A test of wavefunctions for H⁺₂(²Σ⁺_g) via the study of Compton profiles

Abstract

The Compton profiles (CP) of H:('Z,') are calculated using the exact Born-Oppenheimer (BO) wavefunction for various internuclear distances R. By using the rotational-vibrational ( RV) state distribution factors, calculated according to the Franck-Condon ( FC) principle or measured from experiment, the vibrationally averaged values of C P for H;('L,') and D;(2Zl) in the adiabatic approximation are also calculated. Various theoretical values are given for comparison with the CP measured from H;-Ar collisions. The experimental data are most compatible with the exact BO values at R = 2.0 au but the data, with an error of IS%, fail to resolve various theoretical values at either small or large momenta q. It is important to have accurate experimental data (of absolute measurements) with an error of less than 10% in order to determine the accuracy of the theoretical values reported here.

The Bethe theory for dissociative excitations and ionisation of H2+(1sσg) by electron impact

“…The total cross section for the inelastic scattering of fast electrons by H:( lsa,) can be written (Inokuti 1971, Inokuti et a1 1975, Saxon 1973, Liu 1973, 1974, 1987)…”

“…For molecular targets, to calculate crex is comparatively more difficult than vtot (Liu 1973(Liu , 1974(Liu , 1987 because the generalised oscillator strengths (COS) for all the excitations must be calculated. In order to obtain an accurate rex, there are considerable excitations to be considered even for the simplest molecule H: as compared with one-electron atoms.…”

A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors

“…• p := a Since the case p := d represents the case of the class of systems modeled by (4), where the PS algorithm has been extensively studied in previous works, we consider next the case p := a, which belongs to the class of systems modeled by (9), and where the PS algorithm has been not applied yet. For b = 0.15, c = 2 and d = 0.1, as can be seen from the BD in Fig.2(b), system dynamics are more complex than for p := d, presenting several direct and reverse period-doubling bifurcations.…”

“…R n is a nonlinear, at least continuous function and q  1. The great majority of known systems of integer or fractional-order, including systems like: Lorenz, Chen, Rössler, Chua, Rikitake and many others systems, are modeled by the IVP (4). In [24,25] it was proved analytically and verified numerically that the PS algorithm allows the numerical approximation of any desired attractor, by switching the control parameter within a chosen finite set of values while the underlying IVP is numerically integrated with some fixed step size numerical method.…”

“…Fractional-order systems play an important role in many fields of science and engineering (see e.g. [3,4,5,6,7,8,9,10,11] or [12,13] with therein references). Also, piecewise continuous functions are used in the study of nonlinear circuits and systems.…”