Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

Abstract

The confined variational method is used to generate a basis of correlated gaussians to describe the interaction region wave function for positron scattering from the H2 molecule. The scattering length was ≈ −2.7 a0 while the zero energy Z eff of 15.7 is compatible with experimental values. The variation of the scattering length and Z eff with inter-nuclear distance was surprisingly rapid due to virtual state formation at R ≈ 3.4 a0.PACS numbers: 34.10.+x, 34.80.Bm, 34.80.Uv, 03.65.Nk The lack of spherical symmetry makes the calculation of electron or positron scattering from molecules an especially intractable computational problem. The nonspherical potential couples different partial waves resulting in an enormous escalation in the size of the calculation when compared with atomic targets. One consequence of this is that it is difficult to identify a definitive calculation of low energy electron/positron scattering from the simplest of molecules, i.e. H 2 , even under the simplifications of the fixed nucleus approximation.A new approach to compute the wave function for electron/positron scattering from small molecules is developed. It utilizes existing computational technologies from few-body physics that had been used to describe the low energy scattering of simple and composite projectiles from atoms [1,2,3]. The method is applied to the calculation of positron scattering from the H 2 molecule. The cross section for positron annihilation at thermal energies was found to be compatible with experimental values [4,5,6]. This is a significant achievement since the annihilation cross section presents a stringent test to the accuracy of the scattering wave function [7] and its successful prediction solves a previously intractable problem. Our calculations also show the existence of an unexpected virtual state at a H 2 inter-nuclear distance of R ≈ 3.4 a 0 .There have been a number of calculations of low energy e + -H 2 scattering and annihilation [7,8,9,10,11]. At present, all previous calculations significantly underestimate the low energy annihilation cross section. The most sophisticated calculations are the Kohn variational calculations performed by Armour and colleagues at the University of Nottingham (UN) [9,11,12]. Their most recent calculations significantly underestimate the annihilation cross section at thermal energies.We apply a variant of the confined variational method (CVM) [1, 2] to describe low energy positron-H 2 scattering. In the CVM, an artificial confining potential is added to the scattering Hamiltonian thus converting the system into a bound system. This provides a framework that permits the wave function in the interaction region to be obtained with bound state techniques. Of crucial importance to this exercise is the use of the stochastic variational method (SVM) [13,14,15] to describe the interaction region wave function. The SVM and variants [16] constitute a powerful tool for studying few body systems. The SVM uses a wave function that is a linear combination of explicitly correlated...

Muon, positron and antiproton interactions with atoms and molecules

“…Thus the value obtained with the method of models is closer to the experimental value of 14.6 [26] than that obtained without using it. In a very recent, very accurate calculation of Z eff (k) at very low energies, Zhang et al [27] find similar behaviour to the behaviour we find using the method of models as R increases beyond 1.6a 0 . The more accurate value obtained by the method of models, despite using a less accurate target wave function, may be due to the better convergence behaviour that is obtained using this method [28,22].…”

A rigid sphere approach to positron elastic scattering by noble gases, molecular hydrogen, nitrogen and methane

“…However at lower energies, E < 2 eV, the smallest R 0 yields results that are higher than other experiments and theories. On the other hand, the use of the second value of R 0 = 0.9505a 0 gives cross-sections that are consistent with ro-vibrational laboratory-frame close coupling method by Mukherjee and Sarkar [64], CCC method of Zammit et al [66] and density functional calculations (DFT) by Fedus et al [3] below 2 eV, giving the value of the scattering length (see next subsection) comparable with prediction of Zhang et al [81], Zhang and Mitroy [82], Zhang et al [83] obtain with stochastic variational method. Above 2 eV presently calculated cross-sections agree pretty well with other experiments.…”

“…The results obtained with the largest value of R 0 = 0.9912a 0 is included in Figure 7a mainly to show that it is possible to get results that are consistent at very low impact energies (<0.4 eV) with TCS by Zecca et al [73], though this experimental dataset seems to be significantly underestimated at low energies as discussed by Zhang and Mitroy [81]. Figure 7b shows present calculations of elastic crosssections for molecular nitrogen (N 2 ) using three different values of rigid sphere radius: R 0 = 1.2875a 0 , R 0 = 1.3249a 0 and R 0 = 1.4268a 0 .…”

Positron Scattering at Thermal Energies

“…[28] and giving 4πρ e δR ≈ 0.5 and 0.66, respectively. It is expected that the similar results should be obtained for other small molecules with low polarizability, also including H 2 (see for example [33]). The formula of Gribakin (Eq.…”