  By means of high-resolution spectra we have measured radial velocities of the
companion (hereafter COM J1740-5340) to the eclipsing millisecond pulsar PSR
J1740-5340 in the Galactic globular cluster NGC 6397. The radial-velocity curve
fully confirms that COM J1740-5340 is orbiting the pulsar and enables us to
derive the most accurate mass ratio (M_ PSR/M_COM=5.85+/-0.13) for any
non-relativistic binary system containing a neutron star. Assuming a pulsar
mass in the range 1.3-1.9 Msun, the mass of COM J1740-5340 spans the interval
0.22-0.32 Msun, the inclination of the system is constrained within 56 deg <= i
<= 47 deg and the Roche lobe radius is r_RL ~ 1.5-1.7 Rsun. A preliminary
chemical abundance analysis confirms that COM J1740-5340 has a metallicity
compatible with that measured for other stars in this metal-poor globular, but
the unexpected detection of strong He I absorption lines implies the existence
of regions at T>10,000 K, significantly warmer than the rest of the star. The
intensity of this line correlates with the orbital phase, suggesting the
presence of a region on the companion surface, heated by the millisecond pulsar
flux.
