Quasielastic Rayleigh Scattering in Nematic Liquid Crystals

VOLUME 2$, NUMBER 4 PHYSICAL REVIEW LETTERS Veneziano's, although we do not obtain an explicit form. We do not need any restriction stronger than (3) in deriving the correct asymptotic behavior with u fixed. A stronger restriction might be imposed if one requires the good behavior along the real axis. 4 It is necessary for the purpose of physical application to polish our representation so as to validate the asymptotic behavior along the real axis. But we believe that the present formula will be the first step towards constructing more realistic formulas with nonlinear trajectories. The present representation reduces to the beta function in the limit of a linear trajectory AQ. =0. It is straightforward to construct an analog to the Lovelace-Veneziano formula' out of our formula. Since we have introduced widths into resonances, we are in a position to impose elastic unitarity and to fix partly the ambiguity of adding satellites. But the present formula is still imperfect in that the degeneracy is not resolved completely among masses or total widths. The author is grateful to H. Sugawara for help- 28 Juav 1969 ful comments and to K. Kikkawa for useful correspondence. |G. Veneziano, Nuovo Cimento 57A, 190 (1968). We have assumed, in accord with (3), a once-subtracted dispersion relation for e(s) with a linear dependence in front. The restriction will turn out to play an important role later in deriving the Regge behavior. In this connection see R. Z. Roskies, Phys. Rev. Letters 21, 1851 (1968), 3A class of functions satisfying (5) is sometimes called van der Corput's neutralizer. See, for example, E. T. Copson, Asymptotic Uni- is to improve the behavior at the essential singularities a=0 and 1. dispensable ~ +oo This milder behavior at z=0 and 1 is inin deriving the Regge behavior as Ret 4 is also likely that a modification may be necessary for the neutralizer f(z), 5C. Lovelace, Phys. Letters 28B, 265 (1968). 4It ERRATA BROKEN-DUALITY MODEL FOR THE REACTION PP —m'd. V. Barger and C. Michael [Phys. Rev. Letters 22, 1330 (1969)]. The data at 21. 1 GeV/c attributed to Allaby et al. (Ref. 2) were taken from a preliminary ver- sion of the paper. The residue parameters of Eq. (6) obtained from a fit to the data as given in the published version are a(N ) = -0.94, a(N&) =8. 7, b(N ) =-1.40, and b(N&)=0. 23. QUASIELASTIC RAYLEIGH SCATTERING IN NEMATIC LIQUID CRYSTALS. Orsay Liquid Crystal Group [Phys. Rev. Letters 22, 1361 (1969)]. The three textual mentions of Ref. 1 on page 1363 (lines 17 and 24 of the first column, and line 2 of the second column) are erroneous; they should read "Ref. 3. " 208 Expansion (Cambridge versity Press, London, England, 1965), p. 24. Why we use (6) instead of the more familiar form