It is shown that exp(−2 Im($\int p dr$)) is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the transmission coefficient only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. The simplest extension to this formula which is invariant under canonical transformations is proposed. However, it is shown that this gives half the correct temperature for black holes.

In a one-dimensional quantal solution of Schroedinger equation, the general expressions for reflection and transmission coefficients are derived for a potential constituting n number of rectangular wells and barriers. These expressions are readily used for the estimation of eigenvalues of a smooth potential which is simulated by a multi-step potential. The applicability of this method is demonstrated with success in potentials with different forms including the most versatile Ginocchio potential where the widely used numerical method like Runge–Kutta integration algorithm fails to yield the result. Accurate evaluation of eigenvalues free from numerical problem for any form of potentials, whether analytically solvable or not, is the highlight of the present multi-step approximation method in the theory of potential scattering.

We present the spectral properties of supersymmetric shape invariant potentials (SIPs). Although the folded spectrum is completely random, unfolded spectrum shows that energy levels are highly correlated and absolutely rigid. All the SIPs exhibit harmonic oscillator-type spectral statistics in the unfolded spectrum. We conjecture that this is the reflection of shape invariant symmetry.

The possibility to verify the pseudo-Dirac nature of neutrinos is investigated here via the detection of ultra-high energy neutrinos from distant cosmological objects like 𝛾-ray bursts (GRBs). The very long baseline and the energy range from ∼TeV to ∼EeV for such neutrinos invoke the likelihood to probe very small pseudo-Dirac splittings. The expected secondary muons from such neutrinos that can be detected by a kilometer scale detector such as ICECUBE is calculated and compared with the same in the case of mass-flavour oscillations and for no oscillation cases. The calculated muon yields indicate that to probe such small pseudo-Dirac splittings one needs to look for a nearby GRB (red shift $z \sim 0:03$ or less) whereas for a distant GRB ($z \sim 1$) the flux will be much depleted and such phenomenon cannot be distinguished. Also calculated are the muon-to-shower ratios.

An inverse response matrix converts the observed pulse-height distribution of a NaI(Tl) scintillation detector to a true photon spectrum. This also results in extraction of intensity and energy distributions of multiply scattered events originating from interactions of 279 keV photons with thick targets of bronze. The observed pulse-height distributions are a composite of singly and multiply scattered events in addition to bremmstrahlung originating from slowing down of Compton and photo-electrons in thick targets. To evaluate the contribution of multiply scattered events, the spectrum of singly scattered events contributing to inelastic Compton peak is reconstructed analytically. The optimum thickness (saturation depth), at which the number of multiply scattered events saturate, has been evaluated in different energy bin meshes chosen for scintillation detector response unfolding. Monte Carlo calculations based upon the package developed by Bauer and Pattison (Compton scattering experiments at the HMI (1981), HMI-B 364, pp. 1-106) supports the present experimental results.

The mass spectrum of the 𝑃-wave mesons is considered in a non-relativistic constituent quark model. The full Hamiltonian used in the investigation includes the kinetic energy, the confinement potential, the one-gluon-exchange potential (OGEP) and the instanton-induced quark-antiquark interaction (III). A good description of the mass spectrum is obtained. The respective role of III and OGEP in the P-wave meson spectrum is discussed.

The fission decay of highly neutron-rich uranium isotopes is investigated which shows interesting new features in the barrier properties and neutron emission characteristics in the fission process. ²³³U and ²³⁵U are the nuclei in the actinide region in the beta stability valley which are thermally fissile and have been mainly used in reactors for power generation. The possibility of occurrence of thermally fissile members in the chain of neutron-rich uranium isotopes is examined here. The neutron number $N = 162$ or 164 has been predicted to be magic in numerous theoretical studies carried out over the years. The series of uranium isotopes around it with $N = 154-172$ are identified to be thermally fissile on the basis of the fission barrier and neutron separation energy systematics; a manifestation of the close shell nature of $N = 162$ (or 164). We consider here the thermal neutron fission of a typical representative ²⁴⁹U nucleus in the highly neutron-rich region. Semiempirical study of fission barrier height and width shows that ²⁵⁰U nucleus is stable against spontaneous fission due to increase in barrier width arising out of excess neutrons. On the basis of the calculation of the probability of fragment mass yields and the microscopic study in relativistic mean field theory, this nucleus is shown to undergo exotic decay mode of thermal neutron fission (multi-fragmentation fission) whereby a number of prompt scission neutrons are expected to be simultaneously released along with the two heavy fission fragments. Such properties will have important implications in stellar evolution involving 𝑟-process nucleosynthesis.

The phenomenon of proton emission is treated as a process of asymmetric fission through a one-dimensional potential barrier developed due to combined effects of the Coulomb potential, centrifugal potential and various renormalization processes. The barrier is simulated to an asymmetric, smooth and analytically solvable potential with adjustable depth, shape and range. The half-lives of proton emitters in the mass range $A = 105-171$ have been calculated using exact expression for the transmission coefficients. Good agreement with the experimental data is obtained by the adjustment of just one parameter in all the cases.

Phenomenological analysis of the $\pi^{-}- ^{12}C$ elastic scattering differential cross-section at 400, 486, 500, 584, 663, 672 and 766 MeV is presented. The analysis is made in the diffraction model framework using the recently proposed parametrization of the phase-shift function. Good description of the experimental data is achieved at all energies. Microscopic interpretation of the parameters of the phase-shift function is provided in terms of Helm's model density parameters.

This paper presents an analysis of diffraction effects taking place at different Schlieren diffracting elements. Two types of diffraction effects are prominent in the Schlieren schemes. One is diffraction of direct light (source image) at the Schlieren element, which limits the sensitivity and resolution of Schlieren systems. The second type is the diffraction of light deflected from the test object at the Schlieren-diffracting element. This second type of diffraction degrades the quality of Schlieren results. Experimental results showing the effect of diffraction of light deflected from the test object at a phase knife-edge, corner of a square phase aperture and an optical fiber tip as Schlieren diffracting elements have been presented and discussed.

This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit security features in the security hologram can only be read through a key hologram. Key hologram also facilitates in-built repositioning of security hologram. The method of fabrication, the principle of reconstruction and the experimental results are presented.

We have exactly solved a model of equidistant cascade four-level system interacting with a single-mode radiation field both semiclassically and quantum mechanically by exploiting its similarity with Jaynes-Cummings model. For the classical field, it is shown that the Rabi oscillation of the system initially in the first level (second level) is similar to that of the system when it is initially in the fourth level (third level). We then proceed to solve the quantized version of the model where the dressed state is constructed using a six-parameter four-dimensional matrix and show that the symmetry exhibited in the Rabi oscillation of the system for the semiclassical model is completely destroyed on the quantization of the cavity field. Finally, we have studied the collapse and revival of the system for the cavity field-mode in a coherent state to discuss the restoration of symmetry and its implication is discussed.

In this paper, we investigate the existence and variation of complete photonic band gap size with the introduction of asymmetry in the constituent dielectric rods with honeycomb lattices in two-dimensional photonic crystals (PhC) using the plane-wave expansion (PWE) method. Two examples, one consisting of elliptical rods and the other comprising of rectangular rods in honeycomb lattices are considered with a view to estimate the design parameters for maximizing the complete photonic band gap. Further, it has been shown that complete photonic band gap size changes with the variation in the orientation angle of the constituent dielectric rods.

The recent neutron scattering data for spin-wave dispersion in HoMnO₃ are well-described by an anisotropic Hubbard model on a triangular lattice with a planar (XY) spin anisotropy. Best fit indicates that magnetic excitations in HoMnO₃ correspond to the strong-coupling limit $U/t > \sim 15$, with planar exchange energy $J = 4t^{2}/U \simeq 2.5$ meV and planar anisotropy $\Delta U \simeq 0.35 $meV.

Spinal ferrites having the general formula Co$_{1-x}$Zn$_{x}$Fe$_{2-x}$Al$_{x}$O₄ ($x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6$) were prepared using the wet chemical co-operation technique. The samples were annealed at 800°C for 12 h and were studied by means of X-ray diffraction, magnetization and low field AC susceptibility measurements. The X-ray analysis showed that all the samples had single-phase cubic spinel structure. The variation of lattice constant with Zn and Al concentration deviates from Vegard's law. The saturation magnetization $\sigma_{s}$ and magneton number $n_{B}$ measured at 300 K using high field hysteresis loop technique decreases with increasing 𝑥, suggesting decrease in ferrimagnetic behaviour. Curie temperature $T_{C}$ deduced from AC susceptibility data decreases with 𝑥, suggesting a decrease in ferrimagnetic behaviour.

The effect of environmental temperature on neuronal spiking behaviors is investigated by numerically simulating the temperature dependence of spiking threshold of the Hodgkin-Huxley neuron subject to synaptic stimulus. We find that the spiking threshold exhibits a global minimum in a specific temperature range where spike initiation needs weakest synaptic strength, which form the engineering perspective indicates the occurrence of optimal use of synaptic transmission in the nervous system. We further explore the biophysical origin of this phenomenon associated with ion channel gating kinetics and also discuss its possible biological relevance in information processing in neuronal systems.