Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomoment. II

The discrete spectrum of multiparticle Hamiltonians $H_0$ of neutral systems in a homogeneous magnetic field is studied at a fixed pseudomoment. A general theorem is proved, which describes the discrete spectrum of $H_0$ under certain conditions in terms of constructed effective one-dimensional differential operators with a known spectrum structure. Based on this theorem, the conditions for a finite or infinite spectrum and the spectral asymptotic forms of the operator $H_0$ are obtained. The results can be applied to Hamiltonians of any atoms.