Sadhan K. Adhikari

The Phillips and the Girard-Fuda plot for the trinucleon system

Abstract For the S-wave spin doublet neutron-deuteron (n-d) system we suggest and parametrize an effective range expansion which has the correct dependence on the n-d scattering length a at low energies. The present expansion explains the low energy properties of this system and in particular the linear correlation between the trinucleon energies and the scattering length a .

ANOMALIES OF VARIATIONAL PHASE-SHIFTS

Abstract It is demonstrated, contrary to various claims, that the phase shifts calculated via variational principles involving the Green function may exhibit anomalous behavior. These anomalies may appear in variational principles for the K matrix (Schwinger variational principle) of potential V , for ( KV ) (Kohn-type and Newton variational principles), and other variational principles of higher order (Takatsuka—McKoy variational principle).

A new class of antisymmetrized optical potentials

Abstract A new class of antisymmetrized, two-fragment, elastic scattering optical potentials having no elastic unitary cuts is constructed. The construction is based on the wave function equations of many-particle scattering theory and yields potentials differing significantly from those derived recently.

Effective range expansion for systems with small scattering length: Pion-pion and neutron-deuteron systems

Abstract The dramatic failure of the effective range expansion for systems with small scattering length a (| a | ∼ 0) is accounted for theoretically. An alternate expansion is suggested for such systems and is applied successfully to the S wave neutron-deuteron and pion-pion systems where the usual expansion fails because of the appearance of sub-threshold poles in the effective range function.

ON RESOLVENT OPERATORS IN SCATTERING THEORY

Abstract It is shown that, contrary to recent claims, the usual definition of resolvent operators in scattering theory is correct.

Effective range expansion revisited

Abstract For small values of the scattering length a (| a | ∼ 0) the effective range function k cot δ shows a pole for small k 2 . The usual effective range expansion cannot produce such a pole. We provide an alternative expansion which reduces to the usual one for | a | ⪢ 0 and shows a pole for | a | ∼ 0. The present expansion explains the low energy properties of the S-wave spin-doublet trinucleon system and in particular the linear correlation between the trinucleon energy and the neutron-deuteron scattering length.

Surface integrals in the derivation of the Lippmann-Schwinger equation for many-particle systems

Abstract The derivation and interpretation of the many-particle Lippmann-Schwinger (NS) equation are reviewed. The derivation from the Schrodinger equation involves certain surface integrals at infinity, originally examined by Gerjuoy. Reasonable assumptions about the values of these surface integrals at real energies imply that the many-particle LS equation generally has nonunique solutions. Various arguments, including calculations in a model problem, indicate that these surface integrals have been correctly evaluated, despite recent claims to the contrary.

Discretizing the three-body continuum: Interpretation of non-breakup results

Abstract This paper is concerned with understanding the physics responsible for the major result of the preceding article, viz., that the coupled reaction channel (CRC) ansatz responds better than any of the connected-kernel (exact) collision theories to an L 2 (pseudostate) discretization approximation. The analysis is carried out within the framework of the wave function equations equivalent to the transition operator formalisms employed in the preceding article. In an alternate approach comparing the CRC method with an approximate version of a multichannel collision theory, it was argued that since only the CRC ansatz is based directly on the Schrodinger equation and on orderly restrictions of the Hilbert space, then it must be the superior approximation. While this conclusion is correct, the argument underlying it is in fact inadequate. The different argument used in the present analysis is based on the fact that connected-kernel theories require contributions from the full three-body breakup continua in order to determine the two-body transition amplitudes accurately, while the effect of an L 2 discretization approximation on them is to eliminate much of these contributions unless very high-lying pseudostates are employed. In contrast, high-lying pseudostates are much less important for the CRC case. This is demonstrated and its ramifications are explored in some detail herein. In particular, the analyses based on this argument are seen to yield an understanding and interpretation of almost all of the trends exhibited in the results tabulated in the preceding article.

Parametrization of strongly overlapping nuclear resonances

Abstract We compare the parameters involved in two approaches to the study of overlapping nuclear resonances, the first one by Kawai, Kerman, and McVoy and the second one by the present author. We also compare the parameters of these two approaches to those of the approach of Agassi, Weidenmuller, and Mantzouranis.

Nonuniqueness of solutions of three-body Lippmann-Schwinger equations in a soluble model

Abstract Contrary to recent claims we show in a soluble three-body model that the exact scattering wavefunction with incoming wave in a rearrangement channel satisfies the homogeneous Lippmann-Schwinger equation, and hence that the solutions to the Lippmann-Schwinger equation are nonunique.