• Volume 22, Issue 3-4

March 1984,   pages  131-386

• Relativistic particle interactions—A comparison of independent and collective variable models

We present a detailed comparison of two models for relativistic classical particle interactions recently discussed in the literature—one based on independent particle variables, and the other on centre of mass plus relative variables. Basic to a meaningful comparison is a reformulation of the latter model which shows that it makes essential use of the concept of invariant relations from constrained Hamiltonian theory. We conclude that these two models have very different physical and formal structures and cannot be thought of as two equivalent descriptions of the same physical theory.

• Kerr metric in the deSitter background

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein’s equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time—a space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild’s exterior metric with cosmological constant.

• Neutrinos in gravitational collapse: Analysis of the flux profile

The flux profile of the neutrinos emitted from a collapsing spherical object, as seen by a remote observer is studied. The model of the collapsing star consists of the Friedmann dust interior matched onto the Schwarzschild exterior. It is assumed that the neutrino emission occurs from an interior shell in a very short time interval. It is found that the nature of the flux profile falls into four distinct categories depending on the progress of collapse. Interesting features such as bursts, discontinuities, decay, etc are observed when the collapse has sufficiently progressed.

• Nonlinear response theory—I

A general nonlinear response theory for the case of linear coupling of physical systems to arbitrary external fields is formulated for applications in different branches of physics. This is done within the framework of non-relativistic density matrix approach of quantum mechanics. Some simple properties of response functions and other related functions, which are introduced here for convenience, are studied to obtain suitable representations of the nonlinear response functions, including important sum-rules. As an example, the sum rule for the second-order response function is applied to electronic dipole nonlinearity at optical frequencies which includes both the Raman nonlinearity arising from perturbation to the electronic motion from external ionic displacement field and the usual optical sum, difference and harmonic generations. This immediately allows us to visualize a rigorous connection between these two types of non-linearities.

• Perturbation expansions and series acceleration procedures. Part I. ε-convergence and critical parameters

A simple acceleration of convergence technique known as the ‘ε-convergence algorithm’ (ea) is applied to determine the critical temperatures and exponents. Several illustrations involving well-known series expansions appropriate to two- and three-dimensional Ising models, three-dimensional Heisenberg models, etc., are given. Apart from this, a few recently studied ferrimagnetic systems have also been analysed to emphasise the generality of the approach. Where exact solutions are available, our estimates obtained from this procedure are in excellent agreement. In the case of other models, the critical parameters we have obtained are consistent with other estimates such as those of the Padé approximants and group theoretic methods.

The same procedure is applied to the partial virial series for hard spheres and hard discs and it is demonstrated that the divergence of pressure occurs when the close-packing density is reached. The asymptotic form for the virial equation of state is found to beP/ρkT ∼ (1 −ρ/ρc−1 for hard spheres and hard discs.

Apart from the estimation of ‘critical parameters’, we have applied theea and the parametrised Euler transformation to sum the partial, truncated virial series for hard spheres and hard discs. The resulting values of pressure so obtained, compare favourably with the molecular dynamics results.

• Some features of the perturbing effects of gravity near the gas liquid critical point

The effect of gravity on various thermodynamic properties near the gas-liquid critical point has been calculated. Using a simple equation satisfying scaling requirements, an analytic expression for density profile is obtained, using which the effect on different thermodynamic properties can be easily calculated.

The present paper considers the magnifying power and aberration properties of three different catadioptric magnifying systems useful for application as simple hand-held microfiche readers. These are in the form of a plano-convex lens, a meniscus lens and an achromatic doublet lens and all their outer surfaces have been coated with a semi-reflecting film so that they behave like catadioptric elements. These can be designed to give magnification in the range of 15 × to 25 × with sufficient eye relief. Using such magnifiers, it is possible to read microfiche having frame sizes of 16 × 12 mm and 12 × 9 mm. The cemented achromatic doublet coated on the outer surfaces seems to give a very good image for use in microfiche reader.

• Complete mass spectra of$$q\bar q$$ and$$Q\bar q$$ mesons with improved Bethe-Salpeter dynamics of confinementmesons with improved Bethe-Salpeter dynamics of confinement

The Bethe-Salpeter (bs) dynamics of harmonic confinement developed byanm and collaborators over the last three years and already applied with considerable experimental success to various hadron spectra and coupling structures has been significantly improved through (i) a more exact treatment of a certain momentum-dependent operator$$\hat Q_q$$ appearing in thebs equation, using the techniques of SO (2, 1) Lie algebra, and (ii) a sharpened definition of theqcd Coulomb term, so as to yield unambiguous values for different flavour sectors. The resulting mass spectra of light$$(q\bar q)$$ meson towers and semi-heavy$$(Q\bar q)$$ quarkonia which are most sensitive to the improved treatment of$$\hat Q_q$$, reveal excellent agreement with experiment, one in which only slight changes in the reduced spring constant$$(\tilde \omega )$$ and quark masses (mq) over the earlier parametrizations are involved. These changes are however found to have a negligible effect on the (already good) numerical values of the other predictions (electroweak and pionic couplings) depending on the$$q\bar q$$ andqqq wave functions. A critical assessment of the strong and weak points of this method is madevis-a-vis other related approaches.

• A new approach to particle confinement

A new approach to permanent confinement of non-relativistic and relativistic particles inside microscopic regions of space is presented. Motion in suitably chosen energy-dependent potentials turns out to be such that the size of orbits of particles bound in such potentials decreases when energy is supplied to them from external sources and there exists a maximum size of these orbits. The energy spectrum is purely discrete without any continuum. The dynamics of such particles requires the introduction of a space-dependent metric in the Hilbert space of states to ensure conservation of probability.

• Baryon number violating nuclear decay

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.

• A study of pion absorption by16O using realistic interactions—I. Twonucleon emission following bound-pion absorption

Matrix element of the Galilean invariant non-relativistic reduction of the pseudoscalar-pseudovector interaction has been calculated assuming the reaction to be a direct process with boundπ being absorbed by a correlated pair of nucleons. The Hartree-Fock wavefunctions obtained with the unitary-model-operator approach starting with the realistic nucleon-nucleon interaction have been used forπ-capturing nucleon pair in the initial state. The calculations have been done with and without antisymmetrising the initial state wavefunction of the pion absorbing pair. For the final state nucleon-nucleon interaction has been taken into account. The strongπ-nucleus interaction together with the Coulomb interaction with the finite nuclear size on the bound pion wavefunction are taken into account. Angular distributions of the emitted nucleon-pair, the branching ratios and the total absorption rates are calculated for16O with and without antisymmetrisation effect. The calculated results are compared with the experimental and other theoretical work.

• Fusion-fission angular distributions: A new probe of fast fission fractionation in nucleus-nucleus collisions

Fragment angular distributions in heavy ion-induced fission reactions have been analysed in terms of a two component model—fission following compound nucleus formation and fast fission events. It is seen that, contrary to the general assumption, fast fission competes with compound nucleus fission even when the composite system is formed with a spin less than the rotating liquid drop model limit for vanishing fission barrier.

• Study of pulsed fast neutrons in an infinite iron assembly

Using multi-group diffusion equation and eigenfunction expansion method, the results for time- and energy-dependent fast neutron spectra are reported for an infinite iron assembly. The nuclear cross-sections used are taken from vitamin-C nuclear data file. The results are presented at short times (0–50 nsec) as well as at large times (50–500 nsec) after the injection of a mono-energetic pulse of 14.47 MeV. Following the pulse, the time behaviour of neutrons corresponding to different energy groups has been discussed. The values of mean slowing down times and of most probable times have been obtained for each energy group.

• Level-degeneracy effects in resonant nonlinear phenomena: Three-level atomic model

The role of level degeneracy in resonant nonlinear phenomena is examined by considering theJ=1 →J=0 atomic transition. The atomic medium is modelled as a homogeneously broadened three-level system and a closed-form expression for the medium susceptibility is obtained. It is used to discuss several nonlinear phenomena such as saturated absorption, optical bistability, and phase conjugation. The two-photon-induced coupling of the ground-state Zeeman sublevels leads to interesting polarization effects.

• Oscillator models for multiphoton optical bistability and phase conjugacy

Nonlinear oscillator models are constructed to treat the bistability in situations involving elementary excitations in solids. Such models are shown to be useful not only in describing single photon but also multiphoton bistability. The resulting bistability both with and without cavity is considered. The two-photon excitonic bistability in CuCl is in detail. The effect of local field corrections can also be incorporated, in a simple manner, in such models.

• Thermal neutron polarisation

The basic principle for the production of polarised thermal neutrons is discussed and the choice of various crystal monochromators surveyed. Brief mention of broad-spectrum polarisers is made. The application of polarised neutrons to the study of magnetisation density distributions in magnetic crystals, the dynamic concept of polarisation, principle and use of polarisation analysis, the neutron spin-echo technique are discussed.

• Studies on the valence state of Ce and Eu in some new boron and silicon containing rare earth intermetallic compounds

Compounds of the formula RPd3Bx (R=rare earth with 0⩽x⩽1) and RPd3Six (R=La, Ce, Eu with 0⩽x⩽0.3) can be prepared by alloying boron or silicon with parent RPd3 compounds. Addition of boron (silicon) does not change the structure but results in lattice expansion. The valence state of Ce in CePd3 and that of Eu in EuPd3 is strongly influenced by boron and silicon. Ce is known to be in a valence fluctuating state in CePd3 while Eu is trivalent (J=0) in EuPd3. The increase in the lattice parameter as a function of boron concentration is observed to be larger in CePd3Bx and EuPd3Bx compared to that in other RPd3Bx alloys giving the first indication of the change in the valence state of Ce and Eu. This is confirmed from susceptibility measurements. With the addition of boron, susceptibility increases and the effective paramagnetic moments approach the values corresponding to Ce3+ (J=5/2, μeff=2.54 μB) and Eu2+ (J=7/2, μeff=7.94 μB) in the two alloy systems CePd3Bx and EuPd3Bx respectively. In the case of europium alloys,151Eu Mössbauer studies point out the importance of near-neighbour environment effects. Further, in EuPd3B, where all the europium ions are crystallographically equivalent, a single Mössbauer line, with an isomer shift characteristic of europium ions in valence-fluctuating state, is observed at 300 K. However, at 88 K the Mössbauer absorption splits into two lines corresponding to europium ions in two valence states,e.g. divalent- and trivalent-like. Such a behaviour indicates thermally-induced charge ordering of europium ions. Addition of silicon to CePd3, like boron, results in unusual lattice expansion and changes the valency of cerium towards 3+. the valence change is further corroborated by susceptibility measurements. In EuPd3Six alloys, susceptibility and Mössbauer studies indicate that in the limiting single phase alloy EuPd3Si0.25 the europium ions are on the verge of valence instability. Susceptibility results on CeRh3Bx alloys are also presented.

• The crystal fields inα-alums—A high pressure magnetic resonance study

The origin of the crystal field and its variation with temperature in severalα-alums have been studied bynmr of27Al andepr of Cr3+ at high hydrostatic pressures and low temperatures. The results lead to an explanation of the anomalous temperature variation of the axial crystal field at the trivalent ion site. The mechanism of the phase transition in ammonium alum is also explained. A correlation between the axial crystal field as determined bynmr (e2qQ/h) and that determined byepr (D) has been obtained.

• Density wave theory of freezing and the solid

The theory of the liquid to solid transition, in three as well as in two dimensions, is reviewed. The transition can be viewed either as the melting of the solid due to phonon or defect proliferation instabilities or alternatively as freezing of the liquid into a density wave state with crystalline symmetry. A theory due to Yussouff and the author, based on the latter idea, is discussed and its predictions are compared with experiment. It is shown that the theory leads to a new approach to the properties of a deformed (e.g., sheared) solid and of defects such as grain boundaries and dislocations in a solid. The approach brings out explicitly the structural nature of these properties, and is not restricted to small deviations from perfect periodicity (harmonic approximation) since the solid, the liquid and anything in between can be handled theoretically.

• On the possible origins of natural diamonds

A brief survey of the current theories of formation of diamonds in nature leads to the hypothesis which suggests the possibility of natural diamonds having formed metastably—a hypothesis which has not been enjoying much experimental support in its favour. The authors present briefly some aspects of the investigations which have resulted in demonstrating a new process whereby the dissolution and metastable autoepitaxial (re)crystallization of diamond occurs at atmospheric pressure. A comparison of certain reported growth characteristics of natural (terrestrial) and synthetic (high pressure, solvent-catalyst) diamonds with those of the metastable diamond overgrowths reveal many striking similarities. These results therefore serve as evidence to support the metastable origin hypothesis.

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Posted on July 25, 2019