Nuclear Theory·nucl-th

Thursday·November 21, 2019

13 papers—8 primary·5 cross-listed

01
[Submitted on 19 Nov 2019]
Exact T=0 Eigenstates of the Isovector Pairing Hamiltonian
M. Sambataro · N. Sandulescu
We derive the exact $T = 0$ seniority-zero eigenstates of the isovector pairing Hamiltonian for an even number of protons and neutrons. Nucleons are supposed to be distributed over a set of non-degenerate levels and to interact through a pairing force with constant strength. We show that these eigenstates (and among them, in particular, the ground state) are linear superpositions of products of $T = 1$ collective pairs arranged into $T = 0$ quartets. This grouping of protons and neutrons first into $T = 1$ collective pairs and then into $T = 0$ quartets represents the distinctive feature of these eigenstates. This work highlights, for the first time on the grounds of the analytic expression of its eigenstates, the key role played by the isovector pairing force in the phenomenon of nuclear quarteting.
Comments:
10 pages, 4 figures
Subjects:
Nuclear Theory (nucl-th)
arXiv:
1911.08482 [pdf]
J.Phys.G(2020)·6 citations
02
[Submitted on 19 Nov 2019]
Application of Effective Field Theory in Nuclear Physics
Xiaojun Yao🇺🇸
The production of heavy quarkonium in heavy ion collisions has been used as an important probe of the quark-gluon plasma (QGP). Due to the plasma screening effect, the color attraction between the heavy quark antiquark pair inside a quarkonium is significantly suppressed at high temperature and thus no bound states can exist, i.e., they "melt". In addition, a bound heavy quark antiquark pair can dissociate if enough energy is transferred to it in a dynamical process inside the plasma. So one would expect the production of quarkonium to be considerably suppressed in heavy ion collisions. However, experimental measurements have shown that a large amount of quarkonia survive the evolution inside the high temperature plasma. It is realized that the in-medium recombination of unbound heavy quark pairs into quarkonium is as crucial as the melting and dissociation. Thus, phenomenological studies have to account for static screening, dissociation and recombination in a consistent way. But recombination is less understood theoretically than the melting and dissociation. Many studies using semi-classical transport equations model the recombination effect from the consideration of detailed balance at thermal equilibrium. However, these studies cannot explain how the system of quarkonium reaches equilibrium and estimate the time scale of the thermalization. Recently, another approach based on the open quantum system formalism started being used. In this framework, one solves a quantum evolution for in-medium quarkonium. Dissociation and recombination are accounted for consistently. However, the connection between the semi-classical transport equation and the quantum evolution is not clear. In this dissertation, I will try to address the issues raised above. As a warm-up project, I will first study a similar problem: $α$ - $α$ scattering at the $^{8}$ Be resonance inside an $e^{-} e^{+} γ$ plasma. By applying pionless effective field theory and thermal field theory, I will show how the plasma screening effect modifies the $^{8}$ Be resonance energy and width. I will discuss the need to use the open quantum system formalism when studying the time evolution of a system embedded inside a plasma. Then I will use effective field theory of QCD and the open quantum system formalism to derive a Lindblad equation for bound and unbound heavy quark antiquark pairs inside a weakly-coupled QGP. Under the Markovian approximation and the assumption of weak coupling between the system and the environment, the Lindblad equation will be shown to turn to a Boltzmann transport equation if a Wigner transform is applied to the open system density matrix. These assumptions will be justified by using the separation of scales, which is assumed in the construction of effective field theory. I will show the scattering amplitudes that contribute to the collision terms in the Boltzmann equation are gauge invariant and infrared safe. By coupling the transport equation of quarkonium with those of open heavy flavors and solving them using Monte Carlo simulations, I will demonstrate how the system of bound and unbound heavy quark antiquark pairs reaches detailed balance and equilibrium inside the QGP. Phenomenologically, my calculations can describe the experimental data on bottomonium production. Finally I will extend the framework to study the in-medium evolution of heavy diquarks and estimate the production rate of the doubly charmed baryon $Ξ_{cc}^{++}$ in heavy ion collisions.
Comments:
Ph.D dissertation, 235 pages, 56 figures, 2 tables; based on 1602.07298, 1609.00383, 1709.03529, 1801.02652, 1807.06199, 1811.07027, 1811.09644, 1812.02238
Subjects:
Nuclear Theory (nucl-th); High Energy Physics — Phenomenology (hep-ph)
arXiv:
1911.08500 [pdf]
ProQuest Number: 13882375 (2019)·3 citations
03
[Submitted on 17 Nov 2019]
Transport coefficients for the hot quark-gluon plasma at finite chemical potential $μ_{B}$
Olga Soloveva🇩🇪 · Pierre Moreau🇺🇸 · Elena Bratkovskaya🇩🇪
We calculate transport coefficients of the quark-gluon plasma (QGP) within the dynamical quasiparticle model (DQPM) by explicitly computing the parton interaction rates as a function of temperature $T$ and baryon chemical potential $μ_{B}$ on the basis of the DQPM couplings and partonic propagators. The latter are extracted from lattice QCD by matching the equation of state, entropy density and energy density at $μ_{B}$ = 0. For baryon chemical potentials $0 \leq μ_{B} \leq 500 M e V$ we employ a scaling Ansatz for the effective coupling which was shown before to lead to thermodynamic consistent results in this range. We compute the ratio of the shear and bulk viscosities to the entropy density, i.e. $η / s$ and $ζ / s$ , the electric conductivity $σ_{0} / T$ as well as the baryon diffusion coefficient $κ_{B}$ and compare to related approaches from the literature. We find that the ratios $η / s$ and $ζ / s$ as well as $σ_{0} / T$ are in accord with the results from lattice QCD at $μ_{B}$ =0 and only weakly depend on the ratio $T / T_{c} (μ_{B})$ where $T_{c} (μ_{B})$ denotes the critical temperature at finite baryon chemical potential.
Comments:
12 pages, 7 figures. arXiv admin note: text overlap with arXiv:1903.10257
Subjects:
Nuclear Theory (nucl-th); High Energy Physics — Phenomenology (hep-ph)
arXiv:
1911.08547 [pdf]
PRC(2020)·67 citations
04
[Submitted on 20 Nov 2019]
Cluster correlation and nuclear vorticity in low-lying $1^{-}$ states of $^{24}$ Mg
Yohei Chiba · Yoshiko Kanada-En'yo · Yuki Shikata
We investigated cluster correlation and nuclear voricity in low-lying $1^{-}$ states of $^{24}$ Mg within antisymmetrized molecular dynamics framework. We found that the toroidal and compressional dipole modes separately appear as the $K = 1$ and $K = 0$ states. The $1^{-}$ ( $K = 1$ ) state is the toroidal dipole state with the strong nuclear vorticity but no prominent cluster structure, and the $1^{-}$ ( $K = 0$ ) state is the compressional dipole state having enhanced cluster structure but has the weaker vorticity.
Subjects:
Nuclear Theory (nucl-th)
arXiv:
1911.08734 [pdf]
PRC(2021)·6 citations
05
[Submitted on 20 Nov 2019]
Time-evolution of net-baryon density fluctuations across the QCD critical region
Marcus Bluhm🇫🇷 · Marlene Nahrgang (SUBATECH, Nantes & EMMI, Darmstadt)🇫🇷
We investigate the role of a finite surface tension during the time-evolution of fluctuations in the net-baryon density. The systems in this study undergo a temperature evolution across the phase transition in the critical region of the QCD phase diagram. The occuring non-equilibrium effects are discussed.
Comments:
Proceedings for the 18th International Conference on Strangeness in Quark Matter (SQM 2019), June 10-15, 2019, Bari, Italy
Subjects:
Nuclear Theory (nucl-th); High Energy Physics — Phenomenology (hep-ph)
arXiv:
1911.08911 [pdf]
Springer Proc.Phys.(2020)·8 citations
06
[Submitted on 20 Nov 2019]
Isospectral scattering for relativistic equivalent Hamiltonians on a coarse momentum grid
María Gómez-Rocha · Enrique Ruiz Arriola
The scattering phase-shifts are invariant under unitary transformations of the Hamiltonian. However, the numerical solution of the scattering problem that requires to discretize the continuum violates this phase-shift invariance among unitarily equivalent Hamiltonians. We extend a newly found prescription for the calculation of phase shifts which relies only on the eigenvalues of a relativistic Hamiltonian and its corresponding Chebyshev angle shift. We illustrate this procedure numerically considering $π π$ , $π N$ and $N N$ elastic interactions which turns out to be competitive even for small number of grid points.
Comments:
18 pages, 18 figures
Subjects:
Nuclear Theory (nucl-th)
arXiv:
1911.08990 [pdf]
PRD(2020)·5 citations
07
[Submitted on 18 Nov 2019]
A dispersive optical model analysis of $^{208}$ Pb generating a neutron-skin prediction beyond the mean field
M. C. Atkinson · M. H. Mahzoon · M. A. Keim · B. A. Bordelon · C. D. Pruitt · R. J. Charity · W. H. Dickhoff
A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in $^{208}$ Pb. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, the charge distribution, and the binding energy have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator derived from these self-energies, we have determined the charge and matter distributions in $^{208}$ Pb. The predicted spectroscopic factors are consistent with results from the $(e, e^{'} p)$ reaction and inelastic-electron-scattering data to very high spin states. Sensible results for the high-momentum content of neutrons and protons are obtained with protons appearing more correlated, in agreement with experiment and \textit{ab initio} calculations of asymmetric matter. A neutron skin of $0.25 \pm 0.05$ fm is deduced. An analysis of several nuclei leads to the conclusion that finite-size effects play a non-negligible role in the formation of the neutron skin in finite nuclei.
Comments:
15 pages, 14 figures. arXiv admin note: text overlap with arXiv:1808.08895
Subjects:
Nuclear Theory (nucl-th)
arXiv:
1911.09020 [pdf]
PRC(2020)·46 citations
08
[Submitted on 14 Nov 2019]
Asymptotics of the nucleus ground-state and single-hole nature of the bound states of the nuclei
Franco Capuzzi
We consider nuclei composed of nucleons which interact via two-body potentials decreasing exponentially at infinity. Protons and neutrons are not distinguished in order to simplify notations. The basic result is the rigorous mathematical proof that the bound eigenstates of the nuclei belong to the subspace $P H$ spanned by the states of a single hole in the ground state $ψ_{0}$ of the parent nucleus with an extra nucleon, as in the uncorrelated models. This follows from the exponential decay of $ψ_{0}$ when a nucleon is very far apart from the residual nucleus. We prove that the real difference from the uncorrelated models is that $P H$ has an infinite dimension and contains generalized single hole states, distinguishable from the usual ones by the fact that one cannot assign a wave function to the hole. The bound eigenstates of the nuclei are just states of this kind. Some physical consequences are discussed, in particular the unexpected fact that the dynamical part of the single-hole Hamiltonian, although nonnull, does not affect the single-hole overlaps with the bound eigenstates. The decay of $ψ_{0}$ provides the asymptotic behaviours of many single-hole quantities, in particular the nuclear density matrix. Thus a by product of this paper is the rigorous proof of the method developed by Van Neck, Waroquier and Heyde to calculate overlaps and separation energies.
Comments:
43 pages
Subjects:
Nuclear Theory (nucl-th); Mathematical Physics (math-ph); math.MP (math.MP)
arXiv:
1911.09082 [pdf]
0 citations

Affiliations

first authorsco-authorsvia INSPIRE