Nuclear Theory

We propose a method to incorporate the coupling between shape and pairing collective degrees of freedom in the framework of the interacting boson model (IBM), based on the nuclear density functional theory. To account for pairing vibrations, a boson-number non-conserving IBM Hamiltonian is introduced. The Hamiltonian is constructed by using solutions of self-consistent mean-field calculations based on a universal energy density functional and pairing force, with constraints on the axially-symmetric quadrupole and pairing intrinsic deformations. By mapping the resulting quadrupole-pairing potential energy surface onto the expectation value of the bosonic Hamiltonian in the boson condensate state, the strength parameters of the boson Hamiltonian are determined. An illustrative calculation is performed for 122 Xe, and the method is further explored in a more systematic study of rare-earth N=92 isotones. The inclusion of the dynamical pairing degree of freedom significantly lowers the energies of bands based on excited 0 + states. The results are in quantitative agreement with spectroscopic data, and are consistent with those obtained using the collective Hamiltonian approach.

We present our concise notes for the lectures and tutorials on pairing, quasi-spin and seniority delivered at SERB school on Role of Symmetries in Nuclear Physics, AMITY University, 2019. Starting with some generic features of residual nucleon-nucleon interactions, we provide detailed derivation of the matrix elements for the \delta-interaction which is the basis for the standard pairing Hamiltonian. The eigen values for standard pairing Hamiltonian are then obtained within the quasi-spin formalism. The algebra involving quasi-spin operators is performed explicitly using the annihilation and creation operators for single nucleon together with the application of Wicks theorem. These techniques are expected to be helpful in deriving the mean-field equations for the Hartree-Fock, Bardeen-Cooper-Schrieffer and Hartree-Fock Bogoliubov theories.

The consequences of the short range nature of the nucleon-nucleon interaction, which forces the spatial part of the nuclear wave function to be as symmetric as possible, on the pseudo-SU(3) scheme are examined through a study of the collective deformation parameters beta and gamma in the rare earth region. It turns out that beyond the middle of each harmonic oscillator shell possessing an SU(3) subalgebra, the highest weight irreducible representation (the hw irrep) of SU(3) has to be used, instead of the irrep with the highest eigenvalue of the second order Casimir operator of SU(3) (the hC irrep), while in the first half of each shell the two choices are identical. The choice of the hw irrep predicts a transition from prolate to oblate shapes just below the upper end of the rare earth region, between the neutron numbers N=114 and 116 in the W, Os, and Pt series of isotopes, in agreement with available experimental information, while the choice of the hC irrep leads to a prolate to oblate transition in the middle of the shell, which is not seen experimentally. The prolate over oblate dominance in the ground states of even-even nuclei is obtained as a by-product.

Blast wave fits can capture essential features of global properties of systems near kinetic equilibrium. They usually provide temperature fields and collective velocity fields on a given hypersurface. We investigate how faithful the viscous blast wave introduced in [1] (Z. Yang and R. J. Fries, arXiv:1807.03410), can reproduce the given temperature and specific shear viscosity at freeze-out of a viscous fluid dynamic calculation, if the final spectrum and elliptic flow of several particle species are fitted. We focus here on fluid dynamic simulations appropriate for high energy nuclear collisions at current collider energies. We find that specific shear viscosities are reproduced to good accuracy by viscous blast wave fits while temperatures tend to be slightly underpredicted. We quantify the deviations of fitted from true quantities for some examples. The maps we obtain can be used to improve raw results obtained from viscous blast wave fits.

Particle spin polarization is known to be linked both to rotation (angular momentum) and magnetization of a many particle system. However, in the most common formulation of relativistic kinetic theory, the spin degrees of freedom appear only as degeneracy factors multiplying phase-space distributions. Thus, it is important to develop theoretical tools that allow to make predictions regarding the spin polarization of particles, which can be directly confronted with experimental data. Herein, we discuss a link between the relativistic spin tensor and particle spin polarization, and elucidate the connections between the Wigner function and average polarization. Our results may be useful for theoretical interpretation of heavy-ion data on spin polarization of the produced hadrons.

We explore parton collisional effects on the conversion of geometry eccentricities into azimuthal anisotropies in Pb+Pb collisions at s NN ??????????= 5.02 TeV using a multi-phase transport model. The initial eccentricity ε n (n = 2,3) and flow harmonics v n (n = 2,3) are investigated as a function of the number of parton collisions ( N coll ) during the source evolution of partonic phase. It is found that partonic collisions leads to generate elliptic flow v 2 and triangular flow v 3 in Pb+Pb collisions. On the other hand, partonic collisions also result in an evolution of the eccentricity of geometry. The collisional effect on the flow conversion efficiency is therefore studied. We find that the partons with larger N coll show a lower flow conversion efficiency, which reflect differential behaviors with respect to N coll . It provides an additional insight into the dynamics of the space-momentum transformation during the QGP evolution from a transport model point of view.

The change in the energy of the moving heavy (charm and bottom) quarks due to field fluctuations present in the hot QCD medium has been studied. A finite quark chemical potential has been considered while modeling the hot QCD medium counting the fact that the upcoming experimental facilities such as Anti-proton and Ion Research (FAIR) and Nuclotron-based Ion Collider fAcility (NICA) are expected to operate at finite baryon density and moderate temperature. The effective kinetic theory approach has been adopted where the collisions have been incorporated using the well defined collisional kernel, known as Bhatnagar-Gross-Krook (BGK). To incorporate the non-ideal equations of state (EoSs) effects/ medium interaction effects, an extended effective fugacity model has been adopted. The momentum dependence of the energy change due to fluctuation for the charm and bottom quark has been investigated at different values of collision frequency and chemical potential. The results are exciting as the heavy quarks are found to gain energy due to fluctuations while moving through the produced medium at finite chemical potential and collision frequency.

The aim of this work is to present an overview of the derivation of the effective shell-model Hamiltonian and decay operators within many-body perturbation theory, and to show the results of selected shell-model studies based on their utilisation. More precisely, we report some technical details that are needed by non-experts to approach the derivation of shell-model Hamiltonians and operators starting from realistic nuclear potentials, in order to provide some guidance to shell-model calculations where the single-particle energies, two-body matrix elements of the residual interaction, effective charges and decay matrix elements, are all obtained without resorting to empirical adjustments. On the above grounds, we will present results of studies of double-beta decay of heavy-mass nuclei where shell-model ingredients are derived from theory, so to assess the reliability of such a way to shell-model investigations. Attention will be also focussed on the relevant aspects that are connected to the behavior of the perturbative expansion, whose knowledge is needed to establish limits and perspectives of this approach to nuclear structure calculations.

We present a perturbative approach to solving the three-nucleon continuum Faddeev equation. This approach is particularly well suited to dealing with variable strengths of contact terms in a chiral three-nucleon force. We use examples of observables in the elastic nucleon-deuteron scattering as well as in the deuteron breakup reaction to demonstrate high precision of the proposed procedure and its capability to reproduce exact results. A significant reduction of computer time achieved by the perturbative approach in comparison to exact treatment makes this approach valuable for fine-tuning of the three-nucleon Hamiltonian parameters.

The equation of state and phase diagram of strongly interacting matter composed of α particles are studied in the mean-field approximation. The particle interactions are included via a Skyrme-like mean field, containing both attractive and repulsive terms. The model parameters are found by fitting known values of binding energy and baryon density in the ground state of α matter, obtained from microscopic calculations by Clark and Wang. Thermodynamic quantities of α matter are calculated in the broad domains of temperature and baryon density, which can be reached in heavy-ion collisions at intermediate energies. The model predicts both first-order liquid-gas phase transition and Bose-Einstein condensation of α particles. We present the profiles of scaled variance, sound velocity and isochoric heat capacity along the isentropic trajectories of α matter. Strong density fluctuations are predicted in the vicinity of the critical point at temperature T c ≈14 MeV and density n c ≈0.012 fm −3 .