The Reference Scattering State

The reference scattering state can be chosen as a distorted wave (with any level of distortion) or as a free wave, as long as it is regular at the origin and is an eigenstate of the asymptotic Hamiltonian, Ho — lirnH oo H Groenenboom et al 

With this level of distortion, the reference scattering state is the product of a translational state, a vibrational state, and a rotational state  

For the translational function, we choose the spherical Hankel function of the second kind /ip (a ) [45]. properly normalized to give unit incoming flux  

This follows from the fact that the SF and BF angles of r transform via 

It may seem that we are using a two angle rotation, which is inconsistent with the construction of the BF Hamiltonian. In fact, we eventually use a three angle rotation, applying the third rotation trivially as the hnal step in the derivation. 

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