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**

NUMERICALCALCULATIONS ORBITAL BASIS A MOLECULAR Some examples of calculations using a molecular orbital basis of adequate size will now be given. At very low energies, for which a partial wave treatment is appropriate, there have not been extensive investigations into the fully stripped ion - hydrogen atom system. On the other hand, several calculations have been made for certain cases of partially stripped ions in collisions with atomic hydrogen which are of astrophysical interest. A recent study of this kind by Heil et al.

Is the Euler's constant. As seen from Eq. (108), the quantity xo = xo(u, Z ) depends logarithmically on u and is almost independent of Z . 5 X Zln(314/u) (cm2) (109) The basic idea ofthe decay model, namely the existence of a large number of ionic states available for the reaction, may also be formulated in terms of a dense multi-curve-crossingsystem. In that case one can introduce an internuclear distance R,,such that for R > R, all crossings are passed diabatically (with zero transition probability) and for R G R, the capture probability is equal to unity.

A. CLASSICAL TRAJECTORY MONTECARLO METHOD The motion of the three-particle system (p, e, 2) in the classical mechanics is described by Hamilton's equation (Landau and Lifshitz, 1973): (1 59) aHlapi = ii, aHlaq, = -pi where q, and pi are the coordinates and momenta of the particles and His the Hamilton's function. Let (4, , q2, q3)be the Cartesian coordinates of the electron with respect to the proton, (q4, q5, q6) the coordinates of the projectile nucleus (2)with respect to the center of mass of the hydrogen atom (p, e), and (q,, q8,q9)the coordinates the center of mass of the entire system.

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