Nuclear Theory

The connection between the scaling function, directly extracted from the analysis of electron scattering data, and the nuclear spectral function or nuclear momentum density is investigated at depth. The dependence of the scaling function on the two independent variables in the scattering process, the transfer momentum ( q ) and the scaling variable ( y ), is taken into account, and the analysis is extended to both, positive and negative y -values, i.e., below and above the center of the quasielastic peak, respectively. Analytical expressions for the derivatives of the scaling function, evaluated at the finite limits of integration dealing with the kinematically allowed region, are connected with the spectral function. Here, contributions corresponding to zero and finite excitation energies are included. The scaling function is described by the Gumbel density distribution, whereas short-range correlations are incorporated in the spectral function by using some simple models. Also different parametrizations for the nucleon momentum distribution, that are compatible with the general properties of the scaling function, have been considered.

We compute various nucleon polarizabilities in chiral perturbation theory implementing the Δ -full ( Δ -less) approach up to order ϵ 3 + q 4 ( q 4 ) in the small-scale (chiral) expansion. The calculation is carried out using the covariant formulation of χ PT by utilizing the extended on-mass shell renormalization scheme. Except for the spin-independent dipole polarizabilities used to fix the values of certain low-energy constants, our results for the nucleon polarizabilities are pure predictions. We compare our calculations with available experimental data and other theoretical results. The importance of the explicit treatment of the Δ degree of freedom in the effective field theory description of the nucleon polarizabilities is analyzed. We also study the convergence of the 1/m expansion and analyze the efficiency of the heavy-baryon approach for the nucleon polarizabilities.

Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. We demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number of collective S , D , G , ??pairs (i.e., with angular momentum zero, two, four, ??) and if the structure of the pairs is optimally determined either by a conjugate-gradient minimization method or from a Hartree-Fock intrinsic state. We illustrate the procedure for 6 protons and 6 neutrons in the pf ( sdg ) shell and exactly reproduce the level energies and electric quadrupole properties of the ground-state rotational band with SDG ( SDGI ) pairs. The SD -pair approximation without significant renormalization, on the other hand, cannot describe the full SU(3) collectivity. A mapping from Elliott's fermionic SU(3) model to systems with s , d , g , ??bosons provides insight into the existence of a decoupled collective subspace in terms of S , D , G , ??pairs.

We have studied the isoscalar giant quadruple resonance (ISGQR) and the isovector giant dipole resonance (IVGDR) in 208 Pb based on an improved isospin-dependent Boltzmann-Uehling-Uhlenbeck transport approach using an improved isospin- and momentum-dependent interaction. With the isoscalar nucleon effective mass and the nucleon-nucleon cross section which reproduces respectively the excitation energy and the width of the ISGQR strength function, the slope parameter of the symmetry energy and the neutron-proton effective mass splitting are constrained respectively within 36<L<62 MeV and 0.08δ<( m ∗ n0 − m ∗ p0 )/m<0.42δ , by comparing the resulting centroid energy of the IVGDR and the electric dipole polarizability with the experimental data. It is found that nucleon-nucleon collisions have considerable effects on the resulting electric dipole polarizability, which needs to be measured more accurately in order to pin down isovector nuclear interactions.

The quadrupole-octupole coupling and the related spectroscopic properties have been studied for the even-even light actinides 218−238 Ra and 220−240 Th. The Hartree-Fock-Bogoliubov approximation, based on the Gogny-D1M energy density functional, has been employed as a microscopic input, i.e., to obtain (axially symmetric) mean-field potential energy surfaces as functions of the quadrupole and octupole deformation parameters. The mean-field potential energy surfaces have been mapped onto the corresponding bosonic potential energy surfaces using the expectation value of the sdf Interacting Boson Model (IBM) Hamiltonian in the boson condensate state. The strength parameters of the sdf -IBM Hamiltonian have been determined via this mapping procedure. The diagonalization of the mapped IBM Hamiltonian provides energies for positive- and negative-parity states as well as wave functions which are employed to obtain transitional strengths. The results of the calculations compare well with available data from Coulomb excitation experiments and point towards a pronounced octupole collectivity around 224 Ra and 226 Th.

The origin of weakly-bound nuclear clusters in hadronic collisions is a key question to be addressed by heavy-ion collision (HIC) experiments. The measured yields of clusters are approximately consistent with expectations from phenomenological statistical hadronisation models (SHMs), but a theoretical understanding of the dynamics of cluster formation prior to kinetic freeze out is lacking. The competing model is nuclear coalescence, which attributes cluster formation to the effect of final state interactions (FSI) during the propagation of the nuclei from kinetic freeze out to the observer. This phenomenon is closely related to the effect of FSI in imprinting femtoscopic correlations between continuum pairs of particles at small relative momentum difference. We give a concise theoretical derivation of the coalescence--correlation relation, predicting nuclear cluster spectra from femtoscopic measurements. We review the fact that coalescence derives from a relativistic Bethe-Salpeter equation, and recall how effective quantum mechanics controls the dynamics of cluster particles that are nonrelativistic in the cluster centre of mass frame. We demonstrate that the coalescence--correlation relation is roughly consistent with the observed cluster spectra in systems ranging from PbPb to pPb and pp collisions. Paying special attention to nuclear wave functions, we derive the coalescence prediction for hypertriton and show that it, too, is roughly consistent with the data. Our work motivates a combined experimental programme addressing femtoscopy and cluster production under a unified framework. Upcoming pp, pPb and peripheral PbPb data analysed within such a programme could stringently test coalescence as the origin of clusters.

It is shown that the Principal Component Analysis applied to azimuthal single-particle distributions allows to perform flow analysis in ways that are analogous to the traditional approaches based on multi-particle correlations. In particular, symmetric cumulants are considered. It is demonstrated also that statistical fluctuations due to a finite number of particles per event practically do not play a role for higher order PCA-based cumulants.

Non-additive generalisation of relativistic anisotropic anisotropic hydrodynamics is described. In the particular case of 0+1 boost-invariant hydrodynamics additional entropy production due to non-additivity is calculated.

Estimates of QED and dispersion effects on the cross section for elastic electron scattering from a 12C nucleus are provided for collision energies in the range of 120-450 MeV. While in general such corrections are smoothly varying with energy or scattering angle, they show structures in the vicinity of diffraction minima which are very sensitive to details of the theoretical models. This casts doubt on the assertion that the discrepancy between QED background-corrected experimental data and theory in these minima originates solely from dispersion.

We build upon the remarkable, model independent constraints on the equation of state of dense baryonic matter established recently by Annala et al. [1]. Using the quark-meson coupling model, an approach to nuclear structure based upon the self-consistent adjustment of hadron structure to the local meson fields, we show that, once hyperons are allowed to appear in dense matter in \b{eta}-equilibrium, the equation of state is consistent with those constraints. As a result, while one cannot rule out the occurence of quark matter in the cores of massive neutron stars, the available constraints are also compatible with the presence of hyperons.