Papers by Colston Chandler
Few-Body Problems in Physics ’95, 1995
Coupled-channel methods have been employed to calculate reaction probabilities for a number of br... more Coupled-channel methods have been employed to calculate reaction probabilities for a number of breakup reactions, despite the fact that all the methods assume forms of wave functions which do not have the asymptotic behavior necessary to describe such reactions directly. This contribution provides a general conceptual framework for these methods, shows how to extend them to include asymptotic behavior appropriate to breakup reactions, calls attention to a possible reason for their practical success, and points out unresolved problems.
Few-Body Problems in Physics ’99, 2000
The creation of a mathematically rigorous multichannel relativistic quantum scattering theory tha... more The creation of a mathematically rigorous multichannel relativistic quantum scattering theory that includes particle creation and annihilation has been an important goal in theoretical physics for many decades. Even in such a thoroughly worked-over field as pion-nucleon physics the goal has remained unrealized [1]. This basic problem is here reexamined from a perspective that is different in some important respects from the main traditional approaches. In particular, it is not a local quantum field theory [2] nor is it based on the Bakamjian-Thomas construction [3].
Bulletin of the American Mathematical Society, 1975
A time-independent formula recently proposed by Rosenberg for the scattering operator for systems... more A time-independent formula recently proposed by Rosenberg for the scattering operator for systems involving charged particles is shown to be erroneous. Specifically, it is shown that his scattering amplitude is zero. (auth)
Few Body Dynamics, 1976
Publisher Summary This chapter describes a time-independent theory of multichannel quantum mechan... more Publisher Summary This chapter describes a time-independent theory of multichannel quantum mechanical scattering. In the continuing search for computationally viable theories of few body scattering, a number of variants of the Faddeev equations and their many-body generalizations have been proposed. The general method seems to develop equations for the scattering operators in the full N-body Hubert space. Problems such as uniqueness of solution and connectedness of the kernels of the resulting integral equations are dispatched in this full Hilbert space. At the end of the calculation, the projections onto the asymptotic scattering states are made. This chapter presents a study in which the projections onto the asymptotic states are made at the beginning and kept throughout the calculation. This approach is adopted because it is physically more natural, and it is hoped that it would lead to simpler equations for the transition operators.
Physical Review C, 1982
A new connected kernel version of the Chandler-Gibson equations is derived. Both the new and the ... more A new connected kernel version of the Chandler-Gibson equations is derived. Both the new and the original versions of the Chandler-Gibson equations are then modified to incorporate identical particle symmetries. Both types of equations are written down in detail for two different six-body models of alpha-deuteron scattering. Various features of these equations are thin compared. NUCLEAR REACTIONS Connected kernel equations for distinguishable and identical particles; equations for alpha-deuteron scattering.
Physics Letters B, 1985
As a model of p-d elastic scattering, s-wave scattering is studied for a two-body potential that ... more As a model of p-d elastic scattering, s-wave scattering is studied for a two-body potential that consists of a repulsive Coulomb potential and a central potential that decreases at large radius as the inverse fourth power of that radius. It is proved that the usual Coulomb modified s-wave scattering length does not exist for such potentials. We define a different modified scattering length and conjecture that it is the quantity that is to be compared with published calculated and experimental values.
Physics Letters B, 1982
It is shown that the recently proposed energy-independent optical potential is in fact the abstra... more It is shown that the recently proposed energy-independent optical potential is in fact the abstract form of Feshbach's generalized optical potential appropriate for time-dependent scattering theory. Thus the concept carries no new physical content. Recently, Kuo and collaborators [1] have derived an energy-independent optical potential in the form of a folded diagram expansion [2]. Subsequently, Buck and Lipperheide [3] have given a formal algebraic derivation of the energy-independent optical potential U by means of the projection operator technique. The detailed structure of U and its relation to Feshbach's optical potential have been further elucidated by Buck and Lipperheide [3], as well as Londergan and Miller [4], within the context of a model system with separable nonlocal interactions. The comment in ref. [3] that the physical interpretation of the energy-independent optical potential U is "somewhat obscure" motivated us to reconsider both the derivation and physical interpretation of U. For this purpose we chose the framework of time-dependent scattering theory because of its greater physical clarity and mathematical rigor. In particular, we have been able to isolate the assumptions of Buck and Lipperheide [3] in a precise way. Our main result is that the energy-independent optical potential U is just the abstract Hilbert-space version of Feshbach's generalized energy-dependent optical potential [5]. The relation between the two types of optical potentials is reminiscent of the one that exists between the scatterhag operators defined by time-dependent and time-independent scattering theories, respectively. Thus we
Physics Letters B, 1986
A simple formula is derived for the Coulomb modified s-wave scattering length function in the pre... more A simple formula is derived for the Coulomb modified s-wave scattering length function in the presence of long-range polarization potentials. When applied to a model of low-energy p-d scattering, the formula reproduces behavior previously described by Kvitsinskii and Merkuriev [Sov. J. Nucl. Phys. 41 (1985) 4121.
Physical Review Letters, 1994
In the original two-potential formalism the potential was split into two parts which were treated... more In the original two-potential formalism the potential was split into two parts which were treated at different dynamical levels. In the present Letter a multichannel generalization of the method is proposed that also allows various groups of channels to be treated differently. The new formalism is used to devise a dynamically consistent way of treating breakup processes in the framework of coupled-channel calculations.
Physical Review C, 1996
It is shown that the electric polarizability of the deuteron produces negligible effect on the cr... more It is shown that the electric polarizability of the deuteron produces negligible effect on the cross section of deuteron induced rearrangement reactions even at extremely low energies. This assessment is based on simple analytical formulas, derived on the basis of N-particle scattering theory by means of the general two-potential formalism, including Coulomb and exchange effects. It is shown on the basis of general physical arguments that the polarizability effects at very low energies are entirely contained in a multiplicative enhancement factor that differs from 1 by at most a few percent. As a result enhancement of (d, p) relative to (d,n) reactions is not possible by the Oppenheimer-Phillips mechanism.
Nuclear Physics A, 1978
Abstract The problem of spurious solutions to the integral equations of N -particle quantum scatt... more Abstract The problem of spurious solutions to the integral equations of N -particle quantum scattering theory is treated. In particular, the Federbush discussion of the Weinberg-van Winter equation is enlarged. It is shown within this framework that the Narodetzkii-Yakubovskii equations, the Bencze-Redish equations, and the Kouri-Levin-Tobocman equations can all have spurious solutions. Certain model independent results are also presented.
Nuclear Physics A, 1982
... s lim (.IJIIint = 0. (3.20) Gy. Bencze et al. Multiparticle scattering theory 469 Now, if the... more ... s lim (.IJIIint = 0. (3.20) Gy. Bencze et al. Multiparticle scattering theory 469 Now, if the closure of the range of 7 is the same as that of Jl1, the restriction of Hx onto this subspace .JEn is unchanged. The wave operators t = s lim ...
Nuclear Physics A, 1998
Jones, Madison and Konovalov [Phys. Rev. A 55 (1997) 444] have calculated various approximate rea... more Jones, Madison and Konovalov [Phys. Rev. A 55 (1997) 444] have calculated various approximate reaction amplitudes for the ionization of hydrogen by electron impact. It is shown here that their approximate amplitudes are Born approximations to new representations of the transition operator for the reaction.
Journal of Mathematical Physics, 1974
Rigorous derivations are given of two time-independent formulas for the multichannel scattering o... more Rigorous derivations are given of two time-independent formulas for the multichannel scattering operator for nonrelativistic charged particle systems. The derivations are based on Dollard's time-dependent theory and use techniques of spectral integration. The formulas involve a complex power of the resolvent operator, in contrast to short-range formulas. Bilateral Laplace transforms are used to derive a generalized multichannel resolvent equation and to prove existence and uniqueness of the solution. The formulas are applied to recover the well-known two-body Coulomb scattering amplitude.
Journal of Mathematical Physics, 1974
The formulation by Mulherin and Zinnes of two-particle Coulomb scattering theory is extended to t... more The formulation by Mulherin and Zinnes of two-particle Coulomb scattering theory is extended to the multichannel case. The wave operators so obtained are proved by a direct method to be identical with those of Dollard.
Journal of Mathematical Physics, 1973
Rigorous proofs are given of several theorems establishing the connection between time-dependent ... more Rigorous proofs are given of several theorems establishing the connection between time-dependent and time-independent multichannel scattering theory. The method of proof involves a two-Hilbert-space formulation of time-dependent multichannel theory and the theory of spectral integrals. In particular, the time-independent theory in the form proposed by Alt, Grassberger, and Sandhas is derived.
Journal of Mathematical Physics, 1993
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Papers by Colston Chandler