Photoionization of atomic barium subshells in the $4d$ threshold region using the relativistic multiconfiguration Tamm-Dancoff approximation

Photoionization cross sections and photoelectron angular distribution asymmetry parameters are calculated for the $4d^{10},5s^2,5p^6$, and $6s^2$ subshells of atomic barium as a test of the relativistic multiconfiguration Tamm-Dancoff (RMCTD) method. The shape resonance present in the near-threshold region of the $4d$ subshell is studied in detail in the $4d$ photoionization along with the $5s, 5p$, and $6s$ subshells in the region of the $4d$ thresholds, as the $4d$ shape resonance strongly influences these subshells in its vicinity. The results are compared with available experiment and other many-body theoretical results in an effort to assess the capabilities of the RMCTD methodology. The electron correlations addressed in the RMCTD method give relatively good agreement with the experimental data, indicating that the important many-body correlations are included correctly.

Figure 1

Ba $4d$ photoionization cross section vs photoelectron energy. Theoretical results shown are the geometric mean of the present RMCTD results, labeled RMCTD (GM), along with RPAE [1], HF-length (HFL) [4], RRPA [2], the geometric mean of RRPA with relaxation, RRPA-R (GM) [2], and the length forms of MBPT [3] without relaxation (MBPT1) and with relaxation and polarization (MBPT2). The solid circles are the experimental results of Ref. [5], and open circles are from Ref. [6].

Figure 2

Ba $4d$ photoelectron angular distribution β parameter shown along with various theoretical results. Shown are the present RMCTD, which is the geometric mean of length and velocity forms, denoted as RMCTD (GM), RPAE [1], MBPT2, which includes relaxation and polarization effects [3], RRPA, and RRPA-R (GM), which are the results of the present work, as described in the text.

Figure 3

Ba $5s$ photoionization cross section in the region of the $4d$ thresholds. The theoretical curves are labeled as in Fig. 1, with the addition of the RMCDT0 results in which the coupling with the $4d$ photoionization channels is omitted in length (solid line) and velocity (dashed line) formulations, and RPAE-R, which is RPAE with the addition of rearrangement and relaxation [41]. The discontinuities in the theoretical curves are owing to the omission of the regions of autoionizing resonances below the $4d$ thresholds, which have been left out to simplify the comparisons. The theoretical curves are shifted by the difference between the theoretical and experimental $4d_{3/2}$ thresholds. The experimental results shown are open circles [5], open triangles [6], and open squares [42].

Figure 4

Ba $5p$ photoionization cross section. The theoretical curves are labeled as in Fig. 1, with the discontinuities leaving out the autoionization resonances. Experiment is given by closed squares [6], closed circles [5], and open circles [42]. The theoretical curves are shifted by the difference between the theoretical and experimental $4d_{3/2}$ thresholds.

Figure 5

Ba $5p$ photoelectron angular distribution parameter β with the theoretical curves labeled as in Fig. 1, except that the RMCTD (GM) results are shown for several different levels on truncation, as indicated. The experimental values are from Ref. [5].

Figure 6

Ba $6s$ photoionization cross section. Theoretical curves as Fig. 1, experiment, Ref. [6]. The theoretical curves are shifted by the difference between the theoretical and experimental $4d_{3/2}$ thresholds.