DOUBLE-PHASE REPRESENTATION OF ANALYTIC FUNCTIONS
The double phase representation for the elastic scattering amplitude A(s,t,u) as a function of the covariant Mandelstam variables s, t, and u is discussed. Conditions for the existence of the double representation, and their implications, are examined. The asymptotic forms of this double phase representation when some of s, t, and u become infinite are derived in the case when the phase approaches the limit at infinity not too slowly. This is the case when the elastic scattering anrplitude exhibits asymptotically a power behavior in energy (usually called the Regge behavior). In particular, the case when the forward peak of high-energy elastic scattering does not shrink is examined closely. No-shrinkage is found to be the case when the phase in the crossed channel does not diverge logarithmically at infinity in its momentum-transfer plane. If the forward peak shrinks, the above phase diverges logarithmically at infinity ln the case of no-shrinkage, the asymptotic shape of the forward peak is determined solely by the phase in the crossed channel. Furthermore, the above shape assumes a pure exponential function of the covariant momentum-transfer squared when momentum-transfer is small, and approaches a power behavior in the same variable for large momentumtransfer. Some of the specific predictions of the phase representation approach to high-energy elastic scattering are listed. (auth)
- Research Organization:
- Purdue Univ., West Lafayette, IN (United States); Chicago. Univ. Enrico Fermi Inst. for Nuclear Studies; Chicago. Univ.
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AT(11-1)-264
- NSA Number:
- NSA-17-034737
- OSTI ID:
- 4664549
- Report Number(s):
- TID-19142
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-63
- Country of Publication:
- United States
- Language:
- English
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