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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Space-time shifts and cross-sections in collisions between relativistic wave packets

V. S. Olkhovsky, Erasmo Recami

Published Feb 1, 1968• 20 citations
Publisher
DOI
10.1007/bf02721712

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Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.
Antihydrogen-formation cross sections in antiproton-positronium collisions are calculated by using a time-dependent coupled-channel (TDCC) method. Nonuniform grid points are taken in the two-dimensional radial space to obtain accurate wave functions. High numerical accuracy of the TDCC method is demonstrated in a calculation of positronium-formation cross sections in positron-hydrogen collisions. The result is somewhat discrepant with previous results; in the present calculation, the cross section has a maximum of 16.19 in units of $\ensuremath{\pi}{a}_{0}^{2}=0.880\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16} {\mathrm{cm}}^{2}$ at an antiproton energy of 9.2 eV in the center-of-mass frame.