Projection-operator approach to potential scattering

Journal Article · Tue Nov 01 04:00:00 EST 1983 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.28.2777· OSTI ID:5267812

Domcke, W

The projection-operator approach of Feshbach is applied to potential scattering. The aim is to describe single-particle or shape resonances in a mathematically rigorous manner as discrete states interacting with a continuum, in analogy to the well-known description of closed-channel resonances in scattering from targets with internal degrees of freedom. A projection operator Q is defined as Q = summation= 1/sup N/ Vertical Barchi/sub ..nu../>) is an arbitrary orthonormal set of L/sup 2/ functions. The complementary P space is spanned by a set of scattering states obtained in explicit form by orthogonalizing the free continuum to the set )). The free Green's function in P space is constructed explicitly and the P-space scattering problem is solved with the use of separable expansions of the potential. Two standard model problems: s-wave scattering from the square-well potential and the delta-shell potential: are solved exactly, with the use of an arbitrary number of eigenstates of a particle in a spherical box to define the Q space. It is shown that the formalism leads to a decomposition of the exact T matrix and scattering phase shift into an orthogonality scattering, a direct scattering, and a resonant scattering contribution. The pole structure of the corresponding S matrices in the complex momentum plane is analyzed.

• Research Organization: Theoretische Chemie, Physikalisch-Chemisches Institut, Universitat Heidelberg, D-6900 Heidelberg, Federal Republic of Germany
• OSTI ID: 5267812
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 28:5; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
COLLISIONS
ELASTIC SCATTERING
ELECTRON COLLISIONS
ELECTRON-MOLECULE COLLISIONS
FUNCTIONS
GREEN FUNCTION
MATHEMATICAL OPERATORS
MATRICES
MOLECULE COLLISIONS
NUCLEI
POTENTIAL SCATTERING
PROJECTION OPERATORS
RESONANCE
S MATRIX
SCATTERING