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A generalized Morse potential is constructed which describes the interaction of two excitons located near the boundary of the polar crystal and the vacuum. c)n the basis of this potential the first vibrational and rotational levels of the s u rface biexciton a r e estimated.

The Angular Dependences of Two-Photon Transitions to Surface States A.I. BOBRYSHEVA, S.A. MOGKALENKO, andV.T. ZYUKOV BYThe angular dependences of two-photon absorption intensities of polarized beams due to allowed transitions from the totally symmetric ground state of an insulating crystal to excited surface states have been calculated. Any of the sutface states is characterized by an irreducible representation of ten two-periodical point groups. The case is considered when the top of the valence band and the minimum of the conduction band is at the centre of the Brillouin zone and direct band-to-band dipole transitions take place at this point. These angular dependences hold for band-to-band, exciton, and biexciton transitions.Recently surface excitons have been detected in GaAs /l/, Si /2/, ZnO /3/ by means of photoemission spectroscopy. Additional information about properties of surface excitons can be obtained by conventional optical methods / 4 / .On the ground of group-theoretical analysis the polarization dependence of the absorption coefficient due to one-photon transitions to surface states located on the (111) plane of Si was established /5/.

The oscillator strengths are calculated for one-and two-photon absorption by surface state Wannier excitons. The model of two surface bands is used, and excitons and electron-hole pairs a c t as intermediate states. The cases of direot allowed and forbidden dipole transitions are investigated. Numerical calculations of the ratios of two-and one-photon oscillator strengths are performed for (100) GaAs. Es werden die Oszillatorstiirken fur Ein-und Zwei-Photonenabsorption durch Wennier-Exzitonen-Oberfliichenzustiinde berechnet. Das Model1 von zwei Oberflachenbandern wird benutzt, und die Exzitonen und Elektronen-Lochpaare wirken als Zwischenzustiinde. Die Falle von direkten erlaubten und verbotenen Dipolubergangen werden untersucht. Numerische Rechnungen der Verhaltnisse von Zwei-und Ein-Photonen-Oszillatorstarken werden fiir (100) GaAs durchgefuhrt.

The Fourier transform ~( p )of the exciton-exciton interaction energy is derived. The excitons are situated in a semiinfinite polar crystal near the surface. The character of the interaction depends essentially on the symmetry of the spin functions under the permutation of identical particles. On the base of v ( p ) the shift of the surface exciton level with increasing exciton density n,, is obtained. The numerical value is listed for GaAs. The effective Hamiltonian of surface excitons interacting through exchange by virtual surface longitudinal optical phonons is derived. Es wird die Fouriertransformierte v(p) der Exziton-Exziton-Wechselwirkungsenergie abgeleite t.Die Exzitonen befinden sich in einem halbunendlichen polaren Kristall in der Nahe der Ober. flsche. Der Charakter der Wechselwirkung hangt wesentlich von der Symmetrie der Spinfunktionen unter Permutation identischer Teilchen ab. Mittels ~( p ) wird die Verschiebung des Niveaus der OberflLchenexzitonen mit wachsender Exzitonendichte aeX erhalten. Der numerische Wert fur GaAs wird mitgeteilt. Der effektive Hamiltonian der Oberflachenexzitonen, die iiber Austausch mit virtuellen longitudinalen optischen Oberflachenphononen wechselwirken, wird abgeleitet.