### Isospin symmetry breaking in the mirror pair $^{73}$Sr-$^{73}$Br

The recent experimental observation of isospin symmetry breaking (ISB) in the ground states of the $T=3/2$ mirror pair $^{73}$Sr - $^{73}$Br is theoretically studied using large-scale shell model calculations. The large valence space and the successful PFSDG-U effective interaction used for the nuclear part of the problem capture possible structural changes and provide a robust basis to treat the ISB effects of both electromagnetic and non-electromagnetic origin. The calculated shifts and mirror-energy-differences are consistent with the inversion of the $I^{\pi}$= 1/2$^{-}, 5/2^{-}$ states between $^{73}$Sr - $^{73}$Br, and suggest that the role played by the Coulomb interaction is dominant. An isospin breaking contribution of nuclear origin is estimated to be $\approx 25$ keV.

### A field theoretical model for quarkyonic matter

The possibility that nuclear matter at a density relevant to the interior of massive neutron stars may be a quarkynoic matter has attracted considerable recent interest. In this work, we construct a field theoretical model to describe the quarkyonic matter, that would allow quantitative and systematic calculations of its various properties. This is implemented by synthesizing the Walecka model together with the quark-meson model, where both quark and nucleon degrees of freedom are present based on the quarkyonic scenario. With this model we compute at mean-field level the thermodynamic properties of the symmetric nuclear matter and calibrate model parameters through well-known nuclear physics measurements. We find this model gives a very good description of the symmetric nuclear matter from moderate to high baryon density and demonstrates a continuous transition from nucleon-dominance to quark-dominance for the system.

### A New Radioactive Decay Mode, True Ternary Fission, the Decay of Heavy Nuclei Into Three Comparable Fragments

The ternary cluster decay of heavy nuclei has been observed in several experiments with binary coincidences between two fragments using detector telescopes (the FOBOS-detectors, JINR, Dubna) placed on the opposite sides from the source of fissioning nuclei. The binary coincidences at a relative angle of 180$^0$ deg. correspond to binary fission or to the decay into three cluster fragments by registration of two nuclei with different masses (e.g.$^{132}$Sn,$^{52-48}$Ca,$^{68-72}$Ni). This marks a new step in the physics of fission-phenomena of heavy nuclei. These experimental results for the collinear cluster tripartition (CCT), refer to the decay into three clusters of comparable masses. In the present work we discuss the various aspects of this ternary fission (FFF) mode. The question of collinearity is analysed on the basis of recent publications. Further insight into the possible decay modes is obtained by the discussion of the path towards larger deformation, towards hyper-deformation and by inspecting details of the potential energy surfaces (PES). In the path towards the extremely deformed states leading to ternary fission, the concept of deformed shells is most important. At the scission configuration the phase space determined by the PES's leads to the final mass distributions. The possibility of formation of fragments of almost equal size ($Z_i$ = 32, 34, 32, for $Z$=98) and the observation of several other fission modes in the same system can be predicted by the PES. The PES's show pronounced minima and valleys, namely for several mass/charge combinations of ternary fragments, which correspond to a variety of collinear ternary fission (multi-modal) decays. The case of the decay of $^{252}$Cf(sf,fff) turns out to be unique due to the presence of deformed shells in the total system and of closed shells in all three nuclei in the decay.

### Shell Evolution in Neutron-rich Ge, Se, Kr and Sr Nuclei within RHB Approach

The exotic even-even isotopic chains from Z=32 to Z=38 are investigated by means of the relativistic Hartree-Bogoliubov (RHB) approach with the explicit Density Dependent Meson-Exchange (DD-ME2) and Density Dependent Point-Coupling (DD-PC1) models. The classic magic number N=50 is reproduced and the new number N=70 is predicted to be a robust shell closure by analysing several calculated quantities such as: two-neutron separation energies, two-neutron shell gap, neutron pairing energy, potential energy surface and neutron single particle energies with and without the tensor force. The obtained results are corroborated by shell model calculations and compared with the predictions of finite range droplet model (FRDM) and with the available experimental data. A reasonable and satisfactory agreement between the theoretical models and experiment is established.

### Relativistic nuclear collisions: Establishing the non-critical baseline for fluctuation measurements

We study the influence of global baryon number conservation on the non-critical baseline of net baryon cumulants in heavy-ion collisions in a given acceptance, accounting for the asymmetry between the mean-numbers of baryons and antibaryons. We derive the probability distribution of net baryon number in a restricted phase space from the canonical partition function that incorporates exact conservation of baryon number in the full system. Furthermore, we provide tools to compute cumulants of any order from the generating function of uncorrelated baryons constrained by exact baryon number conservation. % The results are applied to quantify the non-critical baseline for cumulants of net proton number fluctuations obtained in heavy-ion collisions by the STAR collaboration at different RHIC energies and by the ALICE collaboration at the LHC. Furthermore, volume fluctuations are added by a Monte Carlo procedure based on the centrality dependence of charged particle production as measured experimentally. % Compared to the predictions based on the hadron resonance gas model or Skellam distribution a clear suppression of fluctuations is observed due to exact baryon-number conservation. The suppression increases with the order of the cumulant and towards lower collision energies. Predictions for net proton cumulants up to the eight order in heavy-ion collisions are given for experimentally accessible collision energies.

### Mean Field Tunneling Dynamics of Superfluid Fermi Systems. Spontaneous and Induced Fission

Existing mean field theories of imaginary time dynamics describing tunneling "bounce" of interacting Fermi systems are of the Hartree-Fock type in which the pairing effects are ignored. Here we extend this theory to the Hartree-Fock-Bogoliubov(HFB) framework and derive the corresponding generalisation of imaginary time dependent Bogoliubov-de Gennes (BdG) mean field equations. We construct a representation of the partition function as a functional integral type of sum over complete sets of states. These states are generated by a trial imaginary time dependent Hamiltonian. Taking this Hamiltonian as describing non interacting BdG quasiparticles we use the convex inequality to optimise its dynamical parameters at any given temperature. A prominent feature of the resulting mean field equations is an inseparable interplay between quantum dynamical and entropic statistical effects. With increasing excitation energy (effective temperature) the decay process is gradually evolving from pure quantum tunneling to statistical "bottle neck" escape mechanism. Correspondingly the resulting bounce action is a sum of two terms - statistically weighted dynamical penetrability action and tunneling entropy. The first (second) term gradually decreases (increases) with increasing effective temperature. BdG equations for the "false ground state" tunneling decay (spontaneous fission in nuclear physics) are obtained in the zero temperature limit of our formalism. At finite temperature our tunneling equations should be useful e.g. to describe tunneling decays of excited microcanonical ensemble of states as a microscopic framework for the phenomenology of induced fission phenomena.

### Diffractive two-meson electroproduction with a nucleon and deuteron target

The diffractive electro- or photo-production of two mesons separated by a large rapidity gap gives access to generalized parton distributions (GPDs) in a very specific way. First, these reactions allow to easily access the chiral-odd transversity quark GPDs by selecting one of the produced vector meson to be transversely polarized. Second, they are only sensitive to the so-called ERBL region where GPDs are not much constrained by forward quark distributions. Third, the skewness parameter $\xi$ is not related to the Bjorken $x_\text{Bj}$ variable, but to the size of the rapidity gap. We analyze different channels ($\rho_L^0\,\rho_{L/T}, \rho^0_L\,\omega_{L/T}$ and $\rho^0_L\,\pi$ production) on nucleon and deuteron targets. The analysis is performed in the kinematical domain where a large momentum transfer from the photon to the diffractively produced vector meson introduces a hard scale (the virtuality of the exchanged hard Pomeron). This enables the description of the hadronic part of the process in the framework of collinear factorization of GPDs. We show that the unpolarized cross sections depend very much on the parameterizations of both chiral-even and chiral-odd quark distributions of the nucleon, as well as on the shape of the meson distribution amplitudes. The rates are shown to be in the range of the capacities of a future electron-ion collider.

### Generalized Rastall's gravity and its effects on compact objects

We present a generalization of Rastall's gravity in which the conservation law of the energy-moment tensor is altered, and as a result, the trace of the energy-moment tensor is taken into account together with the Ricci scalar in the expression for the covariant derivative. Afterwards, we obtain the field equation in this theory and solve it by considering a spherically symmetric space-time. We show that the external solution has two possible classes of solutions with spherical symmetry in the vacuum in generalized Rastall's gravity. The first class of solutions is completely equivalent to the Schwarzschild solution, while the second class of solutions has the same structure as the Schwarzschild--de Sitter solution in general relativity. The generalization, in contrast to constant value $k=8\pi G$ in general relativity, has a gravitational parameter $k$ that depends on the energy density $\rho$. As an application, we perform a careful analysis of the effects of the theory on neutron stars using realistic equations of state (EoS) as inputs. Our results show that important differences on the profile of neutron stars are obtained within two representatives EoS.

### GW190814's secondary component with mass $(2.50-2.67)$ M$_{\odot}$ as a super-fast pulsar

Using Stergioulas's RNS code for investigating fast pulsars with Equation of States (EOSs) on the causality surface (where the speed of sound equals to that of light) of the high-density EOS parameter space satisfying all known constraints from both nuclear physics and astrophysics, we show that the GW190814's secondary component of mass $(2.50-2.67)$ M$_{\odot}$ can be a super-fast pulsar spinning faster than 971 Hz about 42\% below its Kepler frequency. There is a large and physically allowed EOS parameter space below the causality surface where pulsars heavier than 2.50 M$_{\odot}$ are supported if they can rotate even faster with critical frequencies depending strongly on the high-density behavior of nuclear symmetry energy.

### Probing topological order of QCD at Electron Ion Collider

The idea that the nuclear matter may posses long range topological order is supported by the theory and the lattice calculations. At high temperature this order is instrumental in producing anomalous phenomena such as the Chiral Magnetic Effect. In the cold nuclear matter it affects the gluon distribution in the nuclear wave function at low $x$. The effect of the topological order is encapsulated in the unintegrated gluon distribution functions which are proportional, at the leading order, to the square of the gluon propagator at finite topological charge density. It is argued that the Electron Ion Collider is well suited to study the topological order of the cold nuclear matter.