Testing refined shell-model interactions in the sd shell: Coulomb excitation of Na26

Background: Shell-model calculations crucially depend on the residual interaction used to approximate the nucleon-nucleon interaction. Recent improvements to the empirical universal sd interaction (USD) describing nuclei within the sd shell yielded two new interactions—USDA and USDB—causing changes in the theoretical description of these nuclei. Purpose: Transition matrix elements between excited states provide an excellent probe to examine the underlying shell structure. These observables provide a stringent test for the newly derived interactions. The nucleus Na26 with 7 valence neutrons and 3 valence protons outside the doubly-magic 16O core is used as a test case. Method: A radioactive beam experiment with Na26 (T1/2=1,07s) was performed at the REX-ISOLDE facility (CERN) using Coulomb excitation at safe energies below the Coulomb barrier. Scattered particles were detected with an annular Si detector in coincidence with γ rays observed by the segmented MINIBALL array. Coulomb excitation cross sections of the beam have been obtained by normalization to the well known Coulomb excitation cross sections of the Pd104 target. Results: The observation of three γ-ray transitions in Na26 together with available spectroscopic data allows us to determine E2- and M1-transitional matrix elements. Results are compared to theoretical predictions. Conclusion: The improved theoretical description of Na26 could be validated. Remaining discrepancies between experimental data and theoretical predictions indicate the need for future experiments and possibly further theoretical improvements.