The simplest formulas connecting Jacobi elliptic functions with different modulus parameters were first obtained over two hundred years ago by John Landen. His approach was to change integration variables in elliptic integrals. We show that Landen’s formulas and their subsequent generalizations can also be obtained from a different approach, using which we also obtain several new Landen transformations. Our new method is based on recently obtained periodic solutions of physically interesting non-linear differential equations and remarkable new cyclic identities involving Jacobi elliptic functions.

We have studied five-dimensional homogeneous cosmological models with variableG and bulk viscosity in Lyra geometry. Exact solutions for the field equations have been obtained and physical properties of the models are discussed. It has been observed that the results of new models are well within the observational limit.

Within the quasi-particle random phase approximation (QRPA), the method of the self-consistent determination of the isovector effective interaction which restores a broken isotopic symmetry for the nuclear part of the Hamiltonian is given. The effect of the pairing correlations between nucleons on the following quantities were investigated for theA = 208 nuclei: energies of the isobar analog 0⁺ states, the isospin admixtures in the ground state of the even-even nuclei, and the differential cross-section for the²⁰⁸Pb(³He,t)²⁰⁸Bi reaction atE(³He)=450 MeV. Both couplings of the excitation branches withT^z = T⁰ ± 1, and the analog state with isovector monopole resonance (IVMR) in the quasi-particle representation were taken into account in our calculations. As a result of these calculations, it was seen that the pairing correlations between nucleons have no considerable effect on theT = 23 isospin admixture in the ground state of the²⁰⁸Pb nucleus, and they cause partially an increase in the isospin impurity of the isobar analog resonance (IAR). It was also established that these correlations have changed the isospin structure of the IAR states, and shifted the energies of the IVMR states to the higher values.

In this paper intermittent behaviour of the pions from ‘cold’ and ‘hot’ classes of events from¹²C-AgBr interactions at 4.5 A GeV has been studied, separately. The results reveal strong intermittent pattern in case of ‘cold’ class of events.

Chemical effects on the K shell fluorescence yields of Fe, Mn, Co, Cr and Cu compounds were investigated. Samples were excited using 59.5 keV energy photons from a²⁴¹ Am radioisotope source. K X-rays emitted by samples were counted by a Si(Li) detector with a resolution 160 eV at 5.9 keV. Chemical effects on the K shell fluorescence yields (ωk) for Fe, Mn, Co, Cr and Cu compounds were observed. The values are compared with theoretical, semiempirical fit and experimental ones for the pure elements.

We have used non-relativistic and relativistic distorted wave approximation methods to study the excitation of then¹D states of magnesium (n = 3), calcium (n = 4) and strontium (n = 5) from the ground n¹S state. Calculations have been performed for the complete set of parameters (σ,$$\tilde L_ \bot ^ + ,\tilde L_ \bot ^ - ,\tilde \gamma ^ + ,\tilde \gamma ^ - $$). The results are presented for electron impact energies of 20 and 40 eV. We compare our results obtained from both the non-relativistic and relativistic methods with each other. Good agreement is found on comparison and the importance of relativistic effects is also explored.

The paper describes a simple and cost effective method for the realization of an optical interferometer based on holographic optics, which use minimal bulk optical components. The optical arrangement in the proposed method involves a very simple alignment procedure and inexpensive holographic recording material is used in the formation of holographic optical elements. The proposed interferometer set-up is quite suitable for performing optical test studies on phase (transparent) objects in real-time. Recording schemes for the formation of holographic optical elements and the related technique for the realization of the interferometer set-up along with the experimental results have been presented.

A non-linear mirror consisting of a lithium triborate crystal and a dichroic output coupler are used to mode-lock (passively) an Nd : YVO₄ laser, pumped by a diode laser array. The laser can operate both in cw mode-locked and simultaneously Q-switched and mode-locked (QML) regime. The peak power of the laser while operating in QML regime is much higher but pulses suffers from poor amplitude stability. The incorporation of an acousto-optic modulator as an active Q-switch enhances the stability of the QML pulse envelope. The second-order non-linearity of powdered crystalline urea is conclusively measured with respect to KDP while the laser is operating in passively Q-switched and passively mode-locked regime as well as in actively Q-switched and passively mode-locked regime.

A self-consistent and general description of obliquely propagating low-frequency electrostatic dust-modes in a non-uniform magnetized dusty plasma system has been presented. A number of different situations, which correspond to different low-frequency electrostatic dust-modes, namely, dust-acoustic mode, dust-drift mode, dust-cyclotron mode, dust-lower-hybrid mode, and other associated modes (such as, accelerated and retarded dust-acoustic modes, accelerated and retarded dust-lower-hybrid modes, etc.), have also been investigated. It has been shown that the effects of obliqueness and inhomogeneities in plasma particle number densities introduce new electrostatic dust modes as well as significantly modify the dispersion properties of the other low-frequency electrostatic dust associated modes. The implications of these results to some space and astrophysical dusty plasma systems, especially to planetary ring-systems and cometary tails, are briefly mentioned.

For an unmagnetized partially ionized dusty plasma containing electrons, singly charged positive ions, micron-sized massive negatively charged dust grains and a fraction of neutral atoms, dispersion relations for both the dust-ion-acoustic and the dustacoustic waves have been derived, incorporating dust charge fluctuation. The dispersion relations, under various conditions, have been exhaustively analysed. The explicit expressions for the growth rates have also been derived.

Temporal, spatial and spectral characteristics of a multi-keV monochromatic point x-ray source based on vacuum diode with laser-produced plasma as cathode are presented. Electrons from a laser-produced aluminium plasma were accelerated towards a conical point tip titanium anode to generate K-shell x-ray radiation. Approximately 10₁₀ photons/pulse were generated in x-ray pulses of ∼18 to ∼28 ns duration from a source of ∼300 μm diameter, athυ = 4.51 keV (K_α emission of titanium), with a brightness of ∼10²⁰ photons/cm²/s/sr. This was sufficient to record single-shot x-ray radiographs of physical objects on a DEF-5 x-ray film kept at a distance of up to ∼10 cm.

Some previously obtained physical solutions [1–3] of Yang’s equations forSU(2) gauge fields [4], Charap’s equations for pion dynamics [5,6] and their combination as proposed by Chakraborty and Chanda [1] have been presented. They represent different physical characteristics, e.g. spreading wave with solitary profile which tends to zero as time tends to infinity, spreading wave packets, solitary wave with oscillatory profile, localised wave with solitary profile which becomes plane wave periodically, and, wave packets which are oscillatory in nature.

Spectroscopic factors for two-proton emitting nuclei are discussed in the framework of the BCS (Bardeen-Cooper-Schriefer) model. Calculations carried out for the two-proton unstable⁴⁵Fe,⁴⁸Ni and⁵⁴Zn nuclei are presented.

An approximate simple scaling law is obtained for asymmetric (e, 3e) process on helium-like ions for double ionization by fast electrons. It is based on the equation (Z^′3π) exp[-Z(r₁ + r₂)],Z′ = Z – (5/16) for ground state wave function of helium-like ions and Z^′2 scaling of energies. The scaling law is found to work very well if the lower energy electron is ejected along the momentum transfer direction and the other one is ejected in the opposite direction. It also works quite well if this electron is ejected within about 90° of the momentum transfer direction with the other electron going in the opposite direction. The scaling law becomes increasingly accurate as the target nuclear charge and the energy increase.

Three different types of ionization and excitation processes are studied in detail for the scattering of positronium (Ps) by the simplest alkali atom (Li) using a Coulomb-Born approximation for ionization and first-Born approximation for excitation. This is the first work where orthogonalized Coulomb wave is used to represent the ionized electron for Ps-Li scattering using a single-electron and a three-electron prescription of the target. Li is chosen to minimize the effect of intrinsic correlation among the target atomic electrons so that it can extract the basic physics more accurately. All the possible Coulomb interactions are considered exactly. Comparative studies of different cross-sections using two different representations of the target provide us the informations to enrich our ideas about the system and the important role of core electrons.

The resonance Raman (RR) spectra of nickel octaethyl porphyrin, Ni(OEP), in CH₂Cl₂ (solvent) at different excitations such as 514.5, 488.0, 441.6 and 406.7 nm are recorded and analysed. The results of the theory of distortion-induced RR intensity is applied to the observed spectra to determine the excited electronic state symmetry of porphyrin in Ni(OEP). It is concluded that the porphyrin molecule (D_4h structure) attains a non-polar distorted structure of D₂ symmetry rather than S₄ symmetry in CH₂Cl₂ solution.

The energy relaxation between the hot degenerate electrons of a homogeneously photoexcited metal film and the surface phonons (phonon wave vectors in two dimensions) is considered under Debye approximation. The state of electrons and phonons is described by equilibrium Fermi and Bose functions with different temperatures. Two cases for electron scattering by the metal surface, namely specular and diffuse scattering, are considered.

Fit of the experimental data of ZnS : Mn by a modified lucky-drift formula has been performed using the least square algorithm. The fit agrees well with the experimental data only at high field. The best fitting parameters at high field are the mean free path of order 102.74 Å and Keldysh factor,p₀ = 0.0138. A generalized Keldysh formula has been used, due to introduction of a soft threshold factor. The soft lucky-drift theory can also be used to calculate the impact ionization coefficients of high electron energy of ZnS : Mn without losing its physical significance compared to full band-structure Monte Carlo calculation with a remarkably reduced amount of computer resources.

The curvature on semi-log plot of experimental impact ionization coefficient against the inverse of electric field is different from what is observed for other materials at low electric fields due to impact ionization of deep level impurities.