P. Van Isacker
In the framework of the interacting boson model, relations are derived between nuclear charge radii, electric monopole transition rates, and summed magnetic dipole transition in even-even nuclei. The proposed correlations are tested in the rare-earth region.
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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 clos…
The momentum projected SU(3) Chiral Color Dielectric Model (CCDM) is employed to calculate the charge root mean square radii and charge distributions of hyperons. We compare our result with Skyrme, MIT bag and Cloudy Bag model results. The charge distribution of $Λ$ in CCDM is similar to that of Skyrme Model prediction.
The artificial neural networks (ANNs) have emerged with successful applications in nuclear physics as well as in many fields of science in recent years. In this paper, by using (ANNs), we have constructed a formula for the nuclear charge radii. Statistical modeling of nuclear charge radii by using ANNs has been seen as to be successful. Also, the charge radii, binding energies and two-neutron separation energies of Sn isotopes have been calculated by implementing of the new formula in Hartree-Fock-Bogoliubov (HFB) calculations. The results of the study shows that the new formula is useful for …
A feed-forward neural network model is trained to calculate the nuclear charge radii. The model trained with input data set of proton and neutron number $Z,N$, the electric quadrupole transition strength $B(E2)$ from the first excited 2$^+$ state to the ground state, together with the symmetry energy. The model reproduces well not only the isotope dependence of charge radii, but also the kinks of charge radii at the neutron magic numbers $N=82$ for Sn and Sm isotopes, and also $N=126$ for Pb isotopes. The important role of $B(E2)$ value is pointed out to reproduce the kink of the isotope depen…
The shell effect and isospin effect in nuclear charge radii are systematically investigated and a four-parameter formula is proposed for the description of the root-mean-square (rms) charge radii by combining the shell corrections and deformations of nuclei obtained from the Weizsäcker-Skyrme mass model. The rms deviation with respect to the 885 measured charge radii falls to 0.022 fm. The proposed formula is also applied for the study of the charge radii of super-heavy nuclei and nuclear symmetry energy. The linear relationship between the slope parameter L of the nuclear symmetry energy and …
A short review of existing efforts to understand charge radii and related indicators on a global scale within the covariant density functional theory (CDFT) is presented. Using major classes of covariant energy density functionals (CEDFs), the global accuracy of the description of experimental absolute and differential charge radii within the CDFT framework has been established. This assessment is supplemented by an evaluation of theoretical statistical and systematic uncertainties in the description of charge radii. New results on the accuracy of the description of differential charge radii i…
Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, R_mir, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability. In particular, this qu…
Root-mean-square charge radii are discussed in terms of spherical Energy Density Functional (EDF) models corrected for quadrupole deformations. Comparisons between experiment and theory are made for the absolute radii of all even-even nuclei, for the isotonic shift between cadmium and tin isotopes, the isotopic shifts of the calcium isotopes and the isotonic shift for nuclei with $ N=28 $. We conclude that the data are well described in this approach, except for the sharp rise just after the neutron magic numbers.
Quadrupole moments and charge radii in cadmium isotopes are studied from a microscopic perspective. The results obtained from self-consistent deformed Hartree-Fock+BCS calculations with Skyrme forces are compared with isomer and isotope shifts measured from high resolution laser spectroscopy experiments. The microscopic calculations reproduce fairly well the main features observed in those isotopes that include the linear increase with the neutron number of the quadrupole moments of the 11/2- isomers, as well as the parabolic behavior of the mean-square charge radii difference between isomers …
Ab initio charge form factors and radii of light isoscalar nuclei: Role of the two-body charge density
本研究通过从头计算方法，利用双核电荷密度算符，提高了轻同量核电荷形式因子和半径的预测精度，揭示了双核电荷密度在解决核电荷半径低估问题中的关键作用。
We apply the recently proposed RMF(BCS)* ansatz to study the charge radii of the potassium isotopic chain up to $^{52}$K. It is shown that the experimental data can be reproduced rather well, qualitatively similar to the Fayans nuclear density functional theory, but with a slightly better description of the odd-even staggerings (OES). Nonetheless, both methods fail for $^{50}$K and to a lesser extent for $^{48,52}$K. It is shown that if these nuclei are deformed with a $β_{20}\approx-0.2$, then one can obtain results consistent with experiments for both charge radii and spin-parities. We argue…
A simple superfluid model with an effective four body interaction of monopole pairing type is used to explain the staggering of the charge radii in the isotope chains. The contribution of deformation and of the particle number projection are analyzed for the Sn isotopes. Good results are obtained for the staggering parameters and neutron pairing energies.
Correlation between the rms nucleus charge radius and their deformation, isospin asymmetry, mass and charge numbers are presented. Four parameters radius parametrization formula is proposed. Ratio of experimental to theoretical value distribution exhibit variation equal to 0.0044, i.e. it corresponds to the vaule of experimental errors. Observed correlations can impose interesting constraints on the form of the nuclear equation of state.
The interacting boson model (IBM) of Arima and Iachello is applied to calculate nuclear charge radii and electric monopole transitions of even-even nuclei in the rare-earth region. Consistent operators are used for the two observables. A relation between summed M1 strength and $ρ({\rm E0})$ values is pointed out.
Charge radii of Sn, Ba, Yb, and Pb isotopes are calculated within Hartree-Fock-Bogoliubov theory with a Skyrme force and a density-dependent delta-force pairing. We investigate mean field effects of the pairing upon odd-even staggering of isotope shifts. HFB equations are solved in the canonical basis. Odd nuclei are treated in the blocking approximation.
We compute the charge radii of even-mass neon and magnesium isotopes from neutron number N = 8 to the dripline. Our calculations are based on nucleon-nucleon and three-nucleon potentials from chiral effective field theory that include delta isobars. These potentials yield an accurate saturation point and symmetry energy of nuclear matter. We use the coupled-cluster method and start from an axially symmetric reference state. Binding energies and two-neutron separation energies largely agree with data and the dripline in neon is accurate. The computed charge radii have an estimated uncertainty o…
Recently, charge radii and ground-state electromagnetic moments of Li and Be isotopes were measured precisely. We have performed large-scale ab initio no-core shell model calculations for these isotopes using high-precision nucleon-nucleon potentials. The isotopic trends of our computed charge radii and quadrupole and magnetic-dipole moments are in good agreement with experimental results with the exception of the 11Li charge radius. The magnetic moments are in particular well described, whereas the absolute magnitudes of the quadrupole moments are about 10% too small. The small magnitude of t…
The charge radii of calcium isotopes within relativistic density functional theory: nucleon's finite-size and quadrupole shape fluctuation effects
该研究在密度泛函理论中首次自洽考虑核子有限大小和形状零点运动效应，成功解释了钙同位素电荷半径异常，并发现这些效应对锡镉同位素位移同样重要。
The anomalous behaviour of the charge radii of the isotopic chain of Pb nuclei has been studied in the relativistic mean field theory. It has been shown that the relativistic mean field provides an excellent description of the anomalous kink in the isotopic shifts about $^{208}$Pb. This contrasts strongly from the Skyrme mean field, where almost all the known and realistic forces fail to reproduce the observed trend in the empirical data on the charge radii. The results have been discussed in the perspective of differences in the ansätze of the relativistic and the Skyrme mean-field theories.
The analysis of self-consistency and proton-neutron interaction effects in the buildup of differential charge radii has been carried out in covariant density functional theoretical calculations without pairing interaction. Two configurations of the $^{218}$Pb nucleus, generated by the occupation of the neutron $1i_{11/2}$ and $2g_{9/2}$ subshells, are compared with the ground state configuration in $^{208}$Pb. The interaction of added neutron(s) and the protons forming the $Z=82$ proton core is responsible for a major contribution to the buildup of differential charge radii. It depends on the …
In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction. We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei w…
The evolution of the ground-state nuclear shapes in neutron-rich Sr, Zr, and Mo isotopes, including both even-even and odd-A nuclei, is studied within a self-consistent mean-field approximation based on the D1S Gogny interaction. Neutron separation energies and charge radii are calculated and compared with available data. A correlation between a shape transition and a discontinuity in those observables is found microscopically. While in Sr and Zr isotopes the steep behavior observed in the isotopic dependence of the charge radii is a consequence of a sharp prolate-oblate transition, the smooth…
Neutron Magic Numbers in $sd$ Shell from Nuclear Charge Radii within Neutron-Proton Correction around the Fermi Surface
本文用相对论性Hartree-Bogoliubov模型并引入费米面附近中子-质子配对修正，研究$sd$壳层同位素链电荷半径，揭示其对$N=8$、20、28壳闭合及不同有效相互作用计算效果的影响。
Extracting nuclear charge radii from binding energies: a single-parameter empirical formula with structural corrections
研究利用核结合能数据为电荷半径建模，提出单参数公式$\mathrm{BECR}_\mathrm{1p}$，结合能关联与结构修正，在实验电荷半径数据上验证，经多步修正及AKRR处理降低偏差，并用此公式预测大量核的电荷半径。
The charge radii and the decay rates of the pion and kaons are calculated, using the relativistic equation of motion with a linear potential. Those physical quantities are quite well explained with the current quark masses in the case of the pion. It is found that the Van Royen-Weisskopf paradox can be cleared out only in the linear potential model by considering the color degree of freedom of the quark in the meson. The physical quantities for the kaon are not so satisfactory that it should be required to reconsider the Cabibbo-Kobayashi-Maskawa matrix element in the kaon decay.
Radii of charge and neutron distributions are fundamental nuclear properties. They depend on both nuclear interaction parameters related to the equation of state of infinite nuclear matter and on quantal shell effects, which are strongly impacted by the presence of nuclear surface. In this work, by studying the dependence of charge and neutron radii, and neutron skin, on nuclear matter parameters, we assess different mechanisms that drive nuclear sizes. We apply nuclear density functional theory using a family of Skyrme functionals obtained by means of different optimization protocols targetin…
Shell effects in nuclear charge radii based on Skyrme density functionals
本研究基于含SLy5和SkM*有效力的Skyrme密度泛函，引入费米面附近中子对凝聚相关新项，改善了多种同位素链电荷半径变化趋势及壳层效应的描述，验证了该机制对核电荷半径不连续行为的解释作用。
A systematic study of energy spectra throughout the rare-earth region (even-even nuclei from $_{58}$Ce to $_{74}$W) is carried out in the framework of the interacting boson model (IBM), leading to an accurate description of the spherical-to-deformed shape transition in the different isotopic chains. The resulting IBM Hamiltonians are then used for the calculation of nuclear charge radii (including isotope and isomer shifts) and electric monopole transitions with consistent operators for the two observables. The main conclusion of this study is that an IBM description of charge radii and electr…
Charge radii and their deformation correlation for even-$Z$ nuclei in deformed relativistic Hartree-Bogoliubov theory in continuum
本文采用连续介质形变相对论Hartree-Bogoliubov理论（DRHBc）与PC-PK1泛函，研究了偶$Z$核电荷半径及其形变关联，发现引入形变显著提升了对闭壳间原子核电荷半径的描述，并揭示了电荷半径随形变变化的多样性及其与壳结构的联系。
Radial and orbital decomposition of charge radii of Ca nuclei:Comparative study of Skyrme and Fayans functionals
本研究在密度泛函理论框架下分解Ca核电荷半径的径向与轨道贡献，比较Skyrme和Fayans泛函，揭示Fayans泛函在N<20和20≤N≤28区域行为的共同起源，强调需同时描述两个区域。
Radii of nuclear charge distributions carry information about the strong and electromagnetic forces acting inside the atomic nucleus. While the global behavior of nuclear charge radii is governed by the bulk properties of nuclear matter, their local trends are affected by quantum motion of proton and neutron nuclear constituents. The measured differential charge radii $δ\langle r^2_c\rangle$ between neutron numbers $N=28$ and $N=40$ exhibit a universal pattern as a function of $n=N-28$ that is independent of the atomic number. Here we analyze this remarkable behavior in even-even nuclei from c…
Shape deformations and charge radii, basic properties of atomic nuclei, are influenced by both the global features of the nuclear force and the nucleonic shell structure. As functions of proton and neutron number, both quantities show regular patterns and, for nuclei away from magic numbers, they change very smoothly from nucleus to nucleus. In this paper, we explain how the local shell effects are impacting the statistical correlations between quadrupole deformations and charge radii in well-deformed even-even Er, Yb, and Hf isotopes. This implies, in turn, that sudden changes in correlations…
Based on the systematic investigation of the data available for $A \geq 40$, a $Z^{1/3}$ dependence for the nuclear charge radii is shown to be superior to the generally accepted $A^{1/3}$ law. A delicate scattering of data around $R_c/Z^{1/3}$ is infered as owing to the isospin effect and a linear dependence of $R_c/Z^{1/3}$ on $N/Z$ (or $(N-Z)/2$) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. Wit…
We investigate the correlation between nuclear neutron radii and the radius of neutron stars. We use a well-established hadronic SU(3) model based on chiral symmetry that naturally includes non-linear vector meson and scalar meson - vector meson couplings. The relative strengths of the couplings modify the nuclear isospin-dependent interactions. We study the dependence of nuclear and neutron star radii on the coupling strengths. The relevance of the results for parity-violating electron-nucleus scattering and the URCA process in neutron stars is discussed.
We study the nuclear ground-state properties by using the unitary-model-operator approach (UMOA). Recently, the particle-basis formalism has been introduced in the UMOA and enables us to employ the charge-dependent nucleon-nucleon interaction. We evaluate the ground-state energies and charge radii of $^{4}$He, $^{16}$O, $^{40}$Ca, and $^{56}$Ni with the charge-dependent Bonn potential. The ground-state energy is dominated by the contributions from the one- and two-body cluster terms, while, for the radius, the one-particle-one-hole excitations are more important than the two-particle-two-hole …
Electromagnetic radii of light nuclei from variational Monte Carlo calculations
本文基于变分蒙特卡罗和Norfolk相互作用，计算了 $A \le 10$ 轻核的电荷与磁半径，发现电荷半径与实验值误差在5%以内，并呼吁精确测量较重系统的磁半径。
Effects of center-of-mass correction and nucleon anomalous magnetic moments on nuclear charge radii
本文利用相对论Hartree-Bogoliubov模型系统研究质心修正与核子反常磁矩对核电荷半径的影响，发现两者效应量级相当且显著影响轻至重核的电荷半径。
We study the consistency of the description of charge distributions and radii of nuclear clusters obtained with semiclassical nuclear pasta models. These nuclei are expected to exist in the low density outer crust of neutron stars. Properties of the arising clusterized nucleon matter can be compared to realistic nuclear properties as experimentally extracted on earth. We focus on non iso-symmetric light clusters with nucleon number $8 \le A \le 30$ and use Monte Carlo many-body techniques. We simulate isotopic chains for a set of selected nuclei using a model Hamiltonian consisting of the usua…
Octet hyperon charge radii are calculated in a chiral constituent quark model including electromagnetic exchange currents between quarks. In impulse approximation one observes a decrease of the hyperon charge radii with increasing strangeness. This effect is reduced by exchange currents. Due to exchange currents, the charge radius of the negatively charged hyperons are close to the proton charge radius.
We study the effects of short- and long-range correlations on the charge radii of Ca isotopes. We start our investigation with an independent particle model consisting in Hartree-Fock plus Bardeen-Cooper-Schrieffer calculations with finite-range effective nucleon-nucleon interactions of Gogny type. The short-range correlations effects are evaluated by considering all the terms of a cluster expansion containing a single correlation line. The long-range correlations are taken into account by including the coupling with the quasi-particle random phase approximation phonons. While the effects of t…
Potential signature of new magicity from universal aspects of nuclear charge radii
本研究利用相对论Hartree-Bogoliubov模型，通过考虑中子-质子关联，发现$N=28$同中子素链电荷半径呈倒抛物线趋势，并在$Z=22$处观察到突变，为$N=32$和34新幻数的存在提供潜在特征信号。
Charge radii of atomic nuclei and shell effects
本研究分析了球形原子核均方根电荷半径的实验数据，通过相对电荷半径 x(N,N_sh,Z) 揭示了跨越中子壳层时的规律，发现了 N_sh=8,28,50 和 82 壳层的体现，并预测了硫-30 的未知电荷半径。
Charge radii of calcium isotopes within relativistic configuration-interaction density functional theory
研究在ReCD理论框架下探究钙同位素电荷半径，通过纳入超出平均场的关联，改进了对其势能面、四极形变参数等的描述，再现了特殊电荷半径，改进奇偶交错描述，且奇数A同位素势能面有二级局部最小值，为相关研究提供了新认识。
We studied the charge radius, rms radius and neutron skin thickness $Δr_{np}$ in even-even isotopes of Si, S, Ar and Ca and isotones of N =20, 28, 50 and 82. The $Δr_{np}$ in doubly-magic $^{48}$Ca, $^{68}$Ni, $^{120,132}$Sn and $^{208}$Pb nuclei has also been calculated. Theoretical calculations are done with the Hartree-Fock-Bogoliubov theory with the effective Skyrme interactions. Calculated theoretical estimates are in good agreement with the recently available experimental data. The charge radii for Si, S, Ar and Ca isotopes is observed to be minimum at neutron number N =14. The theoretic…
Global prediction of nuclear charge density distributions using deep neural network
本文提出融合相对论密度泛函理论数据与1014个核实验电荷半径的DNN，以全局预测核电荷密度分布，并在验证集和最新实验数据上验证其精度。
Estimation of the slope of nuclear symmetry energy via charge radii of mirror nuclei
本文利用 Hartree-Fock-Bogoliubov 近似和40种 Skyrme 泛函分析镜像核电荷半径差与对称能斜率的关联，并由实验数据给出 L 约束。
Nuclear charge densities in spherical and deformed nuclei: towards precise calculations of charge radii
本研究利用 Skyrme 能量密度泛函与密度依赖对力，评估球形核和形变核电荷密度计算中的相对论自旋－轨道修正，以提升电荷半径及同位素位移的高精度预测。
Logarithmic divergences in pion and proton charge radii associated with chiral loops are investigated to assess systematic uncertainties in current lattice determinations of charge radii. The chiral corrections offer a possible solution to the long standing problem of why present lattice calculations yield proton and pion radii which are similar in size.
Improved description of nuclear charge radii: Global trends beyond $N=28$ shell closure
本文利用相对论平均场理论并考虑费米面np关联，改进了$Z=19$-$29$核素电荷半径的描述，成功重现了超越$N=28$壳闭合的陡峭增加趋势，为识别核素新幻数提供了敏感指标。
Robust correlation between binding energies and charge radii of mirror nuclei
本文基于双参数费米模型电荷密度，提出镜像核结合能与电荷半径之间的稳健关联，实现对丰质子核质量与半径的可靠预测，并表明该关联可灵敏探测壳闭合和质子晕等局部结构异常。
Isotope shifts of the mean square radii (MSR) and electric quadrupole moments of even-even nuclei with 20< Z < 98$ are calculated using a dynamical microscopic model. A single particle Nilsson potential with the Seo set of correction term parameters, the pairing forces in the BCS formalism and a long range interaction in the local approximation are used. A collective hamiltonian is obtained using a generator coordinate method (GCM) with the gaussian overlap approximation (GOA). A potential energy of the nucleus consists of a microscopic-macroscopic Strutinsky energy and a zero point vibrationa…
Radiative decays of decuplet hyperons and octet hyperon charge radii are evaluated in a chiral constituent quark model emphasizing the role of exchange currents. Exchange currents largely cancel for the M1 decay amplitudes, while they dominate the E2 amplitude. Due to the pseudoscalar meson cloud the charge radii of Sigma^- and Xi^- are almost as large as the proton radius, in agreement with recent experimental results from SELEX. Strangeness suppression is weakened by exchange currents for several observables.
The structures and distributions of light nuclei are investigated within a microscopic correlation model. Two particle correlations are responsible for the scattering of model particles either to low momentum- or to high momentum-states. The low momentum states form the model space while the high momentum states are used to calculate the G-matrix. The three and higher order particle correlations do not play a role in the latter calculation especially if the correlations induced by the scattering operator are of sufficient short range. They modify however, via the long tail of the nuclear poten…
The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. We explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neura…
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 para…
Odd-even shape staggering and kink structure of charge radii of Hg isotopes by the deformed relativistic Hartree-Bogoliubov theory in continuum
本文利用DRHBc理论研究了$^{180-186}$Hg同位素电荷半径的奇偶形状交错及$N=126$附近扭结结构，揭示了其分别源于核形状跃迁和特定单粒子态占据概率变化。
Prolate-oblate shape competition and impact on charge radii in Bk isotopes
本文通过DRHBc理论研究Bk同位素长轴-短轴形状竞争，揭示短轴形状对电荷半径的增强效应及其微观机制。
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…
Charge radii of Sn isotopes in the relativistic mean field approximation
研究Sn同位素核电荷半径在N=82附近出现的kink现象，利用NL3*参数集在相对论平均场框架下分析，发现狄拉克旋量的小成分对质子中央势能的贡献是形成kink的关键因素。
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 cl…
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