Abstract
The question of calculating the effective charge for E2 transitions has been quite annoying to the theoretical physicists. In recent years a general theory for the effective transition operators as needed in the nuclear shell model has been formulated (1). The basic idea is to define a model space of dimension d and an operator \({\rm P}\;{\rm ( = }\;\sum\limits_{{\rm i\varepsilon d}} | \;{\rm \phi }_{\rm i} > < {\rm \phi }_{\rm i} |)\) that projects onto this space. Then we can define an operator Q that projects onto the excluded space \(\matrix{ {{\rm Q}\;{\rm = }\;{\rm 1 - P}\;{\rm = }\;{\rm 1}\;{\rm - }\;\mathop \sum \limits_{{\rm i}\varepsilon {\rm d}} |\;{\rm \phi }_{\rm i} > < {\rm \phi }_{\rm i} |\; = \;_{\rm i} \Sigma _{\rm d} |\;{\rm \phi }_{\rm i} > < {\rm \phi |}} & {{\rm where}} & {{\rm |}\;{\rm \phi }_{\rm i} > } \cr } \) are the eigen-functions of the model Hamiltonian H0. As Bruce Barrett mentioned this morning, an effective Hamiltonian can be defined as
where
Heff has the same eigenvalue spectrum as the original total Hamiltonian H.
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References
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© 1972 Plenum Press, New York
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Khanna, F., Harvey, M., Sprung, D.W.L., Jopko, A. (1972). Does an Effective E2 Operator have a Two-Body Part?. In: Austin, S.M., Crawley, G.M. (eds) The Two-Body Force in Nuclei. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8337-6_19
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DOI: https://doi.org/10.1007/978-1-4684-8337-6_19
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