By David Bates, Benjamin Bederson

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**Example text**

For the system H 2, when Z is sufficiently high (say 2 3 lo), one can neglect all nondiagonal elements in the interaction matrix V,,, except those which couple the initial state li} = 10) with the final states lj). Then, the + 25 ELECTRON CAPTURE system (78) reduces to l’ -dao - Z- dt sr Vo( *, R ) exp [-i o o j ( z ) d7] bj [s 1 dbJ i- V,,(R) exp i dt o o J ( 7 )d7 a, The initial conditions are a3)l = 1, bJ(- co) = 0 We also assume that the unitarity is preserved: la,(- lUdt)l2-k lbJ(t)12 (80) =’ (81) J and that VoJis real ( V 6 = V,,).

However, in the region of R [namely (2Z)'I2 < R < 221 giving the main contributions to a&,, Vo,(R, Z) N (4) A(R, Z) exp(-aR2/Z) [see Eq. (30a)], and the ratio R2/Zin the exponent gives rise to a linear Z dependence of the cross section. The same result is obtained also if Vo,(R,Z) exp(-aRZ-1/2). One of the main merits of the M- VPS theory for charge exchange is that it is able to include both the Landau- Zener and the tunneling transitions. It is therefore applicable in a very broad energy range.

H. Bransden and R. K. Janev cluded, have been performed in the context of the charge-exchange atom highly charged ion problem by Presnyakov and Ulantsev (1975) and by Ryufuku and Watanabe (1978, 1979a,b). In both cases the charge-exchange probability has been expressed in terms of the two-state transition probability (or the corresponding transition matrix elements) for the coupling of the initial state with each of the final states. , 1964), Ryufuku and Watanabe (1978) used the distorted wave Born approximation (Bates, 1958).