Fig. 1. Potential curves of BeHe³⁺ molecular ions refer to Table 1.

Fig. 2. Radial coupling matrix elements for BeHe³⁺.

Fig. 3. Rotational coupling matrix elements for BeHe³⁺.

Fig. 4. Potential curves of BHe⁴⁺ molecular ions refer to Table 2.

Fig. 5. Coupling matrix elements for BHe⁴⁺: (a) and (b) radial coupling matrix element between ¹Σ⁺ states, (c) radial coupling matrix element between ¹σ states, (d) rotational coupling matrix element between ¹Σ⁺ and ¹π states, (e) and (f) some important detailed radial coupling matrix element between exit states with the initial state.

Fig. 6. Comparison between the present SEC cross sections for the Be³⁺(1s) + He(1s²) collision with other theoretical results. Present QMOCC calculation considering the ETF effects (solid line with filled squares); semi-classical molecular orbital close coupling (SMOCC) results of Suzuki et al.^[5] (dashed line with filled circles).

Fig. 7. State-selective cross sections of present QMOCC results (considering the ETF effects) and the results of Suzuki et al.^[5] for electron capture to the 1s2s and 1s2p states of Be²⁺ ions.

Fig. 8. Cross sections of present QMOCC results (considering the ETF effects) and the results of Suzuki et al.^[5] for electron capture to singlet and triplet states of Be²⁺ ions.

Fig. 9. Comparison between the present SEC cross sections for the B⁴⁺(1s) + He(1s²) collision with other theoretical^[7,8,10] and experimental^[11] results. Present QMOCC calculation considering the ETF effects (solid line with open squares); AOCC results of Hansen et al.^[7] (dashed line); semi-classical results of Fritsch et al.^[8] (dash dotted line) and Shimakura et al.^[10] (dotted line). Experimental results of Iwai et al.^[11] (filled circles with error bars).

Fig. 10. Comparison between the present state-selective SEC cross sections for the B⁴⁺(1s) + He(1s²) collision with other theoretical^[7,8,10] results. Present QMOCC calculation considering the ETF effects (solid line); AOCC results of Hansen et al.^[7] (dotted line); semi-classical results of Fritsch et al.^[8] (dashed line) and Shimakura et al.^[10] (dash dotted line).

Fig. 11. Comparison between the present DEC cross sections for the B⁴⁺(1s) + He(1s²) collision with other theoretical results.^[7–9] Present QMOCC calculation considering the ETF effects (solid line with open circles); AOCC results of Hansen et al.^[7] (dash dotted line); semi-classical results of Fritsch et al.^[8] (dotted line); and full electron molecular expansion method of Bacchus-Montabonel^[9] (dashed line).

Fig. 12. Comparison between the present state-selective DEC cross sections for the B⁴⁺(1s) + He(1s²) collision with other theoretical results.^[7–9] Present QMOCC calculation considering the ETF effects (solid line); AOCC results of Hansen et al.^[7] (dash dotted line); semi-classical results of Fritsch et al.^[8] (dotted line); and full electron molecular expansion method of Bacchus-Montabonel^[9] (dashed line).

Table 1. Asymptotic separated-atom energies for the states of BeHe³⁺. The bold 5 ²Σ represents the initial state.

Table 2. Asymptotic separated-atom energies for the states of BHe⁴⁺. The bold 13 ²Σ represents the initial state.