HighEnergy Behavior of Total Cross Sections
Abstract
A proof of Pomeranchuk's theorem regarding the highenergy limits of the total cross sections is presented. The proof consists of assuming the usual analyticity for the forward elastic amplitudes and the assumption that these amplitudes become pure imaginary in the highenergy limit. This proof does not require that the total cross sections have finite limits. It is also shown that the total crosssection σ(s) as a function of s, the total c.m. energy squared, behaves asymptotically as σ(s)=σ(∞)+δs^{12}+O(1s) when δ(∞) is nonzero, where δ is some constant. This asymptotic form is based upon a more specific assumption that highenergy elastic scattering is described by an effective complex and energydependent potential which satisfies a dispersion relation in the energy variable. However, the above asymptotic form is valid independently of the dependence of this effective potential on the spacial coordinate. It is argued that the term δs^{12} in the above asymptotic form should be regarded as genuinely asymptotic, while the term of the order of 1s is not. According to this criterion, the available highenergy pp data are not so close to the asymptotic region as the π^{+/}p data in the same laboratory momentum range.
 Publication:

Physical Review
 Pub Date:
 December 1963
 DOI:
 10.1103/PhysRev.132.2724
 Bibcode:
 1963PhRv..132.2724N