EGAS41 - Swansea University

41 st EGAS CP 80 Gdańsk 2009
Multiple scattering approximation in atomic and molecular
physics
S. Pozdneev
P.N. Lebedev Physical Institute, Department of Quantum Radiophysics, Laboratory of
Photochemical Processes, Leninsky pr. 53, Moscow 119991, Russia
E-mail: pozdneev@sci.lebedev.ru
The multiple scattering approximation based on the modified Faddeev-Yakubovsky equations
[1] for charged particles is applied to the calculation of the scattering amplitudes and
cross sections of the different processes ion-atom, ion-molecular and atom-molecular collisions.
In three-body approximation the amplitude may be written in the form [2]: f 2−2 =
f c +Ψ 2−2 v 1 (G 2 V 2 +G 3 V 3 + G 2 V 2 G 3 V 3 +G 3 V 3 G 2 V 2 )Ψ 2−2 - for elastic scattering and f 2−3 =
Ψ 2−3 v 1 (G 2 V 2 + G 3 V 3 + G 2 V 2 G 3 V 3 + G 3 V 3 G 2 V 2 Ψ 2−2 - for break-up processes, where f c =
η exp(−iη lnsin 2 θ/2 + 2iargΓ(1 + iη))/2(| k | sin 2 θ/2) - Coulomb amplitude; cos(θ) =
( ⃗ k, ∧ k′ ⃗ ); Ψ 2−2 = ϕ 2−2 (x)ψ c (y, p); ψ c (y, p) = e −πη/2 Γ(1 + iη)Φ(−η, 1, i | p || ξ |); η =
n/2 | p |; ξ =| y | −(y, p); Ψ 2−3 = ϕ 2−3 (x, k)ψ c (y, p); v i = n i / | x i | +vi s(x i); n i =
γZ i Z j / √ 2µ ij ; µ ij = m i m j /(m i + m j ); V i = Vi 1 + Vi 2 ; V 1
= (1 − χ i (x i , y i , ν))n i / | x i |; x i , y i , k i , p i , m i , Z i - coordinate, momenta and charge of
V 2
i
i = v s i + n i χ i (x i , y i , ν)/ | x i |;
i-particle; ψ 2−2 ,ψ 2−3 -wave functions of the bound and continuous states two particle subsystems;
G i , χ i - Green and cutoff functions defined in [1]. The parameters ν, x i , y i chosen
such that χ tends to unity in the limit x i