Slow isocharged sequence ions with helium collisions: Projectile core dependence

The collisions of the isocharged sequence ions of $q=6$ (${\text{C}}^{6+}$, ${\text{N}}^{6+}$, ${\text{O}}^{6+}$, ${\text{F}}^{6+}$, ${\text{Ne}}^{6+}$, ${\text{Ar}}^{6+}$, and ${\text{Ca}}^{6+}$), $q=7$ (${\text{F}}^{7+}$, ${\text{Ne}}^{7+}$, ${\text{S}}^{7+}$, ${\text{Ar}}^{7+}$, and ${\text{Ca}}^{7+}$), $q=8$ (${\text{F}}^{8+}$, ${\text{Ne}}^{8+}$, ${\text{Ar}}^{8+}$, and ${\text{Ca}}^{8+}$), $q=9$ (${\text{F}}^{9+}$, ${\text{Ne}}^{9+}$, ${\text{Si}}^{9+}$, ${\text{S}}^{9+}$, ${\text{Ar}}^{9+}$, and ${\text{Ca}}^{9+}$) and $q=11$ (${\text{Si}}^{11+}$, ${\text{Ar}}^{11+}$, and ${\text{Ca}}^{11+}$) with helium at the same velocities were investigated. The cross-section ratios of the double-electron transfer (DET) to the single-electron capture (SEC) ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ and the true double-electron capture (TDC) to the double-electron transfer ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ were measured. It shows that for different ions in an isocharged sequence, the experimental cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ varies by a factor of 3. The results confirm that the projectile core is another dominant factor besides the charge state and the collision velocity in slow ($0.35-0.49v_0$; $v_0$ denotes the Bohr velocity) highly charged ions (HCIs) with helium collisions. The experimental cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ is compared with the extended classical over-barrier model (ECBM) [A. Bárány et al., Nucl. Instrum. Methods Phys. Res. B 9, 397 (1985)], the molecular Coulombic barrier model (MCBM) [A. Niehaus, J. Phys. B 19, 2925 (1986)], and the semiempirical scaling laws (SSL) [N. Selberg et al., Phys. Rev. A 54, 4127 (1996)]. It also shows that the projectile core properties affect the initial capture probabilities as well as the subsequent relaxation of the projectiles. The experimental cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ for those lower isocharged sequences is dramatically affected by the projectile core structure, while for those sufficiently highly isocharged sequences, the autoionization always dominates, hence the cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ is always small.

Figure 1

Cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ of the $q=6$ isocharged sequence ions collision with helium. The velocity of ${\text{C}}^{6+}$, ${\text{N}}^{6+}$, and ${\text{O}}^{6+}$ is $0.49v_0$ $\left(6\text{ keV}∕\text{u}\right)$, the velocity of ${\text{Ar}}^{6+}$ and ${\text{Ca}}^{6+}$ is $0.35v_0$ $\left(3\text{ keV}∕\text{u}\right)$, and for ${\text{F}}^{6+}$ and ${\text{Ne}}^{6+}$ both velocities were measured. The cross-section ratio difference induced by different velocities is small and within present experiment uncertainties. The prediction of MCBM, ECBM, and SSL is 0.54, 0.68, and 0.41, respectively.

Figure 2

Cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ of the $q=7$ isocharged sequence ions ${\text{F}}^{7+}$, ${\text{Ne}}^{7+}$, ${\text{S}}^{7+}$, ${\text{Ar}}^{7+}$, and ${\text{Ca}}^{7+}$ collision with helium. The collision velocity is $0.43v_0$ for all ions. The prediction of MCBM, ECBM, and SSL is 0.59, 0.70, and 0.41, respectively.

Figure 3

Cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ of the $q=8$ isocharged sequence ions ${\text{F}}^{8+}$, ${\text{Ne}}^{8+}$, ${\text{Ar}}^{8+}$, and ${\text{Ca}}^{8+}$ collision with helium. The collision velocity is $0.4v_0$ for all ions. ${\text{F}}^{8+}$ was measured two times to conform to system reproducibility. The prediction of MCBM, ECBM, and SSL is 0.63, 0.71, and 0.41, respectively.

Figure 4

Cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ of the $q=9$ isocharged sequence ions ${\text{F}}^{9+}$, ${\text{Ne}}^{9+}$, ${\text{Si}}^{9+}$, ${\text{S}}^{9+}$, ${\text{Ar}}^{9+}$, and ${\text{Ca}}^{9+}$ collision with helium. The collision velocity is $0.42v_0$ for all ions. ${\text{Ar}}^{9+}$ was measured two times to test system reproducibility. The prediction of MCBM, ECBM, and SSL is 0.65, 0.71, and 0.41, respectively.

Figure 5

Cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ of the $q=11$ isocharged sequence ions ${\text{Si}}^{11+}$, ${\text{Ar}}^{11+}$, and ${\text{Ca}}^{11+}$ collision with helium. The collision velocity is $0.47v_0$ for all ions. ${\text{Ar}}^{11+}$ was measured three times to test system reproducibility. The prediction of MCBM, ECBM, and SSL is 0.69, 0.72, and 0.41, respectively.

Figure 6

(Color online) The relation between cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ and charge state $q$. Data from this work are presented by solid symbols (● represents ${\text{C}}^{6+}$ and ${\text{Ar}}^{q+}$, ◆ represents ${\text{Ca}}^{q+}$, ∎ represents ${\text{F}}^{q+}$, $★$ represents ${\text{Ne}}^{q+}$, ▴ represents ${\text{S}}^{q+}$, $▾$ represents ${\text{Si}}^{q+}$, $◀$ represents ${\text{N}}^{6+}$, and $▶$ represents ${\text{O}}^{6+}$). ◇ represents the ${\text{Xe}}^{q+}\text{-He}$ $\left(11\le q\le 31\right)$ collision at $4q\text{keV}$ by Andersson et al. [6], ▵ represents the ${\text{Xe}}^{q+}\text{-He}$ $\left(30\le q\le 42\right)$ collision at $3.8q\text{keV}$ by Selberg et al. [14], and ◯ represents the ${\text{Ta}}^{q+}\text{-He}$ $\left(41\le q\le 49\right)$ collision at $0.3v_0$ by Madzunkov et al. [15].

Figure 7

Cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ of the $q=6$ isocharged sequence ions collision with helium. The velocity of ${\text{C}}^{6+}$, ${\text{N}}^{6+}$, and ${\text{O}}^{6+}$ is $0.49v_0$ $\left(6\text{ keV}∕\text{u}\right)$, the velocity of ${\text{Ar}}^{6+}$ and ${\text{Ca}}^{6+}$ is $0.35v_0$ $\left(3\text{ keV}∕\text{u}\right)$, and for ${\text{F}}^{6+}$ and ${\text{Ne}}^{6+}$ both velocities are measured. The cross-section ratio difference induced by different velocities is small and within present experiment uncertainties.

Figure 8

Cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ of the $q=7$ isocharged sequence ions ${\text{F}}^{7+}$, ${\text{Ne}}^{7+}$, ${\text{S}}^{7+}$, ${\text{Ar}}^{7+}$, and ${\text{Ca}}^{7+}$ collision with helium. The collision velocity is $0.43v_0$ for all ions.

Figure 9

Cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ of the $q=8$ isocharged sequence ions ${\text{F}}^{8+}$, ${\text{Ne}}^{8+}$, ${\text{Ar}}^{8+}$, and ${\text{Ca}}^{8+}$ collision with helium. The collision velocity is $0.4v_0$ for all ions. ${\text{F}}^{8+}$ was measured two times to confirm system reproducibility.

Figure 10

Cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ of the $q=9$ isocharged sequence ions ${\text{F}}^{9+}$, ${\text{Ne}}^{9+}$, ${\text{Si}}^{9+}$, ${\text{S}}^{9+}$, ${\text{Ar}}^{9+}$, and ${\text{Ca}}^{9+}$ collision with helium. The collision velocity is $0.42v_0$ for all ions. ${\text{Ar}}^{9+}$ was measured two times to test system reproducibility.

Figure 11

Cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ of the $q=11$ isocharged sequence ions ${\text{Si}}^{11+}$, ${\text{Ar}}^{11+}$, and ${\text{Ca}}^{11+}$ collision with helium. The collision velocity is $0.47v_0$ for all ions. ${\text{Ar}}^{11+}$ was measured three times to test system reproducibility.

Figure 12

(Color online) The relation between cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ and charge state $q$. Data from this work are presented by solid symbols. ◯ represents the ${\text{Xe}}^{q+}\text{-He}$ $\left(11\le q\le 31\right)$ collision at $4q\text{keV}$ by Andersson et al. [6] and ◇ represents the ${\text{Xe}}^{q+}\text{-He}$ $\left(30\le q\le 42\right)$ collision at $3.8q\text{keV}$ by Selberg et al. [14].