Lippmann-Schwinger Formalism Research Articles

Scattering theory of close-coupling equations.

The scattering theory implied by the close-coupling equations is studied using a Lippmann-Schwinger formalism. The new results derived can be summarized as follows: An alternative form of the equations that ensures there are no spurious solutions in the scattering region can be constructed, and moreover there is an infinite number of such forms. The Neumann- (perturbation-) series expansion diverges in general for most energies for both the old and new forms. The Born limit nevertheless holds and can be recovered by appropriate rearrangement of the Neumann series. The original integral formulation may give convergent scattering amplitudes despite the lack of uniqueness of the solutions. The conditions under which this happens are examined.

Finite-basis-set expansion methods for scattering problems.

A wide variety of finite-basis-set expansion methods is applied to electron--hydrogen-atom scattering in the static-exchange approximation. All these methods are based on the Lippmann-Schwinger formalism. A careful analysis of the numerical results is presented with the aim of selecting efficient approaches to the solution of realistic electron-atom (and electron-molecule) scattering problems. The results show that the efficiency of the expansion methods may depend sensitively on the characteristics of the interaction terms. Some difficulties of the simple method of moments are pointed out. A particular least-squares method is proposed to avoid the spurious singularities encountered in applications of the Schwinger variational method to singlet scattering processes.

An improvement of Coulomb corrections in the phase shift analysis of elastic? �-16O scattering and predictions of cross sections for? ?-16O scattering at low energies

The proper treatment of the pure Coulomb part and the pure hadronic part of the totalπ± -16O amplitude, calls for a realistic description of the Coulomb corrections. Introducing Coulomb corrections, derived within the Lippmann-Schwinger formalism, we are able to describe differential cross sections forπ±-16O scattering in the energy range betweenTπ, lab = 114 and 240 MeV very accurate. In addition we are able to determineπ− -16O differential cross sections from measuredπ+ -16O data at lower energies.

Perturbation of relativistic bootstraps

This paper reports the investigation of two problems: (i) the possibility of bootstrapping boundstate scalar and vector mesons from scalar constituents, in an off-shell model, utilizing the direct interaction theory of Bakamjian and Thomas (1953), and then (ii) the effect of applying a linear perturbation procedure to the masses and coupling constants of these solutions. In (i) the Lippmann-Schwinger formalism and an approximate form of crossing symmetry are used to obtain expressions for the bound-state residues, giving solutions to both the scalar and vector cases with properties in excellent agreement with Bethe-Salpeter and N/D dispersion results of other excellent agreement with Bethe-Salpeter and N/D dispersion results of other workers. In (ii) the author calculates the relative contributions of the 'driving-term' and 'feedback' mechanisms. In the S-wave case he finds that the attractive perturbation increases the binding of the bound state, but in the P-wave case, treated with a cut-off, he obtains a 'sign-reversal' of the mass-shift arising from the 'feedback'.