On the poles of the S-matrix for long range potentials

On the poles of the S-matrix for long range potentials by Erasmo Ferreira Download PDF EPUB FB2

The analytic properties in the complex k plane of the S matrix for scattering by a screened Coulomb potential are studied. Particular attention is given to the limit as the screening radius tends to infinity, so as to show, in an explicit example, the effect of the tail of the potential on the properties of the analytically extended S matrix.

It is shown that the pole configuration obtained in Cited by: The poles of the quantum scattering matrix (S-matrix) in the complex momentum plane have been studied extensively.

Bound states give rise to S-matrix poles, and other poles correspond to non. Table ence of the complex k m wave numbers of the l = 0 poles of the S-matrix on the V 2 strength of the surface term for 56 Fe+n in the GWS potential. Analytical results were calculated by the code BENCZE, the numerical results were calculated by the program corrected k m corr values were calculated using Eq.

The cut-off radius value was R max = 12 by: 7. Abstract. Analytical properties of the S matrix are obtained with respect to the strength of any potential in the radial Schrodinger equation. Some properties of the analogs of Regge trajectories are derived in the same way, which should give information on the radius of convergence of Born expansion.

The inclusion of local singularities and higher order perturbations in the 2-body long-range case, and the 2-body oscillating long-range potentials are also discussed. To test the validity of current ideas on the poles of the S-matrix, a simple example is treated: non-relativistic scattering by a spherically symmetric rectangular potential well (on barrier).The poles of the S-matrix associated with this problem, in the case of zero angular momentum, are determined, and their behaviour as a function of the well depth (barrier height) is by: l = 0 case and compare the distribution of the poles of the scattering matrix S for the two types of the potentials.

In section 2 of the paper we define the poles of the S-matrix on the complex k-plane for zero angular momentum. In section 3 we give analytical formulae of the S-matrix for WS and GWS potentials. Long-range scattering for nonlinear Schrödinger equations in one and two space dimensions Shimomura, Akihiro and Tonegawa, Satoshi, Differential and Integral Equations, Scattering theory for the perturbations of periodic Schrödinger operators Gérard, Christian and Nier, Francis, Journal of Mathematics of Kyoto University, Cited by: Book.

Version 3i, 20th July Title: and as poles of the S-matrix. Poles on the negative imaginary k-axis are classed as virtual states, Finally, transformations of the coupled channels set are shown to handle long-range couplings, by matching at a smaller radius to coupled asymptotic wave functions, and to transform non-local.

Regge trajectories can be obtained for many other potentials, in particular also for the Yukawa potential. [2] [3] [4] Regge trajectories appear as poles of the scattering amplitude or in the related S {\displaystyle S}.

You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Analytical structure of the non-relativistic unitary and non-unitary S -matrix is reviewed for the cases of any interactions with any motion equations inside a sphere of radius a, enclosed by centrifugal and rapidly decreasing (exponentially or by the Yukawian law or by the more rapidly decreasing) potentials.

Some kinds of the symmetry conditions are imposed. "Modification of Effective Range Theory in the Presence of a Long-Range (1/r 4) Potential," Thomas F. O'Malley, Larry Spruch, and Leonard Rosenberg: Box: Folder: 19 "Bounds on Elements of the S Matrix for Elastic Scattering: One Dimensional Scattering," Ralph Bartram and Larry Spruch.

Analytical structure of the non-relativistic unitary and non-unitary S-matrix are investigated for he cases of any interactions with any motion equations inside a sphere of radius a, enclosed by the centrifugal and rapidly decreasing (exponentially or by the Yukawian law or by the more rapidly decreasing) potentials.

Some kinds of the symmetry conditions are imposed. The. Kalf and V. Krishna Kumar, On the absence of positive eigenvalues of Schrödinger operators with long range potentials, Trans. Amer. Math. Soc. () – Google Scholar Cited by: 2.

Singular and long-range potentials, Ann. Phys.– and addendum preprint Bielefeld. Google Scholar V. Enss Quantum scattering theory for two-and three-body systems with potentials of short and long range, Schrödinger Operators, ed. Graffi, Springer Lecture Notes in : I.

Sigal. That each S-matrix element for a potential of finite range has infinitely many poles was first shown by J. Humblet () and independently by H.

Rollnik (). The more general proof given here, as well as the subsequent arguments concerning the distribution of poles if the range of the potential is finite, follows T. Regge (a).Author: Roger G.

Newton. TGD AS A GENERALIZED NUMBER THEORY Matti Pitk¨anen Karkinkatu 3 I 3, Karkkila,Finland Febru PREFACE iii PREFACE This book belongs to a series of online books summarizing the recent state Topological Geometrodynamics (TGD) and its applications.

Strictly finite-range (SFR) potentials are exactly zero beyond their finite range. Single-particle energies and densities, as well as S-matrix pole trajectories, are studied in a few SFR potentials suited for the description of neutrons interacting with light and heavy nuclei.

You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

Free ebooks since. We present a solution in the time-domain to the two-dimensional linear water-wave problem, in which a semi-infinite fluid region is bounded on one side by a vertical elastic plate. The problem is solved using a generalized eigenfunction expansion from the solutions for single frequencies, and we begin with a novel solution of the single-frequency by: Table of contents for issues of Journal of Mathematical Physics Erasmo M.

Ferreira and Antonio F. F. Teixeira On the Poles of the S Matrix for Long-Range Potentials Bounded Portions of the Physical Region H. L. Berk and D. L. Book and .We re-examine the series of resonances found earlier in atomic three-body systems by solving the Faddeev-Merkuriev integral equations.

These resonances are rather broad and line up at each threshold with gradually increasing gaps. This lining up takes place in the same way for all thresholds and is irrespective of the spatial symmetry.

We relate these resonances to the Gailitis mechanism Author: Daniel Diaz, Zoltan Papp, Chi-Yu Hu.