Prog. Theor. Phys. Vol. 34 No. 2 (1965) pp. 274-283
Shrinkage of Effective Core and Large Angle Scattering at High Energy
Institute of Physics, College of General Education, Osaka University, Toyonaka, Osaka
(Received April 10, 1965)
It is shown that, by improving a previous theorem, the first l0(s) partial wave amplitudes determine the scattering amplitude for the scattering angle θ within an error smaller than exp [-const l0(s)sin
θ/lnl0(s)] provided that l0(s)>const lns/sin
θ, s being the square of the center-of-mass energy. The improvement of the error is important for the investigation of the large angle scattering at high energy. In connection with this improvement, a field theoretical model of the high-energy large-angle scattering is presented. The improvement of the lower limit of l0(s) immediately gives us the high energy bound of Kinoshita, Loeffel and Martin. The scattering of particles with spin is also discussed.
DOI : 10.1143/PTP.34.274
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- See the inequality (11) of reference 2).
- We use the slightly different method from that in the reference 1).
However, the improvement of the result is due to only the new step function (2·7).
- The assumption on the analyticity domain may be weakened. For example, even if T(s, cos
θ) is singular at cos
θ=1+(1+i)/s, the theorem will hold.
- The division is not unique.
For example the division used in reference 1) is different from that in reference 3).
The division used in 3) is better.
- Appendix D of reference 5).
- III B of reference 5).
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