Nuclear Theory

We present a simple activity based on the liquid-drop model which allows secondary school students to explore the uses of mathematical models and gain an intuitive understanding of the concept of binding energy, and in particular the significance of positive binding energy. Using spreadsheets provided as Supplementary Material, students can perform simple manipulations on the different coefficients of the model to understand the role of each of its five terms. Students can use the spreadsheets to determine model parameters by optimising the agreement with real atomic mass data. %This will subsequently be used to predict the limit of existence of the Segré chart and to find the minimum mass of a neutron star. This activity can be used as the starting point of a discussion about theoretical models, their validation when it comes to describing experimental data and their predictive power towards unexplored regimes.

Is the secondary component of GW190814 the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system [R. Abbott et al., ApJ Lett., 896, L44 (2020)]? This is the central question animating this letter. Covariant density functional theory provides a unique framework to investigate both the properties of finite nuclei and neutron stars, while enforcing causality at all densities. By tuning existing energy density functionals we were able to: (a) account for a 2.6 Msun neutron star, (b) satisfy the original constraint on the tidal deformability of a 1.4 Msun neutron star, and (c) reproduce ground-state properties of finite nuclei. Yet, for the class of models explored in this work, we find that the stiffening of the equation of state required to support super-massive neutron stars is inconsistent with either constraints obtained from energetic heavy-ion collisions or from the low deformability of medium-mass stars. Thus, we speculate that the maximum neutron star mass can not be significantly higher than the existing observational limit and that the 2.6 Msun compact object is likely to be the lightest black hole ever discovered.

We develop a fully self-consistent subtracted second random-phase approximation for charge-exchange processes with Skyrme energy-density functionals. As a first application, we study Gamow-Teller excitations in the doubly-magic nucleus 48 Ca, the lightest double- β emitter that could be used in an experiment, and in 78 Ni, the single-beta-decay rate of which is known. The amount of Gamow-Teller strength below 20 or 30 MeV is considerably smaller than in other energy-density-functional calculations and agrees better with experiment in 48 Ca, as does the beta-decay rate in 78 Ni. These important results, obtained without \textit{ad hoc} quenching factors, are due to the presence of two-particle -- two-hole configurations. Their density progressively increases with excitation energy, leading to a long high-energy tail in the spectrum, a fact that may have implications for the computation of nuclear matrix elements for neutrinoless double- β decay in the same framework.

β -decay half-lives of neutron-rich nuclei around N=82 are key data to understand the r -process nucleosynthesis. We performed large-scale shell-model calculations in this region using a newly constructed shell-model Hamiltonian, and successfully described the low-lying spectra and half-lives of neutron-rich N=82 and N=81 isotones with Z=42??9 in a unified way. We found that their Gamow-Teller strength distributions have a peak in the low-excitation energies, which significantly contributes to the half-lives. This peak, dominated by ν0 g 7/2 ?�π0 g 9/2 transitions, is enhanced on the proton deficient side because the Pauli-blocking effect caused by occupying the valence proton 0 g 9/2 orbit is weakened.

We investigate the properties of neutral and charged pions in a constant background magnetic field mainly at zero temperature within the Nambu--Jona-Lasinio model. In the previous calculations, the Ritus method, involving Schwinger phases in a fixed gauge, was employed within the momentum-space random phase approximation (RPA)~[Phys. Lett. B 782 , 155-161 (2018)]. However, gauge invariance of the charged pion masses has not yet been examined. In this work, by adopting the linear response theory based on the imaginary-time path integral formalism, we derive the correlation functions for pions in the coordinate space, where the corresponding Schwinger phases show up automatically. At sufficiently large imaginary time τ , the meson correlation function approaches an exponential form ∼exp(− E G τ) , where E G is the ground-state energy of the one-meson state and hence determined as the meson mass. Furthermore, we show that the mass of the charged pions is gauge independent, i.e., independent of the choice of the vector potential for the magnetic field. Actually, we also find that the momentum-space RPA is equivalent to the imaginary-time method used here.

The calculable R -matrix theory has been formulated successfully for regular boundary conditions with vanishing radial wave functions at the coordinate origins [P. Descouvemont and D. Baye, Rept. Prog. Phys. 73, 036301 (2010)]. We generalize the calculable R -matrix theory to the incoming wave boundary condition (IWBC), which is widely used in theoretical studies of low-energy heavy-ion fusion reactions to simulate the strong absorption of incoming flux inside the Coulomb barriers. The generalized calculable R -matrix theory also provides a natural starting point to extend eigenvector continuation (EC) [D. Frame et al., Phys. Rev. Lett. 121, 032501 (2018)] to fusion observables. The 14 N+ 12 C fusion reaction is taken as an example to validate these new theoretical tools. Both local and nonlocal potentials are considered in numerical calculations. Our generalizations of the calculable R -matrix theory and EC are found to work well for IWBC.

In this work, we have studied the isovector giant dipole resonance (IVGDR) in even-even Sm isotopes within time-dependent Hartree-Fock (TDHF) with four Skyrme forces SLy6, SVbas, SLy5 and UNEDF1. The approach we have followed is somewhat similar to the one we did in our previous work in the region of Neodymium (Nd, Z=60) [\href{this https URL}{Physica Scripta (2020)}]. We have calculated the dipole strength of 128??64 Sm , and compared with the available experimental data. An overall agreement between them is obtained. The dipole strength in neutron-deficient 128??42 Sm and in neutron-rich 156??64 Sm isotopes are predicted. Shape phase transition as well as shape coexistence in Sm isotopes are also investigated in the light of IVGDR. In addition, the correlation between the quadrupole deformation parameter β 2 and the splitting ?E/ E ¯ m of the giant dipole resonance (GDR) spectra is studied. The results confirm that ?E/ E ¯ m is proportional to quadrupole deformation β 2

In non-central high energy heavy ion collisions the colliding system posses a huge orbital angular momentum in the direction opposite to the normal of the reaction plane. Due to the spin-orbit coupling in strong interaction, such huge orbital angular momentum leads to the polarization of quarks and anti-quarks in the same direction. This effect, known as the global polarization effect, has been recently observed by STAR Collaboration at RHIC that confirms the theoretical prediction made more than ten years ago. The discovery has attracted much attention on the study of spin effects in heavy ion collision. It opens a new window to study properties of QGP and a new direction in high energy heavy ion physics -- Spin Physics in Heavy Ion Collisions. In this chapter, we review the original ideas and calculations that lead to the predictions. We emphasize the role played by spin-orbit coupling in high energy spin physics and discuss the new opportunities and challenges in this connection.

The initial conditions in heavy-ion collisions are calculated in many different frameworks. The importance of nucleon position fluctuations within the nucleus and sub-nucleon structure has been established when modeling initial conditions for input to hydrodynamic calculations. However, there remain outstanding puzzles regarding these initial conditions, including the measurement of the near equivalence of the elliptical v 2 and triangular v 3 flow coefficients in ultra-central 0-1% Pb+Pb collisions at the LHC. Recently a calculation termed MAGMA incorporating gluonic hot spots via two-point correlators in the Color Glass Condensate framework, and no nucleons, provided a simultaneous match to these flow coefficients measured by the ATLAS experiment, including in ultra-central 0-1% collisions. Our calculations reveal that the MAGMA initial conditions do not describe the experimental data when run through full hydrodynamic SONIC simulations or when the hot spots from one nucleus resolve hot spots from the other nucleus, as predicted in the Color Glass Condensate framework. We also explore alternative initial condition calculations and discuss their implications.

The description of hadron production in relativistic heavy-ion collisions in the statistical hadronization model is very good, over a broad range of collision energy. We outline this both for the light (u, d, s) and heavy (charm) quarks and discuss the connection it brings to the phase diagram of QCD.