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Title: Quantum simulations of nuclei and nuclear pasta with the multiresolution adaptive numerical environment for scientific simulations

Abstract

Background: Neutron star and supernova matter at densities just below the nuclear matter saturation density is expected to form a lattice of exotic shapes. These so-called nuclear pasta phases are caused by Coulomb frustration. Their elastic and transport properties are believed to play an important role for thermal and magnetic field evolution, rotation, and oscillation of neutron stars. Furthermore, they can impact neutrino opacities in core-collapse supernovae. Purpose: In this work, we present proof-of-principle three-dimensional (3D) Skyrme Hartree-Fock (SHF) simulations of nuclear pasta with the Multi-resolution ADaptive Numerical Environment for Scientific Simulations (MADNESS). Methods: We perform benchmark studies of 16O, 208Pb , and 238U nuclear ground states and calculate binding energies via 3D SHF simulations. Results are compared with experimentally measured binding energies as well as with theoretically predicted values from an established SHF code. The nuclear pasta simulation is initialized in the so-called waffle geometry as obtained by the Indiana University Molecular Dynamics (IUMD) code. The size of the unit cell is 24 fm with an average density of about ρ = 0.05 fm -3 , proton fraction of Y p = 0.3 , and temperature of T = 0 MeV. Results: Our calculations reproduce the binding energies andmore » shapes of light and heavy nuclei with different geometries. For the pasta simulation, we find that the final geometry is very similar to the initial waffle state. We compare calculations with and without spin-orbit forces. We find that while subtle differences are present, the pasta phase remains in the waffle geometry. Conclusions: Within the MADNESS framework, we can successfully perform calculations of inhomogeneous nuclear matter. By using pasta configurations from IUMD it is possible to explore different geometries and test the impact of self-consistent calculations on the latter.« less

Authors:
; ; ; ;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1565499
DOE Contract Number:  
AC05-00OR22725; FG02-87ER40365; SC0008808
Resource Type:
Journal Article
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
Physics

Citation Formats

Sagert, I., Fann, G. I., Fattoyev, F. J., Postnikov, S., and Horowitz, C. J. Quantum simulations of nuclei and nuclear pasta with the multiresolution adaptive numerical environment for scientific simulations. United States: N. p., 2016. Web. doi:10.1103/physrevc.93.055801.
Sagert, I., Fann, G. I., Fattoyev, F. J., Postnikov, S., & Horowitz, C. J. Quantum simulations of nuclei and nuclear pasta with the multiresolution adaptive numerical environment for scientific simulations. United States. doi:10.1103/physrevc.93.055801.
Sagert, I., Fann, G. I., Fattoyev, F. J., Postnikov, S., and Horowitz, C. J. Sun . "Quantum simulations of nuclei and nuclear pasta with the multiresolution adaptive numerical environment for scientific simulations". United States. doi:10.1103/physrevc.93.055801.
@article{osti_1565499,
title = {Quantum simulations of nuclei and nuclear pasta with the multiresolution adaptive numerical environment for scientific simulations},
author = {Sagert, I. and Fann, G. I. and Fattoyev, F. J. and Postnikov, S. and Horowitz, C. J.},
abstractNote = {Background: Neutron star and supernova matter at densities just below the nuclear matter saturation density is expected to form a lattice of exotic shapes. These so-called nuclear pasta phases are caused by Coulomb frustration. Their elastic and transport properties are believed to play an important role for thermal and magnetic field evolution, rotation, and oscillation of neutron stars. Furthermore, they can impact neutrino opacities in core-collapse supernovae. Purpose: In this work, we present proof-of-principle three-dimensional (3D) Skyrme Hartree-Fock (SHF) simulations of nuclear pasta with the Multi-resolution ADaptive Numerical Environment for Scientific Simulations (MADNESS). Methods: We perform benchmark studies of 16O, 208Pb , and 238U nuclear ground states and calculate binding energies via 3D SHF simulations. Results are compared with experimentally measured binding energies as well as with theoretically predicted values from an established SHF code. The nuclear pasta simulation is initialized in the so-called waffle geometry as obtained by the Indiana University Molecular Dynamics (IUMD) code. The size of the unit cell is 24 fm with an average density of about ρ = 0.05 fm-3 , proton fraction of Yp = 0.3 , and temperature of T = 0 MeV. Results: Our calculations reproduce the binding energies and shapes of light and heavy nuclei with different geometries. For the pasta simulation, we find that the final geometry is very similar to the initial waffle state. We compare calculations with and without spin-orbit forces. We find that while subtle differences are present, the pasta phase remains in the waffle geometry. Conclusions: Within the MADNESS framework, we can successfully perform calculations of inhomogeneous nuclear matter. By using pasta configurations from IUMD it is possible to explore different geometries and test the impact of self-consistent calculations on the latter.},
doi = {10.1103/physrevc.93.055801},
journal = {Physical Review C},
issn = {2469-9985},
number = 5,
volume = 93,
place = {United States},
year = {2016},
month = {5}
}

Works referenced in this record:

Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure
journal, August 2014


Nuclear “pasta” formation
journal, December 2013


Structure of Matter below Nuclear Saturation Density
journal, June 1983


Appearance of the single gyroid network phase in “nuclear pasta” matter
journal, February 2015


The TDHF code Sky3D
journal, July 2014

  • Maruhn, J. A.; Reinhard, P. -G.; Stevenson, P. D.
  • Computer Physics Communications, Vol. 185, Issue 7
  • DOI: 10.1016/j.cpc.2014.04.008

Multiresolution quantum chemistry: Basic theory and initial applications
journal, December 2004

  • Harrison, Robert J.; Fann, George I.; Yanai, Takeshi
  • The Journal of Chemical Physics, Vol. 121, Issue 23
  • DOI: 10.1063/1.1791051

A comparative study of Hartree-Fock iteration techniques
journal, April 1982


Time-dependent Hartree-Fock approach to nuclear “pasta” at finite temperature
journal, May 2013


Adaptive Solution of Partial Differential Equations in Multiwavelet Bases
journal, October 2002

  • Alpert, B.; Beylkin, G.; Gines, D.
  • Journal of Computational Physics, Vol. 182, Issue 1
  • DOI: 10.1006/jcph.2002.7160

Nuclear matter in the crust of neutron stars
journal, August 2007


Dynamical response of the nuclear “pasta” in neutron star crusts
journal, September 2005


The Ame2003 atomic mass evaluation
journal, December 2003


Supernova mechanisms
journal, October 1990


Neutron star crusts
journal, January 1993


Neutron star matter
journal, November 1971


Disordered Nuclear Pasta, Magnetic Field Decay, and Crust Cooling in Neutron Stars
journal, January 2015


MADNESS applied to density functional theory in chemistry and nuclear physics
journal, July 2007


Variations on a theme by Skyrme: A systematic study of adjustments of model parameters
journal, March 2009


Explosion Mechanisms of Core-Collapse Supernovae
journal, November 2012


Sub-saturation phases of nuclear matter
journal, March 1985


Density as a constraint and the separation of internal excitation energy in TDHF
journal, September 1985

  • Cusson, R. Y.; Reinhard, P. -G.; Strayer, M. R.
  • Zeitschrift f�r Physik A Atoms and Nuclei, Vol. 320, Issue 3
  • DOI: 10.1007/BF01415725

Physics of Neutron Star Crusts
journal, December 2008

  • Chamel, Nicolas; Haensel, Pawel
  • Living Reviews in Relativity, Vol. 11, Issue 1
  • DOI: 10.12942/lrr-2008-10

Light clusters, pasta phases, and phase transitions in core-collapse supernova matter
journal, May 2015


Phase diagram of nuclear “pasta” and its uncertainties in supernova cores
journal, March 2008


Nuclear shapes in the inner crust of a neutron star
journal, August 1993


Nuclear “pasta” structures and the charge screening effect
journal, July 2005

  • Maruyama, Toshiki; Tatsumi, Toshitaka; Voskresensky, Dmitri N.
  • Physical Review C, Vol. 72, Issue 1
  • DOI: 10.1103/PhysRevC.72.015802

Liquid crystals in the mantles of neutron stars
journal, May 1998


Exploring the Nuclear Pasta Phase in Core-Collapse Supernova Matter
journal, October 2012


Application of the imaginary time step method to the solution of the static Hartree-Fock problem
journal, June 1980


Fast multiresolution methods for density functional theory in nuclear physics
journal, July 2009


A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
journal, January 1993

  • Alpert, Bradley K.
  • SIAM Journal on Mathematical Analysis, Vol. 24, Issue 1
  • DOI: 10.1137/0524016

The role of spin–orbit potential in nuclear prolate-shape dominance
journal, August 2011


An Overview of Wavelet Based Multiresolution Analyses
journal, September 1994

  • Jawerth, Björn; Sweldens, Wim
  • SIAM Review, Vol. 36, Issue 3
  • DOI: 10.1137/1036095

Crust-core coupling and r-mode damping in neutron stars: a toy model
journal, July 2001


Multiresolution computational chemistry
journal, January 2005

  • Harrison, Robert J.; Fann, George I.; Gan, Zhengting
  • Journal of Physics: Conference Series, Vol. 16
  • DOI: 10.1088/1742-6596/16/1/032

Hartree-Fock Calculations with Skyrme's Interaction. I. Spherical Nuclei
journal, March 1972


Pasta nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium
journal, June 2015


Formation of Nuclear “Pasta” in Supernovae
journal, September 2009


A highly resistive layer within the crust of X-ray pulsars limits their spin periods
journal, June 2013

  • Pons, José A.; Viganò, Daniele; Rea, Nanda
  • Nature Physics, Vol. 9, Issue 7
  • DOI: 10.1038/nphys2640

Simulation of Transitions between “Pasta” Phases in Dense Matter
journal, January 2005


Phase transitions in core-collapse supernova matter at sub-saturation densities
journal, December 2014


Nonuniform neutron-rich matter and coherent neutrino scattering
journal, December 2004


Finite size effects in neutron star and nuclear matter simulations
journal, January 2015


Self-consistent mean-field models for nuclear structure
journal, January 2003

  • Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard
  • Reviews of Modern Physics, Vol. 75, Issue 1
  • DOI: 10.1103/RevModPhys.75.121

Shape of Nuclei in the Crust of Neutron Star
journal, February 1984

  • Hashimoto, M. -a.; Seki, H.; Yamada, M.
  • Progress of Theoretical Physics, Vol. 71, Issue 2
  • DOI: 10.1143/PTP.71.320

Nuclear “waffles”
journal, November 2014


Neutrino-“pasta” scattering: The opacity of nonuniform neutron-rich matter
journal, April 2004


Structure of the inner crust of neutron stars: Crystal lattice or disordered phase?
journal, April 2002


Direct Urca process in a neutron star mantle
journal, June 2004


Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree–Fock and density functional theory
journal, August 2004

  • Yanai, Takeshi; Fann, George I.; Gan, Zhengting
  • The Journal of Chemical Physics, Vol. 121, Issue 7
  • DOI: 10.1063/1.1768161

Nuclear “pasta matter” for different proton fractions
journal, November 2014


Gyroid Phase in Nuclear Pasta
journal, September 2009


Shear viscosity and thermal conductivity of nuclear “pasta”
journal, September 2008


Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Super fluid Fermi Systems in Large Boxes
journal, December 2012


Upper limits on the observational effects of nuclear pasta in neutron stars: Effects of nuclear pasta in neutron stars
journal, October 2011


The Skyrme interaction in finite nuclei and nuclear matter
journal, April 2007