Upper critical magnetic field HC2 from chemical equilibrium

The fraction of bosons, f(t), is obtained from a standard equilibrium theory in terms of the chemical constant phi (t) by f(t) = 1 - [1 + phi (t)](-1/2). Here t = T/T* and T* is the scaling temperature connected with tile binding energy of bosons 2 Delta by Delta = k(B)T*, independent of magnetic held together with f(t). The transition temperature t(c)(H) is obtained from n(0)f(t,(H)) = n(c)(H) = n(c)(O)[1 + gammaH(mu)], where n(c)(H), the critical density for superconductivity is assumed to be a power law. In the cases where t(0) = t(c)(0) = T-c(0)/T* is small the chemical constant can be approximated by phi (t) = 1/(Pt) and t(c)(H) can be calculated. This is equivalent of knowing H-c2(y), given by H-c2(y) = H-c2(0)[(f(t(0)y) - f(t(0)))/(1 - f(t(0)))](1/mu) y = t(c)(H)/t(c)(0). For several heavy fermions (beta = 13.7 and T* = 150K) data on the quantity mu (-1)ln[H-c2(y)/H-c2(0)] fall on the same curve. For Tl2201 we obtain mu = 2/3 and upwards curvature. In the superfluid state T T,(H) the universal function f becomes magnetic field dependent f = f(S)(T, H). The density of states becomes magnetic field dependent, which explains the low temperature NMR-rate (T-1(H)T)(-1) similar to HP observed experimentally. Contrary to this the NMR-rate is independent of H in the normal state. We predict a specific heat linear term C(T, X)- C(T, 0) similar to THmu /2.