Non-universal critical Casimir force in confined 4He near the superfluid transition

We present the results of a one-loop calculation of the effect of a van der Waals type interaction potential ∼ vertical bar x vertical bar-d-σ on the critical Casimir force and specific heat of confined 4He near the superfluid transition. We consider a 4He film of thickness L. In the region L < or approx. ξ (correlation length) we find that the van der Waals interaction causes a leading non-universal non-scaling contribution of O(ξ2L-d-σ) to the critical temperature dependence of the Casimir force above Tλ that dominates the universal scaling contribution ∼e-L/ξ predicted by earlier theories. For the specific heat we find subleading non-scaling contributions of O(L-1) and O(L-d-σ)