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I analyze the low temperature limit of the BCS theory of s-wave single-bandsuperconductors, when the attraction band may be asymmetric with respect to thechemical potential. I discuss equilibrium systems, taking consistently intoaccount the variation of the energy and of the total number of particles withthe populations of the quasiparticle energy levels. I show that the equationfor the energy gap has two solutions, one of which is stable and the other oneis metastable. When the chemical potential is the center of the attraction band(the standard BCS assumption), the energy gap in the stable solution is$\Delta_0$, whereas in the metastable one is $\Delta_0/3$. If the chemicalpotential is not in the center of the attraction band, then a quasiparticleimbalance appears. If the absolute value of the difference between the chemicalpotential and center of the attraction band is bigger than $2\Delta_0$, thenthe superconducting energy gap cannot be formed. If the number of particles isconserved and the attraction band is asymmetric, then the stable solution isunphysical and only metastable solutions are realized.

New phenomenology from an old theory--new equilibrium states in the BCS model