Nuclear Chart Research Articles

Pathways to new exotic nuclei

The challenge of today’s nuclear physicists is to extend the nuclide chart. We produce and study exotic nuclei to understand the nature of the nuclear force, the origin of chemical elements in the universe and the energy production and evolution of stars. Beyond, exotic nuclei are used in various applications like medicine or compact power sources.

State of the Art of the Theoretical Nuclear Physics

In this contribution, I summarizes the theoretical topics discussed at SOTANCP5, including various cluster states, clusters at the edges of the nuclear chart and in nuclear matter, and clustering aspects in reactions.

New studies and predictions for nuclear clustering and dynamics in the ab initio symmetry-adapted framework

We discuss recent studies and predictions for nuclear clustering and dynamics within the framework of the ab initio symmetry-adapted no-core shell model, which has opened new domains of the nuclear chart. In this framework, we show the emergence from first principles of collectivity and clustering in light to mediummass nuclei, with implications for constructing ab initio optical potentials, for studying clustering in stable and unstable nuclei, for reproducing enhanced deformations without effective charges, and for the formation of clusters and its sensitivity to the underlying inter-nucleon force.

Impact of the Brink-Axel hypothesis on unique first-forbidden β-transitions for r-process nuclei* *J.-U. Nabi is supported by the Higher Education Commission Pakistan through Project (0-15394/NRPU/R&D/HEC/2021)

Key nuclear inputs for the astrophysical r-process simulations are the weak interaction rates. Consequently, the accuracy of these inputs directly affects the reliability of nucleosynthesis modeling. The majority of the stellar rates, used in simulation studies are calculated by invoking the Brink-Axel (BA) hypothesis. The BA hypothesis assumes that the strength functions of all parent excited states are the same as for the ground state, only shifted in energies. However, the BA hypothesis has to be tested against microscopically calculated state-by-state rates. In this project, we study the impact of the BA hypothesis on calculated stellar -decay and electron capture rates. Our investigation include both unique first forbidden (U1F) and allowed transitions for 106 neutron-rich trans-iron nuclei ([27, 77] ≤ [Z, A] ≤ [82, 208]). The calculations were performed using the deformed proton-neutron quasiparticle random-phase approximation (pn-QRPA) model with a simple plus quadrupole separable and schematic interaction. Waiting-point and several key r-process nuclei lie within the considered mass region of the nuclear chart. We computed electron capture and -decay rates using two different prescriptions for strength functions. One was based on invoking the BA hypothesis and the other was the state-by-state calculation of strength functions, under stellar density and temperature conditions ([10, 1] ≤ [ ( ), T( )] ≤ [1011, 30]). Our results show that the BA hypothesis invoked U1F rates are overestimated by 4–5 orders of magnitude as compared to microscopic rates. For capture rates, more than two orders of magnitude differences were noted when applying the BA hypothesis. It was concluded that the BA hypothesis is not a reliable approximation, especially for -decay forbidden transitions.

Atomic masses with machine learning for the astrophysical r process

The astrophysical r process plays a vital role in the production of heavy elements. Modeling of the r process is sensitive to masses and further requires knowledge of masses beyond current experimental reach. Therefore, simulations of the r process offer a unique test bed for predicting mass extrapolations. We take a Machine-Learning (ML) approach to model the masses across the entire chart of nuclides. For the first time, we simulate r-process nucleosynthesis with a physics-based ML mass model. We compare simulated abundances to solar data in order to evaluate the model's performance far from stability. The resulting r-process abundances up to thorium and uranium qualitatively match those of the observed solar system abundance pattern, with the characteristic peaks well positioned. We propagate the mass uncertainties obtained from the ML model to r-process abundance yields to estimate an uncertainty band associated with our approach. The size of the uncertainty band is approximately one order of magnitude which aligns with the uncertainty reported using alternative techniques.

Increasing the rate capability for the cryogenic stopping cell of the FRS Ion Catcher

At the FRS Ion Catcher (FRS-IC), projectile and fission fragments are produced at relativistic energies, separated in-flight, energy-bunched, slowed down, and thermalized in the ultra-pure helium gas-filled cryogenic stopping cell (CSC). Thermalized nuclei are extracted from the CSC using a combination of DC and RF electric fields and gas flow. This CSC also serves as the prototype for the CSC of the Super-FRS, where exotic nuclei will be produced at unprecedented rates making it possible to go towards the extremes of the nuclear chart. Therefore, it is essential to efficiently extract thermalized exotic nuclei from the CSC under high beam rate conditions, in order to use the rare exotic nuclei, which come as cocktail beams. The dependence of the extraction efficiency on the intensity of the impinging beam into the CSC was studied with a primary beam of 238U and its fragments. Tests were done with two different versions of the DC electrode structure inside the cryogenic chamber, the standard 1 m long and a short 0.5 m long DC electrode systems. In contrast to the rate capability of 104 ions/s with the long DC electrode system, results show no extraction efficiency loss up to the rate of 2 × 105 ions/s with the new short DC electrode. This order of magnitude increase of the rate capability paves the way for new experiments at the FRS-IC, including studies of exotic nuclei with in-cell multi-nucleon transfer reactions. The results further validate the design concept of the CSC of the Super-FRS, which was developed to effectively manage beams of even higher intensities.

Deformation versus Sphericity in the Ground States of the Lightest Gold Isotopes.

The changes in mean-squared charge radii of neutron-deficient gold nuclei have been determined using the in-source, resonance-ionization laser spectroscopy technique, at the ISOLDE facility (CERN). From these new data, nuclear deformations are inferred, revealing a competition between deformed and spherical configurations. The isotopes ^{180,181,182}Au are observed to possess well-deformed ground states and, when moving to lighter masses, a sudden transition to near-spherical shapes is seen in the extremely neutron-deficient nuclides, ^{176,177,179}Au. A case of shape coexistence and shape staggering is identified in ^{178}Au which has a ground and isomeric state with different deformations. These new data reveal a pattern in ground-state deformation unique to the gold isotopes, whereby, when moving from the heavy to light masses, a plateau of well-deformed isotopes exists around the neutron midshell, flanked by near-spherical shapes in the heavier and lighter isotopes-a trend hitherto unseen elsewhere in the nuclear chart. The experimental charge radii are compared to those from Hartree-Fock-Bogoliubov calculations using the D1M Gogny interaction and configuration mixing between states of different deformation. The calculations are constrained by the known spins, parities, and magnetic moments of the ground states in gold nuclei and show a good agreement with the experimental results.

Nuclear Shape-Phase Transitions and the Sextic Oscillator

This review delves into the utilization of a sextic oscillator within the β degree of freedom of the Bohr Hamiltonian to elucidate critical-point solutions in nuclei, with a specific emphasis on the critical point associated with the β shape variable, governing transitions from spherical to deformed nuclei. To commence, an overview is presented for critical-point solutions E(5), X(5), X(3), Z(5), and Z(4). These symmetries, encapsulated in simple models, all model the β degree of freedom using an infinite square-well (ISW) potential. They are particularly useful for dissecting phase transitions from spherical to deformed nuclear shapes. The distinguishing factor among these models lies in their treatment of the γ degree of freedom. These models are rooted in a geometrical context, employing the Bohr Hamiltonian. The review then continues with the analysis of the same critical solutions but with the adoption of a sextic potential in place of the ISW potential within the β degree of freedom. The sextic oscillator, being quasi-exactly solvable (QES), allows for the derivation of exact solutions for the lower part of the energy spectrum. The outcomes of this analysis are examined in detail. Additionally, various versions of the sextic potential, while not exactly solvable, can still be tackled numerically, offering a means to establish benchmarks for criticality in the transitional path from spherical to deformed shapes. This review extends its scope to encompass related papers published in the field in the past 20 years, contributing to a comprehensive understanding of critical-point symmetries in nuclear physics. To facilitate this understanding, a map depicting the different regions of the nuclide chart where these models have been applied is provided, serving as a concise summary of their applications and implications in the realm of nuclear structure.

Impact of nuclear rotation corrections on alpha decay half-lives of superheavy nuclei within 98 ≤ Z ≤ 120

The influence of nuclear rotation on the decay half-lives of superheavy nuclei within the range 98≤Z≤120 is investigated using the axially deformed relativistic Hartree-Bogoliubov theory in the continuum (DRHBc) with the PC-PK1 parameter set. The deduced DRHBc decay energies (with and without the rotation effect) are compared with those calculated from the macroscopic-microscopic WS4 and the available experimental binding energies. Six semi-empirical formulae, such as the Viola-Seaborg formula (VSS), the modified Brown formula (mB1), the semi-empirical relationship based on fission theory (SemFIS2), the Royer formula (R), the Wang formula (Wang) and the modified YQZR formula (MYQZR) are employed to estimate the half-lives of α decay. Among these formulae, the half-live predictions of SemFIS2 are found to gradually deviate from the systematic trend beyond Nd=184, showing that the probability of undergoing spontaneous fission is less feasible beyond this point. A minimum is observed at Nd=184, reflecting its neutron shell closure for the mass region considered on the nuclear chart. The results further indicate that, for 98≤Z≤104, the predictions of all semi-empirical formulae are more closely matched to the available experimental data when the rotation effect is taken into account. However, we have demonstrated that the effect of nuclear rotation gradually reduces as the atomic nucleus becomes heavier.

Science brings nations together: Mary Good and the heaviest atoms and nuclei

Abstract The 20th century started with the realization that working together and collaborating expedites new discoveries. The Solvay Conference in 1911 brought together scientists to try to understand the real nature of matter, the new elements, and their properties. Through global conflicts, the scientists stayed in communication and organized IUPAC and IUPAP to stay current in advances internationally in chemistry and physics, respectively. The outcomes include the discovery and naming of the elements that complete the periodic table of elements and the chart of nuclides with the heavy atoms and all of their isotopes. Mary Lowe Good forged new directions in developing tools in the field of radiochemistry. She exemplified cooperation and collaboration nationally and internationally. Now the advances in the heavy elements by Yuri Ts. Oganessian and colleagues staying close to the principles of international cooperation and sharing the new information about the connection of the production of super heavy elements to the main part of the chart of nuclides. The future lies in determining whether there are more elements to be discovered and what are their chemical properties.

Strong Evidence for ^{9}N and the Limits of Existence of Atomic Nuclei.

The boundaries of the chart of nuclides contain exotic isotopes that possess extreme proton-to-neutron asymmetries. Here we report on strong evidence of ^{9}N, one of the most exotic proton-rich isotopes where more than one half of its constitute nucleons are unbound. With seven protons and two neutrons, this extremely proton-rich system would represent the first-known example of a ground-state five-proton emitter. The invariant-mass spectrum of its decay products can be fit with two peaks whose energies are consistent with the theoretical predictions of an open-quantum-system approach; however, we cannot rule out the possibility that only a single resonancelike peak is present in the spectrum.

Proton and Neutron Pairing Properties within a Mixed Volume-Surface Pairing Type Using the Hartree–Fock–Bogolyubov Theory

This work aims at systematic investigations of the proton and neutron pairing properties and Fermi energies in the region from the proton drip-line to the neutron drip-line. In order to obtain a more accurate mass formula with the Skyrme (SKI3) force, the global descriptive power of the Skyrme–Hartree–Fock–Bogoliubov model for pairing properties is applied. Systematic Skyrme–HFB calculations with a mixed volume-surface pairing are carried out to study the ground-state proton pairing gap, neutron and proton pairing energies, and the neutron and proton Fermi energies for about 2095 even-even nuclei ranging from 2 ≤ Z ≤ 110 to 2 ≤ N ≤ 236 . The calculated values of proton pairing gaps are compared with experimental data, by using the difference-point formulas Δ(3), Δ(4), and Δ(5), and compared with the proton pairing gap in the Lipkin–Nogami model. It is shown that the Skyrme (SKI3) force with the mixed volume-surface pairing can be successfully used for describing the ground-state proton pairing gap, proton and neutron pairing energies, and proton and neutron Fermi properties of the investigated nuclei, in particular, the neutron-rich nuclei and the exotic nuclei near the neutron drip-line. On the other hand, the calculated proton pairing gap shows the acceptable agreement with the available experimental values of the proton pairing gap with the use of the difference-point formulas Δ(3), Δ(4), and Δ(5) and with the data of the Lipkin–Nogami model over the whole nuclear chart.

Double-magicity of proton drip-line nucleus 22Si with ab initio calculation

New magic numbers have been discovered in the neutron-rich region of the nuclear chart. However, there has been a lack of research on proton-rich nuclei. 22O, the mirror nucleus of 22Si, is a double-magic nucleus bearing a high E(21+). Whether 22Si exhibits double-magic characters is an intriguing topic. To investigate this matter, we utilized ab initio valence space in-medium similarity renormalization group for 22Si/22O, and their nearby nuclei. Our ab initio calculations provide good descriptions for the double magicity of 22O, as well as the shell evolution of N=14 and Z=14 through E(21+). The computed E(21+) indicate that the closure of Z=14 sub-shell in proton-rich nuclei is weaker than the N=14 sub-shell closure in their mirror nuclei. Particularly, the calculated E(21+) of 22Si is 800 keV lower than the one of 22O. To further explore the magicity of 22Si, the mirror energy difference (MED) of 26Si/26Mg, 24Si/24Ne, as well as 22Si/22O are calculated. The results demonstrate that the calculated MEDs agree well with available experimental data, and the E(21+) values of 22,24,26Si are all lower than their respective mirror nuclei due to the Thomas-Ehrman shift with large s1/2 occupation. Moreover, our calculation provides that the many-body configurations of the low-lying state of 22Si/22O are nearly identical despite the fact that the states bearing large MED. In conclusion, our ab initio results suggest that 22Si is a double magic nucleus, similar to its mirror nucleus 22O, albeit with a lower E(21+).

Expanding proton dripline by employing a number of muons* *Supported by the Natural Science Foundation of China (11775099)

Through mean-field calculations, we demonstrate that, in a large Z nucleus binding multiple muons, these heavy leptons localize within a few dozen femtometers of the nucleus. The mutual Coulomb interactions between the muons and protons can lead to a substantial decrease in proton chemical potential, surpassing 1 MeV. These findings imply that, in principle, the proton-dripline can be expanded on the nuclear chart, suggesting the possible production of nuclei with Z around 120.

β-decay studies in the 220

The experimental study presented in this work aims at providing new inputs to the knowledge of β decay in the 220<A<230 n-rich region.A systematic description of β decay in this region would be useful to probe the predictions of global nuclear models in exotic nuclei beyond N= 126, as an input to models describing r-process nucleosynthesis. The region mentioned is also one of the regions in the nuclear chart where the strongest octupole deformations are supposed to be found, and were measured experimentally in recent years in few selected cases.This work focuses on preliminary results on an experiment performed by the HISPEC-DESPEC collaboration as a part of the FAIR-0 campaing in April 2021. β-decay half lives and γ-ray spectra studies are presented.

β-decay studies across N = 126

With the advent of the first Radioactive Ion Beam facilities of new generation, the investigation of the neutron-rich side of the nuclear chart has experienced an impressive progress. However, the discovery and study of new nuclear species in the region around the heaviest known neutron shell closure, N = 126, is still one of the most coveted experimental challenges. At a slower pace, the exploitation of alternative reaction mechanisms and/or advanced instrumentation has opened the possibility to investigate the isomeric and β decay of new, moderately neutron-rich N ∼ 126 nuclei. These are of relevance for the understanding of the nuclear structure below the doubly-magic 208Pb and for their role in the synthesis of the trans-bismuth fissile elements in the r process. In this contribution, a general overview of the β-decay experiments performed at both sides of N = 126 is provided, with a main focus on the experiments carried out at the fragmentation facilities GSI and RIBF.

Spectroscopic Analysis of the Energy-Level Structure in Rhenium-190

Investigations of neutron-rich nuclei, particularly those that lie in regions of the nuclear chart known for a high probability of isomeric states forming, are of vital importance to the understanding of nuclear astrophysical processes. Studies of these nuclei, such as 190Re, can be used to validate and improve theoretical models of such processes. A polarised-beam experiment has been performed using the Munich Q3D magnetic spectrograph in order to investigate the energy-level structure of 190Re. An excitation-energy spectrum has been produced, allowing for energies to be assigned to observed states. Through comparison between measured and calculated differential cross-sections and vector analysing powers, the process of assigning spin and parity to newly observed states, and confirming the assignments for previously observed states, is underway.

Shape Coexistence in Even–Even Nuclei: A Theoretical Overview

The last decade has seen a rapid growth in our understanding of the microscopic origins of shape coexistence, assisted by the new data provided by the modern radioactive ion beam facilities built worldwide. Islands of the nuclear chart in which shape coexistence can occur have been identified, and the different microscopic particle–hole excitation mechanisms leading to neutron-induced or proton-induced shape coexistence have been clarified. The relation of shape coexistence to the islands of inversion, appearing in light nuclei, to the new spin-aligned phase appearing in N=Z nuclei, as well as to shape/phase transitions occurring in medium mass and heavy nuclei, has been understood. In the present review, these developments are considered within the shell-model and mean-field approaches, as well as by symmetry methods. In addition, based on systematics of data, as well as on symmetry considerations, quantitative rules are developed, predicting regions in which shape coexistence can appear, as a possible guide for further experimental efforts that can help in improving our understanding of the details of the nucleon–nucleon interaction, as well as of its modifications occurring far from stability.

Nuclear linear-chain structure arises in carbon-14

The shape and internal structure of an atomic nucleus can change significantly with increasing excitation energy, angular momentum, or isospin asymmetry. As an example of this structural evolution, linear-chain configurations in carbon or heavier isotopes have been predicted for decades. Recent studies have found non-stability of this structure in 12C while evidenced its appearance in 16C. It is then necessary to investigate the linear-chain molecular structures in 14C to clarify the exact location on the nuclear chart where this structure begins to emerge, and thus to benchmark theoretical models. Here we show a cluster-decay experiment for 14C with all final particles coincidentally detected, allowing a high Q-value resolution, and thus a clear decay-path selection. Unambiguous spin-parity analyses are conducted, strongly evidencing the emergence of the π-bond linear-chain molecular rotational band in 14C. The present results encourage further studies on even longer chain configurations in heavier neutron-rich nuclei.

A proton pairing isomer in 174Hf: Reinterpretation of data and support for the split prolate–oblate pairing approximation for deformed nuclei

The available data on the even–even isotope 174Hf are reinterpreted to conclude that the low-lying 02+ level, usually regarded as a “β vibration”, is actually a proton (2p–2 h) excitation known as a Pairing Isomer. This is the first identification of a Pairing Isomer based on Proton Nilsson Orbitals. Its identification demonstrates that Pairing Isomers can exist anywhere in the Nuclear Chart if the positioning of the Fermi Surface is favourable with respect to relevant Nilsson orbitals.