H + 2 ion in strong magnetic field : an accurate calculation

Using a unique trial function we perform an accurate calculation of the ground state 1σg of the hydrogenic molecular ion H + 2 in a constant uniform magnetic field ranging 0 − 10 G. We show that this trial function also makes it possible to study the negative parity ground state 1σu. PACS numbers: 31.10.+ z, 32.60.+ i, 97.10.Ld, 31.15.Ar, 97.60.Jd E-mail: [email protected] E-mail: [email protected] On leave of absence from the Institute for Theoretical and Experimental Physics, Moscow 117259, Russia E-mail: [email protected], [email protected] This work is supported in part by DGAPA project IN105296 For a long time the behavior of atomic and molecular systems in a strong magnetic field of order B ≥ 10 G has attracted considerable attention. The main interest comes from both astrophysics – studies of white dwarfs and neutron stars (see [1, 2], and also, for example [3, 4], and the review [5] and references therein), as well as from chemistry – formation of unusual chemical compounds whose existence is impossible without strong magnetic fields [6] (for a review, see, for example, [7] and references therein). There are many studies of the hydrogen atom H – the simplest atomic system – in a strong magnetic field, while the hydrogen molecular ion H 2 – the simplest molecular system which is stable with respect to dissociation H 2 → H + p – is much less explored. One of the major drawbacks of many of these studies is a restricted domain of applicability: they are accurate in the weak magnetic field region but are inappropriate for the strong magnetic field region and vice versa. The goal of the present Note is to carry out an accurate variational calculation of H 2 in magnetic fields ranging from 0 up to 10 G 2 using a unique simple trial function equally applicable for any value of the magnetic field strength. We restrict our consideration to the case where the magnetic field is directed along the axis of the molecule, which is evidently the optimal configuration leading to the lowest energy. Our main perception is that the calculations should not be technically complicated and also easily reproduced, while the trial function should be simple enough to allow further analytic and numerical investigations. A constructive criterion for an adequate choice of trial function was formulated in [8] and further development was presented in [9, 10]. In the simplest form the criterion is the following. The trial function Ψt(x) should contain all symmetry properties of the problem in hand. If the ground state is studied, the trial function should not vanish inside of the domain where the problem is defined. The potential Vt(x) = ∆Ψt Ψt , for which the trial function is an eigenfunction, should reproduce the original potential near singularities and also its asymptotic behavior. The use of this simplest possible recipe has led to a unique one-parameter trial function, which, in particular made it possible to carry out the first qualitative study of the ground state of the hydrogen molecule H2 in the region of both weak and strong magnetic fields where the relativistic corrections can still be neglected (see a discussion in [5] and references therein)