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Shiv Nadar University

(SoNS) School of Natural Sciences

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.

Physics

World University root node

Physical Review C

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.

Journal of Physics G: Nuclear Physics

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.

Physical Review D

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.