Elsevier

Nuclear Physics A

Volume 317, Issues 2–3, 9 April 1979, Pages 399-423
Nuclear Physics A

Convergence studies for the one-body mass radius operator of some closed-shell nuclei

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Abstract

The convergence properties of the perturbation series for the mass radius operator are studied in detail using a harmonic oscillator basis. The systems considered are the ground states of the closed shell nuclei 4He, 16O and 40Ca. Calculations are carried out to third order in the nuclear interaction and include up to 4ħω excitations for 4He and 16O, and up to 2ħω excitations for 40Ca. Goldstone graph components are used for graphs with at most 2p-2h intermediate states and Goldstone graphs for graphs with 3p-3h intermediate states. Both, the original and the saturating Sussex matrix elements (SME) are used. Some diagonalizations and inversions are also considered. The mass radius operator results with the original SME give large negative contributions that result in small rms radii. The results with the saturating SME indicate a slow order by order convergence at the value of the size parameter b that gives saturation in the first order energy. However, in this case, the individual perturbation orders and the total corrections, for the mass radius operator, are small for each of the above three nuclei at these values of b, and reasonably good agreement with experimental rms radii is obtained.

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