High energy photons from the decay of giant dipole resonances (GDR) built on excited states provide an excellent probe in the study of nuclear structure properties, damping mechanisms etc., at finite temperatures. The dependence of GDR width on temperature (𝑇) and angular momentum (𝐽) has been the prime focus of many experimental and theoretical studies for the last few decades. The measured GDR widths for a wide range of nuclei at temperatures (1.5 < 𝑇 < 2.5 MeV) and spins (upto fission limit) were well described by the thermal shape fluctuation model (TSFM). But, at low temperatures (𝑇 < 1.5 MeV) there are large discrepancies between the existing theoretical models. The problem is compounded as there are very few experimental data in this region. At Variable Energy Cyclotron Centre, Kolkata, a programme for the systematic measurement of GDR width at very low temperatures has been initiated with precise experimental techniques. Several experiments have been performed by bombarding 7–12 MeV/nucleon alpha beam on various targets (⁶³Cu, ¹¹⁵In and ¹⁹⁷Au) and new datasets have been obtained at low temperatures (𝑇 < 1.5MeV) and at very lowspins (𝐽 < 20$\hbar$). The TSFM completely fails to represent the experimental data at these low temperatures in the entire mass range. In fact, the GDR width appears to be constant at its ground state value until a critical temperature is reached and subsequently increases thereafter, whereas the TSFM predicts a gradual increase of GDR width from its ground state value for 𝑇 > 0 MeV. In order to explain this discrepancy at low 𝑇, a new formalism has been put forward by including GDR-induced quadrupole moment in the TSFM.

Calculations of elastic scattering cross-sections for ^9,10,11Be+⁶⁴Zn at near-Coulomb barrier energy have been performed using a potential obtained from the double folding model and are compared with the experiment. In the framework of the double folding model, the nuclear matter densities of ^9,10,11Be projectiles and a ⁶⁴Zn target are folded with the complex energydependent effective M3Y interaction. The angular distributions of the differential cross-section for ^9,10Be scattering from ⁶⁴Zn at $E_{c.m.} \approx$24.5 MeV agree remarkably well with the data, while in case of ¹¹Be, calculations show a Coulomb–nuclear interference peak which is not observed in the data.

Compact stars such as neutron stars (NS) can have either hadronic or exotic states like strange quark or colour superconducting matter. Stars can also have a quark core surrounded by hadronic matter, known as hybrid stars (HS). The HS is likely to have a mixed phase in between the hadron and the quark phases. Observational results suggest huge surface magnetic field in certain NS. Therefore, we study here the effect of strong magnetic field on the respective equation of states (EOS) of matter under extreme conditions. We further study the hadron–quark phase transition in the interiors of NS giving rise to HS in the presence of strong magnetic field. The hadronic matter EOS is described based on RMF theory and we include the effects of strong magnetic fields leading to Landau quantization of the charged particles. For quark phase, we use the simple Massachusetts Institute of Technology (MIT) bag model, assuming density-dependent bag pressure and magnetic field. The magnetic field strength increases from the surface to the centre of the star. We construct the intermediate mixed phase using Glendenning conjecture. The magnetic field softens the EOS of both the matter phases. We finally study, the mass–radius relationship for such types of mixed HS, calculating their maximum mass, and compare them with the recent observations of pulsar PSR J1614-2230, which is about 2 solar mass.

An equation of state (EoS) for symmetric nuclear matter is constructed using the density-dependent M3Y effective interaction and extended for isospin asymmetric nuclear matter. Theoretically obtained values of symmetric nuclear matter incompressibility, isobaric incompressibility, symmetry energy and its slope agree well with experimentally extracted values. Folded microscopic potentials using this effective interaction, whose density dependence is determined from nuclear matter calculations, provide excellent descriptions for proton, alpha and cluster radioactivities, elastic and inelastic scattering. The nuclear deformation parameters extracted from inelastic scattering of protons agree well with other available results. The high density behaviour of symmetric and asymmetric nuclear matter satisfies the constraints from the observed flow data of heavy-ion collisions. The neutron star properties studied using 𝛽-equilibrated neutron star matter obtained from this effective interaction reconcile with the recent observations of the massive compact stars.

The nature of equation of state for the neutron star matter is crucially governed by the density dependence of the nuclear symmetry energy. We attempt to probe the behaviour of the nuclear symmetry energy around the saturation density by exploiting the empirical values for volume and surface symmetry energy coefficients extracted from the precise data on the nuclear masses.

Recent observations of high mass pulsar PSRJ1614-2230 has raised serious debate over the possible role of exotics in the dense core of neutron stars. The precise measurement of mass of the pulsar may play a very important role in limiting equation of state (EoS) of dense matter and its composition. Indirectly, it may also shape our understanding of the nucleon–hyperon or hyperon–hyperon interactions which is not well known. Within the framework of an effective chiral model, we compute models of neutron stars and analyse the hyperon composition in them. Further related implications are also discussed.

The direct part of real 𝛼−𝛼 interaction potential is calculated in the simple folding model using density-dependent Brink–Boeker effective interaction. The simple folding potentials calculated from the short- and finite-range components of this effective interaction are compared with their corresponding double folding results obtained from the oscillator model wave function to establish the relative accuracy of the model. It is found that the direct part of real 𝛼–𝛼 interaction potential calculated in the simple folding model is reliable.

We searched for the shell closure proton and neutron numbers in the superheavy region beyond 𝑍 = 82 and 𝑁 = 126 within the framework of non-relativistic Skryme–Hartree–Fock (SHF) with FITZ, SIII, SkMP and SLy4 interactions. We have calculated the average proton pairing gap $\Delta_p$, average neutron pairing gap $\Delta_n$, two-nucleon separation energy $S_{2q}$ and shell correction energy $E_{\text{shell}}$ for the isotopic chain of 𝑍 = 112–126. Based on these observables, 𝑍 = 120 with 𝑁 = 182 is suggested to be the magic numbers in the present approach.

By exploiting supersymmetry-inspired factorization method together with a judiciously chosen deuteron ground-state wave function, approximate higher partial wave nucleon–nucleon potentials are generated. In this context, a minor modification is also introduced to the generated potentials. The n–p scattering phase shifts are computed and analysed via the phase function method.

With the discovery of a large number of superheavy nuclei undergoing decay through 𝛼 emissions, there has been a revival of interest in 𝛼 decay in recent years. In the theoretical study of 𝛼 decay the 𝛼-nucleus potential, which is the basic input in the study of 𝛼-nucleus systems, is also being studied using advanced theoretical methods. In the light of these, theWentzel–Kramers–Brillouin (WKB) approximation method often used for the study of 𝛼 decay is critically examined and its limitations are pointed out. At a given energy, the WKB expression uses barrier penetration formula for the determination of the transmission coefficient. This approach utilizes the 𝛼-nucleus potential only at the barrier region and ignores it elsewhere. In the present era, when one has more precise experimental information on decay parameters and better understanding of 𝛼-nucleus potential, it is desirable to use a more precise method for the calculation of decay parameters. We describe the analytic 𝑆-matrix (SM) method which gives a procedure for the calculation of decay energy and mean life in an integrated way by evaluating the resonance pole of the 𝑆-matrix in the complex momentum or energy plane. We make an illustrative comparative study of WKB and 𝑆-matrix methods for the determination of decay parameters in a number of superheavy nuclei.

Heavy-ion collision simulations in various classical models are discussed. Heavy-ion reactions with spherical and deformed nuclei are simulated in a classical rigid-body dynamics (CRBD) model which takes into account the reorientation of the deformed projectile. It is found that the barrier parameters depend not only on the initial orientations of the deformed nucleus, but also on the collision energy and the moment of inertia of the deformed nucleus. Maximum reorientation effect occurs at near- and below-barrier energies for light deformed nuclei. Calculated fusion crosssections for ²⁴Mg + ${}^{208}$Pb reaction are compared with a static-barrier-penetration model (SBPM) calculation to see the effect of reorientation. Heavy-ion reactions are also simulated in a 3-stage classical molecular dynamics (3S-CMD) model in which the rigid-body constraints are relaxed when the two nuclei are close to the barrier thus, taking into account all the rotational and vibrational degrees of freedom in the same calculation. This model is extended to simulate heavy-ion reactions such as ⁶Li + ²⁰⁹Bi involving the weakly-bound projectile considered as a weakly-bound cluster of deuteron and ${}^{4}$He nuclei, thus, simulating a 3-body system in 3S-CMD model. All the essential features of breakup reactions, such as complete fusion, incomplete fusion, no-capture breakup and scattering are demonstrated.

The transverse momentum spectra of the produced hadrons have been compared to a model, which is based on the assumption that a nucleus–nucleus collision is a superposition of isotropically decaying thermal sources at a given freeze-out temperature. The freeze-out temperature in nucleus–nucleus collisions is fixed from the inverse slope of the transverse momentum spectra of hadrons in nucleon–nucleon collision. The successive collisions in the nuclear reaction lead to gain in transverse momentum, as the nucleons propagate in the nucleus following a random walk pattern. The average transverse rapidity shift per collision is determined from the nucleon–nucleus collision data. Using this information, we obtain parameter-free result for the transverse momentum distribution of produced hadrons in nucleus–nucleus collisions. It is observed that such a model is able to explain the transverse mass spectra of the produced pions at SPS energies. However, it fails to satisfactorily explain the transverse mass spectra of kaons and protons. This indicates the presence of collective effect which cannot be accounted for, by the initial state collision broadening of transverse momentum of produced hadrons, the basis of random walk model.

We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of the largest cluster at different $Z_{\text{bound}}$, differential charge distribution and cross-section of neutron-rich nuclei of different projectile fragmentation reactions at different energies are described. Application of nuclear multifragmentation reaction in basic research as well as in other domains is outlined.

The dynamical description of light, intermediate, heavy and superheavy nuclei formed in heavy-ion collisions is worked out using the dynamical cluster decay model (DCM), with reference to various effects such as deformation and orientation, temperature, angular momentum etc. Based on the quantum mechanical fragmentation theory (QMFT), DCM has been applied to understand the decay mechanism of a large number of nuclei formed in low-energy heavy-ion reactions. Various features related to the dynamics of competing decay modes of nuclear systems are explored by addressing the experimental data of a number of reactions in light, intermediate, heavy and superheavy mass regions. The DCM, being a non-statistical description for the decay of a compound nucleus, treats light particles (LPs) or equivalently evaporation residues (ERs), intermediate mass fragments (IMFs) and fission fragments on equal footing and hence, provides an alternative to the available statistical model approaches to address fusion–fission and related phenomena.

Many empirical evidences that point to the existence of preferred magic nucleon numbers for superdeformed (SD) shapes are presented in this paper. We use a simple premise based on the 4-parameter formula fitted using observed 𝛾-rays of SD bands. In particular, plots of 𝛾-ray energy ratios, nuclear softness parameter values and the number of SD bands for given 𝑁 and 𝑍 are used to pinpoint the magicity (𝑁, 𝑍 numbers) that are most favoured as the SD magic numbers. This analysis also leads to several new predictions on the occurrence of SD bands specially in neutron-rich nuclei.