Search for specific chemical signatures of intermittent dissipation of turbulence in diffuse molecular clouds . We observed HCO ^ { + } ( 1-0 ) lines and the two lowest rotational transitions of ^ { 12 } CO and ^ { 13 } CO with an exceptional signal-to-noise ratio in the translucent environment of low mass dense cores , where turbulence dissipation is expected to take place . Some of the observed positions belong to a new kind of small scale structures identified in CO ( 1-0 ) maps of these environments as the locus of non-Gaussian velocity shears in the statistics of their turbulent velocity field i.e . singular regions generated by the intermittent dissipation of turbulence . We report the detection of broad HCO ^ { + } ( 1-0 ) lines ( 10 { mK } < { T _ { A } ^ { * } } < 0.5 K ) . The interpretation of 10 of the HCO ^ { + } velocity components is conducted in conjunction with that of the associated optically thin ^ { 13 } CO emission . The derived HCO ^ { + } column densities span a broad range , 10 ^ { 11 } < N ( { HCO ^ { + } } ) / \Delta v < 4 \times 10 ^ { 12 } { cm } ^ { -2 } /km s ^ { -1 } , and the inferred HCO ^ { + } abundances , 2 \times 10 ^ { -10 } < X ( { HCO ^ { + } } ) < 10 ^ { -8 } , are more than one order of magnitude above those produced by steady-state chemistry in gas weakly shielded from UV photons , even at large densities . We compare our results with the predictions of non-equilibrium chemistry , swiftly triggered in bursts of turbulence dissipation and followed by a slow thermal and chemical relaxation phase , assumed isobaric . The set of values derived from the observations , i.e . large HCO ^ { + } abundances , temperatures in the range of 100–200 K and densities in the range 100–10 ^ { 3 } { cm } ^ { -3 } , unambiguously belongs to the relaxation phase . The kinematic properties of the gas suggest in turn that the observed HCO ^ { + } line emission results from a space-time average in the beam of the whole cycle followed by the gas and that the chemical enrichment is made at the expense of the non-thermal energy . Last , we show that the ” warm chemistry ” signature ( i.e . large abundances of HCO ^ { + } , CH ^ { + } , H _ { 2 } O and OH ) acquired by the gas within a few hundred years , the duration of the impulsive chemical enrichment , is kept over more than thousand years . During the relaxation phase , the H _ { 2 } O /OH abundance ratio stays close to the value measured in diffuse gas by the SWAS satellite , while the OH/ HCO ^ { + } ratio increases by more than one order of magnitude .