Variational Calculation of the Ground State of ClosedShell Nuclei Up to $A$ = 40
Abstract
Variational calculations of groundstate properties of 4He, 16O and 40Ca are carried out employing realistic phenomenological two and threenucleon potentials. The trial wave function includes twoand threebody correlations acting on a product of singleparticle determinants. Expectation values are evaluated with a cluster expansion for the spinisospin dependent correlations considering up to fivebody cluster terms. The optimal wave function is obtained by minimizing the energy expectation value over a set of up to 20 parameters by means of a nonlinear optimization library. We present results for the binding energy, charge radius, point density, singlenucleon momentum distribution, charge form factor, and Coulomb sum rule. We find that the employed threenucleon interaction becomes repulsive for A ≥ 16. In 16O the inclusion of such a force provides a better description of the properties of the nucleus. In 40Ca instead, the repulsive behavior of the threebody interaction fails to reproduce experimental data for the charge radius and the charge form factor. We find that the highmomentum region of the momentum distributions, determined by the shortrange terms of nuclear correlations, exhibit a universal behavior independent of the particular nucleus. The comparison of the Coulomb sum rules for 4He, 16O, and 40Ca reported in this workmore »
 Authors:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Michigan State Univ., East Lansing, MI (United States)
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Publication Date:
 Research Org.:
 Argonne National Lab. (ANL), Argonne, IL (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26); USDOE Office of Science (SC). Nuclear Physics (NP) (SC26)
 OSTI Identifier:
 1378564
 Report Number(s):
 LAUR1723856
Journal ID: ISSN 05562813; 135687
 Grant/Contract Number:
 AC0206CH11357; AC5206NA25396; SC0013617; AC0205CH11231
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review. C, Nuclear Physics
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 2; Journal ID: ISSN 05562813
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Atomic and Nuclear Physics
Citation Formats
Lonardoni, Diego, Lovato, Alessandro, Pieper, Steven C., and Wiringa, Robert B. Variational Calculation of the Ground State of ClosedShell Nuclei Up to $A$ = 40. United States: N. p., 2017.
Web. doi:10.1103/PhysRevC.96.024326.
Lonardoni, Diego, Lovato, Alessandro, Pieper, Steven C., & Wiringa, Robert B. Variational Calculation of the Ground State of ClosedShell Nuclei Up to $A$ = 40. United States. doi:10.1103/PhysRevC.96.024326.
Lonardoni, Diego, Lovato, Alessandro, Pieper, Steven C., and Wiringa, Robert B. 2017.
"Variational Calculation of the Ground State of ClosedShell Nuclei Up to $A$ = 40". United States.
doi:10.1103/PhysRevC.96.024326.
@article{osti_1378564,
title = {Variational Calculation of the Ground State of ClosedShell Nuclei Up to $A$ = 40},
author = {Lonardoni, Diego and Lovato, Alessandro and Pieper, Steven C. and Wiringa, Robert B.},
abstractNote = {Variational calculations of groundstate properties of 4He, 16O and 40Ca are carried out employing realistic phenomenological two and threenucleon potentials. The trial wave function includes twoand threebody correlations acting on a product of singleparticle determinants. Expectation values are evaluated with a cluster expansion for the spinisospin dependent correlations considering up to fivebody cluster terms. The optimal wave function is obtained by minimizing the energy expectation value over a set of up to 20 parameters by means of a nonlinear optimization library. We present results for the binding energy, charge radius, point density, singlenucleon momentum distribution, charge form factor, and Coulomb sum rule. We find that the employed threenucleon interaction becomes repulsive for A ≥ 16. In 16O the inclusion of such a force provides a better description of the properties of the nucleus. In 40Ca instead, the repulsive behavior of the threebody interaction fails to reproduce experimental data for the charge radius and the charge form factor. We find that the highmomentum region of the momentum distributions, determined by the shortrange terms of nuclear correlations, exhibit a universal behavior independent of the particular nucleus. The comparison of the Coulomb sum rules for 4He, 16O, and 40Ca reported in this work will help elucidate inmedium modifications of the nucleon form factors.},
doi = {10.1103/PhysRevC.96.024326},
journal = {Physical Review. C, Nuclear Physics},
number = 2,
volume = 96,
place = {United States},
year = 2017,
month = 8
}

Theory of ground state correlations of closed shell nuclei: a density matrix formulation
A general theory of long range correlations in the ground state of a closed shell nucleus is outlined, using a number of ideas introduced or adumbrated, but not always successfully developed, in previous work of the authors and others. These include the following. (i) Any operator can be formally expressed as a series in particlehole (ph) excitation and destruction operators which should converge rapidly for a suitable choice of singleparticle basis, the closed shells. By means of these relations and with the help of sum rules all observables can be computed without the explicit use of wave functions. (ii) formore »