First measurement of the B(E2;3/2−→1/2− ) transition strength in

S. L. Henderson

¹

,

T. Ahn

²

,

M. A. Caprio

³

et al.

Abstract

Electromagnetic observables are able to give insight into collective and emergent features in nuclei, including nuclear clustering. These observables also provide strong constraints for ab initio theory, but comparison of these observables between theory and experiment can be difficult due to the lack of convergence for relevant calculated values, such as E2 transition strengths. By comparing the ratios of E2 transition strengths for mirror transitions, we find that a wide range of ab initio calculations give robust and consistent predictions for this ratio. In order to experimentally test the validity of these ab initio predictions, we performed a Coulomb excitation experiment to measure the B(E2; 3/2 − → 1/2 − ) transition strength in 7 Be for the first time. A B(E2; 3/2 − → 1/2 − ) value of 26( 6) stat ( 3) syst e 2 fm 4 was deduced from the measured Coulomb excitation cross section. This result is used with the experimentally known 7 Li B(E2; 3/2 − → 1/2 − ) value to provide an experimental ratio to compare with the ab initio predictions. Our experimental value is consistent with the theoretical ratios within 1σ uncertainty, giving experimental support for the value of these ratios. Further work in both theory and experiment can give insight into the robustness of these ratios and their physical meaning.

Quadrupole moments and proton-neutron structure in p-shell mirror nuclei

“…The error introduced by basis truncation may largely cancel in the ratio of these quadrupole moments, providing a more robustly converged prediction for their ratio. Such cancellation and robust convergence has already been noted for the ratio between the mirror E2 transitions (3/2 − → 1/2 − ) in these two nuclei [26] (see Fig. 6 of Ref.…”

“…If the matrix elements entering into the ratio involve structurally similar states, so that convergence properties are similar, errors from truncation of the many-body space can cancel in the ratio. Such behavior has already been noted for E2 matrix elements among states within the same rotational band [18,22], or between rotational bands with related structures [25], and for the E2 strengths of mirror transitions [26]. Prior calculations of the ratio of proton and neutron quadrupole moments [18] have suggested that this ratio may be similarly robust, at least in a limited sampling of rotational states (see Fig.…”

“…6 of Ref. [26]). Indeed the ratio of the calculated quadrupole moments for 7 Be and 7 Li, shown in Fig.…”

“…This observation applies more generally to ratios of electromagnetic matrix elements involving states with similar convergence properties, arising from structural similarities. Examples include (ratios of) transition strengths within a rotational band [18,22], or between rotational bands with related structures [25], or across mirror transitions [26].…”

Emergent Sp(3,R) dynamical symmetry in the nuclear many-body system from an ab initio description

“…The nucleus is a complex many-body system, which nonetheless exhibits simple patterns indicative of emergent collective degrees of freedom [1][2][3][4]. Ab initio nuclear theory now provides accurate quantitative predictions for observables in light nuclei [5][6][7][8][9][10][11][12][13][14]. Signatures of collective phenomena including clustering [14][15][16][17][18][19] and rotation [12,[20][21][22][23] emerge from ab initio calculations.…”