Valence photodetachment of Li${}^{-}$ and Na${}^{-}$ using relativistic many-body techniques

The multiconfiguration Tamm-Dancoff technique (MCTD) is applied to study photodetachment of negative ions of lithium and sodium. A cusplike structure is found in the photodetachment cross section just below the first detachment-plus-excitation threshold of Li${}^{-}$ (Li 2$p$), and of Na${}^{-}$ (Na 3$p$), in qualitative agreement with existing theoretical and experimental results. The current work emphasizes the importance of correlation in the form of configuration interaction in the photodetachment process and demonstrates the utility of MCTD in dealing with highly correlated systems.

Figure 1

Total MCTD length (L) and velocity (V) photodetachment cross sections of Li${}^{-}$ along with earlier close-coupling (CC) [6], $K$-matrix (Kmat) [8], and $R$-matrix (Rmat) [25] calculations and experiment (solid circles [28], open triangles [29], solid squares [30, 31]). Also shown are the results of the present RRPA calculation. The vertical lines indicate the thresholds.

Figure 2

MCTD length (L) and velocity (V) photodetachment cross section of Li${}^{-}$ near the 2$s$ threshold, along with experiment (solid circles) [40].

Figure 3

Photodetachment cross section of Li${}^{-}$ leading to the 2$p$ excited state of neutral Li. In addition to the MCTD length (L) and velocity (V) results, the earlier $K$-matrix (Kmat) [8] and $R$-matrix (Rmat) [25] cross section and experiment (solid circles) [30, 31] are shown.

Figure 4

Total MCTD photodetachment cross section of Na${}^{-}$ along with previous theoretical calculations: Close-coupling (CC) [6], eigenchannel $R$-matrix (ERmat) [26], $R$-matrix (Rmat) [27], and nonrelativistic random-phase approximation (RPAE) [42]. L and V designate length formulation and velocity formulation results. The solid vertical lines indicate the MCTD thresholds, the dashed 3$s$ line is the DF threshold, and the dashed 3$p$ line is the experimental threshold.

Figure 5

Photodetachment cross section of Na${}^{-}$ leading to the 3$p$ excited state of neutral Na in length (L) and velocity (V) formulations.