Bounds On Scattering Phase Shifts for Compound Systems
Bounds On Scattering Phase Shifts for Compound Systems
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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.
What to read after Bounds On Scattering Phase Shifts for Compound Systems?
You can find similar books in the "Read Also" column, or choose other free books by Tony Randall to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after Bounds On Scattering Phase Shifts for Compound Systems?
You can find similar books in the "Read Also" column, or choose other free books by Tony Randall to read onlineMoreLess
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