  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.
