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Zeros of the Partial-Wave Scattering Amplitude

Journal Article · · Physical Review
 [1];  [1]
  1. Brown Univ., Providence, RI (United States)
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In this work, under the general assumptions of analyticity, unitarity, temperedness, and normal threshold behavior, the relation between the number of zeros and the high-energy behavior of the partial-wave scattering amplitude is studied. If the left-hand-cut discontinuity makes a finite number of sign changes, the maximum and minimum numbers of zeros can be determined by the high-energy upper and lower bound of the partial-wave respectively. In particular, for C⁢|s|–1+ε < |fl⁡(s)| < C, the number of zeros is determined. After having determined the number of zeros, the number of subtractions as well as the sign of the scattering length is obtained for given number and character of zeros of the left-hand discontinuity Δ⁢fl⁡(s).
Research Organization:
Brown Univ., Providence, RI (United States)
Sponsoring Organization:
US Atomic Energy Commission (AEC)
NSA Number:
NSA-21-009866
OSTI ID:
4446929
Report Number(s):
NYO--2262-115(Rev)
Journal Information:
Physical Review, Journal Name: Physical Review Journal Issue: 4 Vol. 152; ISSN 0031-899X
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (13)

The threshold behaviour of partial wave scattering amplitudes and theN/D-method journal August 1964
Cuts in the angular-momentum plane - II journal November 1963
Analyticity and crossing for partial waves journal October 1961
Criteria for the solubility of partial-wave dispersion relations journal November 1965
On the Many-Particle Structure of Green's Functions in Quantum Field Theory journal July 1960
Low's Scattering Equation for the Charged and Neutral Scalar Theories journal January 1956
Subtractions in Dispersion Relations journal September 1961
Cross Sections at High Energies journal December 1961
Proof of Partial-Wave Dispersion Relations in Perturbation Theory journal May 1962
Analysis of Partial-Wave Dispersion Relations journal April 1963
Theory of Low-Energy π − π Scattering journal June 1964
Connection Between the Asymptotic Behavior and the Sign of the Discontinuity in One-Dimensional Dispersion Relations journal September 1964
Number of Subtractions in Fixed-Transfer Dispersion Relations journal September 1964

Figures / Tables (6)

Table I(p. 21)table Table I
Table II(p. 22)table Table II
Table III(p. 24)table Table III
Table IV(p. 25)table Table IV
Fig. 1(p. 35)figure Fig. 1
Fig. 2(p. 36)figure Fig. 2

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Related Subjects

ANGULAR MOMENTUM
High Energy Physics
MOMENTUM
PARTIAL WAVES
QUANTUM MECHANICS
SCATTERING
SCATTERING AMPLITUDE
Scattering Theory
UNITARITY