Many-electron character of two-photon above-threshold ionization of Ar

The absolute generalized cross sections and angular distribution parameters of photoelectrons for the two-photon above-threshold $3p$ ionization of Ar were calculated in the exciting photon energy range from 15.76 to 36 eV. The correlation function technique developed earlier was extended for the case when an intermediate-state function is of a continuum-type. We show that two-photon ionization of Ar near the $3p^4$ threshold to a large extent is determined by the ${(3p⤍\varepsilon d)}^2$ two-photon absorption via the giant resonance. This many-electron correlation causes (i) an increase of the photoionization cross sections by more than a factor of 3; and (ii) the appearance of resonances in the exciting-photon energy range of the doubly excited states. The predictions are supported by a good agreement between length and velocity results obtained after taking into account the higher-order perturbation theory corrections.

Figure 1

The $3p$ shell total G2PICS in length ($L$) and velocity ($V$) form for linearly polarized incoming radiation calculated in LOPT below the one-photon $3p$ threshold [10] and in the ATI region (present work). The calculation of [12] and the data obtained in the average $3p^5$ relaxed core are also presented for comparison (see text). The two-photon $3p^5\left({}^{2}P_{3/2}\right)$ and $3p^4\left({}^{3}P_2\right)$ thresholds and one-photon $3p^5\left({}^{2}P_{3/2}\right)$ threshold from [20] are depicted as hatched lines.

Figure 2

Partial G2PICS for the transition to the $3p^5\varepsilon f\left({}^{1}D\right)$ channel, computed in length ($L$) and velocity ($V$) form for linearly polarized incoming radiation in LOPT and with accounting for transitions (I)–(V) [corr (VI) is excluded].

Figure 3

Partial G2PICS for the transition to the $3p^5\varepsilon f\left({}^{1}D\right)$ channel, computed in length ($L$) and velocity ($V$) form for linearly polarized incoming radiation with accounting for transitions (I)–(V) [corr (VI) is excluded] and with accounting for all correlations (I)–(VI) [corr (VI) is included]. The two-photon $3p^4\left({}^{3}P_2\right)$ ionization threshold is indicated by the hatched line. We show the energetically lowest calculated $3p^{4}4s3d$ doubly excited state resonance only.

Figure 4

Partial G2PICS for the transition to the $3p^5\varepsilon f\left({}^{1}D\right)$ channel, computed in length ($L$) and velocity ($V$) form for linearly polarized incoming radiation with accounting for all the correlations (I)–(VI) (corr) and, in addition, the higher-order PT correlations (CIHFCP). The two-photon $3p^4\left({}^{3}P_2\right)$ ionization threshold is indicated by the hatched line. The first calculated $3p^{4}4s3d$ doubly excited state resonance is shown only.

Figure 5

Partial G2PICS for the transitions to the $3p^5\varepsilon p\left({}^{1}D\right)$ channel (a) and to the $3p^5\varepsilon p\left({}^{1}S\right)$ channel (b), computed in length ($L$) and velocity ($V$) form for linearly polarized incoming radiation in LOPT and with taking into account both the correlations (I)–(VI) and higher-order PT correlations (CIHFCP). The two-photon $3p^4\left({}^{3}P_2\right)$ ionization threshold is indicated by the hatched line.

Figure 6

Partial G2PICS for the transition to the $3p^5\varepsilon p\left({}^{1}S\right)$ channel, computed in length ($L$) and velocity ($V$) form for linearly polarized incoming radiation without (CIHFCP shake-up excluded) and with (CIHFCP) taking into account the shake-up correlation (IV). The two-photon $3p^4\left({}^{3}P_2\right)$ ionization threshold is indicated by the hatched line.

Figure 7

The computed total $3p$ shell G2PICS in length ($L$) and velocity ($V$) form for linearly polarized incoming radiation. (a) LOPT approach and considering all the correlations (I)–(VI) (corr); (b) polarization of the atomic core by the photoelectron (corrCP) is included in addition to (a); (c) higher-order PT correlations (CIHFCP) are included in addition to (b). The two-photon $3p^4\left({}^{3}P_2\right)$ ionization threshold is indicated by the hatched line.

Figure 8

Angular-distribution parameters ${\beta }_{\lambda }^q$ for photoelectrons computed for the two-photon $3p$ ATI of Ar in length ($L$) and velocity ($V$) form in the LOPT approximation and with taking into account all the considered correlations (CIHFCP). The two-photon $3p^4\left({}^{3}P_2\right)$ ionization threshold is indicated by the hatched line.