Excitation Amplitudes and Density Matrix of Excited Atoms

Excitation Amplitudes and Density Matrix of Excited Atoms 

In an ideal experiment the excited atoms are prepared in pure states characterized by a wave function 

In a realistic experiment often the initial state of the collision system is not completely determined or the final state of the projectile which caused the excitation is not observed. Since the amplitudes /m may depend on these quantities, the excited atoms in these cases cannot be characterized by a pure state but must be described by a density matrix p = 1 )(, the elements of which are averaged products of excitation amplitudes 

In connection with the observation of angular distributions it is convenient to expand the density matrix in terms of irreducible spherical tensors by writing 

For the tensor components pi of the density matrix this yields 

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