The homogeneous vibrational line shape of an adatom on a surface is de
termined by its interactions with other localized and delocalized mode
s of the adsorbate and substrate. These interactions include anharmoni
c bonds between the adatom and the surface, and also between the subst
rate atoms themselves at the adsorption site. The line width and frequ
ency shift of the perpendicular vibrational mode of an adatom at a bri
dge site is calculated as a function of temperature, due to coupling t
o phonon modes of a semi-infinite elastic continuum. A self energy for
mulation is employed, using perturbative methods in a quantum field th
eory. The effects of anharmonicity of both the adsorption bonds and of
the interatomic bonds between substrate atoms at the bridge site, on
the vibrational line shape, are compared. Energy relaxation by two-pho
non emission is found to describe well the temperature-dependent line
width in the O/Cu(110) system.