Nuclear Theory

Octupole deformations and related collective excitations are analyzed using the framework of nuclear density functional theory. Axially-symmetric quadrupole-octupole constrained self-consistent mean-field (SCMF) calculations with a choice of universal energy density functional and a pairing interaction are performed for Xe, Ba, and Ce isotopes from proton-rich to neutron-rich regions, and neutron-rich Se, Kr, and Sr isotopes, in which enhanced octupole correlations are expected to occur. Low-energy positive- and negative-parity spectra and transition strengths are computed by solving the quadrupole-octupole collective Hamiltonian, with the inertia parameters and collective potential determined by the constrained SCMF calculations. Octupole-deformed equilibrium states are found in the potential energy surfaces of the Ba and Ce isotopes with N??6 and 88. The evolution of spectroscopic properties indicates enhanced octupole correlations in the regions corresponding to N?�Z??6 , Z??8 and Z??6 , and N??6 and Z??4 . The average β 30 deformation parameter and its fluctuation exhibit signatures of octupole shape phase transition around N=56 and 88.

The interplay between quadrupole and octupole degrees of freedom is discussed in a series of U, Pu, Cm and Cf isotopes both at the mean-field level and beyond. In addition to the static Hartree-Fock-Bogoliubov approach, dynamical beyond-mean-field correlations are taken into account via both parity restoration and symmetry-conserving Generator Coordinate Method calculations based on the parametrization D1M of the Gogny energy density functional. Physical properties such as correlation energies, negative-parity excitation energies as well as reduced transition probabilities B(E1) and B(E3) are discussed in detail and compared with the available experimental data. It is shown that, for the studied nuclei, the quadrupole-octupole coupling is weak and to a large extent the properties of negative parity states can be reasonably well described in terms of the octupole degree of freedom alone.

We construct from chiral effective field theory two- and three-body forces a microscopic global nucleon-nucleus optical potential suitable for reactions involving radioactive isotopes. Within the improved local density approximation and without any adjustable parameters, we begin by computing local proton and neutron optical potentials for 1800 target nuclei in the mass range 12<A<242 and for energies between 0MeV<E<200MeV . We then construct a global optical potential parametrization that depends smoothly on the projectile energy as well as the target nucleus mass number and isospin asymmetry. Elastic scattering observables calculated from the global optical potential are found to be in good agreement with available experimental data for a wide range of projectile energies and target nuclei. Compared to traditional phenomenological optical potentials, we find a strong energy dependence and shell structure features in the Woods-Saxon geometry parameters. For target nuclei with small proton-neutron asymmetry, we find that the real and imaginary optical potential depths exhibit a clear linear dependence on the isospin-asymmetry and preserve the well known Lane form up to high projectile energies. For nuclei with larger isospin asymmetries, we find evidence for a novel isoscalar term in the low-energy optical potential proportional to the square of the isospin asymmetry. These insights from microscopic many-body theory may be used to inform next-generation phenomenological optical potentials for proton- and neutron-rich isotopes.

The 8 Li( n,γ ) 9 Li reaction plays an important role in several astrophysics scenarios. It cannot be measured directly and indirect experiments have so far provided only cross section limits. Theoretical predictions differ by an order of magnitude. In this work we study the properties of 9 Li bound states and low-lying resonances and calculate the 8 Li( n,γ ) 9 Li cross section within the no-core shell model with continuum (NCSMC) with chiral nucleon-nucleon and three-nucleon interactions as the only input. The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states well suited to calculate low-energy nuclear scattering and reactions. Our calculations reproduce the experimentally known bound states as well as the lowest 5/ 2 − resonance of 9 Li. We predict a 3/ 2 − spin-parity assignment for the resonance observed at 5.38 MeV. In addition to the a very narrow 7/ 2 − resonance corresponding presumably to the experimental 6.43 MeV state, we find several other broad low-lying resonances. Our calculated 8 Li( n,γ ) 9 Li cross section is within the limits derived from the 1998 National Superconducting Cyclotron Laboratory Coulomb-dissociation experiment [Phys. Rev. C {\bf 57}, 959 (1998)]. However, it is higher than cross sections obtained in recent phenomenological studies. It is dominated by a direct E1 capture to the ground state with a resonant contribution at ∼0.2 MeV due to E2/M1 radiation enhanced by the 5/ 2 − resonance.

A microscopic method for calculating nuclear level densities (NLD) is developed, based on the framework of energy density functionals. Intrinsic level densities are computed from single-quasiparticle spectra obtained in a finite-temperature self-consistent mean-field (SCMF) calculation that takes into account nuclear deformation, and is specified by the choice of the energy density functional (EDF) and pairing interaction. The total level density is calculated by convoluting the intrinsic density with the corresponding collective level density, determined by the eigenstates of a five-dimensional quadrupole or quadrupole plus octupole collective Hamiltonian. The parameters of the Hamiltonian (inertia parameters, collective potential) are consistently determined by deformation-constrained SCMF calculations using the same EDF and pairing interaction. The model is applied in the calculation of NLD of 94,96,98 Mo, 106,108 Pd, 106,112 Cd, 160,162,164 Dy, 166 Er, and 170,172 Yb, in comparison with available data. It is shown that the collective enhancement of the intrinsic level density, consistently computed from the eigenstates of the corresponding collective Hamiltonian, leads to total NLDs that are in excellent agreement with data over the whole energy range of measured values.

For photoproduction reactions with final states consisting of two pseudoscalar mesons and a spin-1/2 baryon, 8 complex amplitudes need to be determined uniquely. A modified version of Moravcsik's theorem is employed for these reactions, resulting in slightly over-complete sets of polarization observables that are able to determine the amplitudes uniquely. Further steps were taken to reduce the found sets to minimal complete sets. As a final result, multiple minimal complete sets without any remaining ambiguities are presented for the first time. These sets consist of 2N=16 observables, containing only one triple polarization observable.

The experimental search for the QCD critical point by means of relativistic heavy-ion collisions necessitates the development of dynamical models of fluctuations. In this work we study the fluctuations of the net-baryon density near the critical point. Due to net-baryon number conservation the correct dynamics is given by the fluid dynamical diffusion equation, which we extend by a white noise stochastic term to include intrinsic fluctuations. We quantify finite resolution and finite size effects by comparing our numerical results to analytic expectations for the structure factor and the equal-time correlation function. In small systems the net-baryon number conservation turns out to be quantitatively and qualitatively important, as it introduces anticorrelations at larger distances. Including nonlinear coupling terms in the form of a Ginzburg-Landau free energy functional we observe non-Gaussian fluctuations quantified by the excess kurtosis. We study the dynamical properties of the system close to equilibrium, for a sudden quench in temperature and a Hubble-like temperature evolution. In the real-time dynamical systems we find the important dynamical effects of critical slowing down, weakening of the extremal value and retardation of the fluctuation signal. In this work we establish a set of general tests, which should be met by any model propagating fluctuations, including upcoming 3+1 dimensional fluctuating fluid dynamics.

We investigate the in-medium properties of hyperons and anti-hyperons in the framework of the Non-Linear Derivative (NLD) model. We focus on the momentum dependence of in-medium strangeness optical potentials. The NLD model is based on the simplicity of the well-established Relativistic Mean-Field (RMF) approximation, but it incorporates an explicit momentum dependence on a field-theoretical level. The extension of the NLD model to the (anti)baryon-octet is formulated in the spirit of SU(6) and G-parity arguments. It is shown that with an appropriate choice of momentum cut-offs the ? , Σ and ? optical potentials are consistent with recent studies of the chiral effective field theory and Lattice-QCD calculations over a wide momentum region. In addition, we present NLD predictions for the in-medium momentum dependence of ? ¯ ¯ ¯ ¯ -, Σ ¯ ¯ ¯ ¯ - and ? ¯ ¯ ¯ ¯ -hyperons. This work is important for future experimental studies such as CBM, PANDA at the Facility for Antiproton and Ion Research (FAIR). It is relevant for nuclear astrophysics too.

Ab initio calculations of bulk nuclear properties (ground-state energies, root mean square charge radii and charge density distributions) are presented for seven complete isotopic chains around calcium, from argon to chromium. Calculations are performed within the Gorkov self-consistent Green's function approach at second order and make use of two state-of-the-art two- plus three-nucleon Hamiltonians, NN + 3N(lnl) and NNLO sat . An overall good agreement with available experimental data is found, in particular for differential energies (charge radii) when the former (latter) interaction is employed. Remarkably, neutron magic numbers N=28,32,34 emerge and evolve following experimental trends. In contrast, pairing gaps are systematically underestimated. General features of the isotopic dependence of charge radii are also reproduced, as well as charge density distributions. A deterioration of the theoretical description is observed for certain nuclei and ascribed to the inefficient account of (static) quadrupole correlation in the present many-body truncation scheme. In order to resolve these limitations, we advocate the extension of the formalism towards incorporating breaking of rotational symmetry or, alternatively, performing a stochastic sampling of the self-energy.

It is shown that recently proposed RMF model with σ and δ meson interaction agrees with the observational data and presents an interesting structure with phase transition in the outer part of neutron star core.