# Bounds On Scattering Phase Shifts for Compound Systems

Bounds On Scattering Phase Shifts for Compound Systems
Tony Randall
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Xi^(i)^dT. (2. 1) vhere q. Is the distance between neutron i and the center of mass of the nucleus which consists of all the particles except neutron i. F. Is the ground state wave function of this nucleus, ^ is the full scattering wave function^ and X „ (i) is the spin function for neutron i. The integral is DO z over all coordinates except q. , and is understood to represent a siimmation over all spin indices as well. The phase shift is defined by treating g(q. ) as a one body wave function a...nd applying one of the standard defini- tions of the phase shift for static potential scattering, namely T^ = lim ( mjt - kq. I m — > oo (m) where q_^^ is the m'th zero in g(q. ) We note that from the relation ? — > const Xjj^(i)F. Sin(kq_^ + ■(]) / q.
22 1 J- J- it follows that g(q.^, ) — > const sin(kq_^, + t\) as qi. — > oo which guarantees that r\ modulo it as defined by Eq, (2. 1) is correct.
An Application: Triplet Electron Hydrogen Scattering It has been stressed that for the purposes of obtaining a bound, the question of the justification of our definition of the phase shift does not arise.

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