Born series in obstacle scattering

Scattering Theory: Born Series

A 2 Scattering Theory: Born Series

Time-dependent Born-series calculations of three-body scattering systems

Time-dependent Born-series calculations are carried out for various short and long range three-body scattering systems. The long range system is a standard s-wave model for electron-atom scattering developed by Temkin @Phys. Rev. 126, 130 ~1962!# and Poet @J. Phys. B 11, 3081 ~1978!#. A direct solution of the timedependent Schrödinger equation yields exact excitation and ionization cross sectio...

Obstacle Scattering as Seen

We recount some of Ralph Kleinman's scientiic achievements in obstacle scattering for time harmonic waves by reporting on two topics where R.K. and R.K. interacted mathematically. The rst topic is the problem of nonuniqueness for the classical boundary integral equations for the direct scattering problem and the second is the development of numerical methods for the inverse scattering problem.

On the Far Field in Obstacle Scattering

We will establish far eld identities for the scattering of time-harmonic acoustic waves from sound-soft and sound-hard obstacles and will illustrate two applications of these identities for the inverse obstacle scattering problem. Firstly, we will provide an alternate proof for the Fr echet diierentiability of the far eld pattern with respect to the boundary. Secondly, we will connect the ident...