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We present a semiclassical laser-coling theory for an ion bound in a quadratic otential well, allowing for an arbitray internal level scheme of the ion and an arbitrary polarization of the light field. The special case that the ion moves in a region much smaller than the wavelength of the exciting light (Lamb-Dicke limit), as well as an additional low-intensity limit, are worked out in detail. Explicit general expressions are given for the damping and diffusion tensors of the center-of-mass motion of the ion, and the light-induced renormalization of the mechanical oscillation freuencies is discussed. The formalism is implemented analytically by using a computer program Mathematica for an ion with a j = 1/2 -> j = 3/2 transition moving in a one-dimensional optical molasses consisting of two counterpropagating laser beams with perpendicular linear polarizations (lin perp lin). For a weakly bound ion at neglibile saturation, the greatest lower limit of excitation energy turns out to be (33/20)^1/2 ~ 0.78 vibrational quanta above the zero-point energy.
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