Volume 48, Issue 5
May 1997, pages 959-1090
pp 959-967 May 1997
The geometric phase and ray space isometries
We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner’s proof is best viewed as an use of the Pancharatnam connection to ‘lift’ a ray space isometry to the Hilbert space.
pp 969-975 May 1997
Thomas rotation and polarized light: A non-abelian geometric phase in optics
We describe anon-abelian Berry phase in polarization optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarized light. The analogy permits a simple optical realization of the non-abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincaré sphere in terms of the Pancharatnam phase.
pp 977-984 May 1997
On periodically kicked quantum systems
The time evolution of a multi-dimensional system which is kicked periodically with a potential is obtained. The most interesting aspects of the investigation are (i) if the operator corresponding to the potential has invariant subspaces (a characteristic property of multi-dimensional systems), the states belonging to these subspace in its evolution are confined to these invariant subspaces respectively and there cannot be any mixing of states between these subspaces. Further, (ii) it leads to the existence of quasi-stationary states (determined again by the potential) which evolves independent of other similar quasi-stationary states. The method followed in the paper is the direct integration of the Schrödinger equation and then to construct the wave function from the initial wave function.
pp 985-995 May 1997
Weak decay constants of light and heavy pseudoscalar mesons
We investigate the weak leptonic decays of light and heavy pseudoscalar mesons in a relativistic quark model of independent quarks. We perform a static calculation of the decay constantf_{M} purely on grounds of simplicity. In order to minimize the possible uncertainty in the static calculation, we estimate the ratios of the decay constants which are found to be in good agreement, in the heavy flavor sector, with the predictions of other models available in the literature and existing experimental data. However, there is a noticeable discrepancy in the current prediction for pion decay constant which demonstrates the inherent limitations of the static approximation in the study of non-strange light mesons.
pp 997-1004 May 1997
Meson spectroscopy with confined one gluon exchange potential
K B Vijaya Kumar A K Rath S B Khadkikar
Confined gluons-exchange among relativistically confined quarks is used to calculate the ground state masses and the radially excited states of pseudo scalar and vector mesons. A good agreement is obtained with the experimental masses. The limitation of the perturbative treatment of estimating theN−Δ andπ−ρ splitting using one-gluon-exchange potential is pointed out.
pp 1005-1013 May 1997
Two body non-leptonic decaysB →Dπ with heavy quark and chiral symmetry
We have analysed the two body non-leptonic charmed-meson decays of heavyB meson based on the factorization assumption. The transition matrix elements and the corresponding decay widths are calculated in the heavy quark and chiral symmetry limit and the Isgur-Wise function present in the expression is determined by the wave function model of Aliet al. The results obtained are quite interesting and agree reasonably well with the experimental data.
pp 1015-1019 May 1997
Solution of approximate gluon evolution equation for small-x at fixed ‘ρ’
A simple method has been applied to solve the approximate gluon evolution equation for small-x at fixedρ(≡√ln(x_{0}/x)/ln[ln(Q^{2}/Λ^{2})/ln(Q_{0}^{2}/Λ^{2})]. Numerical comparison is made with the predictions from ‘double asymptotic scaling’ and fit. Better agreement is found between our solution and fit nearρ=1. The solution gives approximate double scaling in this region having ‘hard’ pomeron with small contamination.
pp 1021-1026 May 1997
Heavy-ion scattering at low energies: First-order correction to the eikonal phase shift
The first-order non-eikonal correction has been applied to calculate heavy-ion reaction cross sections at low energies. The numerical investigations show that, for many heavy-ion systems, reaction cross sections and elastic scattering angular distributions thus calculated, are in good agreement with the optical model calculations.
pp 1027-1034 May 1997
Semi-empirical formulae for Λ-binding energy in hypernuclei using mass distribution
M Z Rahman Khan Nasra Neelofer M A Suhail
Semi-empirical formulae for ground state Λ-binding energy of heavy hypernuclei, in inverse powers of the mass number, using the mass distribution in the folding model, under fairly reasonable assumptions about the range of the Λ-nucleon force are obtained in more than one plausible way. However, they are found to give nearly identical results. A reasonable estimate of the Λ well-depth is obtained from a chi-square fit of the available ground state Λ-binding energy data of medium and heavy nuclei.
pp 1035-1075 May 1997
TheU^{B}(6)⊗U^{F}(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU^{B}(6)⊗U^{F}(20) related to theU^{B}(5) andO^{B}(6) limits of sdIBM (U^{B}(6)) are analysed. Broadly speaking,U^{B}(6)⊗U^{F}(20) admitsU^{BF}(5)⊗U_{s}^{F}(4), Spin^{BF}(5)⊗U_{k}^{F}(5) andU^{BF}(5)⊗U_{s}^{F}(2) limits withU^{B}(5) core and Spin^{BF}(6),O^{BF}(5)⊗U_{s}^{F}(4), Spin^{BF}(6)⊗U_{k}^{F}(5) andO^{BF}(6)⊗U_{s}^{F}(2) limits withO^{B}(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU^{B}(5) andO^{B}(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU^{B}(6)⊗U^{F}(20) symmetry limits are briefly discussed.
pp 1077-1090 May 1997
Photon interaction cross-sections and anomalous scattering factors of Cu and Ag
Sandiago T K Umesh Ramakrishna Gowda
Total attenuation cross sections of copper and silver have been measured in the energy range 5 to 85 keV in a narrow beam good geometry set up using X- andγ-rays emitted from radio isotopes, by employing a high resolution hyper pure germanium detector. From the measured values, the photoeffect cross-sections have been derived by subtracting a small contribution of the sum of the theoretical coherent and incoherent scattering cross sections. The photoeffect cross-sections so obtained are found to be in better agreement with the unrenormalized values of Scofield [10]. These photoeffect cross-sections have been used to evaluate the dispersion corrections (also called anomalous scattering factors)f^{+} andf″ for the forward Rayleigh scattering amplitude by a numerical evaluation of the dispersion integral that relates them at the energies at which the cross-sections have been measured. To thef^{+} values so obtained, the relativistic corrections proposed by different investigators are included separately and the valuesf′ so obtained are compared with the available data and discussed. Possible conclusions are drawn from the present study.
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