Stable complex-rotation eigenvalues that correspond to no full resonances in scattering: Examples in positron scattering by the helium ion

Journal Article · Thu Jul 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.012706· OSTI ID:20643906

Igarashi, Akinori; Shimamura, Isao ^[1]

---

1. Department of Applied Physics, Miyazaki University, Miyazaki 889-2192 (Japan)

Hyperspherical close-coupling calculations for S- and P-wave positron scattering by He{sup +} ions produce no full resonances in the eigenphase sum {delta}(E) in the two regions of energy E where stable eigenvalues E{sub r}-i{gamma}/2 with large {gamma} were found previously by the complex-rotation method (CRM); {delta}(E) increases only by one radian in the lower-E region, and even decreases almost monotonically in the higher-E region, implying time advance, rather than time delay, due to the collision. However, the peaks found in the trace of time-delay matrix, Tr Q(E), are consistent with the CRM eigenvalues. This suggests that these eigenvalues indeed represent S-matrix poles in the complex-E plane, but that their effects on scattering are almost masked by the background {delta} due to the large {gamma}. This work uses a general relation Tr Q(E)=2({Dirac_h}/2{pi})(d{delta}/dE), proved here for any functional form of {delta}(E), and hence, both on and off resonance. This is a generalization of the well-known single-channel time-delay formula and of the multichannel formula proved previously for the Breit-Wigner resonance with a constant background S matrix.

• OSTI ID: 20643906
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BREIT-WIGNER FORMULA
CATIONS
COUPLING
E REGION
EIGENFUNCTIONS
EIGENVALUES
HELIUM
HELIUM IONS
P WAVES
POSITRON-ATOM COLLISIONS
POSITRONIUM
POSITRONS
RESONANCE
ROTATION
S MATRIX
SCATTERING
TIME DELAY