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In this paper we discuss a novel procedure for constructing clusters of boundparticles in the case of a quantum integrable derivative delta-function Bosegas in one dimension. It is shown that clusters of bound particles can beconstructed for this Bose gas for some special values of the coupling constant,by taking the quasi-momenta associated with the corresponding Bethe state to beequidistant points on a single circle in the complex momentum plane. We alsoestablish a connection between these special values of the coupling constantand some fractions belonging to the Farey sequences in number theory. Thisconnection leads to a classification of the clusters of bound particlesassociated with the derivative delta-function Bose gas and allows us to studyvarious properties of these clusters like their size and their stability underthe variation of the coupling constant.

Clusters of bound particles in the derivative delta-function Bose gas