DiracR-Matrix Modeling of Spin-Induced Asymmetry in the Scattering of Polarized Electrons from Polarized Cesium Atoms

Abstract

Recent experiments by Baum, Raith, and co-workers to measure the spin-induced asymmetries in electron scattering from cesium have stimulated theoretical work to interpret these measurements. We present Dirac R-matrix calculations of the interference asymmetry function, and of the spin-orbit and spin-exchange asymmetries, for comparison with experimental data at 7 and 13.5 eV and with nonrelativistic predictions of the spin-exchange asymmetry from the convergent close coupling method. We find that a simple relativistic target model provides a basis for the understanding and analysis of ongoing experiments. [S0031-9007(97)04271-3] PACS numbers: 34.80.Nz, 34.80.Bm, 34.80.Dp Spin polarization effects in elastic electron-atom scattering can be attributed to several different causes. Exchange polarization arises because electrons are indistinguishable; we have no way of knowing if the scattered electron is the same as the incident electron or was initially bound in the target, making the cross section dependent on the relative spin orientations of the incoming and target electrons. Relativistic dynamics, approximated nonrelativistically by the spin-orbit interaction, also makes the scattering cross section spin dependent. Following an analysis by Burke and Mitchell [1], Farago [2] suggested that the interference between the exchange and spin-orbit scattering amplitudes might be detectable. Atomic cesium was proposed as an ideal target with which to investigate this possibility, as it is easy to prepare experimentally and its atomic number, Z 55, is large enough for appreciable spin-orbit effects. A preliminary calculation of elastic scattering from the Cs 6s ground state by Walker [3] suggested that the interference effect should be observable below about 15 eV in the vicinity of a diffraction minimum in the differential cross section.The differential cross section for scattering of polarized electrons from polarized target atoms depends upon the polarization vectors P e and P t of the incident and target electrons, respectively, through the formula [4] s͑u͒ s u ͑u͒ ͓1 2 A ex ͑u͒P e ? P t 1 A s.o. ͑u͒P e ? n 1 A int͑u͒ P t ? n͔ , Here n is normal to the scattering plane containing the tracks of the incident and scattered electrons, and s u ͑u͒ is the differential cross section for the scattering of unpolarized electrons. The asymmetry functions A ex ͑u͒, A s.o. ͑u͒, and A int ͑u͒ can thus be obtained by combining cross sections for four different polarization settings of the target and the incident electron relative to n [4]. While this does not constitute a "perfect scattering experiment" in the sense of Bederson [5], which would require the measurement of 11 parameters [1], the measurement of these asymmetry functions alone constitutes a stringent test of our understanding of the underlying physics [6,7].More than twenty years after Farago's suggestion [2], it has become possible to measure the interference effect in electron scattering from polarized Cs targets, and so to make an experimental verification of this...

Electron collisions with cesium atoms—benchmark calculations and application to modeling an excimer-pumped alkali laser

“…As noted in our previous paper on the subject [1], electron scattering from Cs has received significant attention, both experimentally [2][3][4][5][6][7][8][9] and theoretically [10][11][12][13][14][15][16][17][18][19][20]. Being a heavy target with nuclear charge Z = 55, relativistic effects are expected to be important.…”

Dirac R-matrix collision strengths and effective collision strengths for transitions of Ni xvii

“…(c) Christensen et al (1986). NB -Levels 6, 7, 10, 11, 12, 13, 36 and 37 in the Current work equate to levels 7, 6, 13, 10, 11, 12, 15 and 16 are generated using DARC (Dirac Atomic R-matrix Code) (Ait-Tahar et al 1997), interfaced with the UK APAP asymptotic and utility codes available at http://amdpp.phys.strath. ac.uk/UK_RmaX/.…”

The fully relativistic implementation of the convergent close-coupling method

“…Other relativistic closecoupling scattering theories based on the Dirac equation also exist. The most advanced of them are the Dirac R-matrix method [50][51][52][53], the recently developed Dirac B-spline Rmatrix method (DBRM) [54,55] and the Dirac R-matrix with pseudo-states method (DRMPS) [56]. Time-dependent scattering methods based on the Dirac equation also exist, such as the time-dependent close-coupling method developed by Pindzola et al [57].…”