Physics

<p>Shiv Nadar University is a comprehensive, multidisciplinary, research-focused, and student-centric University offering a full range of academic programs at the undergraduate, postgraduate and doctoral level. With state-of-the-art infrastructure, the University comprises of academic wings, sophisticated labs, international standard sports facilities, amphitheaters, auditorium, conference rooms and smart classrooms. The University&rsquo;s goal is to become internationally recognized for the quality of its research and creative endeavors and their applicability to improving quality of life, generating new insights and expanding the boundaries of human knowledge creativity. Committed to excellence in teaching, research and service, the University aims to serve the higher education needs of India and the world beyond.</p>

Shiv Nadar University

First-principle scattering calculations which include antisymmetrization of a projectile with respect to identical particles in the target result in a nonsymmetric nonlocal effective potential. Such a potential can lead to redundant states in the scattering wave function. In this case the potential is required to satisfy a consistency condition. We discuss this condition and the manner in which it can be imposed. We also discuss the replacement of this potential by a reduced symmetric nonlocal effective potential which does not produce redundant states. This reduced potential generates a scattering wave function orthogonal to the redundant states. If the original equation has one redundant state, the phase shift at zero energy is π, resulting in an extra node in the zero-energy wave function. The reduced effective potential must retain this extra node. This characteristic of the reduced effective potential is illustrated with an example. We show that the extra node produced by the potential in the example comes either from a spurious state or a bound state of that potential. NUCLEAR REACTIONS Scattering by a nonlocal potential, extra nodes, Fredholm determinants and their zeros, redundant states, continuum bound states, spurious states. © 1980 The American Physical Society.

(SoNS) School of Natural Sciences

World University root node

Physical Review C

Redundant states, reduced potentials, and extra nodes in the radial wave function

Within the framework of an extended vector-dominance scheme, the various radiative processes of and are studied. The rates turn out to be generally much smaller than those of the corresponding decays and in some cases too small for direct observation. The off-shell - and - coupling constants are found to be suppressed by about a couple of orders of magnitude compared with their on-shell values. © 1980 The American Physical Society.

Physical Review D

Radiative processes of and and off-shell suppressions

An integral equation for the s-wave bound-state solution is derived and then solved for a square-well potential. It is shown that the scattering solutions continue to exist at negative energies, and when evaluated at the energy of a bound state these solutions do reduce to the bound-state solution. The bound-state energies of a square-well potential are deduced also from orthogonality considerations. Finally, the existence of bound states for an arbitrary short-range potential is related to the occurrence of zeros of the Jost function or poles of the S matrix for that potential. © 1980, American Association of Physics Teachers. All rights reserved.

American Journal of Physics

Integral equations and the bound-state problem

Lettere al Nuovo Cimento

Asymptotic SU 5 and a new mass constraint for the ω, ϕ, ψ and γ mesons

Fulltext

Physics Letters B

Masslessness of the up quark and η→3π0 decay

S-wave scattering solutions of the Schrodinger equation with an arbitrary central local potential are considered. Green’s functions and integral equations are derived for scattering solutions subject to a variety of boundary conditions. Exact solutions are obtained for the case of a finite spherical square-well potential, and properties of these solutions are discussed. © 1979, American Association of Physics Teachers. All rights reserved.

Integral equations and scattering solutions for a square-well potential

We investigate in a chiral SU(4) × SU(4) model the symmetry-breaking parameters, decay constants, D+-D0 mass difference, quark masses, and electromagnetic mass splitting of the charmed baryons by assuming (i) that matrix elements of the type 0|vP|P are SU(4) invariant and alternatively (ii) that these are dominated by the quark mass term. The two approaches are compared in this work and conclusions presented. We also mention possible extensions to the chiral SU(5) × SU(5) scheme and discuss some of the associated problems. © 1979 The American Physical Society.

A quantitative measure of the SU(4) × SU(4) breaking, SU(2) mass splitting of the charmed hadrons, and quark masses

The recent hypothesis of a possible new fifth quark flavour, beauty (or bottom), following from the discovery of the gamma resonances, is considered here in the context of the Weinberg spectral-function sum rules. The authors find as a consequence new equal-spacing mass relations and general mass constraints for the vector mesons with the new flavour. In a restricted symmetry domain they predict the masses of some of these mesons and discuss the results in so far as they shed light on the breaking of SU(5) symmetry and the approximations involved in the Weinberg sum rules.

Journal of Physics G: Nuclear Physics

Asymptotic SU(5) symmetry and spectral-function sum rules

Increasingly, nonsymmetric nonlocal potentials are occurring in formulations which include descriptions of antisymmetrization and other nuclear phenomena. In studying such potentials, it is found that the characteristics of solutions of the scattering equation differ in some cases significantly from those associated with symmetric nonlocal potentials. For example, it has been demonstrated that when redundant solutions are present due to antisymmetrization, a scattering solution does not exist unless a consistency condition is satisfied. In the present paper this and other such aspects of nonsymmetric nonlocal potentials are investigated. The importance of the adjoint potential to these discussions is particularly emphasized. Conditions on scattering solutions for nonsymmetric nonlocal potentials and their adjoints are discussed in detail, and an example is presented. NUCLEAR REACTIONS Antisymmetrization, scattering solutions for a nonlocal potential, nonsymmetric nonlocal potentials, scattering solutions for adjoint potentials, Fredholm determinants, redundant states. © 1979 The American Physical Society.

Redundant solutions, scattering solutions, and nonsymmetric nonlocal potentials

This paper considers the existence of Jost solutions f(k,r) and the Jost functions L(k) in the presence of redundant states. The definition of L(k) directly in terms of Fredholm determinants associated with kernels of integral equations is discussed. Examples are used to stress the importance of this relationship when the Jost solutions do not exist. NUCLEAR REACTIONS Antisymmetrization, redundant states, nonlocal potentials, Jost solutions and Jost functions. © 1979 The American Physical Society.