Nuclear Charge Radii Research Articles

Charge radii of 11−16C, 13−17N and 15−18O determined from their charge-changing cross-sections and the mirror-difference charge radii

Charge-changing cross-sections (CCCSs) of 11−16C, 13−17N and 15−18O on a carbon target have been determined at energies around 300 MeV/nucleon. A nucleon separation energy-dependent correction factor has been introduced to the Glauber model calculation for extracting the nuclear charge radii from the experimental CCCSs. The charge radii of 11C, 13,16N and 15O thus were determined for the first time. With the new radii, we studied the experimental mirror-difference charge radii (ΔRchmirror) of 11B-11C, 13C-13N, 15N-15O, 17N-17Ne pairs for the first time. We find that the ΔRchmirror values of 13C-13N and 15N-15O pairs follow well the empirical relation to the isospin asymmetry predicted by the abinitio calculations, while ΔRchmirror of 11B-11C and 17N-17Ne pairs deviate from such relation by more than two standard deviations.

Smooth trends in fermium charge radii and the impact of shell effects

The quantum-mechanical nuclear-shell structure determines the stability and limits of the existence of the heaviest nuclides with large proton numbers Z ≳ 100 (refs. 1–3). Shell effects also affect the sizes and shapes of atomic nuclei, as shown by laser spectroscopy studies in lighter nuclides4. However, experimental information on the charge radii and the nuclear moments of the heavy actinide elements, which link the heaviest naturally abundant nuclides with artificially produced superheavy elements, is sparse5. Here we present laser spectroscopy measurements along the fermium (Z = 100) isotopic chain and an extension of data in the nobelium isotopic chain (Z = 102) across a key region. Multiple production schemes and different advanced techniques were applied to determine the isotope shifts in atomic transitions, from which changes in the nuclear mean-square charge radii were extracted. A range of nuclear models based on energy density functionals reproduce well the observed smooth evolution of the nuclear size. Both the remarkable consistency of model prediction and the similarity of predictions for different isotopes suggest a transition to a regime in which shell effects have a diminished effect on the size compared with lighter nuclei.

Quantifying mass-dependent isotope fractionation and nuclear field shift effects for the light rare Earth elements in hydrous systems

The improving sensitivity of mass-spectrometers has opened the potential of using stable isotope signatures of the rare Earth elements (REE) as geochemical tracers. However, thus far only limited studies have utilised REE stable isotopes, despite resolvable variations having been observed in a range of systems. An interesting but poorly explored area remains variations in aqueous environments across a range of temperatures including seawater, marine sediments, ion adsorption deposits or hydrothermal systems. Furthermore, the magnitudes and competing effects of mass-dependent isotope fractionation and mass-independent nuclear field shift effects, which can be significant factor for heavy elements especially at high temperatures, remain poorly understood.To contribute to a holistic understanding of REE isotope signatures, we calculated reduced partition function ratios (as 103lnβ) for mass-dependent and nuclear field shift effects for aqueous La, Ce, and Nd complexes from first principles. Theoretical calculations were compared with experimental data, and this demonstrates that calculations involving a combination of two explicit hydration shells and additional implicit solvation effects are required to accurately describe the coordination and molecular vibrations of aqueous complexes. This data was then combined with speciation modelling of seawater and hydrothermal fluids to assess isotope fractionation in hydrous systems. The predicted magnitude of isotope fractionation is significant in low (T = 25 °C) temperature systems (Δ139/138LaMax-Min = 0.20 ‰, Δ142/140CeMax-Min = 0.33 ‰, Δ146/144NdMax-Min = 0.34 ‰) and remains above currently achievable analytical uncertainties even at high (T = 500 °C) temperatures (±0.015 ‰ for δ146/144Nd; ±0.040 ‰ for δ142/140Ce). Unless oxidation occurs, which is only relevant for Ce in terrestrial environments, nuclear field shift effects are negligible even at temperatures up to 500 °C. The large difference in nuclear charge radius between 140Ce and 142Ce strongly enriches the lighter Ce isotope in the higher oxidation state (103lnβCe(IV)-Ce(III) = −0.45 at 25 °C) which almost completely cancels out the opposing mass-dependent effect (103lnβCe(IV)-Ce(III) = +0.46 at 25 °C). This means that variations in δ142/140Ce isotope signatures cannot easily be related to oxidation in ancient or recent environments.

Absolute nuclear charge radius by Na-like spectral line separation in high-Z elements

Abstract We describe a novel technique to determine absolute nuclear radii of high-Z nuclides. Utilizing accurate theoretical atomic structure calculations together with precise measurements of extreme ultraviolet transitions in highly charged ions this method allows for precise determinations of absolute nuclear charge radii based upon the well-known nuclear radii of their neighboring elements. This method can work for elements without stable isotopes, and its accuracy may be competitive with current methods (electron scattering and muonic x-ray spectroscopy).

Nuclear charge radii of germanium isotopes around N = 40

Collinear laser spectroscopy measurements were performed on 68−74Ge isotopes (Z=32) at ISOLDE-CERN, by probing the 4s24p2P13→4s24p5sP1o3 atomic transition (269 nm) of germanium. Nuclear charge radii are determined via the measured isotope shifts, revealing a larger local variation than the neighboring isotopic chains. Nuclear density functional theory with the Fayans functionals Fy(Δr,HFB) and Fy(IVP), and the SV-min Skyrme describes the experimental data for the differential charge radii δ〈r2〉 and charge radii Rc within the theoretical uncertainties. The observed large variation in the charge radii of germanium isotopes is better accounted for by theoretical models incorporating ground state quadrupole correlations. This suggests that the polarization effects due to pairing and deformation contribute to the observed large odd-even staggering in the charge radii of the Ge isotopic chain.

Reconciling mean-squared radius differences in the silver chain through improved measurement and ab initio calculations

Nuclear charge radius differences in the silver isotopic chain have been reported through different combinations of experiment and theory, exhibiting a tension of two combined standard errors. This study investigates this issue by combining high-accuracy calculations for six low-lying states of atomic silver with an improved measurement of the 5s2S1/2−5p2P3/2 transition optical isotope shift. Our calculations predict measured electronic transition energies in Ag at the 0.3% level, the highest accuracy achieved in this system so far. We calculate electronic isotope shift factors by employing analytical response relativistic coupled-cluster theory and find that a consistent charge radius difference between Ag107,109 is returned when combining our calculations with the available optical isotope shift measurements. We therefore recommend an improved value for the mean-squared charge radius difference between Ag107 and Ag109 as 0.207(6) fm2, within one combined error from the value derived from muonic Ag experiments, and an updated set of charge radii differences across the isotopic chain. Published by the American Physical Society 2024

A strategy for high-entropy copper alloys composition design assisted by deep learning based on data reconstruction and network structure optimization

Complex mapping relationships between high-entropy alloy compositions and performances struggle to precisely elucidate by traditional machine learning models, hindering the accurate and efficient design of high-performance alloys. In this work, a novel alloy design strategy combined self-decision deep neural network, data reconstruction with network structure optimization was proposed, which effectively enhanced the model's ability to predict the mapping relationships between high-dimensional composition spaces and mechanical properties of alloy. Compared to other machine learning methods, significantly improves model prediction accuracy (hardness model: 97.98%; strength model: 94.40%). Through above model, the mechanical properties of 308 new (CuNiMn)-X high-entropy copper alloys was studied added other elements such as Al, Ti, Cr, and Fe, which designed and produced a novel (CuNiMn)60Al20Cr20 alloy with high hardness of 474 HV, high compressive strength of 2322 MPa, and high fracture strain of 25.20%. The primary factors influencing alloy performance and their respective thresholds were also quantitatively revealed (hardness: electronegativity deviation (0.02, 0.1) and nuclear charge deviation (0, 0.25); compressive strength: mean nuclear charge (25, 30) and mean atomic radius (134 p.m.)). These findings provide a new perspective and approach for the design and mechanism understanding of high-performance alloys with complex compositions.

Effects of center-of-mass correction and nucleon anomalous magnetic moments on nuclear charge radii

Effects of center-of-mass correction and nucleon anomalous magnetic moments on nuclear charge radii

Evaluating nuclear charge radii based on the mean mass-density parameter using BP neural networks

In this paper, we have successfully obtained the mean mass-density parameter ([Formula: see text]) using the nuclear masses AME2020 database and nuclear charge radius (CR) CR2013 database. The empirical formula is derived based on the relationship between [Formula: see text] and [Formula: see text] (the ratio of the number of neutrons to protons). Subsequently, we obtained an empirical formula for the difference in [Formula: see text] between two neighboring isotopes. By utilizing this empirical formula along with the AME2020 and CR2013 databases, we then calculated 625 charge radii for nuclei with [Formula: see text]. The root-mean-square deviation (RMSD) between the calculated values and the experimental values in the CR2013 database is 0.0075[Formula: see text]fm. The predicted nuclear CR values are comparable to those of other researches, which some predictions closely matching the experimental values measured in recent years. Additionally, this work used the Back Propagation (BP) neural network to establish a model for describing and predicting the difference in the mean mass-density parameter between two neighboring isotopes. The RMSD between the calculated and experimental values obtained using this model is 0.0039[Formula: see text]fm. Some of our predicted values have good accuracy and compared well with experimental values. Both of the above methods indicate that the nuclear CR relationship proposed in this paper based on the difference in mean mass-density parameter has simplicity and reliability.

Kink of the nuclear charge radius isotope shift and overlaps of the neutron and proton orbitals in lead

Within the relativistic mean field approximation, we analyse the kink effect (KE) in the evolution of the charge radius isotope shift of lead isotopes as a function of the neutron number N. We show that if the interactions between neutron and proton states responsible for the KE are assumed to be proportional either to the overlaps of their corresponding wave functions or to those of their corresponding probability density distributions, it is not possible, by themselves, to explain the KE. However, we find that the small component of the single-particle Dirac spinors plays a relevant role in the kink formation. By considering the contribution of the N−126 valence neutrons to the proton central potential, we can explain the generation of the KE and why neutrons in the 1i11/2 orbital are more kinky than when they are in the 2g9/2 orbital.

Nuclear Charge Radii of Silicon Isotopes.

The nuclear charge radius of ^{32}Si was determined using collinear laser spectroscopy. The experimental result was confronted with abinitio nuclear lattice effective field theory, valence-space in-medium similarity renormalization group, and mean field calculations, highlighting important achievements and challenges of modern many-body methods. The charge radius of ^{32}Si completes the radii of the mirror pair ^{32}Ar-^{32}Si, whose difference was correlated to the slope L of the symmetry energy in the nuclear equation of state. Our result suggests L≤60 MeV, which agrees with complementary observables.

Nuclear charge radius predictions based on eXtreme Gradient Boosting

Nuclear charge radii with 8 ≤ Z ≤ 100 are studied based on the eXtreme Gradient Boosting (XGBoost) method. Besides the proton, neutron, and mass numbers, the physical quantities related to the isospin, shell, and pairing effects are important to improve the performance of the XGBoost method by including them as the input variables. The XGBoost method describes the nuclear charge radii better than the Skyrme-Hartree–Fock-Bogoliubov (HFB)-21 model, especially for odd-Z nuclei. The root-mean-square deviation with respect to the experimental data is reduced from 0.025 fm of the HFB-21 model to 0.012 fm of the XGBoost method in the learning set. It is found that the XGBoost method has reliable extrapolation ability at least for the nuclei not far from the learning region, which is verified by comparison with the data in the newly measured experimental data. When extrapolated to the unknown region, the XGBoost predictions of charge radii are close to the HFB-21 results, and the deviations between them are generally less than 0.1 fm even within about 20 steps from the known region.

An improved effective liquid drop model for cluster radioactivity

The effective liquid drop model (ELDM) is improved by introducing an accurate nuclear charge radius formula and an analytic expression for assaulting frequency. Within the improved effective liquid drop model (IMELDM), the experimental cluster radioactivity half-lives of the trans-lead region are calculated. It is shown that the accuracy of the IMELDM is improved compared with that of the ELDM. At last, the cluster radioactivity half-lives that are experimentally unavailable for the trans-lead nuclei are predicted by the IMELDM. These predictions may be useful for searching for new candidates for cluster radioactivity in future experiments.

Nuclear charge radius predictions by kernel ridge regression with odd–even effects

Nuclear charge radius predictions by kernel ridge regression with odd–even effects

Charge radius relations derived from the nuclear masses for two neighboring isotopes

In this paper, we get the nuclear mass-density parameter of known mass and known charge radius by using the AME2020 nuclear mass database and the CR2013 nuclear charge radius database. For the nuclei with [Formula: see text], we obtained an empirical formula of the constant parameter equal to 0 for the difference of nuclear mass-density parameter between two neighboring isotope. That is, the nuclear mass-density parameter of the two neighboring isotopes was equal. By using this empirical formula combined with AME2020 and CR2013 databases, the calculated value of 625 nuclear charge radii was obtained. The root-mean-square deviation (RMSD) of nuclear charge radius that we have successfully obtained is [Formula: see text][Formula: see text]fm. In addition, one of the corrections is the neutron factor. This correction is the key improvement which reduces the RMSD to 0.0077[Formula: see text]fm. Considering the neutron shell effect, the different shell ranges were divided into two categories for correction, and the RMSD was reduced to 0.0056[Formula: see text]fm. Based on the revised empirical formula combined with the AME2020 database, the calculated and predicted values of nuclear charge radius were obtained with high accuracy. Some of these predictions are also very consistent with experimental values measured in recent years. In addition, we use BP neural network to study the difference of nuclear mass-density parameter on the basis of two categories. The RMSDs obtained are 0.0028[Formula: see text]fm and 0.0038[Formula: see text]fm, respectively. It can be seen that such a division has a certain degree of reliability and feasibility. These results show that the new relation proposed in this paper has simplicity and reliability, which can be compared with other local nuclear charge radius relations.

Isospin-dependence of the charge-changing cross-section shaped by the charged-particle evaporation process

We present the charge-changing cross sections (CCCS) of 11−15C, 13−17N, and 15,17−18O at around 300 MeV/nucleon on a carbon target, which extends to p-shell isotopes with N<Z for the first time. The Glauber model, which considers only the proton distribution of projectile nuclei, underestimates the cross sections by more than 10%. We show that this discrepancy can be resolved by considering the contribution from the charged-particle evaporation process (CPEP) following projectile neutron removal. Using nucleon densities from the deformed relativistic Hartree-Bogoliubov theory in continuum, we investigate the isospin-dependent CPEP contribution to the CCCS for a wide range of neutron-to-proton separation energy asymmetry. Our calculations, which include the CPEP contribution, agree well with existing systematic data and reveal an “evaporation peak” at the isospin symmetric region where the neutron-to-proton separation energy is close to zero. These results suggest that analysis beyond the Glauber model is crucial for accurately determining nuclear charge radii from CCCSs.

Revisiting the extraction of charge radii of 40Ca and 208Pb with muonic atom spectroscopy

The extractions of nuclear charge radii from muonic atom spectroscopy for 40Ca and 208Pb are revisited to analyze the model dependencies induced by employing a Fermi-type charge distribution. For that, the charge densities, together with the corresponding muonic transition energies, calculated by the covariant density functional theory are used as a benchmark. The root-mean-square deviation of transition energies is calculated to quantitatively investigate the sensitivities of transition energies to the details of the two-parameter Fermi distribution. It is found that the second and fourth moments of the charge distribution can be extracted accurately from the muonic atom spectroscopy without much model dependencies, whereas the obtained two-parameter Fermi distributions cannot reproduce the details of the benchmarking charge densities and, in particular, its surface-diffuseness parameter cannot be determined accurately with the present experimental uncertainties on the muonic transition energies.

Second flavor of heavy ions

The existence of the Second Flavor of Hydrogen Atoms (SFHA), predicted theoretically in 2001, has been confirmed by four different types of atomic or molecular experiments, and evidenced by two different types of astrophysical observations. The SFHA is based on the second analytical solution of the standard Dirac equation. Despite this solution is singular at small r, it can be matched with the regular solution inside the proton for the S-states, and thus becomes legitimate. The SFHA have only the S-states: so, in accordance to the selection rules of quantum mechanics they do not couple to the electromagnetic radiation (except for the 21 cm spectral line): they remain dark. In the present paper we extended the legitimacy of the second analytical solution of the Dirac equation outside the nucleus to heavy ions. We predicted the existence of the second flavor of heavy ions and thus the flavor symmetry of these ions. These ions have only the S-states, so that they remain dark just as the SFHA. This theoretical result has the fundamental importance in its own right. Also, it could encourage experimentalists to perform experiments for the verification of the existence of the second flavor of heavy ions. The most probable candidates are ions whose nuclei are double-magic and thus spherical. As an application of the above fundamental result, we referred to the comparison between the nuclear charge radius rn,μ, determined experimentally by the muonic x-ray transition energies, and the nuclear charge radius rn,e, determined experimentally from the elastic electron scattering. The comparison was possible for two spherical nuclei: for 40Ca20, as well as for 48Ca20. In each case, rn,e turned out to be by about 1% smaller, than rn,μ, the difference being well beyond the experimental error margin. We showed in both above examples, that a relatively small admixture (∼10%) of the second flavor of heavy ions in the target reconciles the values of the nuclear charge radius, measured by two different methods, in favor of the larger value. Finally, we noted that while the SFHA is one of the leading candidates for dark matter or a part of it, there are still unsuccessful attempts to find Weakly Interactive Massive Particles (WIMP) as a part of dark matter. We suggested that if there are massive dark matter particles, then more realistically they could be the second flavor of heavy ions, described in the present paper: they are really dark.

Nuclear charge radii and shape evolution of Kr and Sr isotopes with the deformed relativistic Hartree-Bogoliubov theory in continuum

Nuclear charge radii and shape evolution of Kr and Sr isotopes with the deformed relativistic Hartree-Bogoliubov theory in continuum

Collision-energy dependence of the Breit-Wheeler process in heavy-ion collisions and its application to nuclear charge radius measurements

The collision energy dependence of the cross section and the transverse momentum distribution of dielectrons from the Breit-Wheeler process in heavy-ion collisions are computed in the lowest-order QED and found to be sensitive to the nuclear charge distribution and the infrared divergence of the ultra-Lorentz-boosted Coulomb field. Within a given experimental kinematic acceptance, the cross section is found to increase while the pair transverse momentum ($\sqrt{\ensuremath{\langle}{p}_{T}^{2}\ensuremath{\rangle}}$) decreases with increasing beam energy. We demonstrate that the transverse-momentum component of Weizs\"acker-Williams photons is due to the finite extent of the charge source and electric field component in the longitudinal direction. We further clarify the connection between the nuclear charge distribution and the kinematics of produced ${e}^{+}{e}^{\ensuremath{-}}$ from the Breit-Wheeler process, and propose a criterion for the validity of the Breit-Wheeler process in relativistic heavy-ion collisions. Following this approach we demonstrate that the experimental measurements of the Breit-Wheeler process in ultrarelativistic heavy-ion collisions can be used to quantitatively constrain the nuclear charge radius. The extracted parameters show sensitivity to the impact parameter dependence, and can be used to study the initial-state and final-state effects in hadronic interactions.