Energy and angular distribution of electrons in ionization of He and Ne by 6-MeV/u bare carbon ions: Comparison with continuum-distorted-wave eikonal-initial-state calculations in prior and post forms

We have measured the absolute double-differential cross sections (DDCS) for electron emission in ionization of He and Ne atoms under the impact of 6-MeV/u ${\mathrm{C}}^{6+}$ ions. Data were collected between 1 and 500 eV for He, while for Ne this range was extended up to 1000 eV. The angular ranges covered in the experiment are ${30}^{\circ }$ to ${150}^{\circ }$ and ${20}^{\circ }$ to ${160}^{\circ }$ for He and Ne, respectively. The DDCS spectra are compared with the prior and the post forms of the state-of-the-art continuum-distorted-wave eikonal-initial-state model. Both the theoretical models show very good agreement with the energy and angular distributions of the DDCS in the case of He. For Ne, at low energies both are going together and matching very well with the data. In the high-energy region, at extreme forward and backward angles, although both the forms are underestimating the experimental data to some extent, the prior form shows much better agreement compared to the post form. This post-prior discrepancy is attributed to the influence of dynamic screening, on the ionized one, produced by the electrons remaining in the target. The single differential cross sections (SDCS) in emission angle $\left(\frac{d\sigma }{d{\Omega }_e}\right)$ and electron energy $\left(\frac{d\sigma }{d{\epsilon }_e}\right)$ are deduced by integrating the electron DDCS spectra. While excellent agreement is obtained for the $\frac{d\sigma }{d{\epsilon }_e}$ spectrum, the $\frac{d\sigma }{d{\Omega }_e}$ provides a further sensitive test to the adequacy of the theoretical model employed. The total cross section obtained from the SDCS spectra is about 11% higher than the prior model for He and about 6% lower for Ne. To get the quantitative picture of the two-center effect, the forward-backward angular asymmetry parameter has been deduced as a function of velocity of the ejected electrons. For both the targets, it is very well reproduced by both the forms of the theory. For the Ne target, $K$-LL Auger angular distribution has also been studied, which shows small asymmetry caused by multiple vacancies in the $L$ shell along with the $K$-shell vacancy.

Figure 1

(a)–(c) Energy distribution of the ratio of the electron count corresponding to background (without target gas) and target gas (Ne), at different observation angles. (d) Absolute DDCS corresponding to $+{90}^{\circ }$ (circle) and $-{90}^{\circ }$ (square). (Inset) Ratio of the corresponding DDCSs.

Figure 2

Energy distribution of DDCS at different emission angles for He. Solid (dash) lines represent CDW-EIS prior (post) form. In the inset (c), the BE region at ${60}^{\circ }$ is displayed. The vertical scale of the inset is to be multiplied by ${10}^{-5}$.

Figure 3

The same as Fig. 2 for the Ne target. In the insets the Auger region is displayed. The vertical scales of the insets are to be multiplied by ${10}^{-4}$.

Figure 4

Energy distributions of the ratio corresponding to the DDCS from experiment with the prior (post) form displayed as a circle (triangle). (Insets) DDCS corresponding to prior and post forms. Dash line is ratio $=1.0$.

Figure 5

Angular distributions of the DDCS at fixed emission energies for He. Solid (dashed) lines represent CDW-EIS prior (post) form.

Figure 6

Same as Fig. 5 for Ne target.

Figure 7

Ejected electron velocity dependence of angular asymmetry parameter $\left(\alpha \right)$ for He (a) and Ne (b). In (c), velocity distribution of the ratio of $\alpha \text{s}$ corresponding to Ne and He is displayed. Solid (dash) lines represent prior (post) form. Dash dot line in (c) is ratio $=1$.

Figure 8

Angular distribution of Auger electron SDCS for Ne.

Figure 9

Absolute electron SDCS as a function of emission angle (a) and electron energy (b). In both graphs the upper set of plots corresponds to Ne and the lower one corresponds to He. (b) Left vertical scale is for He and right vertical scale is for Ne. Solid (dashed) lines represent prior (post) form calculation.