Isospin susceptibility in the O(n) sigma-model in the delta-regime

We compute the isospin susceptibility in an effective O(n) scalar field theory (in d = 4 dimensions), to third order in chiral perturbation theory (chi PT) in the deltaregime using the quantum mechanical rotator picture. This is done in the presence of an additional coupling, involving a parameter eta, describing the effect of a small explicit symmetry breaking term (quark mass). For the chiral limit eta = 0 we demonstrate consistency with our previous chi PT computations of the finite-volume mass gap and isospin susceptibility. For the massive case by computing the leading mass effect in the susceptibility using chi PT with dimensional regularization, we determine the chi PT expansion for eta to third order. The behavior of the shape coefficients for long tube geometry obtained here might be of broader interest. The susceptibility calculated from the rotator approximation differs from the chi PT result in terms vanishing like 1=l for l = Lt/Ls -> infinity. We show that this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant.