Direct Nuclear Reactions

Notational Conventions

antisymmetrization operator

A, a

intrinsic coordinates of nucleus A and a, respectively, of which there are 3(A ?1) and 3(a ?1)

?, ??, ??

different channels in the partition ?, with ? denoting either a typical channel or the ground state channel and ??, ?? channels in which one, the other, or both of nuclei a or A is excited

?, ?,

frequently used to denote different two-body partitions a+A, b+B, , of a many-nucleon system

B, b

similar to A, a, but for nuclei B and b

optical model wave function in channel ? in which the relative motion is distorted by an optical potential (the asymptotic condition of outgoing (+) or incoming ( ?) waves is indicated)

E

eigenvalue of H, eigenfunction ?, or

E ?

kinetic energy in channel ?, eigenvalue of T ? , eigenfunction of exp( i k ? r ?) (E ? =E ?? ? )

? ?

eigenvalue of H ?, eigenfunction ? ?, and where ? A and ? a are eigenvalues of H A and H a with eigenfunction ? A and ? a ( ? ?= ? A+ ? a)

H

total Hamiltonian of the A+a=B+b many-nucleon system, ordered in terms of various partitions (H=H ? +T ? +V ?

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