The phase shift sum rules recently derived by Puff are extended for a general partly non-local momentum dependent potential. In achieving this, one must use Fredholm determinant of the outgoing solution of the Schrodinger equation instead of the Jost function as was done by Puff. The constants appearing in the moment relations are explicitly defined in terms of the momentum representation of the interaction.

A many-body microscopic band-mixing formulation of variation after projection of angular momentum and conservation of nucleon number is used to study the yrast band and first excitedK^π=0⁺ band in the doubly even nuclei^154,156Gd. The computed energy spectra and the interband and intra-band B (E2) values are in good agreement with corresponding experimental data. Connection with the phenomenological model of Stephens and Simon is discussed, bringing out the role played by thei_13/2 neutron pair in the microscopic formalism.

The odd-proton nucleus¹⁵⁵Tb and odd-neutron nucleus¹⁵⁵Dy are studied along with doubly-even nucleus¹⁵⁶Dy using microscopic method of variation after projection of angular momentum and conservation of nucleon number in each projected state. The calculated energies of the ground band in¹⁵⁶Dy and the ground and excited bands in¹⁵⁵Dy and¹⁵⁵Tb are in good agreement with the corresponding experimental data. The role played by thei_13/2 neutron pair in these nuclei is discussed.

The expressions for baryon number violating nuclear partial decay widths are derived from the interactions as predicted by grand unified theories. Theory predicts that the baryon number violating proton decay inside the nucleus is hindered relative to the free proton decay rate. In the case of closed shell nuclei, the meson spin-isospin dependence of the partial width is the same as that for the nucleon decay. The branching ratios of decay amplitudes depend on the nuclear binding energies. Nuclear structure introduces lepton energy spread of ±49.5 MeV for light closed shell nuclei, while it does not affect the back to back emission of lepton-meson pair.

The energy spectra of the even-parity (K^π = 2⁺, 3⁺) and odd-parity (K^π = 3⁻, 4⁻) side-bands in the doubly even nucleus¹⁷⁰Yb are studied in the framework of the microscopic method of variation after angular momentum projection with nucleon number conservation in each projected state. The calculated energy spectra of the ground band and the four side bands in¹⁷⁰Yb are in good agreement with the corresponding experimental results.

Isobaric degrees of freedom δδ in nuclei are determined from the quark cluster model of a nucleus. These additional degrees of freedom are brought in by the coloured quark exchange between different nucleon clusters present in nuclei. They are found to be important in the region of momentum transfer near 3.5 fm⁻¹. The mass dependence of these isobaric degrees of freedom in nuclei turns out to beA^5/6.

The differential cross-sections of atomic hydrogen for elastic scattering of electrons and positrons have been rederived with the help of a method using a single parameter-dependent unitary shift operator for the calculation of the direct contribution. When the parameter approaches zerc the new method leads to the well-known conventional Glauber results. The numerical calculations include polarization effects and the exchange corrections obtained according to alternative approximation methods. Results calculated with Franco’s exchange show a definite improvement over the earlier results for medium energy electrons at large angles of scattering. Total elastic cross-sections have been calculated for 50 and 100eV electrons and positrons.

A microscopic theory has been provided for propagation of solitons in superfluid⁴He films at temperatureT=0°K.

The experimental and theoretical work carried out on electric and magnetic polarizabilities of a nucleon is reviewed. The results of an exactly solvable one-dimensional chiral bag model predicts correct signs and order of magnitudes of polarizabilities supporting the approximations used in their realistic calculations.

Solutions of the Dirac equation in the presence of a static uniform electric fieldɛ in thez-direction and a linear confining potentialAz, are obtained. Generalized reflection and transmission coefficients are derived for such divergent potentials forɛ >A/e. The eigenspectrum and corresponding localized eigenfunctions forɛ <A/e are obtained from the reflection coefficient and the continuum solutions respectively. The rate for the electric field to decay into pairs is derived from the transmission coefficient. Neglecting nonabelian effects in quantum chromodynamics we identify the fieldɛ with a colour electric field and the produced particles with a quark and an antiquark. By considering a cylindrical geometry, we thus obtain a generalization of Schwinger’s formula, for the fieldɛ in a finite spatial region with the quark (antiquark) being confined in thez direction by the linear potentialAz and in the perpendicular direction by the MIT bag boundary condition. The result is used to qualitatively study Schwinger’s mechanism of quark-gluon plasma (QGP) formation in ultrarelativistic heavy ion collisions. It is found that the critical strength of the field required to create$$q\bar q$$ pairs is enhanced,ɛ_c(A) >ɛ_c(A = 0). The rate of pair creation for constantɛ, decreases for non-zeroA, implying longer QGP formation times. Because ofɛ_c(A) >ɛ_c(0), QGP is predicted to be formed in the early stages of the nuclear collision. The finite size effects and the MIT bag boundary condition effects on QGP formation are also discussed.

The reflection and transmission amplitudes are defined from the asymptotic form of the solution of Dirac equation of a charged fermion in the presence of uniform time independent external electromagnetic field (E, H). Schwinger’s effective lagrangian is derived from the reflection and transmission amplitudes. It is found that both the real and imaginary parts of the effective lagrangian agree with Schwinger’s expressions derived from the elegant method of proper time formalism.

Valence nucleon effective mass, which is almost constant, is proposed within the relativistic mean field theories of finite nuclei (closed shell ± one nucleon). It acquires a slight spin-orbit splitting due to relativistic effects. The relativistic Dirac magnetic moment $$\vec \mu _{op} $$ is rewritten analytically in terms of angular momentum-Pauli spin coupled states and the effective mass. Introducing the nucleon effective charge, the iso-scalar and iso-vector corrections to the magnetic moment operator are extracted from the overall one parameter fit of the measured and the calculated values. The calculated values of magnetic moments are in overall fair agreement with the experiment as well as with the other detailed microscopic calculations.