Complex Eigenvalues in Scattering Theory

Journal Article · Tue Nov 17 04:00:00 EST 1959 · Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences

DOI:https://doi.org/10.1098/rspa.1959.0176· OSTI ID:4205603

Peierls, R. E.

The non-relativistic problem of scattering of a particle by a target possessing discrete excited states can be expressed in terms of'physical' resonance states, i.e., solutions of the wave equation for complex energy- in which in the asymptotic form of the wave function in each channel one of the two possible exponential terms (which for real energy represent the incoming and outgoing wave) vanishes. This representation is possible provided the interaction between the particles and the target vanishes exactly beyond a certain distance. If the interaction decreases exponentially a similar representation may in some cases still be obtained by analytic continuation; it contains also 'redundant' eigenstates in which the coefficient of one of the asymptotic waves tends to infinity. Possible generalizations of the method are discussed. (auth)

• Research Organization: Univ. of Birmingham, Eng.
• Sponsoring Organization: USDOE
• NSA Number: NSA-14-006900
• OSTI ID: 4205603
• Journal Information: Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences, Journal Name: Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences Journal Issue: 1272 Vol. 253; ISSN 1364-5021
• Publisher: The Royal Society Publishing
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ENERGY LEVELS
EXCITATION
INTERACTIONS
PHYSICS
QUANTUM MECHANICS
RESONANCE
SCATTERING
TARGETS