  Raman interaction of a trapped ultracold ion with two traveling wave lasers
has been used extensively in the ion trap experiments. We solve this
interaction in the absence of the rotating wave approximation by a continued
fraction, without considering the restriction of the Lamb-Dicke limit and the
weak excitation regime. Some interesting characteristics of the ion-trap
system, particularly for the ion outside the weak excitation regime are found.
Finally, a comparison of our results with the solution under the rotating wave
approximation is made.
