We perform a quark model calculation of the quarkonia bb and
cc spectra using smooth and sudden string breaking potentials. The
screening parameter is scale dependent and can be related to an effective
running gluon mass that has a finite infrared fixed point. A temperature
dependence for the screening mass is motivated by lattice QCD simulations at
finite temperature. Qualitatively different results are obtained for quarkonia
properties close to a critical value of the deconfining temperature when a
smooth or a sudden string breaking potential is used. In particular, with a
sudden string breaking potential quarkonia radii remain almost independent of
the temperature up to the critical point, only well above the critical point
the radii increase significantly. Such a behavior will impact the phenomenology
of quarkonia interactions in medium, in particular for scattering dissociation
processes.Comment: 9 pages, 11 figures. Accepted for publication ijn Eur. Phys. J.