arXiv subjects

Rong An

Publications and source records attributed to Rong An.

At least 19 recordsLinked to original sources

arXiv2026

Constraining tensor force terms with the charge radii difference of mirror-pair nuclei

Charge radii differences of mirror partner nuclei provide an alternative probe to pin down the interaction components in asymmetric nuclear matter. In this work, the differences in the charge radii of almost spherical mirror-paired nuclei $^{54}$Ni-$^{54}$Fe and $^{36}$Ca-$^{36}$S are used to constrain the magnitude of tensor terms in the Skyrme interactions. The calculated results suggest that a linear correlation can be found between the difference of charge radii of mirror partner nuclei and the adopted strengths of the triplet-odd and triplet-even tensor components. Besides, it suggests that charge radii differences of mirror-paired nuclei are more sensitive to the adopted strengths of the triplet-odd parameter $U$ rather than the triplet-even parameter $T$. Combining the quantitative constraint strengths of the triplet-even tensor part obtained from the magnetic dipole (M1) excitations, the charge-exchange Gamow-Teller (GT) states, and the spin-dipole (SD) excitations, the triplet-odd strengths are further constrained for the SLy5 as well as SGII effective interactions. This provides an alternative approach to constrain the appropriate magnitude of tensor force.

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arXiv2026

Input-driven analysis in predicting nuclear charge radii using Monte Carlo dropout Bayesian neural network

Nuclei charge radii play an essential role in understanding the fundamental interactions of finite quantum fermion systems. In this work, input-driven Bayesian neural network based on the Monte Carlo dropout approach has been built to characterize the systematic evolution of charge radii of nuclei with proton number $Z\geq20$ and mass number $A\geq40$. The motivated underlying mechanisms have been introduced into the input structures, which contain pairing effect, isospin asymmetry degree, the correlations between the valence nucleons and valence holes for neutron and proton, quadrupole deformation parameter $\beta_{20}$, and the local shape staggering phenomena of $^{181,183,185}$Hg isotopes.In addition, shell quenching effect is also taken into account by incorporating the modified Casten factor $P^{*}$ into the input structure. The quadrupole deformation parameters $\beta_{20}$ derived from finite-range droplet model (FRDM), relativistic mean field (RMF) theory and Weizs\"{a}cker-Skyrme (WS) approach are employed to analyze the local variations of nuclear charge radii.The hyperparameter is adjusted automatically in the constructed model.The calibrated results give comparable root-mean-square deviations (RMSD) in the training and validation sets with various shape deformation inputs. The abrupt increase in charge radii around N=60 is well reproduced along Z=37-40 isotopic chains, but this trend is less pronounced along Z=36 and 41 chains. This provides a indicator to confirm the rapid shape-phase transition regions around N=60 from the perspective of finite nuclei size. Shell quenching effect of charge radii along the bismuth isotopes are reproduced well at N=126, but slight deviations can be encountered due to the absence of high-order octupole deformation around N=130 regions and shape-staggering phenomena toward neutron-deficient regions, respectively. This means that...

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arXiv2025

Shell effects in nuclear charge radii based on Skyrme density functionals

A unified description of the charge radii throughout the entire nuclide chart plays an essential role for our understanding of nuclear structure and fundamental nuclear interactions. In this work, the influence of new term, which catches the spirit of neutron and proton pairs condensation around Fermi surface, on the charge radii has been investigated based on the Skyrme density functionals with the effective forces SLy5 and SkM$^{*}$. The differential charge radii of even-even Ca, Ni, Sn, and Pb isotopes are employed to evaluate the validity of this theoretical model. Meanwhile, the results obtained by the relativistic density functional with the effective Lagrangian NL3 are also shown for the quantitative comparison. The calculated results suggest that the modified model can improve the trend of changes of the differential charge radii along Ca, Ni, Sn, and Pb isotopic chains, especially the shell closure effect at the neutron numbers $N=28$, 82 and 126. The shell quenching phenomena of charge radii can also be predicted at the neutron number $N=50$ along the corresponding Ni and Sn isotopes, respectively. The inverted parabolic-like shapes between the two fully filled shells can also be observed, but the amplitude is gradually weakened from Ca to Pb isotopic chains. Combining the existing literatures, it suggests that the discontinuous behavior in nuclear charge radii can be described well by considering the influence of neutron Cooper pairs condensation around Fermi surface.

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arXiv2025

Neutron Magic Numbers in $sd$ Shell from Nuclear Charge Radii within Neutron-Proton Correction around the Fermi Surface

Charge radii are sensitive indicators to identify the nuclear structure phenomena throughout the whole nuclide chart. In particular, the shrunken trend of changes of charge radii along a long isotopic chain is intimately associated with the shell quenching effect. In this work, the systematic evolution of charge radii along the proton numbers $Z=8$, $10$, $12$, $14$, $18$ isotopes is investigated by a relativistic Hartree Bogoliubov model. A ansatz about neutron-proton correlation around Fermi surface is considered for describing the abnormal behavior of nuclear charge radii. Our results show that the neutron-proton pairing corrections around the Fermi surface lead to a sudden strengthening of the charge radii of these isotopic chains at $N=8$, 20 and 28, reflecting the fact that this correction enhances the shell closure across $N=8$, 20 and 28. The reproduction of the $N=14$ charge radius in the Mg isotopes is affected by the way in which pairing correlations are handled, with BCS theory overestimating the shell effect of $N=14$, and the Bogoliubov quasiparticle transformation suggests a stronger pairing correlation near the proton Fermi surface, which is more consistent with experimental results. An analysis of the deviations from the theoretical and available experimental data for the charge radii of the 24 selected even-even nuclei shows that the neutron-proton pairing correction around the Fermi surface has an improved effect on the calculation of the charge {radii} using the meson-exchange effective interactions, but it does not help to significantly improve the results calculated by the density-dependent effective interactions.

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arXiv2025

Implication of shell quenching in scandium isotopes around N=20

Shell closure structures are commonly observed phenomena associated with nuclear charge radii throughout the nuclide chart. Inspired by recent studies demonstrating that the abrupt change can be clearly observed in the charge radii of the scandium isotopic chain across the neutron number $N=20$, we further review the underlying mechanism of the enlarged charge radii for $^{42}$Sc based on the covariant density functional theory. The pairing correlations are tackled by solving the state-dependent Bardeen-Cooper-Schrieffer equations. Meanwhile, the neutron-proton correlation around the Fermi surface derived from the simultaneously unpaired proton and neutron is appropriately considered in describing the systematic evolution of nuclear charge radii. The calculated results suggest that the abrupt increase in charge radii across the $N=20$ shell closure seems to be improved along the scandium isotopic chain if the strong neutron-proton correlation is properly included.

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arXiv2024

Potential signature of new magicity from universal aspects of nuclear charge radii

Shell quenching phenomena in nuclear charge radii are typically observed at the well-established neutron magic numbers. However, the recent discovery of potential new magic numbers at the neutron numbers $N = 32$ and $N = 34$ has sparked renewed interest in this mass region. This work further inspects into the charge radii of nuclei around the $N = 28$ shell closure using the relativistic Hartree-Bogoliubov model. We incorporate meson exchange and point-coupling effective nucleon-nucleon interactions alongside the Bogoliubov transformation for pairing corrections. To accurately capture the odd-even staggering and shell closure effects observed in charge radii, neutron-proton correlations around Fermi surface are explicitly considered. The charge radii of Ca and Ni isotopes are used to test the theoretical model and show an improvement with neutron-proton pairing corrections, in particular for neutron-rich isotopes. Our calculations reveal a inverted parabolic-like trend in the charge radii along the $N = 28$ isotones for proton numbers $Z$ between 20 and 28. Additionally, the shell closure effect of $Z = 28$ persists across the $N = 28$, 30, 32, and 34 isotonic chains, albeit with a gradual weakening trend. Notably, the significantly abrupt changes in charge radii are observed across $Z = 22$ along both the $N = 32$ and $N = 34$ isotonic chains. This kink at $Z = 22$ comes from the sudden decrease of the neuron-proton correlation around Fermi surfaces across $Z = 22$ for $N = 30$, 32, and 34 isotones, and might provide a signature for identifying the emergence of neutron magic numbers $N = 32$ and 34. Furthermore, the calculated charge radii for these isotonic chains ($N = 28$, 30, 32, and 34) can serve as reliable guidelines for future experimental measurements.

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arXiv2024

Shell quenching in nuclear charge radii based on Monte Carlo dropout Bayesian neural network

Charge radii can be generally used to encode information about various fine structures of finite nuclei. In this work, a constructed Bayesian neural network based on the Monte Carlo dropout approach is proposed to accurately describe the charge radii of nuclei with proton number $Z\geq20$ and mass number $A\geq40$. More motivated underlying mechanisms are incorporated into this combined model in addition to the basic building blocks with the specific number of protons and neutrons, which naturally contain the pairing effect, the isospin effect, the shell closure effect associated with the Casten factor $P$, the valence neutrons, the valence protons, the quadrupole deformation $\beta_{20}$, the high order hexadecapole deformation $\beta_{40}$, and the local shape staggering effect of $^{181,183,185}$Hg. To avoid the distorted cases of the traditional Casten factor at the fully filled shells, the modified Casten factor $P^{*}$ is introduced into the input structure parameter sets. The standard root-mean-square deviation is reduced to $0.0084$ fm for the training data set and $0.0124$ fm for the validation data set with the modified Casten factor $P^{*}$. Meanwhile, the shell closure effect of nuclear charge radii can be reproduced remarkably well. We have successfully demonstrated the ability of this constructed model to significantly increase the accuracy in predicting the nuclear charge radii.

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arXiv2024

Implication of odd-even staggering in the charge radii of calcium isotopes

Inspired by the profoundly observed odd-even staggering and the inverted parabolic-like shape in charge radii along calcium isotopic chain, the ground state properties of calcium isotopes are investigated by constraining the root-mean-square (rms) charge radii under the covariant energy density functionals with effective forces NL3 and PK1. In this work, the pairing correlations are tackled by solving the state-dependent Bardeen-Cooper-Schrieffer equations. The calculated results suggest that the binding energies obtained by the radius constraint method have been slightly changed by about $0.2\%$. But for charge radii, the corresponding results deriving from NL3 and PK1 forces have been increased by about $1.0\%$ and $2.0\%$, respectively. This means that charge radius is a more sensitive quantity in the calibrated protocol. Meanwhile, it is found that the reproduced charge radii of calcium isotopes are attributed to the rather strong isospin dependence of effective potential. The odd-even oscillation behavior can also be presented in the proton Fermi energies along calcium isotopic family, but keep opposite trends with respect to the corresponding binding energies and charge radii. As encountered in charge radii, the weakened odd-even oscillation behavior is still emerged from the proton Fermi energies at the neutron numbers $N=20$ and $28$ as well, but not in binding energies.

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arXiv2024

Correlation between the charge radii difference in mirror partner nuclei and the symmetry energy slope

A correlation between the charge radii difference of mirror partner nuclei $\Delta{R_{\mathrm{ch}}}$ and the slope parameter $L$ of symmetry energy has been built to ascertain the equation of state of isospin asymmetric nuclear matter. In this work, the influences of pairing correlations and isoscalar compression modulus on the $\Delta{R_{\mathrm{ch}}}$ are systematically investigated based on the Skyrme energy density functional theory. The calculated results suggest that the linear correlation between $\Delta{R_{\mathrm{ch}}}$ and $L$ is decreased by the surface pairing correlations. The slope parameter deduced from the difference of charge radii of mirror-pair nuclei $^{32}$Ar-$^{32}$Si, $^{36}$Ca-$^{36}$S, $^{38}$Ca-$^{38}$Ar, and $^{54}$Ni-$^{54}$Fe falls into the range of $L$=42.57-50.64 MeV, that is, the rather soft equation of state of asymmetric nuclear matter. Besides, the range of the slope parameter can also be influenced by the effective forces classified by various isoscalar incompressibility coefficients.

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arXiv2023

New quantification of symmetry energy from neutron skin thicknesses of $^{48}$Ca and $^{208}$Pb

Precise knowledge of the nuclear symmetry energy can be tentatively calibrated through multimessenger constraints. The neutron skin thickness of a heavy nucleus is one of the most sensitive indicators for probing the isovector components of effective interactions in asymmetric nuclear matter. Recent studies have suggested that the experimental data from the CREX and PREX2 Collaborations are not mutually compatible within existing nuclear models. In this study, we review the quantification of the slope parameter of symmetry energy $L$ from the neutron skin thicknesses of $^{48}$Ca and $^{208}$Pb. Skyrme energy density functionals classified by various isoscalar incompressibility coefficients $K$ are employed to evaluate the bulk properties of finite nuclei. The calculated results suggest that the slope parameter $L$ deduced from $^{208}$Pb is sensitive to the compression modulus of symmetric nuclear matter, but not that from $^{48}$Ca. The effective parameter sets classified by $K=220$ MeV can provide an almost overlaping range of $L$ from $^{48}$Ca and $^{208}$Pb.

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arXiv2023

Improved description of nuclear charge radii: Global trends beyond $N=28$ shell closure

Charge radii measured with high accuracy provide a stringent benchmark for characterizing nuclear structure phenomena. In this work, the systematic evolution of charge radii for nuclei with $Z=19$-$29$ is investigated through relativistic mean field theory with effective forces NL3, PK1, and NL3$^{*}$. The neutron-proton ($np$) correlation around Fermi surface originated from the unpaired neutron and proton has been taken into account tentatively in order to reduce the overestimated odd-even staggering of charge radii. This improved method can give an available description of charge radii across $N=28$ shell closure. A remarkable observation is that the charge radii beyond $N=28$ shell closure follow the similarly steep increasing trend, namely irrespective of the number of protons in the nucleus. Especially, the latest results of charge radii for nickel and copper isotopes can be reproduced remarkably well. Along $N=28$ isotonic chain, the sudden increase of charge radii is weakened across $Z=20$, but presented evidently across $Z=28$ closed shell. The abrupt changes of charge radii across $Z=22$ are also shown along $N=32$ and $34$ isotones, but the latter with a less slope. This seems to provide a sensitive indicator to identify the new magicity of a nucleus with universal trend of charge radii.

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arXiv2023

Constraining nuclear symmetry energy with the charge radii of mirror-pair nuclei

The nuclear charge radius plays a vital role in determining the equation of state of isospin asymmetric nuclear matter. Based on the correlation between the differences in charge radii of mirror-partner nuclei and the slope parameter ($L$) of symmetry energy at the nuclear saturation density, an analysis of the calibrated slope parameter $L$ was performed in finite nuclei. In this study, relativistic and non-relativistic energy density functionals were employed to constrain the nuclear symmetry energy through the available databases of the mirror-pair nuclei $^{36}$Ca-$^{36}$S, $^{38}$Ca-$^{38}$Ar, and $^{54}$Ni-$^{54}$Fe. The deduced nuclear symmetry energy was located in the range 29.89-31.85 MeV, and $L$ of the symmetry energy essentially covered the range 22.50-51.55 MeV at the saturation density. Moreover, the extracted $L_s$ at the sensitivity density $\rho_{s}=0.10~\mathrm{fm}^{-3}$ was located in the interval range 30.52-39.76 MeV.

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arXiv2022

Nuclear charge radii in Bayesian neural networks revisited

In this work, a refined Bayesian neural network (BNN) based approach with six inputs including the proton number, mass number, and engineered features associated with the pairing effect, shell effect, isospin effect, and ``abnormal" shape staggering effect of $^{181,183,185}$Hg, is proposed to accurately describe nuclear charge radii. The new approach is able to well describe the charge radii of atomic nuclei with $A\ge40$ and $Z\ge20$. The standard root-mean-square (rms) deviation is $0.014$ fm for both the training and validation data. In particular, the predicted charge radii of proton-rich and neutron-rich calcium isotopes are found in good agreement with data. We further demonstrate the reliability of the BNN approach by investigating the variations of the rms deviation with extrapolation distances, mass numbers, and isospin asymmetries.

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arXiv2021

Local variations of charge radii for nuclei with even $Z$ from 84 to 120

Pronounced changes of nuclear charge radii provide a stringent benchmark on the theoretical models and play a vital role in recognizing various nuclear phenomena. In this work, the systematic evolutions of nuclear charge radii along even $Z$=84-120 isotopic chains are firstly investigated by the recently developed new ansatz under the covariant density functional. The calculated results show that the shell closure effects of nuclear charge radii are remarkably shown at the neutron numbers $N=126$ and 184. Interestingly, the arch-like shapes of charge radii between these two strong neutron closed shells are naturally observed. Across the $N=184$ shell closure, the abrupt increase in charge radii is still evidently emerged. In addition, the rapid raise of nuclear charge radii from the neutron numbers $N=138$ to $N=144$ is also disclosed clearly in superheavy regions due to the enhanced shape deformation.

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arXiv2021

Novel Bayesian neural network based approach for nuclear charge radii

Charge radius is one of the most fundamental properties of a nucleus. However, a precise description of the evolution of charge radii along an isotopic chain is highly nontrivial, as reinforced by recent experimental measurements. In this paper, we propose a novel approach which combines a three-parameter formula and a Bayesian neural network. We find that the novel approach can describe the charge radii of all $A\ge40$ and $Z\ge20$ nuclei with a root-mean-square deviation about 0.015 fm. In particular, the charge radii of the calcium isotopic chain are reproduced very well, including the parabolic behavior and strong odd-even staggerings. We further test the approach for the potassium isotopes and show that it can describe well the experimental data within uncertainties.

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arXiv2021

Enhancement of electron-positron pairs in combined potential wells with linear chirp frequency

The effect of linear chirp frequency on the process of electron-positron pairs production from vacuum in the combined potential wells is investigated by computational quantum field theory. Numerical results of electron number and energy spectrum under different frequency modulation parameters are obtained. By comparing with the fixed frequency, it is found that frequency modulation has a significant enhancement effect on the number of electrons. Especially when the frequency is small, appropriate frequency modulation enhances multiphoton processes in pair creation, thus promoting the pair creation. However, the number of electrons created by high frequency oscillating combined potential wells decreases after frequency modulation due to the phenomenon of high frequency suppression. The contours of the number of electrons varying with frequency and frequency modulation parameters are given, which may provide theoretical reference for possible experiments.

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arXiv2021

Odd-even staggering and shell effects of charge radii for nuclei with even $Z$ from $36$ to $38$ and from $52$ to $62$

A unified theoretical model reproducing charge radii of known atomic nuclei plays an essential role in making extrapolations for unknown nuclei. Recently developed new ansatz which phenomenologically takes into account the neutron-proton short-range correlations ($np$-SRCs) can describe the discontinuity properties and odd-even staggering (OES) effect of charge radii along isotopic chains remarkably well. In this work, we further review the modified root-mean-square (rms) charge radii formula in the framework of relativistic mean field (RMF) theory. The charge radii are calculated along various isotopic chains that include the nuclei featuring the $N=50$ and $82$ magic shells. Our results suggest that RMF with and without considering a correction term give an almost similar trend of nuclear size for some isotopic chains with open proton shell, especially the abrupt increases across the strong neutron closed shells and the OES behaviors. This reflects that the $np$-SRCs have almost no influence for some nuclei due to the strong coupling between different levels around Fermi surface. The weakening OES behavior of nuclear charge radii is observed generally at completely filled neutron shells and this may be proposed as a signature of magic indicator.

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arXiv2021

Evolution of nuclear charge radii in copper and indium isotopes

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton ($np$) correlations, is here applied for the first time to the study of odd-$Z$ copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3$^{*}$ parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across $N=50$ and $82$ shell closures are clearly reproduced in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be described remarkably well between two neutron magic numbers, namely $N=28$ to $50$ for copper isotopes and $N=50$ to $82$ for indium isotopes. This implies that the $np$-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-$Z$ isotopic chains. Also, our conclusions have almost no dependence on the effective forces.

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