A conventional tandem Van de Graaff accelerator is used to produce charged carbon cluster beams. The unique capability of the method for studying highly charged clusters unaccessible to other methods of producing cluster beams is demonstrated.

Thesdg interacting boson model (sdgIBM), which includes monopole (s), quadrupole (d) and hexadecupole (g) degrees of freedom, enables one to analyze hexadecupole (E4) properties of atomic nuclei. Various aspects of the model, both analytical and numerical, are reviewed emphasizing the symmetry structures involved. A large number of examples are given to provide understanding and tests, and to demonstrate the predictiveness of thesdg model. Extensions of the model to include proton-neutron degrees of freedom and fermion degrees of freedom (appropriate for odd mass nuclei) are briefly described. A comprehensive account ofsdgIBM analysis of all the existing data on hexadecupole observables (mainly in the rare-earth region) is presented, includingβ₄ (hexadecupole deformation) systematics,B(IS4; 0_GS⁺→4_γ⁺) systematics that give information about hexadecupole component in γ-vibration,E4 matrix elements involving few low-lying 4⁺ levels,E4 strength distributions and hexadecupole vibrational bands in deformed nuclei.

Exact solutions of the potentialV(r)=−Ze²/(r+β),β>0 are obtained in theN-dimensional space for certain values ofβ by means of factorization of infinite Hill determinant. We discuss some features of the radial wave Schrödinger equation in theN-dimensional space.

We consider the scattering problem for absorptive interactions within the framework of phase-function method. A Green’s function approach is used to derive the phase equation. As a case study we apply the algorithm presented on a shallow α-α potential, the real and imaginary parts of which have been deduced from experimental data. The real and imaginary parts of theS-wave phase shift are found to vary smoothly with energy while those forD andG waves show some fluctuations in the low-energy region. It is shown that studies in spatial behaviour of the phase function provide a plausible explanation for the dynamical origin of these fluctuations.

The influence of time-dependent periodic optical drive in the Fabry-Perot interferometer system has been investigated using a theoretical model equation. A variety of features such as different routes to chaos, multiperiodic oscillations, coexistence of multiple attractors and mode-locking with devil’s staircase are found to occur for a certain range of parametric values.

The first order perturbative correction to the energy levels of a boson realization of aq-oscillator due to a quartic term in the potential energy is evaluated. We also discuss the statistical mechanics ofq-anharmonic oscillators in the case where the parameterq deviates slightly from unity.

We present an analytic perturbative method for calculatingf(α) and the generalized dimensionD_q of the critical invariant circle of the polynomial circle map. The scaling behaviour is found to depend onz, the exponent defining the map. The asymptotic bounds of the scaling constantsα(z) andδ(z) are verified analytically.

A SU(2)_H symmetric variant of Zee model of lepton flavor violation is presented and is shown to lead to neutrino transition magnetic moment of the order required to explain the solar neutrino deficit and the possible anticorrelation of solar neutrino flux with sunspot activity via VVO mechanism. The use of horizontal symmetry leads to totally degenerate neutrino states which may be combined to form a ZKM Dirac neutrino with naturally small mass.

The real part of the polarization potential which depends on both energy and angular momentum is calculated in a simple way using dispersion relation. A barrier penetration model (BPM) has been used to explain the fusion cross-section and compound nucleus spin distribution for³²S+⁶⁴Ni system in the energy range 50–75 MeV. It is also shown that the polarization potential which only depends on energy, is not adequate to give rise to correct spin distribution even after including any radial dependence. The proposed polarization potential with implicitE andl dependences is able to explain both fusion cross-section and average spin values.

The finite size effects of nucleons inside a nucleus is investigated. This new approach is entirely different from Hagedorn’s volume correction method and is more rigorous. The size of the nucleon is varied and the magnitude of the hard-core potential is extracted by minimising the energy with respect to the nuclear radius.

The lambda binding energy difference between two mirror hypernuclei_Λ⁴He and_Λ⁴He is studied by incorporating the quark structure of nucleons, specially the six quark cluster effects. A small contribution in the binding energy difference (59 keV in the non-relativistic quark model and 29 keV in the bag model) is obtained in the present work.

The electron capture probabilities to 690.70 and 580.37 keV levels and theK-conversion coefficients of 205.9 and 316.5 keV transitions in the decay of Ir-192 have been determined from the measurement of gamma-ray intensities in conjunction with an analysis of theKX-ray-γ-ray sum peaks observed with a co-axial HPGe detector. TheK-capture probability to 690.70 keV level was determined by an approach which is independent ofK-shell fluorescence yield and absolute detection efficiency forKX-rays. TheK-shell fluorescence yields of the daughter products, namely, Os and Pt of Ir-192 have also been determined by the same technique and were found to be 0.964±0.077 and 0.969±0.068 respectively.