Nuclear Theory·nucl-th

Thursday·November 21, 2019

13 papers—8 primary·5 cross-listed

01
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.
nucl-thJ.Phys.G(2020)·6 citations
02
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.
nucl-thhep-phProQuest Number: 13882375 (2019)·3 citations
03
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.
nucl-thhep-phPRC(2020)·67 citations
04
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.
nucl-thPRC(2021)·6 citations
05
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.
nucl-thhep-phSpringer Proc.Phys.(2020)·8 citations
06
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.
nucl-thPRD(2020)·5 citations
07
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.
nucl-thPRC(2020)·46 citations
08
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.
nucl-thmath-phmath.MP0 citations
09
New Flavor-Kinematics Dualities and Extensions of Nonlinear Sigma Models
Ian Low🇺🇸 · Zhewei Yin🇺🇸
Nonlinear sigma model (NLSM) based on the coset $SU (N) \times SU (N) / SU (N)$ exhibits several intriguing features at the leading $O (p^{2})$ in the derivative expansion, such as the flavor-kinematics duality and an extended theory controlling the single and triple soft limits. In both cases the cubic biadjoint scalar theory plays a prominent role. We extend these features in two directions. First we uncover a new extended theory for $SO (N + 1) / SO (N)$ NLSM at $O (p^{2})$ , which is a cubic bifundamental/biadjoint scalar theory. Next we provide evidence for flavor-kinematics dualities up to $O (p^{4})$ for both $SU (N)$ and $SO (N)$ NLSM's. In particular, we introduce a new duality building block based on the symmetric tensor $δ^{ab}$ and demonstrate several flavor-kinematics dualities for 4-point amplitudes, which precisely match the soft blocks employed to soft-bootstrap the NLSM's up to $O (p^{4})$ .
↳ hep-thhep-phnucl-thPLB(2020)·37 citations
10
Refined analysis on the parton distribution functions of the proton
X. G. Wang🇦🇺 · A. W. Thomas🇦🇺
We explore the application of a two-component model of proton structure functions in the analysis of deep-inelastic scattering (DIS) data at low $Q^{2}$ and small $x$ . This model incorporates both vector meson dominance and the correct photo-production limit. The CJ15 parameterization is applied to the QCD component, in order to take into account effects of order $1/ Q^{2}$ effects, such as target mass corrections and higher twist contributions. The parameters of the leading twist parton distribution functions and higher twist coefficient functions are determined by fitting deep inelastic scattering data. The second moments of the parton distribution functions are extracted and compared with other global fits and lattice determinations.
↳ hep-phnucl-thJ.Phys.G(2020)·4 citations
11
The $ϕ$ meson with finite momentum in a dense medium
HyungJoo Kim🇰🇷 · Philipp Gubler🇯🇵
The dispersion relation of the $ϕ$ meson in nuclear matter is studied in a QCD sum rule approach. In a dense medium, longitudinal and transverse modes of vector particles can have independently modified dispersion relations due to broken Lorentz invariance. Employing the full set of independent operators and corresponding Wilson coefficients up to operator dimension 6, the $ϕ$ meson QCD sum rules are analyzed with changing densities and momenta. The non-trivial momentum dependence of the $ϕ$ meson mass is found to have opposite signs for the longitudinal and transverse modes. Specifically, the mass is reduced by 5 MeV for the longitudinal mode, while its increase amounts to 7 Mev for the transverse mode, both at a momentum scale of 1 GeV. In an experiment which does not distinguish between longitudinal and transverse polarizations, this could in principle be seen as two separated peaks at large momenta. Taking however broadening effects into account, the momentum dependence will most likely be seen as a small but positive effective mass shift and an increased effective width for non-zero momenta.
↳ hep-phnucl-thPLB(2020)·44 citations
12
Measurement and microscopic description of odd-even staggering of charge radii of exotic copper isotopes
R. P. de Groote🇧🇪 · J. Billowes🇬🇧 · C. L. Binnersley🇬🇧 · M. L. Bissell🇬🇧 · T. E. Cocolios🇧🇪 · T. Day Goodacre🇨🇭 · G. J. Farooq-Smith · D. V. Fedorov🇷🇺 · K. T. Flanagan🇬🇧 · S. Franchoo🇫🇷 · R. F. Garcia Ruiz🇬🇧 · W. Gins🇧🇪 and 14 other authors
The mesoscopic nature of the atomic nucleus gives rise to a wide array of macroscopic and microscopic phenomena. The size of the nucleus is a window into this duality: while the charge radii globally scale as $A^{1/3}$ , their evolution across isotopic chains reveals unanticipated structural phenomena [1-3]. The most ubiquitous of these is perhaps the Odd-Even Staggering (OES) [4]: isotopes with an odd number of neutrons are usually smaller in size than the trend of their even-neutron neighbours suggests. This OES effect varies with the number of protons and neutrons and poses a significant challenge for nuclear theory [5-7]. Here, we examine this problem with new measurements of the charge radii of short-lived copper isotopes up to the very exotic $^{78}$ Cu $(Z = 29, N = 49)$ , produced at only 20 ions/s, using the highly-sensitive Collinear Resonance Ionisation Spectroscopy (CRIS) method at ISOLDE-CERN. Due to the presence of a single proton outside of the closed Z=28 shell, these measurements provide crucial insights into the single-particle proton structure and how this affects the charge radii. We observe an unexpected reduction in the OES for isotopes approaching the $N = 50$ shell gap. To describe the data, we applied models based on nuclear Density Functional Theory [2,8] (DFT) and ab-initio Valence-Space In-Medium Similarity Renormalization Group (VS-IMSRG) theory [9,10]. Through these comparisons, we demonstrate a relation between the global behavior of charge radii and the saturation density of nuclear matter, and show that the local charge radii variations, which reflect the many-body polarization effects due to the odd neutron, naturally emerge from the VS-IMSRG calculations.
↳ nucl-exnucl-thNat.Phys.(2020)·131 citations
13
Three pion spectrum in the $I = 3$ channel from lattice QCD
Chris Culver🇺🇸 · Maxim Mai🇺🇸 · Ruairí Brett🇺🇸 · Andrei Alexandru🇺🇸 · Michael Döring🇺🇸
Three-body states are critical to the dynamics of many hadronic resonances. We show that lattice QCD calculations have reached a stage where these states can be accurately resolved. We perform a calculation over a wide range of parameters and find all states below inelastic threshold agree with predictions from a state-of-the-art phenomenological formalism. This also illustrates the reliability of the formalism used to connect lattice QCD results to infinite volume physics. Our calculation is performed using three positively charged pions, with different lattice geometries and quark masses.
↳ hep-latnucl-thPRD(2020)·106 citations

Affiliations

first authorsco-authorsvia INSPIRE