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The young planetary system {\beta} Pictoris is surrounded by a circumstellardisk of dust and gas. Because both dust and gas have a lifetime shorter thanthe system age, they need to be replenished continuously. The gas compositionis partly known, but its location and its origin are still a puzzle. The gassource could be the exocomets (or so-called falling and evaporating bodies,FEBs), which are observed as transient features in absorption lines ofrefractory elements (Mg, Ca, and Fe) when they transit in front of the star atseveral tens of stellar radii.  Nearly 1700 high-resolution spectra of {\beta} Pictoris have been obtainedfrom 2003 to 2015 using the HARPS spectrograph. In these spectra, thecircumstellar disk is always detected as a stable component among the numerousvariable absorption signatures of transiting exocomets.  Summing all the 1700 spectra allowed us to reach a signal-to-noise ratiohigher than 1000, which is an unprecedentedly high number for a {\beta}Pictoris spectrum. It revealed many weak Fe I absorption lines of thecircumstellar gas in more than ten excited states. These weak lines bring newinformation on the physical properties of the neutral iron gas in thecircumstellar disk. The population of the first excited levels follows aBoltzmann distribution with a slope consistent with a gas temperature of about1300 K; this temperature corresponds to a distance to the star of ~ 38 RStarand implies a turbulence of {\xi} ~ 0.8 km/s.

Fe I in the {\beta} Pictoris circumstellar gas disk I. Physical properties of the neutral iron gas