Search for η<i>_c</i>(2<i>S</i>) → 2(π<SUP>+</SUP> π<SUP>-</SUP>) and improved measurement of χ<i>_cJ</i> → 2(π<SUP>+</SUP> π<SUP>-</SUP>)

We search for the hadronic decay eta(c)(2S) -> 2(pi(+) pi(-)) in the psi(3686) -> gamma eta(c)(2S) radiative decay using (27.12 +/- 0.14) x 10(8) psi(3686) events collected by the BESIII detector at the BEPCII collider. No significant signal is found, and the upper limit of B[psi(3686) -> gamma eta(c)(2S)]B[eta(c)(2S) -> 2(pi(+) pi(-))] is determined to be 1.43 x 10(-6) at the 90% confidence level. Using psi(3686) -> gamma chi(cJ) transitions, we also measure the branching fractions of B[chi(cJ(J=0,1,2)) -> 2(pi(+) pi(-))], which are B[chi(c0) -> 2(pi(+) pi(-))] = (2.127 +/- 0.002(stat) +/- 0.101(syst))%, B[chi(c1) -> 2(pi(+) pi(-))]=(0.685 +/- 0.001(stat) +/- 0.031(syst))%, and B[chi(c2) -> 2(pi(+) pi(-))] = (1.153 +/- 0.001(stat) +/- 0.063(syst))%.