Annihilation rate in positronic systems by quantum Monte Carlo: e+LiH as test case

Abstract

An accurate method to compute the annihilation rate in positronic systems by means of quantum Monte Carlo simulations is tested and compared with previously proposed methods using simple model systems. This method can be applied within all the quantum Monte Carlo techniques, just requiring to accumulate the positron-electron distribution function. The annihilation rate of e + LiH as a function of the internuclear distance is studied using a model potential approach to eliminate the core electrons of Li, and explicitly correlated wave functions to deal with all the remaining particles. These results allow us to compute vibrationally averaged annihilation rates, and to understand the effect of the Li + electric field on positron and electron distributions.

Non-Born–Oppenheimer study of positronic molecular systems: e+LiH

“…There has been considerable interest in the literature in small positronic systems such as HPs [5][6][7][8] and e ϩ LiH. [9][10][11][12][13] While calculations of the former system have not presented much difficulty using both finite-mass and infinite-mass approaches concerning the hydrogen nucleus, the calculations of e ϩ LiH have appeared to be much more challenging particularly when methods going beyond the BornOppenheimer approximation were employed. 11 At the core of the difficulty encountered in Ref.…”

Configuration interaction calculations of annihilation rates for positronic complexes of alkali hydrides

“…When these results are compared with the more accurate data obtained in the QMC calculations [19], it is found that they are generally lower by more than a factor of two. Such an underestimation is expected based on the previous experience with the corresponding potential curves mentioned above.…”

“…The slope of the d +À curve is decreasing at this point, however and so there is at least an indication that the minimum found in both MRD-CI treatments would simply be replicated at a shorter r value if QMC calculations had been carried out in this range of LiH distance while maintaining the same general level of accuracy as for the values reported at larger distances. The fact that no QMC results are given for r < 2.0 a 0 may also be an indication that numerical difficulties were encountered in this region in the rather delicate procedure that has been employed to compute these expectation values for such a short-range operator [19]. Overall, it seems safe to conclude that the underestimation of the d +À expectation values in the present calculations is largely independent of bond distance, again as one would expect if the effect were predominantly atomic in nature.…”

“…For example, at the dissociation limit in which the positronium hydride PsH system is formed, a d +À value of 0.02056 a 3 0 is obtained for the 2e CI treatment and 0.0195 a 3 0 for the 4e CI. The corresponding QMC value [19] is 0.04794 a 3 0 (at r = 20.0 a 0 ). The QMC data have the same general variation with bond distance, however, as would be expected if the correlation error in the MRD-CI calculations is atomic-like in nature, as has already been indicated in the potential energy calculations mentioned above [3,4].…”

“…The e + LiH complex is a convenient test case for the above procedure because relatively accurate AR values for this five-particle system have been previously computed for it as a function of LiH bond distance by several groups employing a variety of methods: Mella et al (QMC [19]), Strasburger (ECG [10]) and Mitroy and Ryzhikh (SVM [11]). Two sets of MRD-CI calculations have been carried out for the ground state, one in which the 1s electrons of Li are kept in a frozen core (2e CI) and one in which all electrons are involved in the excitation process (4e CI).…”