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The collective structure of $^{106}$Cd is elucidated by multi-step Coulomb excitation of a 3.849 MeV/$A$ beam of $^{106}$Cd on a 1.1 mg/cm$^2$ $^{208}$Pb target using GRETINA-CHICO2 at ATLAS. Fourteen $E2$ matrix elements were obtained. The nucleus $^{106}$Cd is a prime example of emergent collectivity that possesses a simple structure: it is free of complexity caused by shape coexistence and has a small, but collectively active number of valence nucleons. This work follows in a long and currently active quest to answer the fundamental question of the origin of nuclear collectivity and deformation, notably in the cadmium isotopes. The results are discussed in terms of phenomenological models, the shell model, and Kumar-Cline sums of $E2$ matrix elements. The ${\langle 0_2^+ ||E2||2_1^+ \rangle}$ matrix element is determined for the first time, providing a total, converged measure of the electric quadrupole strength, $\langle Q^2 \rangle$, of the first-excited $2_1^+$ level relative to the $0_1^+$ ground state, which does not show an increase as expected of harmonic and anharmonic vibrations. Strong evidence for triaxial shapes in weakly collective nuclei is indicated; collective vibrations are excluded. This is contrary to the only other cadmium result of this kind in $^{114}$Cd by C. Fahlander et al., Nucl. Phys. A485, 327 (1988), which is complicated by low-lying shape coexistence near midshell., 7 pages, 4 figures

Isomers in $^{66}$Ga, $^{67}$Ge, and $^{69}$Ge were recoil-implanted into ferromagnetic hosts of iron and gadolinium at $\approx 6$~K, and the hyperfine magnetic fields were determined by Time Differential Perturbed Angular Distribution (TDPAD) measurements. The hyperfine field strengths at $\approx 6$~K are compared to the results of previous higher-temperature measurements and the amplitudes of the $R(t)$ functions are compared to empirical expectations. The results show that gadolinium can be a suitable host for high-precision in-beam $g$-factor measurements. The results of new $g$-factor measurements for isomers in $^{66}$Ga and $^{67}$Ge are $g(^{66}$Ga$,7^{-}) = +0.126(4)$, supporting a $[\pi_{f5/2} \otimes \nu g_{9/2}]_{7^-}$ configuration assignment, and $g(^{67}$Ge$,\frac{9}{2}^{+})=-0.1932(22)$, derived from a new measurement of the ratio $g(^{67}\mathrm{Ge})/g(^{69}\mathrm{Ge}) = 0.869(9)$. These values are in agreement with previous results. The $R(t)$ amplitudes indicate that the nuclear alignment produced in the isomeric states was significantly lower than the empirically expected $\sigma/I \approx 0.35$., Comment: 10 pages, 10 figures

The electric monopole ($E0$) transition strength $\rho^2$ for the transition connecting the third 0$^+$ level, a "superdeformed" band head, to the "spherical" 0$^+$ ground state in doubly magic $^{40}$Ca has been determined via $e^+e^-$ pair-conversion spectroscopy. The measured value, $\rho^2(E0; 0^+_3 \to 0^+_1)~=~2.3(5)\times10^{-3}$, is the smallest $\rho^2(E0; 0^+ \to 0^+)$ found in $A

Radioactive $^{129}$Sb, which can be treated as a proton plus semi-magic $^{128}$Sn core within the particle-core coupling scheme, was studied by Coulomb excitation. Reduced electric quadrupole transition probabilities, $B(E2)$, for the $2^+$ $\times$ $\pi g_{{7/2}}$ multiplet members and candidate $\pi d_{{5/2}}$ state were measured. The results indicate that the total electric quadrupole strength of $^{129}$Sb is a factor of 1.39(11) larger than the $^{128}$Sn core, which is in stark contrast to the expectations of the empirically successful particle-core coupling scheme. Shell-model calculations performed with two different sets of nucleon-nucleon interactions suggest that this enhanced collectivity is due to constructive quadrupole coherence in the wavefunctions stemming from the proton-neutron residual interactions, where adding one nucleon to a core near a double-shell closure can have a pronounced effect. The enhanced electric quadrupole strength is an early signal of the emerging nuclear collectivity that becomes dominant away from the shell closure., Comment: Accepted, Physical Review Letters

Complex systems often comprise many kinds of components which vary over many orders of magnitude in size: Populations of cities in countries, individual and corporate wealth in economies, species abundance in ecologies, word frequency in natural language, and node degree in complex networks. Here, we introduce `allotaxonometry' along with `rank-turbulence divergence' (RTD), a tunable instrument for comparing any two ranked lists of components. We analytically develop our rank-based divergence in a series of steps, and then establish a rank-based allotaxonograph which pairs a map-like histogram for rank-rank pairs with an ordered list of components according to divergence contribution. We explore the performance of rank-turbulence divergence, which we view as an instrument of `type calculus', for a series of distinct settings including: Language use on Twitter and in books, species abundance, baby name popularity, market capitalization, performance in sports, mortality causes, and job titles. We provide a series of supplementary flipbooks which demonstrate the tunability and storytelling power of rank-based allotaxonometry., 34 pages, 10 figures, 1 table; online appendices: http://compstorylab.org/allotaxonometry/

The Time Differential Perturbed Angular Distribution technique with LaBr$_3$ detectors has been applied to the $I^\pi = \frac{11}{2}^-$ isomeric state ($E_x = 846$ keV, $\tau=107$~ns) in $^{107}$Cd, which was populated and recoil-implanted into a gadolinium host following the $^{98}$Mo($^{12}$C, $3n$)$^{107}$Cd reaction. The static hyperfine field strength of Cd recoil implanted into gadolinium was thus measured, together with the fraction of nuclei implanted into field-free sites, under similar conditions as pertained for a previous implantation perturbed angular distribution $g$-factor measurement on the $I^\pi = 10^+$ state in $^{110}$Cd. The $^{110}$Cd $g(10^+)$ value was thereby re-evaluated, bringing it into agreement with the value expected for a seniority-two $\nu h_{\frac{11}{2}}$ configuration.

Excited-state spectroscopy from the first Facility for Rare Isotope Beams (FRIB) experiment is reported. A 24(2)-$\mu$s isomer was observed with the FRIB Decay Station initiator (FDSi) through a cascade of 224- and 401-keV $\gamma$ rays in coincidence with $^{32}\textrm{Na}$ nuclei. This is the only known microsecond isomer ($1{\text{ }\mu\text{s}}\leq T_{1/2} < 1\text{ ms}$) in the region. This nucleus is at the heart of the $N=20$ island of shape inversion and is at the crossroads of spherical shell-model, deformed shell-model, and ab initio theories. It can be represented as the coupling of a proton hole and neutron particle to $^{32}\textrm{Mg}$, $^{32}\textrm{Mg}+\pi^{-1} + \nu^{+1}$. This odd-odd coupling and isomer formation provides a sensitive measure of the underlying shape degrees of freedom of $^{32}\textrm{Mg}$, where the onset of spherical-to-deformed shape inversion begins with a low-lying deformed $2^+$ state at 885 keV and a low-lying shape-coexisting $0_2^+$ state at 1058 keV. We suggest two possible explanations for the 625-keV isomer in $^{32}$Na: a $6^-$ spherical shape isomer that decays by $E2$ or a $0^+$ deformed spin isomer that decays by $M2$. The present results and calculations are most consistent with the latter, indicating that the low-lying states are dominated by deformation., Comment: 7 pages, 5 figures, accepted by Physical Review Letters