By Per-Olov Löwdin; et al
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Additional resources for New perspectives in quantum systems in chemistry and physics, part 2
5 Target isotope effects Stancil and Zygelman (21) have derived a simple formula, based on the LandauZener approximation, for the influence of a kinematic isotope effect on low-energy total charge transfer cross sections. Their predictions have since been verified for various systems. Taking as a representative example the electron capture into 46 David L. Cooper et aL Si2÷(3s2) from Si3+(3s), the ratio of cross sections for 3He and 4He targets is given by: G(3He) 1 - 2 V/(~t(3He)v2) a(4He) ~ l_2V/(~t(4He)v2) where V is the diabatic potential for the entrance channel at the crossing point, v is the collision velocity in the centre-of-mass frame, and tt("I-Ie) is the reduced mass of the SiI-Ie3+ quasimolecule based on isotope %Ie.
Cooper et aL relative to N~(~D), with the discrepancy being largest at low collision energies. Using the electronic wave functions obtained by Lafayatis et al. (14), Sun et al. (16) evaluated charge transfer cross sections using a close-coupling formalism, constructing a particular diabatic representation by diagonalizing, at each value of R, the adiabatic transition dipole matrix. There remains substantial quantitative disagreement with experiment for the N+(3P)/N~(ID) ratio at collision energies of a few eV.
T? (201 i=l i=1 where L L -1 8i e -1 s'~ = M T - l m ~ j=l Bq j=l (211 so that using (20) X can be eliminated in favour of X T whenever necessary. In much of what follows it will be convenient to use X as a short-hand, but no approximation is implied. a "J _ ~ ; + j=l e N 0 a r m M T _ l o x To G~j .. w j=l Vi3 0~y (22) a + m i M T -1 c~X T (23) T h e H a m i l t o n i a n operator w i t h electrons identified The translationally invariant kinetic energy operator is in three parts /~(t)--*/~e(te) + / ~ " ( t ") + / ~ ( t " , t ~) (24) 24 Brian Sutcliffe Here ~2 ~L ~ i j ~V(t~).
New perspectives in quantum systems in chemistry and physics, part 2 by Per-Olov Löwdin; et al