Bound states of the Yukawa potential from hidden supersymmetry

Abstract In this work, we present a phenomenological study of the complete analytical solution to bound eigenstates and eigenvalues Yukawa potential obtained previously using hidden supersymmetry system systematic expansion in terms ? = 0 ?D, where is Bohr radius D screening length. The eigenvalues, ?nl(?), are given form Taylor series which can be systematically calculated desired order ?k. Coulomb l-degeneracy broken by effects and, for n, ?nl(?) larger higher values l causes crossing levels n ? 4. convergence enlarged up critical Padé approximants technique allows us calculate with high precision whole rage states exist, reach precise determination lengths, ?nl. Eigenstates have similar solutions potential, associated Laguerre polynomials replaced new ?k r-dependent coefficients which, turn, r. general find sizable deviations from radial probabilities only lengths close their values. We use these squared absolute value at origin wave function 0, derivatives 1, lowest states, as functions ?, enter phenomenology dark matter gauge theories light mediator.