Nuclear Theory

The microscopic origin of the spin-orbit (SO) potential in terms of sub-baryonic degrees of freedom is explored and discussed for application to nuclei and hyper-nuclei. We thus develop a chiral relativistic approach where the coupling to the scalar- and vector-meson fields are controlled by the quark substructure. This approach suggests that the isoscalar and isovector density dependence of the SO potential can be used to test the microscopic ingredients which are implemented in the relativistic framework: the quark substructure of the nucleon in its ground-state and its coupling to the rich meson sector where the ρ meson plays a crucial role. This is also in line with the Vector Dominance Model (VDM) phenomenology and the known magnetic properties of the nucleons. We explore predictions based on Hartree and Hartree-Fock mean field, as well as various scenarios for the ρ -nucleon coupling, ranked as weak, medium and strong, which impacts the isoscalar and isovector density dependence of the SO potential. We show that a medium to strong ρ coupling is essential to reproduce Skyrme phenomenology in N=Z nuclei as well as its isovector dependence. Assuming an SU(6) valence quark model our approach is extended to hyperons and furnishes a microscopic understanding of the quenching of the NΛ spin-orbit potential in hyper-nuclei. It is also applied to other hyperons, such as Σ , Ξ and Ω .

The particle momentum anisotropy ( v n ) produced in relativistic nuclear collisions is considered to be a response of the initial geometry or the spatial anisotropy ϵ n of the system formed in these collisions. The linear correlation between ϵ n and v n quantifies the efficiency at which the initial spatial eccentricity is converted to final momentum anisotropy in heavy ion collisions. We study the transverse momentum, collision centrality, and beam energy dependence of this correlation for different charged particles using a hydrodynamical model framework. The ( ϵ n ??v n ) correlation is found to be stronger for central collisions and also for n=2 compared to that for n=3 as expected. However, the transverse momentum ( p T ) dependent correlation coefficient shows interesting features which strongly depends on the mass as well as p T of the emitted particle. The correlation strength is found to be larger for lighter particles in the lower p T region. We see that the relative fluctuation in anisotropic flow depends strongly in the value of η/s specially in the region p T <1 GeV unlike the correlation coefficient which does not show significant dependence on η/s .

We study the influence of the Coulomb force on the Fermi beta-decays in nuclei. This work is composed of two main parts. In the first part, we calculate the Coulomb corrections to super-allowed beta decay. We use the notion of the isovector monopole state and the self-consistent charge-exchange Random Phase Approximation to compute the correction. In the second part of this work, we examine the influence of the anti-analog state on isospin mixing in the isobaric analog state and the correction to the beta-decay Fermi transition.

In present work, we discuss the effect of Coulomb interaction to the dynamics of two-particle system bound in various traps. The strategy of including Coulomb interaction into the quantization condition of trapped system is discussed in a general and non-perturbative manner. In most cases, Coulomb corrections to quantization condition largely rely on numerical approach or perturbation expansion. Only for some special cases, such as the spherical hard wall trap, a closed-form of quantization condition with all orders of Coulomb corrections can be obtained.

During the study of Bose-Einstein correlations in heavy ion collisions one has to take into account the final state interactions, amongst them the Coulomb interaction playing a prominent role for charged particles. In some cases measurements have shown that the correlation function can be best described by Lévy sources, and three dimensional measurements have indicated the possibility of deviation from spherical symmetry. Therefore, one would like to study the Coulomb interaction for non-spherical Lévy sources. We resort to numerical methods which are most commonly used in order to take into account the Coulomb interaction such measurements. Here, we utilize the Metropolis-Hastings algorithm. The symmetric Lévy distribution that describes the source can be characterized by three Lévy scale parameters and the Lévy exponent. We investigate the roles of these parameters in the correlation function. We show the results for the Bose-Einstein correlation functions for ellipsoidal Lévy sources with Coulomb interaction. We also compare our results with previous ways to treat the Coulomb interaction in the presence of Lévy sources.

We demonstrate the capability of coupled-cluster theory to compute the Coulomb sum rule for the 4 He and 16 O nuclei using interactions from chiral effective field theory. We perform several checks, including a few-body benchmark for 4 He. We provide an analysis of the center-of-mass contaminations, which we are able to safely remove. We then compare with other theoretical results and experimental data available in the literature, obtaining a fair agreement. This is a first and necessary step towards initiating a program for computing neutrino-nucleus interactions from first principles and supporting the experimental long-baseline neutrino program with a state-of-the-art theory that can reach medium-mass nuclei.

Given the established 2 alpha structure of 8Be, a realistic model of 4 interacting alpha clusters must be used to obtain a 8Be+8Be interaction potential. Such a four-body problem poses a challenge for the determination of the 8Be+8Be optical potential (OP) that is still unknown due to the lack of the elastic 8Be+8Be scattering data. The main goal of the present study is to probe the complex 8Be+8Be optical potential in the coupled reaction channel (CRC) study of the alpha transfer 12C(alpha,8Be) reaction measured at 65 MeV, and to obtain the spectroscopic information on the alpha+8Be cluster configuration of 12C. The 3- and 4-body Continuum-Discretized Coupled Channel (CDCC) methods are used to calculate the elastic alpha+8Be and 8Be+8Be scattering at the energy around 16 MeV/nucleon, with the breakup effect taken into account explicitly. Using the CDCC-based OP and alpha spectroscopic factors given by the cluster model calculation, a good CRC description of the alpha transfer data without any adjustment of the (complex) potential strength.

The E1 contribution to the capture reaction 7 Li(n,γ ) 8 Li is calculated at low energies. We employ a coupled-channel formalism to account for the 7 Li ⋆ excited core contribution. The halo effective field theory calculations show that the contribution of the 7 Li ⋆ degree of freedom is negligible at momenta below 1 MeV and significant only beyond the 3 + resonance energy, though still compatible with a next-to-next-to-leading order correction. A power counting that accounts for the size of this correction is proposed. We compare our formalism with a previous halo effective field theory [Zhang, Nollett, and Phillips, Phys. Rev. C {\bf 89}, 024613 (2014)] that also treated the 7 Li ⋆ core as an explicit degree of freedom. Our formal expressions and analysis disagree with this earlier work in several aspects.

We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-beta decay of 48 Ca. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For 48 Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-beta decay of 48 Ca with a quenching factor deduced from two-body currents in recent ab-initio calculation of the Ikeda sum-rule in 48 Ca [Gysbers et al., Nature Physics 15, 428-431 (2019)].

Recent progress in the numerical solution of the nuclear many-body problem and in the development of nuclear Hamiltonians rooted in Quantum Chromodynamics, has opened the door to first-principle computations of nuclear reactions. In this article, we discuss the current status of ab initio calculations of nucleon-nucleus optical potentials for medium-mass systems, with a focus on results obtained with the coupled-cluster method.