The problem of a condensate of a relativistic neutral vector boson gasconstituted of particles bearing a magnetic moment is discussed. Such a vectorboson system is expected to be formed either by parallel spin-pairing ofneutrons in a sufficiently strong magnetic field, or by neutral atoms underspecific conditions of magnetic field strength and density. A strongself-magnetization arises due to a Bose-Einstein-like condensation. Then thesystem, which may resemble the superfluid said to exist in the core of neutronstars, becomes more unstable under transverse collapse than the ordinaryfermion gas. In the nonrelativistic limit of laboratory conditions, an analogywith the behavior of exploding Bose-Einstein condensates for critical values ofmagnetic field strength and particle density; reported by several authors, isbriefly discussed.
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