Stronger constraints for nanometer scale Yukawa-type hypothetical interactions from the new measurement of the Casimir force

Hypothetical interactions of Yukawaand power-types have been discussed actively in recent years (for a collection of references on this subject, see [1]). They may be considered as specific corrections to the classical gravitational force at small distances [2]. An alternative interpretation comes from the elementary particle physics. According to the unified gauge theories, supersymmetry and supergravity [3], there would exist a number of light or massless elementary particles (for example, axion, scalar axion, graviphoton, dilaton, arion, and others). The exchange of such particles between two atoms gives rise to an interatomic force described by Yukawa or power-law effective potentials. The interaction range of this force is to be considered from one angström to hundreds of kilometers. Because of this, it is called a “long-range force” (in comparison with the nuclear size). The constraints for the constants of these hypothetical long-range interactions lead to new knowledge about the parameters of associated elementary particles. Such constraints are obtainable from Galileo-, Eötvösand Cavendishtype experiments, from the measurements of the van der Waals and Casimir force, transition probabilities in exotic atoms, etc [4]. The pioneering studies in the application of the Casimir force measurements to the problem of long-range interactions were made in Refs. [5–7]. There it was shown that the Casimir effect leads to the strongest constraints on the constants of Yukawa-type interactions with a range of action of 10−8 m < λ < 10−4 m [4,5,7]. In the beginning of 1997 the results on the demonstration of the Casimir force between the metallized surfaces of a flat disc and a spherical lens were published [8]. The absolute error of the force measurements was ∆F ≈ 10−11 N for distances between the disc and the lens from one to six micrometers. This corresponds to the relative error of approximately 5% at the smallest surface separation. Some tentative conclusions from experimental observations of [8] were made in [9,10] concerning the possible constraints on long-range interactions. The detailed and accurate analyses of constraints following from [8] was given in [11] for both Yukawaand power-type interactions with account of all different corrections to the Casimir force. It was established that the constraints for Yukawa-type interactions following from [8] are the best ones within a range 2.2 × 10−7 m ≤ λ ≤ 1.6× 10−4 m. The fact was emphasized that they surpass the previously known constraints in this range up to factor of 30.