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5.5 Partial wave expansion

The form factors may be written in a partial wave expansion in the variable . We consider a definite isospin state. Suppressing isospin indices, one has [56,57]

 

where

 

The partial wave amplitudes and depend on and . Their phase coincides with the phase shifts in elastic scattering (angular momentum l, isospin I). More precisely, the quantities

 

are real in the physical region of decay. The form factors and therefore have a simple expansion

 

On the other hand, the phase of the projected amplitudes

 

is not given by , e.g., is not real in the isospin one case. A similar remark applies to .



Carlos E.Piedrafita