PaperPanorama
FAQ

Nuclear Theory·nucl-th

Tuesday·May 14, 2019

14 papers—6 primary·8 cross-listed

All14Primary6Cross-lists8
  1. 01

    Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem

    Amol V. Patwardhan🇺🇸 · Michael J. Cervia🇺🇸 · A. Baha Balantekin🇺🇸

    We demonstrate a method to systematically obtain eigenvalues and eigenstates of a many-body Hamiltonian describing collective neutrino oscillations. The method is derived from the Richardson-Gaudin framework, which involves casting the eigenproblem as a set of coupled nonlinear "Bethe Ansatz equations", the solutions of which can then be used to parametrize the eigenvalues and eigenvectors. The specific approach outlined in this paper consists of defining auxiliary variables that are related to the Bethe-Ansatz parameters, thereby transforming the Bethe-Ansatz equations into a different set of equations that are numerically better behaved and more tractable. We show that it is possible to express not only the eigenvalues, but also the eigenstates, directly in terms of these auxiliary variables without involving the Bethe Ansatz parameters themselves. In this paper, we limit ourselves to a two-flavor, single-angle neutrino system.

    nucl-thastro-ph.HEhep-phquant-phPRD(2019)·46 citations
  2. 02

    Valence Neutron-Proton Orientation in Atomic Nuclei

    J. G. Wang🇨🇳 · M. L. Liu🇨🇳 · C. M. Petrache🇫🇷 · K. K. Zheng🇨🇳 · X. H. Zhou🇨🇳 · Y. H. Zhang🇨🇳

    It is shown that the renormalized nuclear deformations in different mass regions can be globally scaled by two probability partition factors of Boltzmann-like distribution, which are derived from the competing valence and like-nucleon interactions. The partition factors are simply related to the probabilities of anti-parallel and fully-aligned orientations of the angular momenta of the neutrons and protons in the valence pairs, responsible for spherical- and deformed-shape phases, respectively. The partition factors derived from the renormalized deformations are also present in the new scaling law for the energies of the first states. A striking concordance between the distributions of the renormalized deformations and of the newly introduced parameter for the energies of the first states over the extended mass region from Ge to Cf is achieved, giving strong support to the existence of two phases: anti-aligned and fully-aligned subsets of pairs.

    nucl-th0 citations
  3. 03

    Mean-Field Theory for Fermion Pairs and the ab initio Particle-Vibration-Coupling Approach

    Peter Schuck🇫🇷

    A Dyson Bethe-Salpeter equation (Dyson-BSE) for fermion pairs is presented whose kernel has a static and a one frequency dependent contribution, analogous to the self energy of the single particle Dyson equation with the (static) mean field term and the energy dependent correlation term. The static part of the Dyson-BSE is the self-consistent mean field for the vibrations. At the same time, for the correlated single particle self-energy a full particle-vibration coupling (PVC) scattering equation is established where the vibration is the same as obtained from the Dyson-BSE. Both equations, single particle Dyson equation and Dyson-BSE, are coupled through self-consistency. Numerical results for Lipkin and 1D Hubbard chain are very promising.

    nucl-thEPJA(2019)·7 citations
  4. 04

    Parity Doubling and the Dense Matter Phase Diagram under Constraints from Multi-Messenger Astronomy

    Michał Marczenko🇵🇱 · David Blaschke🇵🇱 · Krzysztof Redlich🇵🇱 · Chihiro Sasaki🇵🇱

    We extend the recently developed hybrid quark-meson-nucleon model by augmenting a six-point scalar interaction and investigate the consequences for neutron-star sequences in the mass-radius diagram. The model has the characteristic feature that, at increasing baryon density, the chiral symmetry is restored within the hadronic phase by lifting the mass splitting between chiral partner states (parity doubling), before quark deconfinement takes place. At low temperature and finite baryon density, the model predicts a first-, second-order chiral phase transition, or a crossover, depending on the expectation value of the scalar field, and a first-order deconfinement phase transition. We discuss two sets of free parameters, which result in compact-star mass-radius relations that are at tension with the combined constraints for maximum-mass () and the compactness (GW170817). We find that the most preferable mass-radius relations result in isospin-symmetric phase diagram with rather low temperature for the critical point of the chiral phase transition.

    nucl-thUniverse(2019)·37 citations
  5. 05

    Direct comparison between Bayesian and frequentist uncertainty quantification for nuclear reactions

    G. B. King · A. E. Lovell · L. Neufcourt · F. M. Nunes

    Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence intervals. Although there are statistical arguments to prefer the Bayesian approach, no direct comparison is available. In this work, we compare, directly and systematically, the frequentist and Bayesian approaches to quantifying uncertainties in direct nuclear reactions. Starting from identical initial assumptions, we determine confidence intervals associated with the elastic and the transfer process for both methods, which are evaluated against data via a comparison of the empirical coverage probabilities. Expectedly, the frequentist approach is not as flexible as the Bayesian approach in exploring parameter space and often ends up in a different minimum. We also show that the two methods produce significantly different correlations. In the end, the frequentist approach produces significantly narrower uncertainties on the considered observables than the Bayesian. Our study demonstrates that the uncertainties on the reaction observables considered here within the Bayesian approach represent reality more accurately than the much narrower uncertainties obtained using the standard frequentist approach.

    nucl-thPRL(2019)·63 citations
  6. 06

    -dimensional Lüscher's formula and the near-threshold three-body states in a finite volume

    Shangguo Zhu · Shina Tan

    We study two particles colliding in a -dimensional finite volume and generalize Lüscher's formula to arbitrary spatial dimensions. We obtain the - and -wave approximations of the generalized Lüscher's formula. For resonant - or -wave interactions, we analytically determine the energies of the low-lying states at large box size . At -wave resonance, we discover two low-lying states with nearly opposite energies, which are proportional to for , or for . This provides important insights into the near-threshold states of three bosons at a three-body resonance in a 2- or higher-dimensional finite volume.

    nucl-thcond-mat.quant-gasphysics.atom-ph10 citations

Affiliations

first authorsco-authorsvia INSPIRE