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Within the self-gravitating Bose-Einstein condensate (BEC) model of darkmatter (DM), we argue that the axionlike self-interaction of ultralight bosonsensures the existence of both rarefied and dense phases in the DM halo core of(dwarf) galaxies. In fact, this stems from two independent solutions of theGross-Pitaevskii equation corresponding to the same model parameters. For asmall number of particles, this structure disappears along with thegravitational interaction, and the Gross-Pitaevskii equation reduces to thestationary sine-Gordon equation, the one-dimensional antikink solution of whichmimics a single-phase DM radial distribution in the halo core. Quantummechanically, this solution corresponds to a zero-energy bound state of twoparticles in a closed scattering channel formed by the domain-wall potentialwith a finite asymptotics. To produce a two-particle composite with lowpositive energy and a finite lifetime, we appeal to the resonant transition ofone asymptotically free particle of a pair from an open channel (with a modelscattering potential) to the closed channel. Using the Feshbach resonanceconcept, the problem of two-channel quantum mechanics is solved in the presenceof a small external influence which couples the two channels, and an analyticalsolution is obtained in the first approximation. Analyzing the dependence ofscattering data on interaction parameters, we reveal a long-lived two-particlecomposite (dimer) possessing a lifetime of millions of years. This result israther surprising and supposes important implications of dimers' being involvedin forming large DM structures. It is shown that the dimers' appearance isrelated with the regime of infinite scattering length due to resonance. Therevealed dependence of the DM scattering length $a$ on the parameters ofinteractions can theoretically justify variation of $a$ in the DM dominatedgalaxies.

Axionlike Dark Matter Model Involving Two-Phase Structure and Two-Particle Composites (Dimers)