A trace formula for the oscillating part of the level density for a spherical billiard has been obtained in spherical polar coordinates. The Jacobian of stability and the length of the orbits are obtained from the classical mechanics of the problem. The same formula is applicable to both the planar and the diametric orbits. Numerical results have been obtained with this formula and compared with the results from exact quantum theory, EBK quantization, and Balian and Bloch.

In this paper, we consider an inhomogeneous dust collapse, and extend earlier works of Jhingan, Joshi, and Singh to the case where initial density and velocity distributions are finitely differentiable functions of co-moving coordinate r. We study the occurrence of naked singularities under various conditions on the derivatives of initial density and velocity distributions in marginally as well as non-marginally bound case. We then study their stability and genericity with respect to perturbations in the initial data in an appropriate topological sense.

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.

The decay of 2.76y ¹²⁵Sb to levels of ¹²⁵Te has been studied using an HPGe detector for gamma-ray and a mini orange electron spectrometer for conversion electron measurements. We identify 38 transitions in this decay, including 13 gamma rays and 4 conversion electron lines being reported for the first time. New results also include E1 multipolarity assignments to 3 newly observed transitions and M-shell conversion coefficient for the 109 keV M4 transition. A revised ¹²⁵Te level scheme is constructed using Ritz combination principle. While confirming the existence of 10 well established levels below 700 keV excitation, we introduce 3 other levels at 402.0, 538.6 and 652.9 keV. Interpretation of the observed levels in terms of various theoretical approaches is briefly discussed. The newly introduced 538.6 keV (1/2⁺) and 652.9 keV (3/2⁺) levels are seen as the two missing members of the (s_1/2 ⊗ 2⁺) and (d_3/2 ⊗ 2⁺) sextuplet in the quasiparticle-phonon coupling scheme.

An alternative approach is suggested to determine the spot-size of a multi-mode laser beam. It has been shown by simulations that the suggested approach can give the beam quality factor and characteristic radius with less than 5% error. Unlike the power content method, the proposed method is applicable to the beams even with diameter one tenth of the CCD size. The new approach has been applied to a multi-mode diode laser output and it is shown that the ABCD matrix analysis can be used for beam propagation, with the measured parameters of the laser.

Noncollinear difference frequency mixing of dye laser and Nd:YAG second harmonic (fundamental) radiation from a commercial laser system is employed for the generation of 2.7–5.3 µm (1.6–1.7 µm) radiations in a flux-grown KTiOAsO₁ crystal. The generated radiation is used to scan the methane absorption in the fundamental (v₃) and its first overtone (2v₃) band at pressure 90 torr in a laboratory made single pass gas cell of length 33 cm.

It is reiterated that without a Gibbs-Duhem equation no thermodynamic description of irreversible and reversible processes exists. It is shown with the help of Gibbs-Duhem equation of extended irreversible thermodynamics that the physical contents of intensive quantities, the temperature and the pressure, do not change in going from reversible to irreversible processes. This confirms well with the earlier demonstrations of Eu and García-Colín.

DC magnetization, neutron depolarization and neutron diffraction (with both polarized and unpolarized neutrons) measurements have been reported for the Co_1.1−xZn_xGe_0.1Fe_1.2O₁ spinels with x=0.5, 0.6 and 0.7. Neutron depolarization and neutron diffraction measurements confirm the presence of a long range ferrimagnetic ordering of the local canted spins in these ferrite samples. The observed features of low field magnetization have been explained under the framework of thermally activated domain wall movement of ferrimagnetic arrangement of local canted spins. An important role of magnetic anisotropy (due to the presence of Co²⁺ ions) in establishing the magnetic ordering and domain kinetics in these ferrites has been observed.

Mössbauer spectroscopic studies of [Fe(di(amH)-sar)](NO₃)_4·H₂O where di(amH)-sar represents 1,8 diamino 3,6,10,13,16,19-hexaza bicyclo [6,6,6] icosane in the temperature range of 4.2 to 300 K suggest that it undergoes a dynamic Jahn-Teller effect as revealed from the plots of temperature dependent quadrupole coupling constant, chemical shift and line width values. The spectrum down to 4.2 K, shows a quadrupole doublet with no magnetic hyperfine splitting.