Imaging of continuum states of the $\mathrm{He}_2{}^{2+}$ quasimolecule

Using cold target recoil ion momentum spectroscopy (COLTRIMS) we have investigated the production of one free electron in slow ${\mathrm{He}}^{2+}+\mathrm{He}\left(1s^2\right)$ collisions. At projectile velocities between 0.6 and $1.06\text{a.u.}$ (9–$28\mathrm{keV}∕u$), the fully differential cross section was measured state selective with respect to the second electron, which is bound either at the target or the projectile. We provide a comprehensive data set comprising state selective total cross section, scattering angle dependent single differential cross sections, and fully differential cross section. We show that the momentum distribution of the electron in the continuum image the relevant molecular orbitals for the reaction channel under consideration. By choosing the bound electron final state at the target or projectile and the impact parameter we can select these orbitals and manipulate their relative phase.

Figure 1

Total cross sections of single and double capture into different electronic states: SC1 [$\mathrm{He}(1s{)}^{+}+\mathrm{He}(1s{)}^{+}$, open triangle], SC2 [$\mathrm{He}(1s{)}^{+}+\mathrm{He}(2l{)}^{+}$ and $\mathrm{He}(2l{)}^{+}+\mathrm{He}(1s{)}^{+}$, open inverted triangle], SC3 [$\mathrm{He}(1s{)}^{+}+\mathrm{He}(3l{)}^{+}$ and $\mathrm{He}(3l{)}^{+}+\mathrm{He}(1s{)}^{+}$, open circles], DC1 [$\mathrm{He}\left(1s^2\right)+{\mathrm{He}}^{2+}$, full squares], DC2 [$\mathrm{He}(1s,2l)+{\mathrm{He}}^{2+}$, full circles], TI2 [$\mathrm{He}(2l{)}^{+}+e^{-}+{\mathrm{He}}^{2+}$, open diamonds] the solid lines are drawn to guide the eye. Our data have been normalized to experimental results of Afrosimov et al. [42] (dashed lines).

Figure 2

(Color online) Transfer ionization at $v_p=0.86\text{a.u.}$ Momentum distribution of (a) the recoil ion and (b) the electron in the laboratory system (projectile moves from left to right along $z$). (c) Momentum change of the projectile. (d) Expanded electron distribution projected onto the nuclear scattering plane $(x^{\prime },z^{\prime }=z)$ on linear color scale.

Figure 3

Recoil-ion transverse momentum distributions for electron emission in ${\mathrm{He}}^{2+}+\mathrm{He}$ collisions at four projectile velocities $v_p$ between 0.71 and $1.06\text{a.u.}$: SI1 (solid lines), SI2 (circles), TI1 (dashed lines), and TI2 (squares). Total cross sections are normalized to [42]. Autoionizing double capture for $v_p=0.90\text{a.u.}$ scaled by an arbitrary factor (triangles).

Figure 4

(Color online) Electron momentum distribution of TI1 at $v_p=0.84\text{a.u.}$ The $z$ axis is defined by the incoming beam direction and $p_{r,e}$ is the radial component of the electron momentum. The circular arc marks the position where electrons emitted with $35\mathrm{eV}$ from the projectile are found. The hatched area was not detected.

Figure 5

(Color online) “Top view” of the electron distribution for TI1 at six projectile velocities $v_p$ between $0.64\text{a.u.}$ and $1.06\text{a.u.}$ The normalized electron velocities are projected onto the plane of nuclear motion (projectile motion from left to right). At the initial state the projectile is located at (1,0) and the target at (0,0). During the reaction the projectile is scattered downwards and the target upwards.

Figure 6

(Color online) TI at $v_p=0.84\text{a.u.}$: Electron velocity distribution in the $x^{\prime },y^{\prime }$ plane (i.e., normal to the projectile beam axis) for $0.3v_p<v_{z,e}<0.7v_p$. (a) Density plot of $d^2\sigma ∕\left(d{v}_{x^{\prime },e}d{v}_{y^{\prime },e}\right)$. The recoil ion is scattered to the right side. (b) Polar presentation of $d^2\sigma ∕\left(d\varphi d{v}_{r,e}\right)$ for $v_{r,e}=\sqrt{v_{x^{\prime },e}^2+v_{y^{\prime },e}^2}=0.2v_p$ (circles) and $v_{r,e}=0.4v_p$ (squares). For $v_{r,e}=0.2v_p$, the measured data can be described by $d^2\sigma ∕\left(d\varphi d{v}_{r,e}\right)\propto 0.66{\cos }^2\varphi +0.33$ (dashed line) and for $v_{r,e}=0.4v_p$ with $d^2\sigma ∕\left(d\varphi d{v}_{r,e}\right)\propto 0.66{\cos }^2\varphi +0.66\cos \varphi +0.33$ (solid line).

Figure 7

(Color online) Top view as Fig. 4 (projection of the electron velocity distribution onto the scattering plane) but (a) TI1, (b) SI1, (c) TI2, and (d) SI2 at $v_p=0.9\text{a.u.}$

Figure 8

$v_{x^{\prime },e}$ distribution at $v_p=0.9\text{a.u.}$ for electrons with $-0.2v_p<v_{z^{\prime },e}<0.2v_p$. (a) TI1 (line), TI2 (open circles), and SI2 (full triangles). (b) Total SI1 (line) and events with $p_{r,rec}<5\text{a.u.}$ (full inverted triangles) and with $p_{r,rec}>7\text{a.u.}$ (open squares).

Figure 9

(Color online) Top view of SI1 at $v_p=0.9\text{a.u.}$: (a) distant collisions with $0.3\text{a.u.}<p_{r,rec}<2\text{a.u.}$, (b) close collisions with $2.5\text{a.u.}<p_{r,rec}<15\text{a.u.}$