Cubic anharmonicity and strong sidebands: An experimental test for vibrational phase relaxation at surfaces?

For a localized vibration of linearly bonded adsorbate with displacement coordinate u interacting with a substrate atom of coordinate v, we propose a new dephasing contribution to the vibrational linewidth arising from the cubic term $u^2$v by going to fourth-order perturbation theory. Such a contribution is shown through a specific example to be equally as important as the leading-order dephasing contribution of the quartic term $u^2$ $v^2$, which has been considered by others. It is shown that this cubic term produces much stronger sidebands than the quartic term; it is suggested that this fact may be used in some cases to verify or eliminate phonon dephasing as the linewidth mechanism.