Volume 24, Issue 5
May 1985, pages 663-812
pp 663-672 May 1985 Mathematical Physics
The construction of invariants up to fourth order in velocities has been carried out for one-dimensional, time-dependent classical dynamical systems. While the exact results are recovered for the first and second order integrable systems, the results for the third and fourth order invariants are expressed in terms of nonlinearpotential equations. Noticing the separability of the potential in space and time variables these nonlinear equations are reduced to a tractable form. A possible solution for the third order case suggests a new integrable systemV(q, t) ∼t−4/3q1/2.
pp 673-684 May 1985 Quantum Mechanics
An entropic formulation of uncertainty relations is obtained for the case of successive measurements. The lower bound on the overall uncertainty, that is obtained for the case of successive measurements, is shown to be larger than the recently derived Deutsch-Partovi lower bound on the overall uncertainty in the case of distinct measurements.
pp 685-693 May 1985 Quantum Mechanics
The even and odd parity eigenvalues for the bounded potentialµx2 +λx2m with both positive and negative values ofμ andm=2, 3, 4, 5, 6 are obtained by the method of series solution for any positive value of the coupling constantλ. Whenμ is negative the lower order eigenvalues are closely bunched in pairs in the low-λ regime (λ≪1). The results agree well with existing results.
pp 695-699 May 1985 Quantum Mechanics
For the potentialV(x)=V0 tan2x, the corrections to the lowest orderjwkb (Bohr-Sommerfeld) energy quantization rule are non-zero. These higher order corrections are explicitly computed using the formalism of Dunham. The resultingjwkb series for the energy eigenvalues is summable, and yields the exact bound state spectrum.
pp 701-706 May 1985 General Relativity And Cosmology
An isotropic homogeneous cosmological model with Robertson-Walker line element is studied in general scalar tensor theory where the parameterω is a function of the scalar field. The model consists of perfect fluid with the equation of statep=ερ. Exact solutions are obtained in Dicke’s conformally transformed units forε=1 andε=1/3 assuming a functional relationship betweenω and the scalar fieldφ. The properties are compared with vacuum models in this theory.
pp 707-713 May 1985 Particle Physics
Incorporating chiral-symmetry to the potential model of quarks with confining potentialU(r)=1/2 (1 +γ°)ar2 with mq=10 MeV anda=2.273 fm−3 that gives a reasonable quark-core contribution to μp, 〈r2 〉p1/2 andgA, the quark-pion coupling constant for quarks in a nucleon is estimated.Gqqπ2/4π obtained between 0.4 and 0.5 is consistent with those extracted from experimental vector meson decay-width ratios by Suzuki and Bhaduri. The nucleon-pion coupling constantGNNπ2/4π comes out to be of the order of 13.1 in reasonable agreement with the experimental value.
pp 715-726 May 1985 Nuclear Physics
Single channel single levelR-matrix plus potential analysis of the resonances observed in the32S(n, n) reaction for the neutron energy lying from 20–1100 keV has been carried out to determine the properties of these resonances. This analysis is further supported by a single channel multilevelR-matrix analysis of the data. Spectroscopic factors for the resonances have also been calculated by ourR-matrix method. Its comparison with those obtained bydwba analysis of the (d, p) data is discussed.
pp 727-736 May 1985 Nuclear Physics
The mechanism of target fragmentation phenomena is explored in a statistical model. It is shown that peripheral interaction arising out of large impact parameter can describe the mass yield distribution of the products from the fragmentation of63Cu by the bombardment ofp,12C and40Ar with energies of 28, 25 and 80 GeV respectively. Important insights into the dynamics is obtained from these reactions as the target remaining the same, the projectile mass varies by forty units and the incident energy per nucleon by fourteen units. Surface properties of the target and projectile are shown to play an important role. Other features like limiting fragmentation and projectile dependence are also borne out in this study.
pp 737-741 May 1985 Atomic And Molecular Physics
An application of the semi-empirical CNDO/2 and INDO methods to calculate the molecular dipole moment of iodine compounds has been made with all-valence electron scheme. Equilibrium geometries are obtained using experimental bond lengths and the various semi-empirical parameters required inscf-mo scheme are obtained from atomic Hartree-Fock calculations and by comparison withab initio calculations. Bothsp andspd valence basis sets are used.
pp 743-748 May 1985 Atomic And Molecular Physics
Differential cross-sections for Compton scatterig of 0.279 MeV gamma rays fromK-shell electrons of lead are measured at scattering angles ranging from 30 to 150° to study the effect of binding on the scattering process. Measurements are made employing two Nal(Tl) scintillation spectrometers and a slow-fast coincidence set-up of 30 nsec resolving time. The experimental results are compared with the available theoretical data. The totalK-shell Compton scattering cross-section is 34% of the free electron Compton cross-section.
pp 749-755 May 1985 Atomic And Molecular Physics
The Raman spectrum of polycrystalline α-naphthylamine was recorded in the region 100–4000 cm−1. Polarisation measurements were made in CS2 and CHCl3 solutions. The infrared spectrum was recorded in nujol mull in the region 200–4000 cm−1. The resolution was better than 2 cm−1 and the accuracy of the measurements was within ± 2 cm−1 for all the spectra. Vibrational assignments have been proposed for the observed frequencies. Out of the 54 normal modes of vibrations, 51 modes could be observed experimentally.
pp 757-771 May 1985 Solid State Physics
The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron by making use of simple co-ordinate axes transformations and lattice symmetry in the case of hcp and ccp structures. It is shown that the expressions for the interference factor,S(q,t) of hcp structure are complex while those of ccp structure are real, even when both atomic arrangements are referred to the same orthorhombic co-ordinate axes, and in each case, lattice atom contributions could be distinguished from basis atom contributions toS(q,t). By comparing these expressions with each other as well as with those obtained by approximating their atomic polyhedra by an ellipsoid of equivalent volume, apparent differences between interference factors of hcp and ccp structures, validity of Wigner-Seitz approximation for a diatomic lattice and the manner in which the electron-ion interactions contribute to the different modes of vibration in a hexagonal lattice are discussed.
pp 773-780 May 1985 Solid State Physics
Theoretical evaluations of frequency moments and second order Doppler shifts have been made for dilute57Fe impurities in the high temperature limit for a harmonic solid. The resonant energy shifts have been calculated from the Green’s function of the impure crystal containing both mass disordering and force constant change terms in the crystal Hamiltonian. High temperature frequency moments for the impurity in different metallic solids are obtained from Mc-Millan ratios using standard Mössbauerf-values at room temperature.
The effect of mass disordering predominates over the force constant change term in the evaluations of second order Doppler shifts and hence the frequency moments for dilute57Fe impurities. The variation of frequency moments for the impurity with mass modified Debye-temperature of the hosts is shown for a number of metallic solids.
pp 781-786 May 1985 Solid State Physics
Considering the htermal conduction through molecular collisions an expression for the effective thermal conductivityλe of loose and granular two-phase materials at different interstitial air pressure has been derived. The dependence ofλe on pore and particle sizes, characteristic pressure and radiative heat transfer is also discussed. Calculated values ofλe of glass beads and loose building materials are compared with reported results.
pp 787-795 May 1985 Solid State Physics
A study of theEXAFS associated with theK x-ray absorption discontinuity of germanium in pure germanium and in the rare-earth germanides RGe2 (where R=La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Y) has been carried out. The Ge-Ge distances have been obtained in these compounds. Considering the phase to the RGe2 system, the bond lengths in these compounds have been determined. The values obtained by us for the RGe2 compounds (R=La, Ce, Pr, Nd, Sm, Gd, Dy and Y) agree with those obtained earlier by crystallographic methods. The bond lengths for the compounds TbGe2, HoGe2 and ErGe2 are also being reported.
pp 797-812 May 1985 Solid State Physics
A simple mechanism of replica symmetry breaking for spin-glass, as suggested by Parisi, has been used to solve the anisotropic spin-glass model of Sherrington and Ghatak. Temperature variation of the correlation parameters and the resulting variations with the temperature of the thermodynamic quantities like internal energy, specific heat and entropy have been evaluated. It is found that the anisotropy has considerable effect on the properties of the spin system. At low temperatures, the specific heat varies asT2. However, the entropy is positive for temperatures above 0.1°K, which is a considerable improvement on the results of Sherrington and Ghatak. The results are expected to be in good agreement with experiment or computer simulation studies near transition temperatures.
Volume 93 | Issue 5
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