to the Fermi energy. The pairing field resulting from the summed interaction is strongly peaked at the nuclear surface. It is possible to reproduce the detailed spatial dependence of this field by using either a local approximation, which fully takes into account finite size effects, or a contact interaction, with parameters that are quite different from those commonly used in moremore »

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