Results: We report the detection of broad HCO+(1-0) lines (10 mK < T < 0.5 K). The interpretation of 10 of the HCO+ velocity components is conducted in conjunction with that of the associated optically thin 13CO emission. The derived HCO+ column densities span a broad range, $10^{11}< N(HCO+)/Delta v <4 times 10^{12} rm cm^2/(km/s^{-1}$, 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--1000 cm3, 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+, H20 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 wat/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.
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