  The quantum dynamics of a localized spin-$\frac{1}{2} $ Particle interacting
with an absorbing environment is investigated. The quantum
Langevin-Schr\"odinger equation for spin-$\frac{1}{2} $ is obtained. The
susceptibility function of the environment is calculated in terms of the
coupling function of the spin and the environment. it is shown that the
susceptibility function satisfies the Kramers-Kronig relations. Spontaneous
emission and the shift frequency of the spin is obtained in terms of the
imaginary part of the susceptibility function in frequency domain. Some
transition probabilities between the spin states are calculated when the
absorbing environment is in the thermal state.
