Nuclear physics research is growing on several fronts, along energy and intensity frontiers, with exotic projectiles and targets. The nuclear physics facilities under construction and those being planned for the future make the prospects for research in this field very bright.

Based on the general analysis of the grand canonical partition function in the 𝑆-matrix framework, a method is presented to calculate the equation of state of dilute warm nuclear matter. The result is a model-independent virial series for the pressure and density that systematically includes contributions from all the ground and excited states of all the stable nuclear species and their scattering channels. The multiplicity distribution of these species to keep the matter in statistical equilibrium is found out and then the pressure, incompressibility and the symmetry energy of the system are evaluated. The calculated symmetry energy coefficients are found to be in fair agreement with the recent experimental data.

A simple form for nucleon–nucleon (NN) potential is introduced as an alternative to the popular M3Y form using the relativistic mean field theory (RMFT) with the non-linear terms in 𝜎 -meson for the first time. In contrast to theM3Y form, the new interaction becomes exactly zero at a finite distance and the expressions are analogous with the M3Y terms. Further, its applicability is examined by the study of proton and cluster radioactivity by folding it with the RMFT-densities of the cluster and daughter nuclei to obtain the optical potential in the region of proton-rich nuclides just above the double magic core ¹⁰⁰Sn. The results obtained were found comparable with the widely used M3Y $NN$ interactions.

Recently, a digital data acquisition system with 96 channels has been set up for the Indian National Gamma Array (INGA) consisting of 24 Compton-suppressed clover detectors. The digital system provides higher throughput, better energy resolution and better stability for the multidetector Compton-suppressed clover array compared to the previous conventional system with analog shaping. A number of nuclear spectroscopic experiments have been carried out using the array. Selected results from this array will be presented which highlight different excitations of nuclei near-shell gaps.

The deformed configurations and rotational band structures in $N=50$ Ge and Se nuclei are studied by deformed Hartree–Fock with quadrupole constraint and angular momentum projection. Apart from the `almost’ spherical HF solution, a well-deformed configuration occurs at low excitation. A deformed well-mixed $\Omega = 1/2^+$ neutron orbit comes down in energy (from the shell above $N = 50$) to break the $N = 50$ spherical shell closure. A 𝐾 = 7⁻ isomer is predicted in ⁸⁴Se at fairly low excitation energy. At higher excitation energies (8 MeV), a deformed band with 𝛺 = 7/2⁺–1/2⁻ (based on $h_{11/2}$) neutron 1p–1h excitation, for ⁸²Ge and ⁸⁴Se, is shown in our calculation. Our study gives insight into possible deformed structures at spherical shell closure.

Experimental evidence accumulated during the last two decades indicates that the fission of excited heavy nuclei involves a dissipative dynamical process. We shall briefly review the relevant dynamical model, namely the Langevin equations for fission. Statistical model predictions using the Kramers’ fission width will also be discussed.

Three different types of experiments have been performed to explore the complete and incomplete fusion dynamics in heavy-ion collisions. In this respect, first experiment for the measurement of excitation functions of the evaporation residues produced in the ²⁰Ne+¹⁶⁵Ho system at projectile energy ranges ≈2–8 MeV/nucleon has been done. Measured cumulative and direct crosssections have been compared with the theoretical model code PACE-2, which takes into account only the complete fusion process. It has been observed that, incomplete fusion fraction is sensitively dependent on projectile energy and mass asymmetry between the projectile and the target systems. Second experiment for measuring the forward recoil range distributions of the evaporation residues produced in the ²⁰Ne+¹⁶⁵Ho system at projectile energy ≈8MeV/nucleon has been done. It has been observed that, some evaporation residues have shown additional peaks in the measured forward recoil range distributions at cumulative thicknesses relatively smaller than the expected range of the residues produced via complete fusion. The results indicate the occurrence of incomplete fusion involving the breakup of ²⁰Ne into ⁴He+¹⁶O and/or ⁸Be+₁₂C followed by one of the fragments with target nucleus ¹⁶⁵Ho. Third experiment for the measurement of spin distribution of the evaporation residues produced in the ¹⁶O+¹²⁴Sn system at projectile energy ≈6 MeV/nucleon, showed that the residues produced as incomplete fusion products associated with fast 𝛼 and 2𝛼-emission channels observed in the forward cone, are found to be distinctly different from those of the residues produced as complete fusion products. The spin distribution of the evaporation residues also inferred that in incomplete fusion reaction channels input angular momentum ($J_0$) increases with fusion incompleteness when compared to complete fusion reaction channels. Present observation clearly shows that the production of fast forward 𝛼-particles arises from relatively larger angular momentum in the entrance channel leading to peripheral collision.

Cluster knockout reactions are expected to reveal the amount of clustering (such as that of 𝛼, d and even of heavier clusters such as ¹²C, ¹⁶O etc.) in the target nucleus. In simple terms, incident medium high-energy nuclear projectile interacts strongly with the cluster (present in the target nucleus) as if it were existing as a free entity. Theoretically, the relatively softer interactions of the two outgoing particles with the residual nucleus lead to optical distortions and are treated in terms of distorted wave (DW) formalism. The long-range projectile–cluster interaction is accounted for, in terms of the finite range (FR) direct reaction formalism, as against the more commonly adopted zero-range (ZR) distorted wave impulse approximation (DWIA) formalism. Comparison of the DWIA calculations with the observed data provide information about the momentum distribution and the clustering spectroscopic factor of the target nucleus. Interesting results and some recent advancements in the area of (𝛼, 2𝛼) reactions and heavy cluster knockout reactions are discussed. Importance of the finite-range vertex and the final-state interactions are brought out.

We present here, an overview and progress of the theoretical works on the isomeric state 𝛼 decay, 𝛼 decay fine structure of even–even, even–odd, odd–even and odd–odd nuclei, a study on the feasibility of observing 𝛼 decay chains from the isotopes of the superheavy nuclei $Z = 115$ in the range $271 \leq A \leq 294$ and the isotopes of $Z = 117$ in the range $270 \leq A \leq 301$, within the Coulomb and proximity potential model for deformed nuclei (CPPMDN). The computed half-lives of the favoured and unfavoured 𝛼 decay of nuclei in the range $67 \leq Z \leq 91$ from both the ground state and isomeric state, are in good agreement with the experimental data and the standard deviation of half-life is found to be 0.44. From the 𝛼 fine structure studies done on various ranges of nuclei, it is evident that, for nearly all the transitions, the theoretical values show good match with the experimental values. This reveals that CPPMDN is successful in explaining the fine structure of even–even, even–odd, odd–even and odd–odd nuclei. Our studies on the 𝛼 decay of the superheavy nuclei ${}^{271−294}$115 and ${}^{270−301}$117 predict 4𝛼 chains consistently from ${}^{284,285,286}$115 nuclei and 5𝛼 chains and 3𝛼 chains consistently from ${}^{288−291}$117 and ${}^{292}$117, respectively. We thus hope that these studies on ${}^{284−286}$115 and ${}^{288−292}$117 will be a guide to future experiments.

A general decay formula for the emission of charged particles from metastable nuclei is developed based on the basic phenomenon of resonances occurring in quantum scattering process under Coulomb-nuclear potential. It relates the half-lives of radioactive decays with the 𝑄 values of the outgoing elements with masses and charges of the nuclei involved in the decay. The relation is found to be a generalization of the Geiger–Nuttall law in 𝛼 radioactivity and explains well all the known emissions of charged particles including clusters, alpha and proton.

Study of intermediate mass fragments (IMFs) and light charged particles (LCPs) emission has been carried out for a few reactions involving 𝛼-cluster and non-𝛼-cluster systems to see how the emission processes are affected by nuclear clustering. Li, Be, B and 𝛼-particles have been studied from α-clustered system ¹⁶O + ¹²C for 117, 125, 145 and 160 MeV bombarding energies respectively. The enhanced yields of near-entrance channel fragment B and large quadrupole deformation of the produced composite ²⁸Si$^{\ast}$ extracted from LCP spectra indicate the survival of orbiting-like process in ¹⁶O + ¹²C system at these energies. The same IMFs emitted from the 𝛼-cluster system ¹²C (77 MeV) + ²⁸Si and nearby non-𝛼 cluster ¹¹B (64 MeV) + ²⁸Si and ¹²C (73 MeV) + ${}^{27}$Al (all having the same excitation energy of ∼67 MeV) have also been studied. The fully energy damped (fusion–fission) and the partially energy damped (deep inelastic) components of the fragment energy spectra have been extracted. It has been found that the yields of the fully energy damped fragments for all the above reactions are in conformity with the respective statistical model predictions. The time-scales of various deep inelastic fragment emissions have been extracted from the angular distribution data. The angular momentum dissipation in deep inelastic collisions has been estimated from the data and it has been found to be close to the corresponding sticking limit value.

In this paper, an overview of some aspects of quantum phase transitions (QPT) in nuclei is given and they are: (i) QPT in interacting boson model ($sd$IBM), (ii) QPT in two-level models, (iii) critical point 𝐸(5) and 𝑋(5) symmetries, (iv) QPT in a simple solvable model with three-body forces. In addition, some open problems are also given.

The spectroscopic properties of ⁶⁴Zn and ⁶⁴Ni are calculated within the framework of the deformed shell model (DSM) based on Hartree–Fock states. GXPF1A interaction in 1 $f_{7/2}$, 2$p_{3/2}$, 1$f_{5/2}$ and 2$p_{1/2}$ space with ⁴⁰Ca as the core is employed. After ensuring that DSM gives good description of the spectroscopic properties of low-lying levels in these two nuclei considered, nuclear transition matrix elements (NTME) for the neutrinoless positron double beta decay (0$\nu \beta^+$ and $0\nu \beta^+$EC) of ⁶⁴Zn are calculated. The two-neutrino positron double beta decay halflife is also calculated for this nucleus.

A multidetector gamma array (GDA), for studying nuclear structure was built with ancillary devices namely gamma multiplicity filter and charged particle detector array. This facility was designed for in-beam gamma spectroscopy measurements in fusion evaporation reactions at Inter-University Accelerator Centre, New Delhi. Description of the facility and in-beam performance with two experimental studies done are presented. This array was used in a number of nuclear spectroscopic and reaction investigations.