Nuclear Theory·nucl-th

Thursday·June 17, 2021

9 papers—3 primary·6 cross-listed

01
Causality and stability analysis of first-order field redefinition in relativistic hydrodynamics from kinetic theory
Sukanya Mitra
In this work, the causality and stability of a first-order relativistic dissipative hydrodynamic theory, that redefines the hydrodynamic fields from a first principle microscopic estimation, have been analyzed. A generic approach of gradient expansion for solving the relativistic transport equation has been adopted using the Chapman-Enskog iterative method. Next, the momentum dependent relaxation time approximation (MDRTA) has been employed to quantify the collision term for analytical estimation of the field correction coefficients from kinetic theory. At linear regime, in local rest frame the dispersion relations are observed to produce a causal propagating mode. However, the acausality and instability reappear when a boosted background is considered for linear analysis. These facts point out relevant aspects regarding the methodology of extracting the causal and stable first order hydrodynamics from kinetic theory and indicate the appropriate approach to construct a valid first order theory with proper justification.
nucl-thPRC(2022)·11 citations
02
Shape of atomic nuclei in heavy ion collisions
Jiangyong Jia🇺🇸
In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flow $v_{n}$ are linearly related to the strength of the multi-pole shape of the distribution of nucleons in the transverse plane $ε_{n}$ , $v_{n} \propto ε_{n}$ . The $ε_{n}$ , for $n = 1, 2, 3, 4$ , are sensitive to the shape of the colliding ions, characterized by the quadrupole $β_{2}$ , octupole $β_{3}$ and hexadecapole $β_{4}$ deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, $⟨ ε_{n}^{2} ⟩ = a_{n}^{'} + b_{n}^{'} β_{n}^{2}$ , for events in a fixed centrality. The $⟨ ε_{1}^{2} ⟩$ has a contribution from $β_{3}$ and $β_{4}$ , and $⟨ ε_{3}^{2} ⟩$ from $β_{4}$ . In the ultra-central collisions, there are little cross contributions between $β_{2}$ and $ε_{3}$ and between $β_{3}$ and $ε_{2}$ , but clear cross contributions are present in non-central collisions. Additionally, $⟨ ε_{n}^{2} ⟩$ are insensitive to non-axial shape parameters such as the triaxiality. This is good news because the measurements of $v_{2}$ , $v_{3}$ and $v_{4}$ can be used to constrain simultaneously the $β_{2}$ , $β_{3}$ , and $β_{4}$ values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical $a_{n}^{'}$ , to obtain simple equation that relates the $β_{n}$ of the two species. This opens up the possibility to map the shape of the atomic nuclei at a timescale ( $< 1 0^{- 24}$ s) much shorter than probed by low-energy nuclear structure physics ( $< 1 0^{- 21}$ s), which ultimately may provide information complementary to those obtained in the nuclear structure experiments.
nucl-thhep-phnucl-exPRC(2022)·122 citations
03
Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $s d$ -shell
Adrián Sánchez-Fernández · Benjamin Bally · Tomás R. Rodríguez
We study the ability of variational approaches based on self-consistent mean-field and beyond-mean-field methods to reproduce exact energies and electromagnetic properties of the nuclei defined within the $s d$ -shell valence space using the non-trivial USD Hamiltonian. In particular, Hartree-Fock-Bogoliubov (HFB), variation after particle-number projection (VAPNP) and projected generator coordinate methods (PGCM) are compared to exact solutions {obtained by} the full diagonalization of the Hamiltonian. We analyze the role played by the proton-neutron ( $p n$ ) mixing as well as the quadrupole and pairing degrees of freedom (including both isoscalar and isovector channels) in the description of the spectra of even-even, even-odd and odd-odd nuclei in the whole $s d$ -shell.
nucl-thPRC(2021)·24 citations

Affiliations

first authorsco-authorsvia INSPIRE

Causality and stability analysis of first-order field redefinition in relativistic hydrodynamics from kinetic theory

Shape of atomic nuclei in heavy ion collisions

Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the sd-shell

Affiliations

Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $s d$ -shell