  We discuss a possible spectral realization of the Riemann zeros based on the
Hamiltonian $H = xp$ perturbed by a term that depends on two potentials, which
are related to the Berry-Keating semiclassical constraints. We find
perturbatively the potentials whose Jost function is given by the zeta function
$\zeta(\sigma - i t)$ for $\sigma > 1$. For $\sigma = 1/2$ we find the
potentials that yield the smooth approximation to the zeros. We show that the
existence of potentials realizing the zeta function at $\sigma = 1/2$, as a
Jost function, would imply that the Riemann zeros are point like spectrum
embedded in the continuum, resolving in that way the emission/spectral
interpretation.
