Using 980 fb(-1) of data collected on and around the Upsilon(nS) (n = 1, 2, 3, 4, 5) resonances with the Belle detector at the KEKB collider, we measure the cross section of e(+) e(-) -> eta phi from threshold to 3.95 GeV via initial state radiation. There are clear phi(1680) and J/psi signals but no significant phi(2170) signal in the eta phi final state.
The branching fraction B[J/psi -> eta phi] is measured to be (7.2 +/- 0.8 +/- 0.5) x 10(-4). The resonant parameters of phi(1680) are determined to be m(phi(1680)) = (1696 +/- 8 +/- 10) MeV/c(2) (statistical and systematic errors, respectively), Gamma(phi(1680)) = (175 +/- 13 +/- 16) MeV and, depending on the possible presence of predominantly constructive or destructive interference between phi(1680) and continuum production, Gamma(e+e-)(phi(1680))center dot B[phi(1680) -> eta phi] and B[phi(1680) -> eta phi] are determined to be (75 +/- 10 +/- 11) eV and (25 +/- 12 +/- 2)% or (207 +/- 16 +/- 20) eV and (23 +/- 10 +/- 2)%, respectively.
The upper limit for Gamma(e+e-)(phi(2170)) center dot B[phi(2170) -> eta phi] is determined to be either 0.17 or 18.6 eV at the 90% confidence level.