Open AccessTHE ASYMPTOTIC BEHAVIOUR OF THE S-MATRIX ELEMENT IN HIGHLY SINGULAR POTENTIAL SCATTERING FOR LARGE IMAGINARY VALUES OF ANGULAR MOMENTUM
Author(s) -
Chqu Lon-Shiang
Publication year - 1966
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.22.1046
Subject(s) - physics , scattering , infinity , angular momentum , scattering amplitude , mathematical analysis , mathematical physics , matrix (chemical analysis) , classical mechanics , quantum mechanics , mathematics , materials science , composite material
For the highly singular potential satisfying the conditions of ref. (Ⅰ), it is proved that the partial wave S-matrix element posseses the asymptotic behaviour S(λ,k)Ce-nImλ as the imaginary values of angular momentum tending to infinity. From this we obtained the following conclusions:(1) The WATSON-SOMMERFELD transformation of the scattering amplitude does not hold.(2) Using the result of ref. (I) and above equation, we get existance of REGGE poles with real part tending to infinity in the little angle neighbourhood of the imaginary axis.