PhysicsLettersA 171 (1992) 349—354 PHYSICS LETTERS A North-Holland High-frequency asymptotics of optical activity and energy difference of chiral molecules LB. Khriplovich’ and M.E. Pospelov 2 Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russian Federation Received 6 October 1992; accepted for publication 26 October 1992 Communicated by V.M. Agranovich The asymptotics of optical activity n÷ — n_ at co ~ Ry are co ‘ for oriented chiral molecules and crystals, and as ~ for isotropic media of chiral molecules and polycrystals. However, with a further increase of cv both fall-offs change to cv 3 due to spin—orbit interaction. The expectation value in the numerator ofthe last asymptotics practically coincides, up to an overall factor, with that of the weak interaction responsible for the P-odd energy difference of right- and left-handed molecules. 1. Introduction Optical isomers are molecules or crystals that are mirror images of one another. An isotropic medium ac- quires optical activity (OA) when the concentration of an optical isomer of one sign exceeds that of the isomer of opposite sign. We will investigate the asymptotics of OA, i.e., of the rotation of the polarization plane of light, at frequencies w>~ Ry, where Ry= ~ ma~ = 13.6 eV is the characteristic atomic energy. The refraction index n(w) is related to the forward-scattering amplitudef(w) through the well-known formula (1) where N/V is the concentration. The usual asymptotics of the refraction index is determined by the Thomson amplitudef= — a/rn. Optical activity is caused by the term inf(a)) linear in the degree of circular polarization: 2= —i(e~xe)~n-+iabeae~. (2) Here e is the photon polarization, n is the unit vector of its momentum. The last form of this equation cor- responds to the choice of the direction n along the axis 3. Then a, b=l, 2, ab= Cba, ~12=l. Substituting the photon density matrix for the product of its polarizations, eae~—+pab=~(ôab—12eab) , (3) one easily gets the 2-dependent scattering amplitude 2a . (<lIpbe_zlk><kIpae~wzIl> <lIpa&Ik><kIpbe~’°~I1> Ji(W)=j1Eab~l — . (4) 2m O)—Wkl Here Pa,b are the electron momentum operator components, and Wkl is the frequency of the transition from the initial state 1 to the intermediate one k. Obviously, the amplitude f~ is an odd function of frequency. E-mail: khriplovich@inp.nsk.su. 2 E-mail: pospelov@inp.nsk.su. Elsevier Science Publishers B.V. 349