B. D. DAY 1 t12+ ~13 2 (t12+ 41S)l23 t12(18+ 3 Kg 2($34$ (9) ACKNOWLEDGMENT I am grateful to B. H. Brandow for his suggestion This is the correct result, and it has been obtained of a simple derivation of such results as Eq. (9). here much more easily than in previous work. "' This idea led directly to the results of this note. *Work performed under the auspices of the U. S. Atomic Energy Commission. ~K. A. Brueckner and J. L. Gammel, Phys. Rev. 109, 1023 (1958); 109, 1040 (1958). 2J. Goldstone, Proc. Roy. Soc. (London) A239, 267 (1957) . . ~B. D. Day, Rev. Mod. Phys. 39, 719 (1967}. 4B. H, Brandow, Phys. Rev. 152, 863 (1969). 5E. Feenberg, Theory of Quantum Eluids (Academic, New York, 1969); Am. J. Phys. 38, 684 (1970). J. W. Clark and P. Westhaus, Phys. Bev. 141, 833 (1966). 7 The reaction-matrix treatment of the many-boson system has recently been worked out by B. H. Brandow, Phys. Rev. Letters 22 173 (1969); Ann. Phys. (¹Y. ) (to be published). S. -O. BKckman, D. A. Chakkalakal, and J. W. Clark, Nucl. Phys. A130, 635 (1969). 9C. W. Wong, Phys. Bev. C3, 1058 (1971). ~OH. -K. Sim, C. -W. Woo, and J. R. Buchler, Phys. Bev. Letters 25, 1094 (1970); Phys. Rev. A 2, 2024 (1970); H. -K. Sim and C. -W. Woo, ibid. ~2 2032 (1970). ~B. D. Day, Phys. Rev. 151, 826 (1966). B. D. Day, Phys. Rev. 187, 1269 (1969). ~3F. Y. Wu and E. Feenberg, Phys. Rev. 128, 943 (1962). M. W. Kirson, Nucl. Phys. A99, 353 (1967). ~5G. V. Chester and L. Beatto, Phys. Letters 22, 276 (1966); L. Reatto and G. V. Chester, Phys. Rev. 155, 88 (1967); W. P. Francis, G. V. Chester, and L. Reatto, Phys. Rev. A 1, 86 (1970). ~6See, e. g. , K. A. Brueckner and K. Sawada, Phys. Rev. 106, 1117 (1957). PHYSICAL REVIEW A VOLUME 4, NUMB ER 2 AUGUST 1971 Collective Effects in the Optical Absorption of Diatomic Molecules in Simple Liquids* M. Gillant and J. Woods Halley ~~&ool of I'&p»~s University of Minnesota, Minneapolis, Minnesota 55455 (Received 9 November 1970) We develop a theory of optical absorption of a diatomic molecule in a simple monatomic liquid. Using approximations appropriate to the case of a light molecule like H2, we show that the absorption spectrum near an infrared-inactive vibrational transition of the molecule can be interpreted to give information about collective effects in the fluid. W'e show that some features of existing experimental results on H2-Ar mixtures are consistent with the theory, although no direct evidence of collective effects is seen in these experiments. I. INTRODUCTION A primary motivation for the study of optical properties of liquids is the possibility that collective properties of the liquid may be studied optically. This possibility has recently been realized in Ra- man scattering experiments, ' but no collective ef- fects have yet been identified in optical absorption spectra in liquids. In an earlier study we showed that sidebands analogous to those seen in intrinsic optical absorption in solids would not be observed in optical absorption in pure liquids, and hence that phonons in liquids could not be studied by this meth- od as they are in solids. The physical reason for this result is the following: In an insulating solid, when the electron-phonon coupling is weak, the one- exciton no-phonon peak is narrow because absorp- tion takes place only into the k = 0 exciton mode. In a liquid, even if the coupling is weak, the one-exci- ton peak will be greatly broadened because in the weak-coupling limit the excitons cannot be charac- terized by a k vector. The absorption correspond- ing to the one-exciton peak in a solid is then broad- ened in a liquid because absorption takes place into many exciton modes corresponding to various solu- tions of the exciton problem in a system of amor- phously distributed fixed sites. The bandwidth of this spectrum of solutions is of the order of the transfer rate of excitations from site to site through the Coulomb interactions between electronic states on different sites. In liquid helium both theory and experiment indicate that this width is of the order of a few tenths of an electron volt. Thus, the one- exciton peak is broadened to swamp the phonon side-