Deconvolution and characteristics of cusp spectra for electron transfer to the projectile’s continuum (ETC): Extraction of a generic cross section

Observed cusp spectra for electron transfer to the continuum (ETC) of 0.6-MeV/u ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{He}}^{2+}$ ions from hydrocarbon gaseous targets (${\mathrm{CH}}_4$, ${\mathrm{C}}_3$${\mathrm{H}}_6$, and ${\mathrm{C}}_7$${\mathrm{H}}_{16}$) are fitted to a generic expression of Meckbach, Nemirovsky, and Garibotti [Phys. Rev. A 24, 1793 (1981)]. Six leading terms of this formula are given here analytically. They were derived after the convolution of the assumed expression for the ETC cross section with an analytical function that accounts for the electron transmission through the electron spectrometer of specified longitudinal and transverse velocity resolution. With given angles that determine the angular acceptance as instrumental parameters, formulas for these terms are expressed as universal functions of a single variable which is the ratio of electron speed v to ion speed $v_i$. The least-squares fit of these functions to experimental cusps allows for reconstruction of the generic ETC cross section, which is not ‘‘polluted’’ by finite resolution of the electron spectrometer.

Key characteristics, the asymmetry and relative width of deconvoluted cross sections, are discussed. The skewness in observed cusp spectra is traced to the scattering angles that, relative to the spectrometer’s half-angle of acceptance ${\theta }_0$, are small; this is particularly seen in electron capture to continuum (ECC) data, while the spectra dominated by electron loss to continuum (ELC) are more symmetric and less dependent in their asymmetry on the scattering angle θ. The relative full widths at half maximum, (Δv/v${)}_{\mathrm{FWHM}}$, for the deconvoluted ECC cross sections rise significantly faster with the increasing θ than for the ELC cross sections; this difference is obscured in observed cusp spectra by the finite velocity resolution of the spectrometer. Relatively narrow resolution results in the preferential detection of the highly forward scattered electrons whose velocity distribution conforms with the leading term, 1/‖${\mathrm{v}\mathrm{-}\mathrm{v}}_i$‖, for ETC cross sections.

Hence, for all projectile-target combinations, the observed spectra have the relative widths which are of comparable magnitude and in very good agreement with Dettmann’s prediction, i.e., 1.5${\theta }_0$. A comment on wakes as possible contributors to cusps observed in ETC from large hydrocarbon molecules is made.