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The paper advances the suggestion by Odake and Sasaki to re-writeeigenfunctions of rationally deformed Morse potentials in terms of Wronskiansof Laguerre polynomials in the reciprocal argument. It is shown that theconstructed quasi-rational seed solutions of the Schrodinger equation with theMorse potential are formed by generalized Bessel polynomials withdegree-independent indexes. As a new achievement we can point to theconstruction of the Darboux-Crum net of isospectral rational potentials usingWronskians of generalized Bessel polynomials with no positive zeros. It wasthen proved that any solvable rational Darboux-Crum transform of the Morsepotential can be re-expressed in terms of Wronskians of the latter polynomialsaccompanied by juxtaposed pairs of Romanovski-Bessel polynomials.

Quantization of rationally deformed Morse potentials by Wronskian transforms of Romanovski-Bessel polynomials