Semiclassical Coupled Channels Theory

Abstract

1)eIL Annulen dpr Physik zum 200. Geburtstag yeioidmrt.A b s t r a e t. A semiclassical theory for heavy ion scattering in the Fresnel diffrwtion regime cowring coupled elastic and inelastic channels is developed. The scattering is described ils diffraction off the rninbow triijcvtory along which the development of the internal degrees of freedom is calcu-Ititcd. Simplc formulw for the transition amplitudes are derived and interpreted in terms of miitching conditions, timr scalw iind potentiid strengths ilt closest approach. Polarization potentials comprising of r e d iind itbsorptivr tcrms and of tensors of various ranks are constructed. Aniilyzing power data for c-lostic and iwliistic sciitterinq of polarized 'Li on W3n are analyzed. Suirii klirssischu 'l'tieoric gekopgeltur Katiiilc[nliiil tsii bersiclit. Eine semiklassische Theorie fiir die Streiiung von Schwerionen wird entwickelt, die el:ist.isclio irnd inclastische Streuung im Bereich der Fresnel-Beiigung besclrreibt. I)er Strc.uprt,zc.IJ wird ills Heiigiing von der Re,o~nbogen-Trojektorie weg verstanden, und entlimg dieser 13iilrn \vircl clic zcitliclir Hntwicklung der inncren Preiheitsgrade berechnet. Einfilche anolytischc Formcln fiir dir Uberg;mgsirmplituden wcrden abgeleitet und mit Hilfe von Anpassiings-(~Iatching-) I%c~tlingtingcn. Zeitskiilctl und Potentiitlstlrken tim Punkt nachster Annaherung interpretiert. Polariwtionspotentiillr werdcn konstruiert, die sowohl reelle als niich absorptive Anteile und Tensortermc versclriodcner Stufm critlialten. Experimentelle Daten fur die .4nalysierstlrken fiir ehstischc untl inc~l;istischr Strcuitng voti polnrisiertem 'Li an l%n werdcn tlieomtisch nnidysiert.

Dynamic spin-orbit interaction of heavy ions in semiclassical calculations of elastic scattering

“…Matching conditions are a useful tool in understanding the mechanism of direct reactions as first demonstrated for nucleon transfer in [19]. The matching condition for inelastic scattering reads [7] mf-mi+ E~RR/hvR~-O (4.2) for excitation of the state x with energy E~, the spin projection flipping from m e to my. This condition is derived from the supposition that inelastic scattering must be favoured when the classical conservation laws for energy and total angular momentum hold at the distance of closest approach [7].…”

“…The matching condition for inelastic scattering reads [7] mf-mi+ E~RR/hvR~-O (4.2) for excitation of the state x with energy E~, the spin projection flipping from m e to my. This condition is derived from the supposition that inelastic scattering must be favoured when the classical conservation laws for energy and total angular momentum hold at the distance of closest approach [7]. Consequently, the argument Z~q, (3.10), of the B-functions can be understood as a measure of the mismatch of the inelastic reaction since q is the difference of final and initial spin projection, cf.…”

“…In order to simplify the time integrations of (3.3) performed along the rainbow orbit according to (2.11) we approximate [6,7] (3.5) Two time scales are introduced here: firstly r~ the characteristic time for passage through the interaction region. It is determined by b R, the radial acceleration at the rainbow orbit closest approach and by a, the diffuseness of the real nuclear potential.…”

“…The central ingredients of the semiclassical picture are as follows [5][6][7]. The central nuclear and Coulomb interactions determine classical trajectories along which transitions between spin substates and projectile states of various energies are calculated.…”