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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.

Physics

(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.

Redundant states and Jost functions for nonlocal potentials

A comparison of two two-term separable Λ-N potentials which have been used in three-body calculations of the hypertriton binding energy is reported. The potentials compared are approximately on-shell T matrix equivalent, but yield quite different values for the hypertriton binding energy. It is shown that the radial wave function for one of the potentials has an extra node due to a spurious state. The comparison is based on a Fredholm determinant approach to the radial wave equation for a nonlocal potential. NUCLEAR STRUCTURE Two-term separable Λ-N potentials, Fredholm determinants, spurious states, extra nodes and separable potential three-body calculations. © 1978 The American Physical Society.

Comparison of two-term separable λ-N potentials

A class of radiative decays of psi particles is studied in the vector-meson dominance model to determine the behaviour of the off-shell vector-meson-photon coupling constants. It is found that these are suppressed by about a couple of orders of magnitude compared with their on-shell values and the suppression thus obtained may be much larger than is usually believed. Different approaches for the incorporation of the suppression in simple VDM are discussed, and the necessity of considering suppression due to off-shell effects at both the hadronic and photonic vertices is emphasised. While the authors' model is constructed in the constructive interference scheme, the parallel arguments in the cancellation hypothesis are closely examined in an appendix to the paper; it is found that in this hypothesis also off-shell suppression factors are necessary to give currently acceptable numbers, and some of the problems associated with this approach are indicated.

Off-mass-shell coupling constants and radiative decays of ψ particles in VDM

Lettere Al Nuovo Cimento Series 2

A new sum rule for pseudoscalar mesons

The recent measurements of V→Pγ decays have led to a number of theoretical formulations to explain the low rates. In the vector-meson-dominance model this is accomplished by introducing a suppression factor at one of the vertices of the off-shell vector meson, but this leads to inconsistencies when compared with experimental data. For the case of new mesons we have found that suppression factors need to be introduced at both vertices to give a good fit to the data. In this paper we show that this scheme, applied to the case of the old mesons assuming only simple SU(3), gives fits that are as good as or better than other generally more complicated models. © 1978 The American Physical Society.

Radiative decays of vector mesons and off-shell factors in the vector-dominance model

A local derivative coupling model is used to study the φ′→ππ and other dipionic decays of φ and φ″, as an alternative to the ε-model. The results obtained are quite satisfactory. We findt hat the existence of the ε-resonance is not essential in order to understand the dipionic decays of the psions at the present level of experimental data available. © 1978 Indian Academy of Sciences.

Pramana

Dipionic decays of psions in a local derivative coupling model

On the masslessness of the u-quark

This paper examines the presence of extra nodes in the scattering wave function for a nonlocal potential. Extra nodes are known to result from the nonlocality of an effective potential which incorporates the Pauli principle. It is shown that an extra node is directly linked to the existence of a continuum bound state or a spurious state in the scattering spectrum. Thus the presence of extra nodes occurs in conjunction with zeros of the Fredholm determinants D±(k) and D(k) associated with the integral equations for the physical and regular scattering solutions, respectively. The behavior of the nodes due to spurious states and continuum bound states is differentiated. Two possible definitions of the phase shift for a nonlocal potential are discussed in connection with this behavior. Both are consistent with the local limit. The definition of the phase shift as the negative of the phase of the Jost function L+(k) is suggested as preferable. This definition is shown to be in accord with the nodal behavior of the wave function and its interpretation in terms of an absolute value of the phase shift. Examples of potentials with a spurious state and of potentials with a continuum bound state are given. The nodal behavior of the wave function and the associated phase shift behavior are examined for each. NUCLEAR REACTIONS Scattering by a nonlocal potential, extra nodes, Fredholm determinants and their zeros, continuum bound states, spurious states, phase shifts. © 1977 The American Physical Society.

Extra nodes and the phase shift of the scattering wave function for a nonlocal potential

Nonlocality is characteristic of potentials describing processes in which degrees of freedom are eliminated, and provides for a description of a much wider variety of phenomena than that encountered with short range local potentials. In this paper, properties of the radial equation for symmetric nonlocal potentials are investigated, using a configuration space approach and restricting the analysis to real k. Emphasis is placed on identifying those constraints associated with a local potential which are relaxed in going from a local to a nonlocal potential. The Fredholm determinants associated with the integral equations for the physical, regular, and Jost solutions are central to the development. Unlike the case for a short range local potential, for a nonlocal potential these Fredholm determinants can vanish for real k 0. It is shown that when D±(k)=0 the other Fredholm determinants are zero as well. The properties of the solutions at the zeroes of the Fredholm determinants are discussed in this context, and the concepts "spurious state" and "continuum bound state" are clarified. The behavior of solutions is illustrated with examples. NUCLEAR REACTIONS Scattering by a nonlocal potential, Fredholm determinants and their zeroes, continuum bound states, spurious states. © 1976 The American Physical Society.

Solutions of the radial equation for scattering by a nonlocal potential

In an earlier paper we considered scattering of all partial waves from a wide class of separable nonlocal potentials, and obtained in configuration space exact analytic solutions for the wave functions and phase shifts. In this paper these solutions are used to construct exact expressions for the half-off-shell and off-shell T matrices for this class of potentials. As an illustration, we compare the off-shell T matrix for the one-term Yamaguchi potential calculated by the method presented here with the expression obtained by standard techniques. NUCLEAR REACTIONS Off-shell T matrices. Separable nonlocal potentials. © 1974 The American Physical Society.

Off-shell T matrices for a class of separable nonlocal potentials

In this paper we consider scattering of all partial waves from a wide class of separable nonlocal potentials and obtain in configuration space exact analytic expressions for the wave functions and phase shifts. These expressions simplify some of the difficulties associated with finding a potential which fits phase shift data, with the analytic expressions for the scattering length and effective range being particularly useful. Employing these results, we obtain a two-term separable nonlocal potential with three adjustable parameters which gives a reasonable fit to the S01 n-p phase shifts and a very good scattering length and effective range. NUCLEAR REACTIONS Separable nonlocal potentials. Analytic expressions for wave functions, phase shifts. S01(n-p) phase shift fit. © 1974 The American Physical Society.