Adiabatic approximation and the other (lower) bound on the scattering length

Journal Article · Tue Jan 01 04:00:00 EST 1974 · Physical Review, A (General Physics)

DOI:https://doi.org/10.1103/PhysRevA.9.226· OSTI ID:4354672

Hahn, Yukap; Spruch, Larry

The static approximation, which neglects the distortion of the (complex) target, that is, virtual excitations, during the collision of a particle with the target, was shown previously to give an upper bound on the scattering length when the number of bound states supported by the static and true Hamiltonians are the same. It represents an underadjustment of the target to the field of the scattering particle. It is perhaps then to be expected that the adiabatic approximation, in which the target wave function is calculated for each value of the incident particle coordinate as if the incident particle were fixed at the given point and which represents therefore an overadjustment of the target to the field of the incident particle, might provide the opposite bound, the lower bound, on the scattering length. This possibility is explored for the determination of scattering lengths. The bound property is shown to hold in cases where both the true and adiabatic Hamiltonians support the same number of bound states; some (reasonable) subsidiary conditions must also be satisfied. Possible extensions of the formulation to scattering with nonzero energy and with exchange are briefly mentioned. The theory is then applied to e+H and e+He scattering at zero incident energy; a reasonably acccurate bound for the latter system is obtained, but the adiabatic approximation gives only a very crude, though rigorous, bound on the e+H seattering length. A connection between the generalized optical potential and the adiabatic potential is derived using projection-opeeator techniques, thus further clarifying the physical content of the adiabatic picture. Bounds are also obtained for atom-atom and ion-atom collisions; they are interesting only if the electron-proton mass ratio is not thought of as vanishingly small. Some consideration is given to pH scattering. Lower bounds on electron-atom scattering lengths are more difficult to obtain. (auth)

• Research Organization: Physics Department, University of Connecticut, Storrs, Connecticut 06268
• Sponsoring Organization: USDOE
• NSA Number: NSA-29-025195
• OSTI ID: 4354672
• Journal Information: Physical Review, A (General Physics), Journal Name: Physical Review, A (General Physics) Journal Issue: 1 Vol. 9; ISSN PLRAAN; ISSN 0556-2791
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

*HELIUM-- POSITRON COLLISIONS
*HYDROGEN-- POSITRON COLLISIONS
ADIABATIC APPROXIMATION
BOUNDARY CONDITIONS
N60400* --Physics (Atomic & Molecular)--Collision Phenomena
OPTICAL MODELS
PROJECTION OPERATORS
SCATTERING LENGTHS POSITRON COLLISIONS