R-matrix calculation of photoionisation from Rydberg states in strontium

Abstract

This paper presents the first detailed theoretical calculation of numerous observables investigated in Sr using stepwise laser excitation techniques. Measurements concern the 5p12/ns and 5p32/ns J=1 autoionising levels excited through the 5sns 1S0 Rydberg states; isolated resonances as well as interacting autoionising 5pns levels have been investigated. Results on the excitation spectra, the positions and widths of the levels as well as on the branching ratios and the angular distributions of the photoelectrons have been reported. All the above-mentioned observables are calculated through a combination of the eigenchannel R matrix and the multichannel quantum defect (MQDT) methods. Short-range parameters used by MQDT to describe final-state channel interactions are determined by performing R-matrix calculations in LS coupling and including spin-orbit effects through a geometric (jj/LS) frame transformation. The calculation of the required dipole matrix elements is based on the isolated core excitation approximation. All the measured quantities are accurately reproduced except the asymmetry parameters characterising the angular distributions of electrons ejected to the Sr+ 5s level, these latter quantities being found to be the most sensitive to the interseries interaction. In addition, the calculated MQDT parameters are compared with those previously obtained empirically from experiment.

4pnp J=0e-2e autoionizing series of calcium: experimental and theoretical analysis

“…Despite the fact that the 4snp P levels extend outside the reaction volume, only a MQDT description of their wavefunctions in terms of channel mixing can be given by our theoretical treatment. The photoionization cross sections are then calculated in the ICE approximation [8]. This approximation relies on a negligible excitation of the open channels, j, and expresses the transition dipole moment D G for the excitation of the closed channel i as the product of the transition moment for the inner electron with the overlap integral for the outer electron [13].…”

“…First, the consecutive excitations are one-electron, one-photon resonant transitions efficiently induced by low laser power. Second, the complexity of the recorded spectra is greatly minimized, since direct excitation of Rydberg series is limited to series resulting from the excitation of the inner electron, the outer one remaining a spectator and direct excitation of the continuum being almost negligible [8]. This inherent simplification of the autoionization spectra through the ICE technique not only allows the direct and accurate determination of the properties of the autoionizing states (energies, autoionization widths) but also reflects and reveals the interaction between states belonging to different Rydberg series converging to the same or different ionization thresholds.…”

“…Then, the eigenchannel MQDT formulation is used to impose the proper boundary conditions at large r and to calculate observables. In particular, the calculation of the excitation spectra relies on the ICE approximation, assuming negligible continuum excitation, as well as excitation of only the inner valence electron [8].…”

The even-parity J=0 autoionizing spectrum of strontium below the 4d5/2threshold: observation and theoretical analysis

“…Extensions of the observations to other J values have been performed by using multistep laser spectroscopy (Xu et a/ 1986 On the theoretical side, several works have demonstrated recently that a good description of doubly excited states of alkaline earths can be obtained by combining the eigenchannel R-matrix method, developed by Greene (1985) with the multichannel quantum defect theory (MQDT) (Seaton 1983, Fano andRau 1986). This approach has been successfully employed in Sr to analyse energy level positions, autoionization profiles (Aymar et al 1987, Aymar 1987, Kompitsas et al 1990 and photoelectron spectra (Aymar and Lecomte 1989).…”

A relativistic C.I. study on theJ=1/2 even spectrum of Sr II

“…Processes related to the interaction of radiation with matter have been recently [34,35] investigated by combining the eigenchannel R-matrix [36] and MQDT methods [37,38]. The relativistic Random Phase approximation [39] or MBPT [40] have also been suggested for providing approximate solutions to the many-body problem which are necessary for the treatment of these processes.…”