Fully-stripped-beryllium-ion collisions with $2\ell m$ states of atomic hydrogen: Total and state-selective electron-capture cross sections

Integrated total and state-selective electron-capture cross sections are calculated for bare beryllium ion scattering on atomic hydrogen initially configured in the $2\ell m$ states (where $n=2, \ell$, and $m$ are the principal, angular momentum, and magnetic quantum numbers, respectively). This is done using the wave-packet convergent close-coupling approach which solves the three-body Schrödinger equation by employing a two-center expansion for the total scattering wave function. These calculations are performed within a projectile-energy range of 1 to 500 keV/u. The results suggest that at low energies, collisions with hydrogen in each of the $2\ell m$ states produce a total electron-capture cross section approximately an order of magnitude larger than for scattering on the ground state. However, as projectile energy increases, the cross section for capture from the excited states falls well below the $\mathrm{H}(1s$) electron capture cross section. A possible reason for this observation could be related with the way the target electron radial densities are distributed in different initial states. The results obtained in this work are compared to previous calculations where available. In terms of the $n$-resolved charge-exchange cross sections, significant disagreement is found between our results and some preceding calculations available in the literature to warrant further investigations.

Figure 1

The weighted probability distributions for total electron capture in ${\mathrm{Be}}^{4+}$ collisions with $\mathrm{H}(2s$), $\mathrm{H}(2p_0$), and $\mathrm{H}(2p_1$) at projectile energies 20, 100, and 500 keV/u.

Figure 2

The total cross section for electron capture in ${\mathrm{Be}}^{4+}$ collisions with atomic hydrogen initially in the $2s$ state: The present WP-CCC results are shown alongside previous calculations by Errea et al. [14] and Shimakura et al. [23] using the MOCC method, Igenbergs [25] with the AOCC approach, Hoekstra et al. [22] and Ziaeian and Tökési [21] using the CTMC method, and Jorge et al. [20] with the GTDSE and CTMC approaches. The WP-CCC results for $\mathrm{H}(1s$) are also shown.

Figure 3

The total cross section for electron capture in ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2p_0$) collisions: the present WP-CCC results are shown alongside previous calculations by Igenbergs [25] with the AOCC approach and Ziaeian and Tökési [21] using the CTMC method. The WP-CCC results for $\mathrm{H}(1s$) are also shown.

Figure 4

The total cross section for electron capture for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2p_1$) collisions: The present WP-CCC results are shown alongside previous calculations by Igenbergs [25] with the AOCC approach and Ziaeian and Tökési [21] using the CTMC method. The WP-CCC results for $\mathrm{H}(1s$) are also shown.

Figure 5

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2s$) collisions at projectile energy of 20 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 6

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2p_0$) collisions at projectile energy of 20 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 7

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2p_1$) collisions at projectile energy of 20 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 8

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}$ scattering on $\mathrm{H}(2s$) (top panel) and $\mathrm{H}(2p_0$) and $\mathrm{H}(2p_1$) (bottom panel) at projectile energy of 20 keV/u: The present WP-CCC results for collisions with $\mathrm{H}(2s$) are shown alongside the MOCC calculations made by Errea et al. [14] and results by Jorge et al. [20] using the GTDSE and CTMC approaches.

Figure 9

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2s$) collisions at projectile energy of 100 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 10

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2p_0$) collisions at projectile energy of 100 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 11

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2p_1$) collisions at projectile energy of 100 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 12

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}$ scattering on $\mathrm{H}(2s$) (top panel), $\mathrm{H}(2p_0$) (middle panel), and $\mathrm{H}(2p_1$) (bottom panel) at projectile energy of 100 keV/u: The current WP-CCC results are shown alongside the AOCC calculations by Igenbergs [25] along with the GTDSE and CTMC calculations by Jorge et al. [20].

Figure 13

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2s$) collisions at projectile energy of 500 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 14

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2p_0$) collisions at projectile energy of 500 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 15

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}\text{−}\mathrm{H}(2p_1$) collisions at projectile energy of 500 keV/u: convergence of the WP-CCC results with respect to ${\ell }_{\max }$ (top panel) and $N_{\mathrm{c}}$ (bottom panel) of the basis states included in the expansion.

Figure 16

$n$-partial electron-capture cross sections for ${\mathrm{Be}}^{4+}$ scattering on $\mathrm{H}(2s$) (top panel), $\mathrm{H}(2p_0$) (middle panel), and $\mathrm{H}(2p_1$) (bottom panel) at projectile energy of 500 keV/u: The current WP-CCC results are shown alongside the AOCC calculations by Igenbergs [25].

Figure 17

3$\ell$-partial cross sections for electron capture in ${\mathrm{Be}}^{4+}$ collisions with $\mathrm{H}(2s$) (top panel), $\mathrm{H}(2p_0$) (middle panel), and $\mathrm{H}(2p_1$) (bottom panel): The current WP-CCC results are shown alongside the CTMC calculations by Ziaeian and Tökési [21] and GTDSE results by Jorge et al. [20].

Figure 18

6$\ell$-partial cross sections for electron capture in ${\mathrm{Be}}^{4+}$ collisions with $\mathrm{H}(2s$) (top panel), $\mathrm{H}(2p_0$) (middle panel), and $\mathrm{H}(2p_1$) (bottom panel): The current WP-CCC results are shown alongside the GTDSE calculations by Jorge et al. [20].