The natural or radiative lineshape

The radiation reaction force. We return to a consideration of the classical atomic model which was introduced in sections 4.1 and 4.2. We found that there was a loss of energy in the form of radiation which occurred slow ly over many cycles of the electron s motion. However, this loss of energy was not taken into account in the mechanical equation of motion of the electron. This situation can be remedied by introducing a radiation reaction force, F, such that the work done by the reaction force in one cycle of the oscillation is equal to the energy emitted into the radiation field  

The classical lineshape. The modified equation of motion for the oscillating electron may now be written in the form 

It can be easily shown (Problems 8.1 and 8.2) that the radiation reaction force is small compared with the binding force at the angular frequencies in which we are interested. Thus the equation of motion of the electron oscillator may, to a good approximation, be written in the form 

It follows from equation (2.70) that the electric field radiated by the classical atom has a similar time-dependence  

Since the emitted wave is no longer of infinite extent, it 

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