Bordism of semifree circle actions on Spin manifolds

Using traditional methods in bordism theory, an almost complete description of the rational bordism groups of semifree circle actions on Spin manifolds is given. The single remaining problem, to describe the ideal of $\Omega _ \ast ^{{\operatorname{Spin}}}\, \otimes \,\mathbf{Q}$, generated by bordism classes of Spin manifolds admitting a semifree action of odd type, has been recently solved by S. Ochanine $[\mathbf{O}]$.