Transition Matrix Elements for Large Momentum or Energy Transfer
Abstract
The radial matrix element M=∞R_{kl'}(r)j_{L}(qr)R_{nl}(r)r^{2}dr, which appears in collision theory and photon absorption (L=1, q~0), has been studied in the past for hydrogenic wave functions. Its behavior for large q or large k is now shown to depend only on the expansion of the wave functions near the nucleus and on an application of selection rules. For large q, the trend is M~q^{(l+l'+4)} and for large k and normalization per unit energy, M~k^{(l+L+72)}q^{L}. The asymptotic trend of Altshuler's equivalent forms of the matrix elements is discussed.
 Publication:

Physical Review
 Pub Date:
 October 1967
 DOI:
 10.1103/PhysRev.162.68
 Bibcode:
 1967PhRv..162...68R