# Effective operators in a single-$j$ orbital

Abstract : We present an analysis of effective operators in the shell model with up to three-body interactions in the Hamiltonian and two-body terms in electromagnetic transition operators when the nucleons are either neutrons or protons occupying a single-j orbital. We first show that evidence for an effective three-body interaction exists in the N = 50 isotones and in the lead isotopes but that the separate components of such interaction are difficult to obtain empirically. We then determine higher-order terms on more microscopic grounds. The starting point is a realistic two-body interaction in a large shell-model space together with a standard one-body transition operator, which, after restriction to the dominant orbital and with use of stationary perturbation theory, are transformed into effective versions with higher-order terms. An application is presented for the lead isotopes with neutrons in the 1g 9/2 orbital.
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Journal articles

Cited literature [19 references]

http://hal.in2p3.fr/in2p3-01686464
Contributor : Michel Lion <>
Submitted on : Wednesday, January 17, 2018 - 2:12:36 PM
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### Citation

E Derbali, P. van Isacker, B. Tellili, C. Souga. Effective operators in a single-$j$ orbital. Journal of Physics G: Nuclear and Particle Physics, IOP Publishing, 2018, 45, pp.035102. ⟨10.1088/1361-6471/aaa4c9⟩. ⟨in2p3-01686464⟩

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