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Title: Superscaling in a dilute Fermi gas and the nucleon momentum distribution in nuclei

Abstract

The superscaling observed in inclusive electron scattering is described within the dilute Fermi gas model with interaction between the particles. The comparison with the relativistic Fermi gas (RFG) model without interaction shows an improvement in the explanation of the scaling function f({psi}{sup '}) in the region {psi}{sup '}<-1, where the RFG result is f({psi}{sup '})=0. It is found that the behavior of f({psi}{sup '}) for {psi}{sup '}<-1 depends on the particular form of the general power-law asymptotics of the momentum distribution n(k){approx}1/k{sup 4+m} at large k. The best agreement with the empirical scaling function is found for m{approx_equal}4.5 in agreement with the asymptotics of n(k) in the coherent density fluctuation model where m=4. Thus, superscaling gives information about the asymptotics of n(k) and the NN forces.

Authors:
;  [1];  [1];  [2];  [3];  [2]
  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784 (Bulgaria)
  2. (Spain)
  3. Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid (Spain)
Publication Date:
OSTI Identifier:
20995132
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevC.75.034319; (c) 2007 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; COMPARATIVE EVALUATIONS; DENSITY; DISTRIBUTION; ELECTRON-NUCLEON INTERACTIONS; ELECTRONS; FERMI GAS; FERMI GAS MODEL; FLUCTUATIONS; NUCLEAR FORCES; NUCLEI; NUCLEONS; RELATIVISTIC RANGE; SCALING

Citation Formats

Antonov, A. N., Ivanov, M. V., Gaidarov, M. K., Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Guerra, E. Moya de, and Departamento de Fisica Atomica, Molecular y Nuclear, Facultad de Ciencias Fisicas, Universidad Complutense de Madrid, E-28040 Madrid. Superscaling in a dilute Fermi gas and the nucleon momentum distribution in nuclei. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.034319.
Antonov, A. N., Ivanov, M. V., Gaidarov, M. K., Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Guerra, E. Moya de, & Departamento de Fisica Atomica, Molecular y Nuclear, Facultad de Ciencias Fisicas, Universidad Complutense de Madrid, E-28040 Madrid. Superscaling in a dilute Fermi gas and the nucleon momentum distribution in nuclei. United States. doi:10.1103/PHYSREVC.75.034319.
Antonov, A. N., Ivanov, M. V., Gaidarov, M. K., Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Guerra, E. Moya de, and Departamento de Fisica Atomica, Molecular y Nuclear, Facultad de Ciencias Fisicas, Universidad Complutense de Madrid, E-28040 Madrid. Thu . "Superscaling in a dilute Fermi gas and the nucleon momentum distribution in nuclei". United States. doi:10.1103/PHYSREVC.75.034319.
@article{osti_20995132,
title = {Superscaling in a dilute Fermi gas and the nucleon momentum distribution in nuclei},
author = {Antonov, A. N. and Ivanov, M. V. and Gaidarov, M. K. and Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid and Guerra, E. Moya de and Departamento de Fisica Atomica, Molecular y Nuclear, Facultad de Ciencias Fisicas, Universidad Complutense de Madrid, E-28040 Madrid},
abstractNote = {The superscaling observed in inclusive electron scattering is described within the dilute Fermi gas model with interaction between the particles. The comparison with the relativistic Fermi gas (RFG) model without interaction shows an improvement in the explanation of the scaling function f({psi}{sup '}) in the region {psi}{sup '}<-1, where the RFG result is f({psi}{sup '})=0. It is found that the behavior of f({psi}{sup '}) for {psi}{sup '}<-1 depends on the particular form of the general power-law asymptotics of the momentum distribution n(k){approx}1/k{sup 4+m} at large k. The best agreement with the empirical scaling function is found for m{approx_equal}4.5 in agreement with the asymptotics of n(k) in the coherent density fluctuation model where m=4. Thus, superscaling gives information about the asymptotics of n(k) and the NN forces.},
doi = {10.1103/PHYSREVC.75.034319},
journal = {Physical Review. C, Nuclear Physics},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • The scaling functions f({psi}{sup '}) and F(y) from the {psi}{sup '}- and y-scaling analyses of inclusive electron scattering from nuclei are explored within the coherent density fluctuation model (CDFM). In addition to the CDFM formulation in which the local density distribution is used, we introduce a new equivalent formulation of the CDFM based on the one-body nucleon momentum distribution (NMD). Special attention is paid to the different ways in which the excitation energy of the residual system is taken into account in y and {psi}{sup '} scaling. Both functions, f({psi}{sup '}) and F(y), are calculated using different NMDs and comparedmore » with the experimental data for a wide range of nuclei. The good description of the data for y<0 and {psi}{sup '}<0 (including {psi}{sup '}<-1) makes it possible to show the sensitivity of the calculated scaling functions to the peculiarities of the NMDs in different regions of momenta. It is concluded that the existing data on {psi}{sup '} and y scaling are informative for NMDs at momenta not larger than 2.0-2.5 fm{sup -1}. The CDFM allows us to study simultaneously and on the same footing the role of both basic quantities--the momentum and density distributions--for the description of scaling and superscaling phenomena in nuclei.« less
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  • The dependence upon momentum k and upon energy E of the self-energy of a dilute Fermi gas is studied up to terms of order (k/sub F/ c)/sup 2/, where k/sub F/ denotes the Fermi momentum and c is the positive scattering length. Algebraic expressions are derived for the imaginary part W (k;E) of the self-energy in the whole (k,E) plane. They are compared with a conjecture recently made by Orland and Schaeffer in their analysis of single-particle states in nuclei. The contributions of core polarization and of ground state correlations to the real part V (k;E) of the self-energy aremore » calculated with the help of subtracted dispersion relations which connect them with W (k;E'). Algebraic expressions are derived for the momentum distribution in the correlated ground state. It is shown that the effective mass of a quasiparticle with momentum k is equal to the bare particle mass at k=0 and reaches a local maximum for k close to k/sub F/. This maximum is ascribed to the dependence of V (k;E) upon E, which is described in terms of an E mass. We compute the contributions of core polarization and of ground state correlations to this E mass. The dependence of V (k;E) upon k reflects the nonlocality of the self-energy. It is characterized by a k mass that we also calculate. These results shed light on some nuclear matter properties and on the meaningfulness and limitation of nuclear matter calculations that have recently been performed in the framework of the Brueckner-Hartree-Fock approximation.« less