  QCD theory predicts the existence of glueballs, but so far all experimental
endeavors have failed to identify any such states. To remedy this discrepancy
between QCD, which has proven to be a successful theory for strong
interactions, and the failure of experimental searches for glueballs, one is
tempted to accept the promising interpretation that the glueballs mix with
regular $q\bar q$ states of the same quantum numbers. The lattice estimate of
the masses of pure $0^{++}$ glueballs ranges from 1 to 2 GeV, which is the
region of the $f_0$ family. Thus many authors suggest that the $f_0$ mesonic
series is an ideal place to study possible mixtures of glueballs and $q\bar q$.
In this paper, following the strategy proposed by Close, Farrar and Li, we try
to determine the fraction of glueball components in $f_0$ mesons using the
measured mass spectra and the branching ratios of $J/\psi$ radiative decays
into $f_0$ mesons. Since the pioneering papers by Close et al., more than 20
years has elapsed and more accurate measurements have been done by several
experimental collaborations, so it is time to revisit this interesting topic
using new data. We suppose $f_0(500)$ and $f_0(980)$ to be pure quark states,
while for $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, to fit both the
experimental data of $J/\psi$ radiative decay and their mass spectra, glueball
components are needed. Moreover, the mass of the pure $0^{++}$ glueball is
phenomenologically determined.
