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Register a new userFirst Measurement of the $B(E2; 3/2^- rightarrow 1/2^-)$ Transition Strength in $^7$Be: Testing Ab Initio Predictions for $A=7$ Nuclei
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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. To experimentally test the validity of these ab initio predictions, we performed a Coulomb excitation experiment to measure the $B(E2; 3/2^- rightarrow 1/2^-)$ transition strength in $^7$Be for the first time. A $B(E2; 3/2^- rightarrow 1/2^-)$ value of $26(6)(3) , e^2 mathrm{fm}^4$ was deduced from the measured Coulomb excitation cross section. This result is used with the experimentally known $^7$Li $B(E2; 3/2^- rightarrow 1/2^-)$ value to provide an experimental ratio to compare with the ab initio predictions. Our experimental value is consistent with the theoretical ratios within $1 sigma$ 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.
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The large reported $E2$ strength between the $2^+$ ground state and $1^+$ first excited state of $^8$Li, $B(E2; 2^+ rightarrow 1^+)= 55(15)$ e$^2$fm$^4$, presents a puzzle. Unlike in neighboring $A=7-9$ isotopes, where enhanced $E2$ strengths may be understood to arise from deformation as rotational in-band transitions, the $2^+rightarrow1^+$ transition in $^8$Li cannot be understood in any simple way as a rotational in-band transition. Moreover, the reported strength exceeds textit{ab initio} predictions by an order of magnitude. In light of this discrepancy, we revisited the Coulomb excitation measurement of this strength, now using particle-$gamma$ coincidences, yielding a revised $B(E2; 2^+ rightarrow 1^+)$ of $25(8)(3)$ e$^2$fm$^4$. We explore how this value compares to what might be expected in rotational, Elliott SU(3), and textit{ab initio} descriptions, including no-core shell model (NCSM) calculations with various internucleon interactions. While the present value is a factor of $2$ smaller than previously reported, it remains anomalously enhanced.
Background: Recent developments in {it ab initio} nuclear theory demonstrate promising results in medium- to heavy-mass nuclei. A particular challenge for many of the many-body methodologies, however, is an accurate treatment of the electric-quadrupole, $E2$, strength associated with collectivity. Purpose: In this work we present high-precision $E2$ data for the mirror nuclei $^{23}$Mg and $^{23}$Na for comparison with such theory. We interpret these results in combination with other recent measurements performed by the collaboration and the available literature. Methods: Coulomb-excitation measurements of $^{23}$Mg and $^{23}$Na were performed at the TRIUMF-ISAC facility using the TIGRESS spectrometer and were used to determine the $E2$ matrix elements of mixed $E2$/$M1$ transitions. Results: $E2$ transition strengths were extracted for $^{23}$Mg and $^{23}$Na. Transition strength ($B(E2)$) precision was improved by factors of approximately six for both isotopes, while agreeing within uncertainties with previous measurements. Conclusions: A comparison was made with both shell-model and {it ab initio} valence-space in-medium similarity renormalization group calculations. Valence-Space In-Medium Similarity-Renormalization-Group calculations were found to underpredict the absolute $E2$ strength - in agreement with previous results - but a full analysis of $sd$-shell nuclei found no indication of an isovector component to the missing strength. Comparison with full configuration interaction and coupled cluster calculations in the case of $^{14}$C indicates that correlated multi-particle multi-hole excitations are essential to the reproduction of quadrupole excitation amplitudes.
The form factor of the electromagnetic excitation of $^{12}$C to its 2$^+_1$ state was measured at extremely low momentum transfers in an electron scattering experiment at the S-DALINAC. A combined analysis with the world form factor data results in a reduced transition strength $B(E2; 2^+_1rightarrow 0^+_1) =7.63(19)$ e$^2$fm$^4$ with an accuracy improved to 2.5%. In-Medium-No Core Shell Model results with interactions derived from chiral effective field theory are capable to reproduce the result. A quadrupole moment $Q(2^+_1) = 5.97(30)$ efm$^2$ can be extracted from the strict correlation with the $B((E2)$ strength emerging in the calculations.
The calcium isotopes have emerged as an important testing ground for new microscopically derived shell-model interactions, and a great deal of focus has been directed toward this region. We investigate the relative spectroscopic strengths associated with $1f_{7/2}$ neutron hole states in $^{47, 49}$Ca following one-neutron knockout reactions from $^{48,50}$Ca. The observed reduction of strength populating the lowest 7/2$^{-}_{1}$ state in $^{49}$Ca, as compared to $^{47}$Ca, is consistent with the description given by shell-model calculations based on two- and three-nucleon forces in the neutron $pf$ model space, implying a fragmentation of the $l$=3 strength to higher-lying states. The experimental result is inconsistent with both the GXPF1 interaction routinely used in this region of the nuclear chart and with microscopic calculations in an extended model space including the $ u1g_{9/2}$ orbital.
To test the predictive power of ab initio nuclear structure theory, the lifetime of the second 2+ state in neutron-rich 20O, tau(2+_2 ) = 150(+80-30) fs, and an estimate for the lifetime of the second 2+ state in 16C have been obtained, for the first time. The results were achieved via a novel Monte Carlo technique that allowed us to measure nuclear state lifetimes in the tens-to-hundreds femtoseconds range, by analyzing the Doppler-shifted gamma-transition line shapes of products of low-energy transfer and deep-inelastic processes in the reaction 18O (7.0 MeV/u) + 181Ta. The requested sensitivity could only be reached owing to the excellent performances of the AGATA gamma-tracking array, coupled to the PARIS scintillator array and to the VAMOS++ magnetic spectrometer. The experimental lifetimes agree with predictions of ab initio calculations using two- and three-nucleon interactions, obtained with the valence-space in-medium similarity renormalization group for 20O, and with the no-core shell model for 16C. The present measurement shows the power of electromagnetic observables, determined with high-precision gamma spectroscopy, to assess the quality of first-principles nuclear structure calculations, complementing common benchmarks based on nuclear energies. The proposed experimental approach will be essential for short lifetimes measurements in unexplored regions of the nuclear chart, including r-process nuclei, when intense ISOL-type beams become available.
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