The nuclear shell structure was motivated by the atomic model, which Jensen and his co-worker originally proposed. The high binding energy for some specific nuclei was at specific nucleon numbers; these are called ‘magic numbers'. The study of nuclear structure has been advanced on the basis of the shell structure associated with the magic numbers. These magic numbers are 2, 8, 10,28, 50, 82, 126. These magic numbers are truly near the valley of beta stability. But as we go towards drip-line new phenomena appear like melting of traditional magic numbers and emergence of new shell closure, neutron halo, skin, and different radioactivity decay modes like proton decay and beta decay, beta delayed particle emission.

The studies on exotic nuclei far from the stability line have started owing to the development of radioactive nuclear beams. The magic numbers in such exotic nuclei can be quite an intriguing issue. New magic numbers appear, and some disappear when moving from stable to exotic nuclei in a novel manner due to a particular part of the nucleon-nucleon interaction.

The development of collectivity, the island of inversion, and single-particle versus collective phenomena is the research topic of my research. The nucleus exists not only in spherical but also in prolate, oblate, and quadrupole shapes. Also, the conventional magic number of neutrons N = 28 has been broken down in the region of neutron-rich nuclei.

The Gamow Teller (GT) transitions, B(GT) values, allowed and forbidden beta decays, and electron capture reactions are important tools for the study of nuclear structure. In the recent past, nuclear structure study becomes more important to study electron capture rate and to predict nuclear transition matrix elements and finally half-lives of double beta decay and neutrinoless double beta decay.

1. Perform the modern large-scale calculation for the different mass regions of the nuclear chart using different effective interactions available.

2. Develop and tune a new effective interaction to explain the collectivity around N ~ 40 and also tune the existing effective interactions in this region

3. Perform the shell model calculations for

• Excitation energy states,
• Magnetic dipole moments,
• Electric dipole moments,
• Spectroscopic factor strengths,
• Gamow-Teller transitions strength,
• Q values, branching ratio,
• Log ft values,
• Beta decay half-lives of single beta decay and double beta decay, and
• Forbidden beta decay with newly developed interactions as well as with existing effective interactions.