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Recent experiments announced an observation of topological superconductivityand Majorana quasiparticles in Shiba chains, consisting of an array of magneticatoms deposited on top of a superconductor. In this work we study helical Shibachains and generalize the microscopic theory of subgap energy bands to a regimewhere the decoupled magnetic impurity energy and the hybridization of differentimpurity states can be significant compared to the superconducting gap of thehost material. From exact solutions of the Bogoliubov-de Gennes equation weextract expressions for the topological phase boundaries for arbitrary valuesof the superconducting coherence length. The subgap spectral problem can beformulated as a nonlinear matrix eigenvalue problem from which we obtain ananalytical solution for energy bands in the long coherence length limit.Physical consequences and departures from the previously obtained results inthe deep-dilute impurity limit are discussed in detail.

Topological properties of helical Shiba chains with general impurity strength and hybridization