We present a theoretical and experimental study on the transfer of angular momentum from a light beam to a nematic liquid crystal film. In the angular momentum transfer process photons are not destroyed, but scattered in a different angular momentum state: a process known as self-induced stimulated light scattering (Santamato E, Daino B, Romagnoli M, Settembre M and Shen Y R 1988 Phys. Rev. Lett. 61 113-16). Each photon in the incident beam transfers to the material only the change of its angular momentum, producing a torque on the body. Under the action of this torque, the body starts to rotate, changing, in turn, the amount of angular momentum extracted from the light beam. The process is intrinsically nonlinear and, as proved by the experiments reported in this paper, it can be initiated by a light beam carrying no angular momentum at all.

The cross section for one-electron transfer H − + He + → H(1s) + He * (1s, nlm) is calculated in this paper. The collisional system is treated as a three-electron one and matrix elements for the formation of excited helium He * (1s, nlm) in both singlet and triplet states (1S, 2 1,3 S, P and 3 1,3 S, P, D) are obtained. Close-coupling calculations were done for the 27 1s, nlm| (1S, 2 1,3 S, P and 3 1,3 S, P, D) final states covering the range 1-10 × 10 7 cm s −1 of the relative collision velocity. An approximation is used for the effective potential of H − and Coulomb Green's functions are used to describe the weakly bound electron of H − . A satisfactory agreement is obtained with the experimental cross section.

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The authors solve the competition problem for two enterprises. The problem reduces to an antagonistic dynamic game on a fixed time interval with a convex compact objective set. The problem is solved in the interests of one enterprise. The set of initial positions is constructed, for which an enterprise necessarily attains the objective at a given finite instant of time under the worst behavior of the competitive enterprise.

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