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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength β 2 and triaxiality γ. The deformation can be accessed in high-energy heavy ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity ε 2 and the density gradient d ⊥ in the initial state. Using an analytical estimate and a Glauber model, I show that the variances $\langleε^{2}_{2}\rangle$ or $\langle$(δd ⊥ /d ⊥ ) 2 $\rangle$ and skewnesses $\langleε^{2}_{2}δd_{⊥}/d_{⊥}\rangle$ or $\langle(δd_{⊥}/d_{⊥})^{3}\rangle$ have a simple analytical form of a'+b'β$^{2}_{2}$ and a'+[b'+c' cos(3γ)]β$^{3}_{2}$, respectively. From these, I constructed several normalized skewnesses to isolate the γ dependence from that of β 2 and show that the correlations between a normalized skewness and a variance can constrain simultaneously β 2 and γ. Assuming a linear relation with elliptic flow v 2 and mean-transverse momentum [p T ] of final-state particles, v 2 ∝ ε 2 and δ [p T ] / [p T ] ∝ δd ⊥ /d ⊥ , similar conclusions are also expected for the variances and skewnesses of v 2 and [p T ], i.e., a + bβ$^{2}_{2}$ for $\langle v^{2}_{2}\rangle$ and $\langle(δ[p_{T}] / [p_{T}])^{2}\rangle$ and a + [b + c cos (3γ)] β$^{3}_{2}$ for $\langle v^{2}_{2}δ [p_{T}] / [p_{T}]\rangle$ or $\langle(δ[p_{T}] / [p_{T}])^{3}\rangle$. My findings motivate a dedicated system scan of high-energy heavy ion collisions at RHIC and LHC to measure triaxiality of atomic nuclei: one first determines the coefficients b and c by collisions of isobaric near prolate nuclei, cos (3γ) ≈ 1, and near oblate nuclei, cos (3γ) ≈ –1 , with known β 2 values, followed by collisions of other species of interest with similar mass number. The (β 2 , γ) values for this species can be inferred directly from the measured variance and skewness observables from these collisions. Finally, the results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Longitudinal Wobbling Motion in Au 187

The rare phenomenon of nuclear wobbling motion has been investigated in the nucleus 187Au. A longitudinal wobbling-bands pair has been identified and clearly distinguished from the associated signature-partner band on the basis of angular distribution measurements. Theoretical calculations in the framework of the particle rotor model are found to agree well with the experimental observations. This is the first experimental evidence for longitudinal wobbling bands where the expected signature partner band has also been identified, and establishes this exotic collective mode as a general phenomenon over the nuclear chart.

150 ≤ A ≤ 189↗
DOE OSTI2026

Triaxiality of neutron-rich ruthenium nuclei studied by lifetime measurements

The breaking of axial symmetry in nuclei enables otherwise precluded behaviours, making it an interesting phenomenon to study. Experimental fingerprints such as very low-lying $2^+_2$ states suggest pronounced triaxial deformation for the neutron-rich ruthenium isotopes. Nevertheless, theoretical calculations differ in the description of the triaxial deformation and its evolution with neutron number, making experimental data crucial to understanding it. We investigated the evolution of the degree of triaxiality and $γ$ rigidity in neutron-rich ruthenium isotopes by measuring lifetimes of excited states in 108-112 Ru with the recoil distance Doppler-shift method. The experiment was carried out at the Grand Accélérateur National d’Ions Lourds using the Advanced Gamma Tracking Array coupled to the Variable Mode Spectrometer. We obtained B(E2) values for 29 transitions in the studied nuclei and compared them with fully microscopic symmetry conserving configuration mixing calculations, and phenomenological generalized triaxial rotor and triaxial particle-rotor models. The models generally reproduce the measured transition strengths, and show an increase in triaxiality with neutron number, reaching near maximum triaxiality in 112 Ru. The results are consistent with a transition from soft to rigid motion as the neutron number increases.

Heines, Johannes Sorby [Univ. of Oslo (Norway); No↗
DOE OSTI2026

Evolution of chirality from transverse wobbling in 135 Pr

Chirality is a distinct signature that characterizes triaxial shapes in nuclei. We report the first observation of chirality in the nucleus 135 Pr using a high-statistics Gammasphere experiment with the 123 Sb( 16 O, 4n) 135 Pr reaction. Two chiral-partner bands with the configuration π(1h11/2 )1 ⊗ ν(1h 11/2 ) −2 have been identified in this nucleus. Angular distribution analyses of the ΔI = 1 transitions connecting the two bands reveal a dominant dipole character, and quasiparticle triaxial rotor model calculations show good agreement with the data. Since the simultaneous observation of chirality and transverse wobbling in 135 Pr relies critically on these angular distribution results, we also address and refute the experimental and theoretical criticisms raised in a recent work by Lv et al., presenting additional evidence that further strengthens our interpretation. Furthermore, this marks the first observation of both hallmarks of triaxiality—chirality and wobbling—in the same nucleus.

90 ≤ A ≤ 149↗
DOE OSTI2026

Shape evolution in neutron-rich odd-even 105–109 Nb isotopes

Background: Neutron-rich nuclei around 𝑍 ≈ 40 are well known for exhibiting multiple shape transitions. Here, this region shows one of the sharpest shape transitions in the nuclear chart, evolving from a spherical vibrator at 𝑁 = 58 to a strongly deformed prolate shape at 𝑁 = 60. The largest deformations are observed for 38 Sr and 40 Zr . This abrupt shape transition disappears at 𝑍 = 36 and below, where a shape transition from spherical to oblate nuclei is predicted. On the other hand, for 𝑍 ≥ 42 and 𝑁 ≥ 60, the shape is known to evolve from axial to triaxial. While the even-𝑍 nuclei in this region have already been extensively studied, new insights can be gained from the studies of odd-𝑍 isotopes for a better understanding of the underlying mechanisms driving these phenomena. Purpose: The 41 Nb nuclei lie at the boundary between axially deformed Zr and triaxially deformed Mo nuclei. This work investigates the nuclear structure of very neutron-rich Nb nuclei up to 𝑁 = 68. The goal is to understand how the nuclear shape evolves as a function of isospin in this isotopic chain and provide new insights into the emergence of triaxial deformation. Methods: The structure of the neutron-rich Nb isotopes was investigated using state-of-the-art high-resolution 𝛾-ray spectroscopy of fission fragments produced via two different fission reactions. The use of 9 Be ⁢( 238 U, 𝑓) inverse kinematics, with a detection system comprising AGATA, EXOGAM, and VAMOS++, enabled the measurement of prompt and delayed 𝛾 rays from isotopically identified fission fragments, and 𝛾−𝛾−𝛾−𝛾 highfold data were obtained from a spontaneous fission source of 252 Cf using the Gammasphere array. Results: The level scheme of 105 Nb has been significantly extended, with the addition of two negative-parity bands observed for the first time. A new level scheme is proposed for 107 Nb, which is not in agreement with an earlier measurement, and new levels and transitions have been added to the very neutron-rich 109 Nb. The degree of triaxiality of the new bands is discussed on the basis of signature splitting analysis. The recently reported level scheme of 99 Nb has been revised. Conclusions: This systematic study on the Nb isotopic chain, compared to Zr and Mo, indicates that while the ground-state band exhibits a triaxial deformation, attributed to a proton hole coupled to a triaxially deformed Mo core, the negative-parity bands, based on isomeric bandheads, display an axially symmetric deformed structure, similar to that observed in the Zr isotopes, revealing the existence of a shape coexistence in the neutron-rich Nb nuclei.

Abushawish, M. [Université Claude-Bernard Lyon 1 (↗
DOE OSTI2025

Excited levels in odd-A silver isotopes populated rn fission of {sup 252}Cf

Excited levels in 111−121 Ag , odd-𝐴 isotopes populated following spontaneous fission of 252 Cf have been studied using high-fold 𝛾 coincidences measured with Gammasphere array of Compton-suppressed Ge spectrometers at Argonne National Laboratory. The experimental information on these nuclei reported before has been corrected and extended. In the work we discuss the evolution of triaxiality in odd-Ag nuclei. Relative positions of the 𝜋⁢𝑝1/2 and 𝜋⁢𝑔9/2 shells defining the 𝑍=40 gap when approaching the 𝑁=82 closure, the 𝜋⁢1/2+⁢[431] intruder bands, the three-quasiparticle configurations, and the so called 𝑗−1 anomaly in odd-Ag nuclei are also discussed.

Urban, W.↗
DOE OSTI2020

Shape evolution of neutron-rich 106,108,110 Mo isotopes in the triaxial degree of freedom

Background: Neutron-rich nuclei with mass number between 100 and 110 attract much attention, since several kinds of shapes, such as spherical, prolate, oblate, and triaxial shapes, are predicted. In particular, for neutron-rich Mo isotopes, different models predict different magnitudes and rigidity of triaxial deformation. Previous interpretations of experimental results based solely on low-lying $2^+_2$ states are insufficient to distinguish between the rigid triaxial shape, $\gamma$ vibration, or $\gamma$-soft rotor. Purpose: The shape evolution of 106 Mo, 108 Mo, and 110 Mo is investigated through their $2^+_1$-state lifetimes, decay-branching ratios of the $2^+_2$ state, and energies of the low-lying collective excited states with $K^π = 0^+, 2^+$, and $4^+$. Method: $\beta$-delayed $\gamma$-ray spectroscopy was employed for neutron-rich Nb and Zr isotopes produced at the RIKEN RI Beam Factory to populate excited states in 106 Mo, 108 Mo, and 110 Mo. The EUroball-RIKEN Cluster Array was used for high-resolution $\gamma$-ray detection and lifetimes of the $2^+_1$ states were determined using the UK fast-timing array of LaBr 3 (Ce) detectors. Results: New $\gamma$-ray transitions and levels are reported, including newly assigned $0^+_2$ states in 108,110 Mo. Quadrupole deformations were obtained for 106,108,110 Mo from their $2^+_1$ energies and lifetimes. The $\beta$-delayed neutron-emission probabilities of 108 Nb and 110 Nb were determined by examining the $\gamma$ rays of their respective daughter decays. Conclusions: In this work, the even-odd energy staggering in the $2^+_2$ band was compared with typical patterns of the $\gamma$-vibrational band, rigid triaxial rotor, and $\gamma$-soft rotor. The very small even-odd staggering of 106 Mo, 108 Mo, and 110 Mo favors a $\gamma$-vibrational band assignment. The kinematic moment of inertia for the $2^+_2$ band showed a trend similar to the ground-state band, which is as expected for the $\gamma$-vibrational band. Beyond-mean-field calculations employing the constrained Hartree-Fock-Bogoliubov and local quasiparticle-random-phase approximation method using the SLy5 + T interaction reproduced the ground and $2^+_2$ bands in 106 Mo and 108 Mo. The collective wave functions are consistent with the interpretation of the $2^+_2$ band as the $\gamma$-vibrational band of the prolate shape. However, the staggering pattern observed in 110 Mo differs from the one suggested in the calculations which predict a $\gamma$-soft rotor. There was no experimental indication of the oblate shape or the $\gamma$-soft rotor predicted in these Mo isotopes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Nucleon-pair truncation of the shell model for medium-heavy nuclei

Background: Establishing computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations. Purpose: Here, we propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum. Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast. Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: 44,46,48 Ti, 48,50 Cr, 52 Fe, 60,62,64 Zn, 66,68 Ge, 68 Se, and 108,110 Xe. We predict low-lying states of 112–114 Ba and 116–120 Ce, nuclei difficult to reach by large-scale SM calculations. Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

E2 rotational invariants of 0$^{+}_{1}$ and 2$^{+}_{1}$ states for 106 Cd: The emergence of collective rotation

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 < 0$^{+}_{2}$ ||E2||2$^{+}_{1}$ > matrix element is determined for the first time, providing a total, converged measure of the electric quadrupole strength, < Q 2 >, 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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Imaging nuclear shape through anisotropic and radial flow in high-energy heavy-ion collisions

Most atomic nuclei exhibit ellipsoidal shapes characterized by quadrupole deformation β 2 and triaxiality γ, and sometimes even a pear-like octupole deformation β 3 . The STAR experiment introduced a new ‘imaging-by-smashing’ technique to image the nuclear global shape by colliding nuclei at ultra-relativistic speeds and analyzing outgoing debris. Features of nuclear shape manifest in collective observables like anisotropic flow vn and radial flow via mean transverse momentum [p T ]. We present new measurements of the variances of v n (n = 2, 3, and 4) and [p T ], and the covariance of $v$$^{2}_{n}$ with [p T ], in collisions of highly deformed 238 U and nearly spherical 197 Au. Ratios of these observables between the two systems effectively suppress common final-state effects, isolating the strong impact of uranium’s deformation. By comparing results with state-of-the-art hydrodynamic model calculations, we extract β 2U and γ U values consistent with those deduced from low-energy nuclear structure measurements. Measurements of v 3 and its correlation with [p T ] also provide the first experimental suggestion of a possible octupole deformation for 238 U. These findings provide significant support for using high-energy collisions to explore nuclear shapes on femtosecond timescales, with implications for both nuclear structure and quark-gluon plasma studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Nuclear states projected from a pair condensate

Atomic nuclei exhibit deformation, pairing correlations, and rotational symmetries. To meet these competing demands in a computationally tractable formalism, we revisit the use of general pair condensates with good particle number as a trial wave function for even-even nuclei. After minimizing the energy of the condensate, allowing for general triaxial deformations, we project out states with good angular momentum with a fast projection technique. To show applicability, we present example calculations from pair condensates in several model spaces and compare against angular-momentum projected Hartree-Fock and full configuration-interaction shell-model calculations. This approach successfully generates spherical, vibrational, and rotational spectra, demonstrating potential for modeling medium- to heavy-mass nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Reaching the prolate-oblate boundary at 𝑁=116 via first fragmentation of a 198 Pt beam: Sharp transition to triaxiality in 189 Ta

High-spin isomers in very-neutron-rich 𝐴≈190 Hf-Ta-W nuclei were populated via the pioneering fragmentation of a 198 Pt primary beam at the National Superconducting Cyclotron Laboratory. The nuclei were implanted in a Si detector stack surrounded by the Gamma-Ray Energy Tracking In-beam Nuclear Array (GRETINA) to detect delayed 𝛾 rays, providing first level schemes using 𝛾−𝛾 coincidence data from isomeric decays in this previously inaccessible region of the nuclear chart. Here, a sudden transition to a strong triaxial shape is observed in the very-neutron-rich 189 Ta (𝑁 = 116) nucleus from axially prolate shapes in lighter Ta isotopes, providing a critical experimental benchmark for competing theoretical predictions of nuclear-shape evolution.

150 ≤ A ≤ 189↗
DOE OSTI2026

Shape evolution in neutron-rich Rh isotopes: First measurement of negative-parity isomers in 117,119 Rh

The β-delayed γ-ray spectroscopy of neutron-rich 117,119 Rh isotopes has been investigated at the Radioactive Isotope Beam Factory of RIKEN. The 1/2 − isomers in 117,119 Rh have been identified for the first time. The systematics of energy differences between the 9/2 + and 1/2 − states have been extended up to N = 74, which shows a tendency to first increase with the neutron number N, then reach a maximum at N ≈ 68, and subsequently decrease. Self-consistent triaxial relativistic Hartree-Bogoliubov (TRHB) calculations highlight the crucial role of triaxial deformation, particularly in the positive-parity states, in driving the observed evolution of energy differences. A shape transition from axially symmetric to triaxial and back to symmetric deformation is suggested along the Rh isotopic chain. These findings provide new insights into the structure of neutron-rich nuclei in the A ∼ 110 region and motivate further studies of exotic isotopes in this region to explore the interplay between triaxiality and shell evolution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IIb. Fission properties of BSkG2

Large-scale models of nuclear structure are currently the only way to provide consistent datasets for the many properties of thousands of exotic nuclei that are required by nucleosynthesis simulations. In [W. Ryssens et al., Eur. Phys. J. A 58, 246 (2022)], we recently presented the new BSkG2 model based on an energy density functional of the Skyrme type. Relying on a flexible three-dimensional coordinate representation of the nucleus, the model takes into account both triaxial deformation and time-reversal symmetry breaking. BSkG2 achieves a state-of-the-art global description of nuclear ground state (g.s.) properties and reproduces in particular the known masses with a root-mean-square (rms) deviation of 678 keV. Moving beyond g.s. properties, the model also reproduces all empirical values for the primary and secondary barriers as well as isomer excitation energies of actinide nuclei with rms deviations below 500 keV, i.e. with unprecedented accuracy. Here we discuss in detail the extension of our framework to the calculation of the fission barriers of 45 actinide nuclei, including odd-mass and odd-odd systems. We focus in particular on the impact of symmetry breaking which is key to the accuracy of the model: we allow systematically for axial, reflection and time-reversal symmetry breaking. The effect of the latter on the fission properties of odd-mass and odd-odd nuclei is small, but we find that allowing for shapes with triaxial or octupole deformation, as well as shapes with both, is crucial to achieving this accuracy. Here, the numerical accuracy of our coordinate space approach, the variety of nuclear configurations explored and the simultaneous successful description of fission properties and known masses makes BSkG2 the tool of choice for the large-scale study of nuclear structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Effective field theory for deformed odd-mass nuclei

We develop an effective field theory (EFT) for deformed odd-mass nuclei. These are described as an axially symmetric core to which a nucleon is coupled. In the coordinate system fixed to the core the nucleon is subject to an axially symmetric potential. Power counting is based on the separation of scales between low-lying rotations and higher-lying states of the core. In leading order, core and nucleon are coupled by universal derivative terms. These comprise a covariant derivative and gauge potentials which account for Coriolis forces and relate to Berry-phase phenomena. At leading order, the EFT combines the particle-rotor and Nilsson models. Here, we work out the EFT up to next-to-leading order and illustrate the results in 239 Pu and 187 Os . At leading order, odd-mass nuclei with rotational bandheads that are close in energy and differ by one unit of angular momentum are triaxially deformed. For bandheads that are well separated in energy, triaxiality becomes a subleading effect. The EFT developed in this paper presents a model-independent approach to the particle-rotor system that is capable of systematic improvement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions

In heavy ion collisions, elliptic flow v2 and radial flow, characterized by eventwise average transverse momentum [p T ], are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between v 2 and [p T ], ρ 2 , was found to be particularly sensitive to the quadrupole deformation parameter β that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation β>0 reduces the ρ 2 in ultracentral collisions (UCC), we show that the prolate deformation β<0 enhances the value of ρ 2 . As β>0 and β<0 are the two extremes of triaxiality, the strength and sign of v 2 2 -[pT] correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short timescale (<10 -24 s).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1982

The dynamics of the nucleus of M31

Self-consistent dynamic models of the M31 nucleus were constructed which satisfy Stratoscope II and ground-based photometry, as well as ground-based velocity dispersion measurements. Two models designed to yield the highest and lowest mass-to-light ratios (M/L) consistent with observations are concentrated on. It is found that self-consistent static models of the M31 nucleus can be constructed with a nuclear mass-to-blue magnitude ratio between 0 and 50, and that it is very difficult to construct high M/L models with plausible evolutionary histories. The low values of M/L that were found suggest that the nucleus must be composed of stars on nearly radial orbits whose apocenters lie well outside the observable part of the nucleus. Such nuclei may be formed either during core collapse of a preexisting dense nucleus or by orbital decay of globular clusters in a triaxial bulge.

Tremaine, S.↗