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Deviations from the Porter-Thomas Distribution due to Nonstatistical 𝛾 Decay below the 150 Nd Neutron Separation Threshold

We introduce a new method for the study of fluctuations of partial transition widths based on nuclear resonance fluorescence experiments with quasimonochromatic linearly polarized photon beams below particle separation thresholds. It is based on the average branching of decays of 𝐽=1 states of an even-even nucleus to the 2$^{+}_{1}$ state in comparison to the ground state. Between 5 and 7 MeV, a constant average branching ratio for 𝛾 decays from 1 − states of 0.490(16) is observed for the nuclide 150 Nd. Assuming 𝜒 2 -distributed partial transition widths, this average branching ratio is related to a degree of freedom of 𝜈 = 1.93⁢(12), rejecting the validity of the Porter-Thomas distribution, requiring 𝜈 = 1. The observed deviation can be explained by nonstatistical effects in the 𝛾-decay behavior with contributions in the range of 9.4(10)% up to 94(10)%.

150 ≤ A ≤ 189

Persistence of collectivity in the low-lying states of 30,31 Na inside the 𝑁 = 20 island of inversion

Near the 𝛽-stability line, nuclei with magic numbers are expected to exhibit spherical ground states. However, mass measurements of neutron-rich nuclei near the 𝑁 = 20 island of inversion have indicated an excess in the binding energies. These results, together with subsequent spectroscopic studies and theoretical works, point to the structural evolution from normal configurations to intruder-deformed configurations characterized by particle-hole excitations across the shell gap. Despite evidence of intruder-dominant ground states for the 30,31 Na isotopes in the vicinity of 𝑁 = 20, a question remains as to whether the deformation persists into the ground-state bands beyond the first excited states. Here, in this work, we report on a heavy-ion inelastic scattering measurement performed with GRETINA, the TRIPLEX device, and the S800 spectrograph to study the low-lying excitations in neutron-rich 30,31 Na . The observed gamma rays for the (4 + ) → (3 + ), (3 + ) → 2$^+_{g.s.}$, and (4 + ) → 2$^+_{g.s.}$ decays in 30 Na and for the (7/2 + ) → (5/2 + ) and (5/2 + )→3/2$^+_{g.s.}$ decays in 31 Na were used to extract the reduced transition probabilities 𝐵⁡(𝐸⁢2↑). We report the first measurement of the 𝐵⁡(𝐸⁢2↑) between the 3/2$^+_{g.s.}$ and the (7/2 + ) states in 31 Na . The results from this study are compared to shell-model calculations, confirming the persistence of large collectivity in the low-lying excited states consistent with the formation of the well-deformed ground-state bands in 30,31 Na .

collective models

Determination of proton and neutron contributions to the 0$^+_{𝑔⁡𝑠}$ → 2$^+_{1}$ excitations in 42 Si and 44 S using inelastic proton scattering in inverse kinematics and intermediate-energy Coulomb excitation

Here, we have measured the 0$^+_{𝑔⁡𝑠}$ → 2$^+_1$ transition in the neutron-rich 𝑁 = 28 isotope 42 Si using the probes of intermediate-energy Coulomb excitation and inelastic proton scattering in inverse kinematics at the Facility for Rare Isotope Beams with beam particle rates of ≈ 5 particles/s. The results of these two measurements allowed us to determine 𝑀 𝑛 /𝑀 𝑝 , the ratio of the neutron and proton transition matrix elements for the 0$^+_{𝑔⁡𝑠}$ → 2$^+_1$ transition. In addition, we have measured the 0$^+_{𝑔⁡𝑠}$ → 2$^+_1$ transition in the isotone 44 S using inverse kinematics inelastic proton scattering. By comparing the 44 S proton-scattering result with a recent intermediate-energy Coulomb excitation result on the same transition, we were able to determine 𝑀 𝑛 /𝑀 𝑝 for the 0$^+_{𝑔⁡𝑠}$ → 2$^+_1$ transition in this nucleus as well. This work strengthens the evidence that 42 Si has a stable quadrupole deformation in its ground state and that 44 S does not. Both conclusions are further supported by shell-model calculations carried out with the FSU interaction.

39 ≤ A ≤ 58

Experimental study of 53 Cr via the (𝑑, 𝑝⁢𝛾) reaction

Excited states in 53 Cr were studied via the 52 Cr ⁢(𝑑, 𝑝⁢𝛾) reaction up to the neutron-separation threshold. Proton-𝛾 angular correlations and 𝛾 decay branching ratios were measured in particle-𝛾 coincidences between the Super-Enge Split-Pole Spectrograph (SE-SPS) and CeBr 3 Array (CeBrA) demonstrator of the John D. Fox Accelerator Laboratory at Florida State University. Previous spin-parity assignments from a (𝑑,𝑝) singles experiment at the SE-SPS are supported and 𝛾-ray transitions in 53 Cr are reported. We firmly assign higher-lying excited states to 53 Cr because overlapping excited states and contaminants could be identified better due to the complementary 𝛾-decay information. We also correct some of the previously reported excitation energies and present a reanalysis of previously measured 52 Cr (𝑑, 𝑝)⁢ 53 Cr angular distributions guided by the complementary 𝛾-ray information. Based on this reanalysis, the fragmentation of the neutron 2⁢𝑝 3/2 , 2⁢𝑝 1/2 , 1⁢𝑓 5/2 , 1⁢𝑔 9/2 , and 2⁢𝑑 5/2 single-particle strengths is reassessed for 53 Cr. Here, a comparison to the corresponding strengths in 55 Fe is presented.

39 ≤ A ≤ 58

Rotational bands in 249 Md

Rotational structures in 249 Md have been observed for the first time. One set of states forms a pair of strongly coupled bands with relatively strong E2 transitions and no identifiable M1 transitions between the two signature partners. Another set of states suggests a decoupled sequence of E2 transitions. Furthermore, these bands are assigned as based on the 7/2 − [514] and on the favored signature of the 1/2 - [521] Nilsson level, respectively. Based on previous decay studies, these levels are thought to be the ground state and first excited state of 249 Md, which also agrees with theoretical predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Universal Effective Charges in the 𝑠⁢𝑑 and 𝑓⁡𝑝 Shells

The 247-keV state in 54 Sc, populated in the 𝛽 decay of 54 Ca, is reported here as a nanosecond isomer with a half-life of 26.0(22) ns. The state is interpreted as the 1 + member of the 𝜋⁢𝑓 7/2 ⊗ 𝜈⁢𝑓 5/2 spin-coupled multiplet, which decays to the 3 + ,𝜋⁢𝑓 7/2 ⊗ 𝜈⁢𝑝 1/2 ground state. The new half-life corresponds to a pure 𝐸⁢2 transition with a strength of 1.93(16) W.u., providing the most precise, unambiguous 𝐵⁡(𝐸⁢2) value in the neutron-rich 𝑓⁡𝑝 region to date for a nucleus with valence protons above 𝑍 = 20. Notably, it is roughly 4 times larger than the 𝐵⁡(𝐸⁢2;1/2 − → 5/2 − ) value in 55 Ca. The results, as compared to semiempirical and ab initio shell-model calculations, indicate (1) a weak 𝑁 = 34 subshell gap relative to 𝑁 = 32, (2) a large 𝐸⁢2 enhancement in Sc as compared to Ca due to 1⁢𝑝 − 1⁢ℎ proton excitations across 𝑍 = 28, and (3) empirical effective proton and neutron charges 𝑒 𝜋 = 1.30⁢(8)⁢𝑒 and 𝑒 𝜈 = 0.452⁢(7)⁢𝑒, respectively, that are in contrast to reports of 𝑒 𝜋 ≈1.1–1.15⁢𝑒 and 𝑒 𝜈 ≈ 0.6–0.8⁢𝑒 for 𝑓⁡𝑝-shell nuclei near 𝑁 = 𝑍. Here, we demonstrate that these reports are erroneous and that, in fact, a universal set of effective charges can be used across the 𝑠⁢𝑑 and 𝑓⁡𝑝 shells.

Beta decay

Dynamic mode decomposition for gyrokinetic eigenmode analysis

Dynamic mode decomposition (DMD) is a post-processing approach to decompose a complex time series into a set of modes via spectral analysis. DMD provides a new and powerful method to recover gyrokinetic drift-wave eigenfrequencies and eigenfunctions based only on the solution of the gyrokinetic-Maxwell initial value problem with almost no added cost to the initial value solver. In the present paper, DMD is applied to the CGYRO gyrokinetic code using a newly-developed CGYRO-DMD post-processor. CGYRO-DMD is numerically efficient, even on a single CPU. It does not set any restrictions on the plasma shape, beta (ratio of the plasma pressure to the magnetic field pressure), collisionality or number of species, and allows one to resolve numerous eigenmodes, even of comparable growth rates. In addition, DMD is not limited to unstable modes, but rather can capture stable and unstable branches simultaneously. In this work, we illustrate the accuracy of DMD through gyrokinetic analysis of mode transition for electromagnetic drift wave instabilities.

drift-wave eigenmodes

Multiple valence-space and core-excited band terminations in Ho and Er isotopes

High-spin structures of holmium (𝑍 = 67) and erbium (𝑍 = 68) isotopes are presented near mass 160, a region where collective and single-particle modes of excitation compete in the generation of angular momentum at the highest experimentally attainable spins in atomic nuclei. The level schemes of the 156,157,158 Ho isotopes have been significantly extended, reaching spins in the 40⁢ℏ to 55⁢ℏ range, through multiple experiments utilizing the Gammasphere spectrometer. In particular, several new noncollective band-terminating states are reported for these nuclei. The nature of these states, including both valence-space terminations and core-excited oblateconfigurations, is discussed in terms of proton particle-hole (p-h) excitations across the semimagic 𝑍 = 64 shell closure. Cranked-Nilsson–Strutinsky (CNS) calculations have been used to interpret the nature of these noncollective states. The corresponding terminating states in 154–159 Er are also included, providing a systematic description of band termination in this mass region. In addition, three weak rotational structures have been assigned to 157 Ho at the highest spins. These collective bands are proposed to be based on a triaxial strongly deformed nuclear shape, involving neutron p-h excitations across the 𝑁 = 82 shell gap.

150 ≤ A ≤ 189

Quadrupole strength in isobaric triplets

The dependence of the 𝐸⁢2 matrix elements on isospin projection 𝑇 𝑧 is linked to the conservation of the isospin symmetry. To study this conjecture, we calculated the 𝐵⁡(𝐸⁢2 : 2 + →0 + ) rates for the even-even 𝑇=1 mirror nuclei with 42 ≤ 𝐴 ≤ 98 within nuclear density functional theory, employing the generalized Bohr Hamiltonian, and carrying out angular momentum projection. We demonstrated that collective effects are crucial for describing experimental data near the 𝑁=𝑍 line without invoking explicit beyond-Coulomb isospin symmetry-breaking corrections. We also determined the 𝐵⁡(𝐸⁢2↓) values for odd-odd 𝑇 𝑧 =0 nuclei 70 Br and 78 Y in doubly blocked configurations. We discussed the requirements for accurately describing isobaric analog states and emphasized how current theoretical results should be interpreted within the study of isospin symmetry across isospin triplets.

collective levels

First observation of a high-𝐾 band structure in 162 Er and implications in the context of the identical bands phenomenon

The first ever identification of a high-𝐾 band structure in 162 Er is reported. Based on a 𝐾 𝜋 = 7 (−) isomer, it is found to be identical in nature to the corresponding 𝐾 𝜋 = 7 − sequence in 164 Er up to its highest observed spin. Furthermore, the phenomenon of identical high-K bands built on a two-quasiparticle configuration in an isotopic chain is reported here for the first time. While this is a notable addition to the systematics of known identical bands in nuclei at normal deformation, a satisfactory global understanding of the phenomenon remains elusive.

150 ≤ A ≤ 189

𝑙-forbidden 𝑀⁢1 strengths near 100 Sn from knockout reactions in Cd and Sn

Neutron knockout reactions on beams of 104,102 Cd and 104 Sn are presented. States in the residual 103,101 Cd and 103 Sn nuclei are populated, including low-lying 7/2 + states of 𝜈⁢𝑔 7/2 character. These states have half-lives ≈ 400 ps due to their low energy and hindered 𝐵⁡(𝑀⁢1;7/2 + →5/2 + ) strengths. The excited-state half-lives were measured using their Doppler-shifted line shapes, and the resulting 𝐵⁡(𝑀⁢1) strengths are compared to valence space in medium similarity renormalization group (VS-IMSRG) calculations. Lastly, the VS-IMSRG calculations underpredict the 𝑙-forbidden 𝑀⁢1 strengths in the 100 Sn region, as well as in other regions of the nuclear chart near 40 Ca and 208 Pb.

90 ≤ A ≤ 149

Multipole responses in fissioning nuclei and their uncertainties

Electromagnetic multipole responses are key inputs to model the structure, decay, and reactions of atomic nuclei. With the introduction of the finite amplitude method (FAM), large-scale calculations of the nuclear linear response in heavy deformed nuclei have become possible. This work provides a detailed study of multipole responses in actinide nuclei with Skyrme energy density functionals. We quantify both systematic and statistical uncertainties induced by the functional parametrization in FAM calculations. We also extend the FAM formalism to perform blocking calculations with the equal filling approximation for odd-mass and odd-odd nuclei, and analyze the impact of blocking configurations on the response. In conclusion, by examining the entire plutonium isotopic chain from the proton to the neutron drip line, we find a large variability of the response with the neutron number and study how it correlates with the deformation of the nuclear ground state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Magnetic dipole γ-ray strength functions in the crossover from spherical to deformed neodymium isotopes

We calculate the magnetic dipole $\gamma$-ray strength functions in a chain of even-mass neodymium isotopes $^{144-152}$Nd in the framework of the configuration-interaction (CI) shell model. We infer the strength function by applying the maximum entropy method (MEM) to the exact imaginary-time response function calculated with the shell-model Monte Carlo (SMMC) method. The success of the MEM depends on the choice of a good strength function as a prior distribution. We investigate two choices for the prior strength function: the static path approximation (SPA) and the quasiparticle random-phase approximation (QRPA). We find that the QRPA is a better approximation at low temperatures (i.e., near the ground state), while the SPA is a better choice at finite temperatures. We identify a low-energy enhancement (LEE) in the MEM deexcitation $M1$ strength functions of the even-mass neodymium isotopes and compare with recent experimental results for the total deexcitation $\gamma$-ray strength functions. The LEE is already seen in the SPA strength function but not in the QRPA strength function, indicating the importance of large-amplitude static fluctuations around the mean field in reproducing the LEE. Our method is currently the only one which can reproduce LEE in heavy open-shell nuclei where conventional CI shell model calculations are prohibited. With the onset of deformation as number of neutrons increases along the chain of neodymium isotopes, we observe that some of the LEE strength transfers to a low-energy excitation, which we interpret as a finite-temperature ``scissors'' mode. Here, we also observe a finite-temperature spin-flip mode.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Measurement of the 175 Hf half-life

Hafnium-175 is a useful radioisotope for numerous applications; however, its evaluated half-life (70 ± 2 days) has a large uncertainty. To enable a new measurement of the half-life, 175 Hf was produced via proton irradiation of natural lutetium and chemically purified. The 175 Hf sample was counted approximately once a month with three high-purity germanium detectors for 13 months (~5.5 half-lives). A 133 Ba standard was counted in an identical manner to quantify systematic uncertainties over the measurement period. In conclusion, the measured 175 Hf half-life is 69.90 ± 0.07 days, in agreement with the evaluated value, but with significantly reduced uncertainty.

150 ≤ A ≤ 189

Reinvestigation of the level structures of the even-even nuclei 90 Zr and 92 Zr

Excited states of 90 Zr and 92 Zr were investigated using the fusion reactions 6 Li + 89 Y and 14 N + 82 Se , respectively. Based on the experimental data, 5 and 18 new 𝛾 rays have been added to the level schemes of 90 Zr and 92 Zr , respectively. The level structures of 90 Zr and 92 Zr have been interpreted with shell-model calculations using the GWBXG and SNET effective interactions. The neutron core-breaking and the importance of the 1⁢𝑔 7/2 and 1⁢ℎ 11/2 orbits for high-spin states of 92 Zr were discussed. Finally, the excitation energy of the neutron core-breaking of nuclei in the 𝐴=90 region was compared.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Data-driven analysis of dipole strength functions using artificial neural networks

Here, we present a data-driven analysis of dipole strength functions across the nuclear chart, employing an artificial neural network to model nuclear dipole responses. We train the network on a dataset of experimentally measured dipole strength functions for 216 different nuclei. To assess its predictive capability, we test the trained model on an additional set of 10 new nuclei, where experimental data exist. We demonstrate that the artificial neural network not only accurately reproduces known data but also identifies potential inconsistencies in experimental datasets, indicating which results may warrant further review or possible rejection. For nuclei where experimental data are sparse or unavailable, the network confirms theoretical calculations, reinforcing its utility as a predictive tool in nuclear physics. Finally, utilizing the predicted electric dipole polarizability, we extract the value of the symmetry energy at saturation density and find it consistent with results from the literature.

artificial neural networks

Measurement of the Isolated Nuclear Two-Photon Decay in Ge 72

The nuclear two-photon or double-gamma (2 γ ) decay is a second-order electromagnetic process whereby a nucleus in an excited state emits two gamma rays simultaneously. To be able to directly measure the 2⁢ γ decay rate in the low-energy regime below the electron-positron pair-creation threshold, we combined the isochronous mode of a storage ring with Schottky resonant cavities. The newly developed technique can be applied to isomers with excitation energies down to ~100 keV and half-lives as short as ~10 ms. The half-life for the 2⁢ γ decay of the first-excited 0 + state in bare 72 Ge ions was determined to be 23.9(6) ms, which strongly deviates from expectations.

59 ≤ A ≤ 89