Multiconfigurational Hartree-Fock close-coupling ansatz: Application to the argon photoionization cross section and delays

We present a robust, ab initio method for addressing atom-light interactions and apply it to photoionization of argon. We use a close-coupling ansatz constructed on a multiconfigurational Hartree-Fock description of localized states and $B$-spline expansions of the electron radial wave functions. In this implementation, the general many-electron problem can be tackled thanks to the use of the atsp2k libraries [C. Froese Fischer et al., Comput. Phys. Commun. 176, 559 (2007)]. In the present contribution, we combine this method with exterior complex scaling, thereby allowing for the computation of the complex partial amplitudes that encode the whole dynamics of the photoionization process. The method is validated on the $3s3p^{6}np$ series of resonances converging to the $3s$ extraction. Then, it is used for computing the energy dependent differential atomic delay between $3p$ and $3s$ photoemission, and agreement is found with the measurements of Guénot et al. [Phys. Rev. A 85, 053424 (2012)]. The effect of the presence of resonances in the one-photon spectrum on photoionization delay measurements is studied.

Figure 1

Diagram of the neutral argon levels and ionization thresholds accessible through one-photon transitions. Data are taken from the NIST atomic database [42]. The red level is the Ar ground state, and the blue states are singly excited bound and autoionizing states. Black lines are ionization thresholds that are included in our analysis. Gray lines are other ionization thresholds which are neglected in the present paper (cf. the Appendix).

Figure 2

Radial perturbed function for the $3p\to \epsilon d$ channel, in length gauge, for $\epsilon =-q$ in the vicinity of the $3s3p^{6}4p$ resonance. The red and dashed blue curves are its real and imaginary parts, respectively.

Figure 3

Top panel: Details of the complex energies of the field-free Hamiltonian of argon calculated for the ${}^1{P}^o$ symmetry with $\theta =0.055$ rad (red circles) and $0.11$ rad (black squares). Bottom panel: Comparison of the total calculated cross sections (thick lines), in length (full red curve) and velocity (dashed blue curve) gauges. The empty circles are the experimental values of Berrah et al. [29], in arbitrary units, scaled as in the original paper. The black squares are absolute cross-section measurements from Samson and Stolte [53]. The thin lines are the cross sections computed by including only the $3s3p^{6}np$ resonances in the basis set.

Figure 4

Top panel: partial cross sections for $3p$ ionization and total cross section, in length gauge. Bottom panel: relative error of the sum of the above partial cross sections with respect to the total cross section computed with Eq. (8), for $R_0=65a_0$ and ${\theta }_0=0.055$ rad.

Figure 5

Norm, in atomic units, and argument of the partial photoionization complex amplitudes versus the reduced energy of the $3s3p^{6}4p$ resonance. (a) $3p\to \epsilon d$ channel. (b) $3p\to \epsilon s$ channel. The crosses show 1 on 7 computed values. The lines are obtained from Eq. (29). Red dashed curves and $+$ signs indicate length gauge, and blue full lines and × signs indicate velocity gauge.

Figure 6

Calculated beta parameter ($\beta$) in length (full red line) and velocity (broken blue line) compared to experiment [29] (black dots). The vertical dashed line indicates a change of photon energy scale.

Figure 7

(a) Wigner-like delays for photoionization from argon. There is no perceptible gauge dependence for photoionization from the $3p$ orbital. For the $3s$ photoionization, the results from velocity (blue broken) and length gauge (red dashed) are shown. (b) Wigner-like delay difference between photoionization from the $3p$ and $3s$ orbitals in argon. The thin curves are obtained with the full model that exhibit a pseudoresonance at 39.4 eV. The thick curves are obtained with the truncated model for velocity (blue dashed) and length (red full) gauge, respectively. The experimental values of Ref. [9] are given with error bars. The experimental data point obtained using the ${\tau }_{\text{cc}}$ from Eq. (33) and Ref. [59] are given by the circles and squares, respectively.

Figure 8

Relative Wigner-like delays using a model including some doubly excited resonances (see the Appendix). (a) The probe field bandwidth is 60 meV and 0.6 eV, respectively, for the top and bottom panels. Length (continuous red) and velocity (dashed blue) gauge results are shown. The thicker, light curves correspond to the reduced model used in Fig. 7. Experimental points are shown with the same notation as in Fig. 7.