  The goal of the present work is to obtain a reliable estimate of the masses
of the ground and radially excited states of fully-heavy tetraquark systems. In
order to do this, we use a nonrelativistic model of tetraquarks which are
assumed to be compact and consist of diquark-antidiquark pairs. This
nonrelativistic model is composed of Hulthen potential, a linear confining
potential and spin-spin interaction. We computed ground, first, and second
radially excited $cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$ tetraquark masses.
It was found that predicted masses of ground states of $cc\bar{c}\bar{c}$ and
$bb\bar{b}\bar{b}$ tetraquarks are significantly higher than the thresholds of
the fall-apart decays to the lowest allowed two-meson states. These states
should be broad and are thus difficult to observe experimentally. First
radially excited states are considerably lower than their corresponding (2S-2S)
two-meson thresholds. We hope that our study may be helpful to the experimental
search for ground and excited $cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$
tetraquark states.
