By David Bates, Benjamin Bederson

ISBN-10: 0080564798

ISBN-13: 9780080564791

ISBN-10: 0120038196

ISBN-13: 9780120038190

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**Extra resources for Advances in Atomic and Molecular Physics, Vol. 19**

**Example text**

More recently, a number of calculations including translational factors of different kinds have been performed and a list of those which have basis sets of adequate size is shown in Table I. Comparison with experiments (where these exist) suggests that the MO expansion method is accurate, at least for total capture cross sections for velocities ofat least up to = 1, good agreement is obtained for 2 = 2 and 2 = 6, but only fair agreement for Z = 3 (illustrated in Fig. 2), perhaps because only a limited basis of 6 terms was used (Kimura and Thorson, 1981b).

Is the initial distance of Z from the center of mass of the hydrogen atom. (In the calculations R. is usually taken to be about 10-20 times Z . ) The initial conditions for the electronic coordinates are taken to be re sin 8 cos 4 qy = q4 = re sin 8 sin q5 (164) q$ = re cos 8 where (re,O,$) are the spherical coordinates of the electron. lntroducing the angle between the plane of the orbit and the plane containing both the z axis and the major axis of the orbit, the initial conditions for the electron < ELECTRON CAPTURE momenta can be written as p oI = -p,(cos 8 cos 4 cos { pg = -p,(cos 8 sin 4 cos 53 + sin 4 sin {) < - cos 4 sin t) (165) pg = p , sin 8 cos 5 wherep,is the magnitude ofthe electron momentum in the hydrogen atom.

Cross sections for electron capture by Li3+ from H(ls) at low velocities. (A) Experimental data of Seim et a/. (1980). Theoretical cross sections: (-) atomic expansion (Bransden and Noble, 1982); (---) molecular orbital expansion (Kimura and Thorson, I981 b): (----) UDWA (Ryufuku and Watanabe, 1979a,b). grounds one would expect the larger partial cross sections to be accurate, but smaller cross sections might not be so reliable. D. APPROXIMATE TREATMENTS OF THE DIABATIC PSS EQUATIONS In a diabatic representation of electronic states, the coupled equations in the PSS approximation for the expansion coefficients have the following forms (assuming no rotational coupling and denoting the direct and exchange amplitudes by a, and b,) respectively: i -db, - C V,,(R)exp dt , v,,= (ilW), 0, = vll- v, - (rll - rl,) - (78c) where R = R(t) is the classical trajectory and ql (q,) is the binding energy of the electron in the state i ( j ) when R m.

### Advances in Atomic and Molecular Physics, Vol. 19 by David Bates, Benjamin Bederson

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