Research Journey
The High Spin Back-bending phenomenon
My early training and Ph.D. research work led me towards the field of “nuclear structure studies of deformed nuclei”. Seventies was a time when high spin physics was thriving. My Ph.D. thesis involved developing a simple exponential pairing model for back-bending phenomenon in even-even deformed rare-earth nuclei (Physical Review C18, 1906, 1978; Journal of Physics G4, 81, 1978). I followed this topic for many years, publishing several papers.
Symmetries and Identical Bands in normal deformed nuclei
I also became quite interested in the symmetries observed in the rotational structures and their close relationship with the Lie group algebra. This was also the time when the Interacting Boson Model was thriving. I will sit with loads of nuclear level structure data and try to look for some visible symmetries in the spectra. This led me to the first observation of “identical” band (IB) patterns on a wide scale in normal rotational bands around 1980. These were interpreted as “strongly decoupled bands” in odd-A deformed nuclei. First published in 1984 (Z. Physik A317, 2050, 1984; Phys. Rev. C30, 2050, 1984), it was followed up by the observation of identical band structures in a group of nuclei and interpreted in terms of SU(7) Lie group (Z. Physik A320, 648, 1985), with partial success. Later on, we tried to provide an interpretation in terms of F-spin multiplets (Modern Physics Letters A3, 743, 1988). We found many examples of the IB structures in the rare-earths (Reviews of Modern Physics 62, 393-509, 1990) and the actinide region (At. Data & Nucl. Data Tables 50, 269- 342, 1992).
Odd-Odd Nuclei, the GM splitting, and the odd-even effects
My interests shifted to 2-quasi particle and multi-quasi particle structures in deformed Odd- Odd Nuclei and even-even nuclei in the 80s. We noticed for the first time a significant odd- even effect in the K – bands in doubly odd nuclei. This was quite unusual and we could explain it in terms of higher-order Coriolis couplings in odd-odd nuclei (Phys. Lett. B209, 19, 1988; Phys. Rev. C40, 4320, 1989). These studies were further extended to explain the phenomenon of signature inversion in odd-odd nuclei also (Phys. Lett. B277, 233, 1992; Nucl. Phys. A620, 265, 1997; Reviews of Modern Physics 70, 843-895, 1998, Atomic Data & Nuclear Data Tables, 69, 239-348, 1998; 69, 239-348, 1998).
Multi-Quasiparticle States
My work on the odd-odd nuclei (which largely exhibit 2qp n-p states at low energies) was further extended to more complex states like two and three quasiparticle (2qp, 3qp) states and multi quasiparticle (MQP) states in even-even and odd-A nuclei. We observed a new phenomenon of signature reversal in 2qp states of some even-even nuclei and also explained it in terms of higher order Coriolis effects (Physics Letters B337, 240-244, 1994). The G-M rules applicable to odd-odd nuclei were generalized by to three quasi-particle states and a model was proposed for the same (Physical Review C45, 3013-3016, 1992; Physical Review C75,067301,2007). We recently developed a model for the three-quasi- particle states (3qp plus rotor model) which is being used to understand the high spin features of the 3qp bands (At. Data & Nucl. Data Tables 92, 1, 2006; Physica Scripta T125, 186, 2006; Phys. Rev. C75, 067301, 2007).
Super-deformed Bands
Experimental observation of the high spin super-deformed (SD) bands was one of the most surprising discoveries in nuclear structure physics in the last decade of the 20 th century. These bands display some very unusual properties like near rigid-rotor behaviour and total disconnectedness with normal level structures. We pointed out many new features of the SD bands like a weak oscillation in the gamma ray energies, and negative alignment (J. Korean Phys. Soc. 29, S361-S365, 1996; Physics Letters B412, 14-18,1997).
Semi-classical Methods in Nuclear Physics
Continuing this work on SD bands, we successfully applied the semi-classical methods to understand the high spin super-deformed (SD) bands. A semi-classical analysis of the conventional models such as the Particle-Rotor model and the Cranking model was carried out and several new features of SD bands were pointed out (Physics Letters B392, 243-248, 1997; Physics Letters B370, 1, 1996). In particular, a large starting spin for the band-head of the SD bands, weak oscillations and no linking transitions to normal states were shown to be closely related to the generally ignored non-linearity in the model Hamiltonian and the ensuing second order phase transition (Int. J. Mod. Phys. E9, 487-506, 2000). We have also used the new and powerful technique of the Periodic Orbit Theory (POT) to understand the dynamics of deformed nuclei. A complete periodic orbit theory of deformed systems was worked out and the role of three-dimensional periodic orbits was brought out in the context of SD bands (Int. J. Mod. Phys. E11, 1-17, 2002). We also obtained the level density of spherical systems in a novel way by using the periodic orbit dynamics (Pramana – J. Phys. 53, 243, 1999).
Magnetic Rotation Bands
One does not expect rotational spectra in nearly spherical nuclei. It was, therefore, a big surprise when well-developed quasi-rotational bands were seen in many Pb isotopes which are known to be nearly spherical in nature. The levels of the bands were strongly linked by magnetic transitions rather than electric transitions. It has now been recognized that this rotation is not of the charge density as in deformed nuclei but is rather of currents (a magnetic top). We completed a review of this area and identified as many as 178 candidates for the magnetic rotation (MR) bands all across the chart of nuclides (Atomic Data Nucl. Data Tables, 74, 283-331 (2000); http://www.nndc.bnl.gov/publications/preprints/mag-dip- rot-bands.pdf, 2007). We have used the particle-rotor model as well as the self-consistent Tilted Axis Cranking model in pursuing a theoretical understanding of this phenomenon. We also started an experimental program in this area and were successful in discovering many new MR bands along with new features like shape mixing, and crossing of two magnetic bands (Nucl. Phys. A732, 13 (2004); Nucl. Phys. A761, 1-21 (2005); Phys. Rev. C69, 014319 (2004); Phys. Rev. C66, 041303 (R), 2004). More recently, we have reviewed this phenomenon again and identified confirmed as well as not so well confirmed examples of 248 MR bands in 123 nuclides (https://arxiv.org/ftp/arxiv/papers/2303/2303.00499.pdf, 91 pages).
Anti-Magentic Rotation (AMR) bands
A phenomenon closely related to the magnetic rotation bands was also proposed by Stefan Frauendrof, in an analogy to anti-ferromagnetism in solids. This leads to a new kind of phenomenon termed as 'Anti-magnetic Rotation' (AMR). An AMR band was first observed in an odd-A nucleus 105Cd in 2010 by our group (Phys. Rev. C (Rapid Comm) 82, 061308, 2010). This was later followed by the first example of more than one AMR band in a single nucleus, in 107Cd (Phys. Rev. C 87, 034304, 2013). Also, the first observation of an AMR and a MR band coexisting together was also made in 107Cd by us in 2015 (Phys. Rev. C 91, 014318, 2015). A more recent work compiles the present situation of the MR bands and AMR bands together in our article Atomic Data & Nuclear Data Tables 165, 101735 (2025).
Nuclear Isomers and Generalized Seniority
We formally started to work in the field of nuclear isomers in a focussed way in 2012, with the joining of Bhoomika in our group as a Ph.D. student. We prepared the first “Atlas of Nuclear Isomers” and produced a reliable data book in 2015 (Nuclear Data Sheets 128, 1, 2015). This work has now been updated, and more comprehensive Second Edition of the Atlas has also been published in 2023 (At. Data & Nucl. Data Tables 150, 101546, 2023). The idea behind this effort was to arrive at a global view of nuclear isomers and discover a new type of isomerism. Eventually, we discovered a new type of seniority isomer, which have multi-j configuration and decay by odd tensor electric transitions (Physics Letters B 753, 122 2016). We used the generalized seniority formalism to carry out many new calculations and have been able to explain the long-standing puzzle of double hump behavior of BE2 values in Sn isotopes (Nuclear Physics A 952, 62, 2016). This work has been greatly expanded to explain features of the chain of Sn isotopes, and isotopes and isotones around magic numbers and has led to a series of publications. We have also published the first book on nuclear isomers entitled “Nuclear Isomers- A Primer” in 2021 (Springer-Verlag).
Isospin dominance in n-rich systems and nuclear fission
I was attracted to exploring the possible role of isospin in neutron rich fission fragment distribution from an experiment carried out at B.A.R.C. (Mumbai) by the group of D. Biswas. It led me to propose signatures of isospin dependence in the fission fragment mass distribution of heavy nuclei, which proceeded by the path of compound nucleus formation, first published in a conference proceeding (Nucl. Data Sheets 120C, 123, 2014). This novel finding was later expanded to include the effect of weight factors of different channels in the various partitions of fission fragments (Physica Scripta 92, 2017, 094001; Physica Scripta 93, 14008, 2018; Pramana – J. Phys. 92, 35, 2019; European Physical Journal – Special Topics, 229, 2527, 2020). Application of this method to thermal neutron fission has also yielded reasonable results (Phys. Rev. C 103, 044322,2021). This is not so surprising when we realize that the isopsin becomes increasingly pure with the rise in neutron richness in nuclei. Since one of the fission fragments is always neutron rich, the isospin conservation must show up in a strong way.
Applications of Nuclear Physics to Hydrological problems and Nuclear Security
I have also applied the nuclear techniques to problems of societal applications. One of the important applications was made by using the technique of stable isotopes to trace the movement of rain over India. A primary study was made to study the isotopic composition of atmospheric moisture and isotopic fractionation of evaporating water of different isotopic composition (Isotopes in Environmental and Health Studies 51, 426, 2015; Journal of Radioanalytical Nuclear Chemistry 302, 975, 2014). Lately, I have also been providing full support and advice to the development of a nuclear security education lab at the Amity University since 2019 and providing expertise to hold a series of meetings in this area (International Journal of Nuclear Security 7, Article 11, 2022).
Nuclear Data Program in India
I established the first nuclear data program in India around 2004 and started the Nuclear Data Centre India under the aegis of IAEA. After getting a training at a workshop at IAEA in 2004 and working with Dr. Balraj Singh for more advanced experience in nuclear structure and decay data evaluation (we together evaluated the A=165 mass chain), I began a program of evaluation and training others in India. Since then, I have been involved in evaluating a large number of mass chains and many horizontal evaluations. The Nuclear Data Centre has now been shifted from IIT Roorkee to VECC Kolkata. I continue to be an expert member in the Nuclear Structure and Decay Data Network of IAEA. (EPJ Web of Conf. 239, 15004, 2020)