We study the physical features of a class of exact solutions for cold compact anisotropic stars. The effect of pressure anisotropy on the maximum mass and surface red-shift is analysed in the Vaidya–Tikekar model. It is shown that maximum compactness, red-shift and mass increase in the presence of anisotropic pressures; numerical values are generated which are in agreement with observation.

With a view to obtain exact analytic solutions to the time-dependent Schrödinger equation for a few potentials of physical interest in three dimensions, transformation-group method is used. Interestingly, the integrals of motion in the new coordinates turn out to be the desired invariants of the systems.

Quantum effects which have usually been associated with micro-scale phenomena can also arise on the macro-scale in situations other than the well-known macro-quantum phenomena of superconductivity and superfluidity. Such situations have been shown here to arise in processes involving inelastic scattering with bound or partially bound systems (not bound in all degrees of freedom), and the macro-quantum behaviour is associated with the state of the total system in transition in the process of scattering. Such a state is designated as a `transition-state'. It is pointed out that we have already observed such manifestations for a particular system, the charged particles in a magnetic field where interference effects involving macro-scale matter waves along the magnetic field have been reported [R K Varma et al, Phys. Rev. E65, 026503 (2002)].

We have theoretically studied the collective modes of a quasi-two-dimensional (Q2D) Bose condensate in the large gas parameter regime by using a formalism which treats the interaction energy beyond the mean-field approximation. The results show that incorporation of this higher order term leads to significant modifications in the mode frequencies.

We calculate the physical mass and the width of the sigma meson by considering that it couples in vacuum to two virtual pions. The mass is calculated by using the spectral function, and we find that it is about 600 MeV. In addition, we obtained 220 MeV as the value for the width of its spectral function. The value obtained for the mass is in good agreement with that reported in the Particle Data Book for the σ-meson, which is also named $f_{0}$(600). This result also shows that 𝜎-meson can be considered as a two-pion resonance.

We explore the possibility of distinguishing the SM-like MSSM Higgs boson from the SM Higgs boson via Higgs boson pair production at future muon collider. We study the behavior of the production cross-section in SM and MSSM with Higgs boson mass for various MSSM parameters tan 𝛽 and $m_{A}$. We observe that at fixed CM energy, in the SM, the total cross-section increases with the increase in Higgs boson mass whereas this trend is reversed for the MSSM. The changes that occur for the MSSM in comparison to the SM predictions are quantified in terms of the relative percentage deviation in cross-section. The observed deviations in cross-section for different choices of Higgs boson masses suggest that the measurements of the cross-section could possibly distinguish the SM-like MSSM Higgs boson from the SM Higgs boson.

The $\Lambda \Lambda$ binding energy ($B_{\Lambda \Lambda}$) of the s- and p-shell hypernuclei are calculated variationally in the cluster model and multidimensional integrations are performed using Monte Carlo. A variety of phenomenological 𝛬-core potentials consistent with the 𝛬-core energies and a wide range of simulated s-state $\Lambda \Lambda$ potentials are taken as input. The $B_{\Lambda \Lambda}$ of $_{\Lambda \Lambda}^{6}$He is explained and $_{\Lambda \Lambda}^{5}$He and $_{\Lambda \Lambda}^{5}$H are predicted to be particle stable in the $\Lambda \Lambda$-core model. The results for s-shell hypernuclei are in excellent agreement with those of non-VMC calculations. The $_{\Lambda\Lambda}^{10}$Be in $\Lambda \Lambda \alpha \alpha$ model is overbound for combinations of $\Lambda \Lambda$ and $\Lambda \alpha$ potentials. A phenomenological dispersive three-body force, $V_{\Lambda \alpha \alpha}$, consistent with the $B_{\Lambda}$ of $_{\Lambda}^{9}$Be in the $\Lambda \alpha \alpha$ model underbinds $_{\Lambda \Lambda}^{10}$Be. The incremental $\Delta B_{\Lambda \Lambda}$ values for the s- and p-shell cannot be reconciled, consistent with the finding of earlier analyses.

A new empirical four-parameter function is proposed for the construction of potential curves of 15 stable states of diatomic molecules. The parameters are evaluated in terms of experimentally known spectroscopic constants. On comparing its performance with other functions, the proposed function is found to be simple and reliable for a wide range of molecules.

We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and orbital angular momentum are still constants of motion. We find the exact solutions by introducing the concept of an image ellipse. The quadratic effect leads to a dilation of space–time, and a one-to-one correspondence is observed for pairs of physical quantities like energy and angular momentum, and the maximum and minimum distances from the Coulomb center for the Zeeman orbit and the corresponding pairs for the image ellipse. Thus, instead of finding additional conserved quantities, we find constants of motion for an additional dynamics, namely, the image problem. The trajectory is open, in agreement with Bertrand's theorem, but necessarily bound. A stable unbound trajectory does not exist for real values of energy and angular momentum. The radial distance, the angle covered in the plane of the orbit, and the time are uniquely determined by introducing further the concept of an image circle. While the radial distance is defined in a closed form as a transcendental function of the image-circular angle, the corresponding orbit angle and time variables are found in the form of two convergent series expansions. The latter two variables are especially contracted, thereby leading to a precession of the open cycles around the Coulomb center. It is expected that the space–time dilation effect observed here would somehow influence the solution of the quantum mechanical problem at the non-relativistic level.

We have studied fast ion–atom and electron–atom collision processes using a reconditioned high resolution X-ray spectrometer. The X-rays, generated by the collisions, are dispersed by a curved ADP crystal (Johansson geometry) and detected by a gas proportional counter. A self-written LabVIEW based program has been used to give precise and controlled movement to the crystal and for data acquisition. The performance was tested by detecting the K𝛼 diagram and satellite lines of several elements. The K𝛼 satellite lines of Al have been studied in collision with 3–12 keV electrons and 40 MeV C⁴⁺ ions. In ion collisions as large as four L-vacancies are created simultaneously with the K-vacancy, compared to two satellites in case of the e-impact. In addition, we have measured the X-rays from H-, He- and Li-like Si ions which arise due to the electron loss/capture process in highly charged 80 MeV Si⁷⁺ ions in collision with thin carbon foil. Approximate charge state distribution has been obtained using this new technique.

Linear electro-optical tensor coefficients and optical susceptibility of tetragonal KNbO₃ are calculated using a formalism based on bond charge theory. Results are in close agreement with the experimental data. The covalent Nb–O bonding network comprising the distorted NbO₆ octahedral groups in the structure is found to be a major contributor to the electro-optic coefficients making these groups more sensitive to these properties than the KO₁₂ groups. The orientations of the chemical bonds play an important role in determining these properties.

The cosmic ray (CR) intensity data recorded in Deep River Neutron Monitoring Station have been investigated on quietest days (QD) for third harmonics of daily variation during solar cycles 21 and 22. It has been observed that in spite of abrupt change in the amplitude and phase of tri-diurnal anisotropy in CR intensity, the amplitude is quite significant throughout the period of investigation with larger amplitude during the years 1980 and 1985. Thus, tri-diurnal anisotropy clearly shows 11-year variation at the mid latitude neutron monitoring station.

The Hartree–Bogoliubov (HB) framework of calculations has been applied for calculating various nuclear structure quantities for ^154−166Dy mass chains. In this framework, the intrinsic quadrupole moments, the low-lying yrast states ($E_{2}^{+}$ and $E_{4}^{+}$) and occupation numbers for various shell model orbits have been obtained. The calculated results indicate that the observed onset of deformation in going from ¹⁵⁴Dy to ¹⁶⁶Dy arises due to enhanced occupation of $(h_{11/2})_{\pi}$ orbit, increased polarization of $(d_{5/2})_{\pi}$ orbit and increase in the occupation of down-slopping $`k'$ components of $(i_{13/2})_{v} and $(h_{9/2})_{υ}$ orbits.