An experiment on coherent control of energy and angular distribution of autoionized electrons of calcium performed by van Leeuwen et al (van Leeuwen, Bajema and Jones 1999 Phys. Rev. Lett. 82 2852) using the Ramsey pump-probe technique is investigated theoretically. The peculiar features observed in this experiment are ascribed to the fact that three overlapping resonances are excited by the isolated core excitation process (ICE) 4s14s → 4p3/214s, leading to interference in the decay of the 4p3/214s wavepacket created by the pump and probe short pulses. Predictions dealing with the ICE excitation of two isolated resonances 4p1/2ns from the 4s20s level are presented. The dynamics of autoionizing wavepackets of calcium created by one or two short pulses is analysed by calculating the time dependence of radial electron flux at fixed macroscopic distances from the atom. Some results on radial flux obtained by using a chirped pulse are also reported.

In this paper we will show how the approach combining the eigenchannel R-matrix method to the techniques of multichannel quantum-defect theory (MQDT) is a very powerful method to obtain realistic descriptions of complex spectra of alkaline-earth atoms in the energy domain and to study the dynamics of various processes in these spectra. Several illustrations will be presented. Those on structure will concern photoionization spectra of barium and strontium at high energy and two-photon ionization processes in magnesium and strontium. Then, recent results on the dynamics of coherent ionization processes will be presented.

A quantitative analysis of part of the experimental data reported by Wang, Chen and Elliott [1,3] who studied in barium coherent control through two-color resonant interfering paths is reported. Dynamics of the two-color photoionization process, described as an adiabatic process in the rotating wave approximation, is governed by the coherent excitation of the 6s6p and 6s7p 1P1 intermediate states. Interference effects are found to play a minor role. The required atomic parameters are obtained from a theoretical approach based on a combination of jj-coupled eigenchannel R-matrix and Multichannel Quantum Defect Theory.

We have investigated theoretically the asymmetrical photoionization yields into the 6s1/2, 5d3/2 and 5d5/2 continuum channels of atomic barium observed by Wang, Chen and Elliott [Phys. Rev. Lett. 77, 2416 (1996)] in the study of coherent control through two-color resonant interfering paths. The atomic parameters obtained from a theoretical approach based on a combination of jj-coupled eigenchannel R-matrix and Multichannel Quantum Defect Theory are used to analyze the photoionization spectra from the \(\) and 6s7p\(\) states with polarized light beams. The studied energy range includes the 6p7p autoionizing resonances. The dynamics of the two-color photoionization is governed by the coherent excitation of the 6s6p and \(\) intermediate states. This excitation is described as an adiabatic process in the rotating wave approximation. The influence of the radiative decay, spatial distribution of the intensities of the laser beams and hyperfine interaction is discussed.

Two-photon ionization processes from the ground state of strontium are studied employing the jj-coupled eigenchannel R-matrix approach combined with the multichannel quantum-defect theory (MQDT). The calculations satisfactorily reproduce the experimental spectra corresponding to two-photon excitation of the and low-lying autoionizing resonances, confirming that the method is suitable to account for the spin-orbit interaction effects in the multiphoton excitation of heavy atoms. It is also shown that the dielectronic core polarization cannot be disregarded in the description of these highly correlated resonances, as it affects significantly both their energy positions and autoionization widths.

Absolute photoabsorption cross sections of strontium have been measured in the energy range extending from the threshold up to above the 6s threshold. The synchrotron radiation source of the Synchrotron Radiation Research Center at Hsin-Chu was used as the background continuum. Strontium vapour was confined in a heatpipe oven. The absolute column density was determined by simultaneously measuring the temperature distribution profiles and the total pressure in the heatpipe. Absolute cross sections were determined using the Beer-Lambert law. The observed spectrum was analysed using a combination of a recent extension of the jj-coupled eigenchannel R-matrix adapted to handle highly correlated levels and the phase-shifted multichannel quantum defect theory. The main features of the observed spectrum, dominated by the presence of many window-type resonances, are well reproduced and the structures are identified. The observed absorption windows result from the fact that only continua are directly excited from the ground state.

The approach based on the eigenchannel R-matrix method and multichannel quantum-defect theory, introduced by Robicheaux and Gao to calculate two-photon processes in light alkaline-earth atoms, has been implemented in jj-coupling introducing explicitly spin-orbit effects and employing both the length and velocity forms of the electric dipole transition operator. Emphasis is placed on the identification of the intermediate-and final-state resonances appearing in the cross sections. The efficiency and potential of the method are demonstrated in magnesium, by calculating two-photon ionization cross sections, branching ratios and photoelectron angular distributions for an extended photon energy range, including above-threshold ionization. The contributions of electronic correlation, core-polarization and spin-orbit effects are investigated by a systematic comparison with experimental results and earlier theoretical calculations.

Two-step polarized laser excitation of the barium ground state through 5d7p 3P1 and 3D1 intermediate states produces photoelectrons which are analysed in two groups of energy-resolved continua 6s, 5d3/2,5/2 epsilon l and 6p1/2,3/2 epsilon l. Even-parity autoionizing resonances are investigated systematically over a large energy range (71400-84500 cm-1) extending from the bottom of the 6p3/2 threshold up to the 7s threshold. Experimental results are analysed using an extension of the variational eigenchannel R-matrix approach. This method allows the structures to be identified. They correspond to intrashell states 6d2 3F2 or 7p2 3P2 and to Rydberg states such as 7snd. Experimental partial photoionization cross sections are compared with R-matrix calculations.

The positions and autoionization widths of the 7sng J=4 levels of barium have been calculated using various procedures based on the eigenchannel R-matrix method. The calculations perfectly reproduce the experimental data recently obtained for the 7sng 1G4 levels. The localized perturbers of the 7sng series are unambiguously identified. The anomalous behaviour of energy positions and widths of high lying 7sng levels are ascribed to 4f8p levels. Line narrowing effects are predicted for 7sng 3G4 levels near n=17.

The 4fnf J=4, 5, 6 series of barium have been investigated through a combination of the eigenchannel R-matrix and the multichannel quantum defect theory (MQDT) methods. The energy positions and autoionization widths for the 4f2 levels are predicted. The intermediate 4fnf levels, 5or=8, the theoretical results agree with a recent experiment. The investigation of the whole series from their bottom end allows the determination of the entire part of the quantum defects. The strong mixing between the 4f5/2f7/2 and 4f7/2f5/2 series observed for J=4-6 is shown to primarily originate from the large exchange electrostatic interaction.

A method is presented for adapting the streamlined eigenchannel R-matrix approach to the analysis of 6d2 and 7p2 autoionizing resonances of Ba. The doubly excited states are assumed to be confined within the reaction volume. R-matrix calculations are carried in LS coupling for the 1S, 3P, 1D, 3F and 1G symmetries and in jj coupling for J = 0e to J = 4e. For each symmetry, an R-matrix restricted to open channels is constructed using a variational basis allowing the identification of the doubly excited states. From the R-matrix we deduce a scattering S-matrix which is expressed as the sum of resonant and non-resonant parts, i.e. in a form suited to resonance analysis. The positions and autoionization widths of 6d2 and 7p2 levels are predicted from the energy dependence of the density of states matrix, equivalent to the time-delay matrix. The approach is connected with other theories, in particular with Fano's configuration interaction method which treats bound levels embedded in continua.

The 6dng, 6dni and 7sni J=6 autoionizing Rydberg series of barium have been investigated using the eigenchannel R-matrix method together with multichannel quantum defect theory. For the 6dng and 6dni J=6 series, results concern the energy positions, autoionization widths and autoionization branching ratios as well as the perturbations of these series by 4fnl J=6e levels. For the 7sni series, results restricted to the energy positions. The theoretical results are compared with recent experimental results and show good agreement for the 6dng and 7sni series. A possible explanation for the discrepancies between theory and experiment for 6dni series is proposed.

The 6pnf J=2,3,4 autoionizing levels of barium are studied through a combination of the eigenchannel R-matrix and the multichannel quantum defect theory (MQDT) methods. The calculation reproduces well the spectra of 6pnf series observed in excitation from 5d6p levels and confirms that the 6pnf levels have very large autoionization rates. Calculated MQDT parameters are compared with those obtained empirically from experiment and used to analyse channel interactions.

The 7d5/2nt double-Rydberg states of bariunl have been studied for n = ii to 14 and £ = 7 to n I using the Isolated Core Excitation technique along with a Stark switching nlethod to populate the high t states. The resulting spectra show resolved structures due to the correlation between the two excited electrons, identified by the (j£)K angular nlonlentunl coupling between thenl. The spectra are conlpared to energy positions and linewidths calculated using a perturbative approach, including the dipole and quadrupole interaction ternls. The agreenlent between exper1nlent and theory is very good for high £ > 9, but less so for lower £-

We report on autoionisation decay of di-excited states of barium atom including one Rydberg electron with different l angular momentum values. When l is low (l less-than-or-equal-to 2) the great part of the large autoionisation linewidth is due to core penetration of the Rydberg electron. At the opposite, when l is large, the autoionisation decay is considerably reduced and mostly depends on the large range interaction between both excited electrons. In the first case, all the spectra caracteristics of the 7p(j1) nd series are well interpreted using an independent electron model based on the quantum defect theory. In the second case, because of the narrower autoionisation linewidths 6p(j1) nl and 7d5/2 nl series with l = n - 1, n - 2, ... exhibit resolved (j1 - l) K splittings due to correlation effects between both excited electrons.

6p32/nl (n=11 to 15, l=5 to n-1) and 6d52/nl (n=11 to 14, l=6 to n-1) doubly excited Rydberg states of barium have been studied using a multistep laser excitation technique. The excitation is via the bound 6s12/nl states which are populated using an electric-field switching method which allows the selective population of high-l angular momentum states. The resulting spectra clearly demonstrate the presence of dielectronic correlation. The authors show that this correlation is well described in terms of the (j-l)K coupling scheme, taking into account in a perturbative way the dipole and quadrupole interaction terms.

The authors present the excitation of highly excited 7p1/2nd and 7p3/2nd states (1016) have a strong autoionisation channel towards the 7p1/2 state of Ba+. This result confirms that autoionisation occurs predominantly to excited states of Ba+ with the emission of low-energy electrons.

In Ba, we report the first experimental result on highly excited double-Rydberg states Ns(or d)n’p(or d) 22 < N < 34, 40 < n’ < 60) which lie only ~ 0.1 eV below the Ba2+ threshold. These results have been obtained using a selective microwave field ionisation in a double time-of-flight mass spetrometer (D.T.O.E.) which allows the detection of highly excited Rydberg states of the Ba+ ion.

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.