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 nonrelativistic 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 p_(s)=0.10 fm^(-3) was located in the interval range 30.52–39.76 MeV.

Predictions of nuclear charge radii based on the convolutional neural network

In this study, we developed a neural network that incorporates a fully connected layer with a convolutional layer to predict the nuclear charge radii based on the relationships between four local nuclear charge radii. The convolutional neural network(CNN) combines the isospin and pairing effects to describe the charge radii of nuclei with A ≥ 39 and Z ≥ 20. The developed neural network achieved a root mean square(RMS) deviation of 0.0195 fm for a dataset with 928 nuclei. Specifically, the CNN reproduced the trend of the inverted parabolic behavior and odd–even staggering observed in the calcium isotopic chain, demonstrating reliable predictive capability.

Analytical solutions for characteristic radii of circular roadway surrounding rock plastic zone and their application

In the non-uniform stress field, the surrounding rock plastic zone of the circular roadway shows different shapes under the different confining pressure conditions. Based on the boundary shape characteristics of the plastic zone, the characteristic radii of the plastic zone were proposed, namely the horizontal,longitudinal and medial axis radii, which could reflect the plastic zone shapes characteristics and classify the sizes of the key parts. On the theoretical basis of elastic-plastic mechanics, analytical solutions for the characteristic radii were obtained by theoretical deduction, and the relationships between the characteristic radii and key influencing factors were analyzed. Finally, the evaluation criterion of the circular roadway surrounding rock plastic zone shapes, evaluation criterion of the location of potential hazards caused by the roadway surrounding rock and evaluation critical points of roadway dynamic disasters based on characteristic radii were proposed. This work could provide a theoretical basis for stability analysis of the surrounding rock, support design, and guide the prevention and control of dynamic roadway disasters.

Crystal Radii and Their Application on the Study of Electronic Structures of LaX(X=N,P,As,Sb)

以Ｐｈｉｌｉｐｓ－ＶａｎＶｅｃｈｔｅｎ理论和晶体光学性质为基础，计算了ＬａＸ（Ｘ＝Ｎ，Ｐ，Ａｓ，Ｓｂ）晶体的离子半径（单位：ｎｍ）：（Ｌａ：Ｎ）为（０．１４１４，０．１２３６），（Ｌａ：Ｐ）为（０．１５１８，０．１４８９），（Ｌａ：Ａｓ）为（０．１５３６，０．１５２６），（Ｌａ：Ｓｂ）为（０．１５８６，０．１６５１）．用ＬＭＴＯ－ＡＳＡ方法对ＬａＸ系列晶体的能带结构进行了计算．所得到的能隙是：ＬａＮ为２．３０ｅＶ，ＬａＰ为２．０５ｅＶ，ＬａＡｓ为１．６６ｅＶ，ＬａＳｂ为１．３４ｅＶ．与实验结果相符．这也证明了作者得到的半径的合理性．

Polymer Radii and Moments in the Polycondensation Reaction of A_a Type

For the polycondensation reaction of A. type, the kth radius for k>2 can be expressed in terms of polymer moments.

Representations of Real and Complex Stability Radii of 2-Dimensional LinearSystems

Rigorous proofs are given for the representations of real and complex stability' radii of 2-dimensional linear systems. This representations can be used to analyze the robustness of a nominal 2-dimensional linear system under pelturbation of the system parameters, in particular testing the effect of numerical algorithms which are used to calculate the real stability radii of higher dimensional piecewise-linear systems.

Nuclear Interaction Radii for Light Exotic Nuclei

We developed a simple model to calculate the interaction radii for light neutron-rich nuclei based on Coulomb-modified Glauber model.Considering a relation of surface diffuseness of neutron distribution with the neutron separation energy of nucleus,the large increasing of nuclear interaction radii for exotic nuclei(such as ^(6)He,^(8)He,^(11)Li,^(11)Be)on ^(12)C target can be reasonably explained.

Magnetic Moments and Electromagnetic Radii of Nucleon and △（1232） in an Extended Goldstone-Boson-Exchange Model

We derive the exchange currents of pseudoscalar, vector, and scalar mesons from Feynman diagrams, and use them to calculate the magnetic form factors of nucleon and △(1232). The magnetic moments and electromagnetic radii are obtained by using those form factors and the parameters determined from the masses of nucleon and △(1232).We find the magnetic moments and electromagnetic radii of nucleon and △(1232) can be produced very well in the extended Goldstone-Boson-exchange model in which all of pseudoscalar, vector, and scalar meson nonet are included.The magnetic moments of △(1232) are closer to experiment values and results from lattice calculation than the results obtained by the model without other mesons except for pion and sigma.

Semi-Empirical Formulas for Nuclear Charge Radii

Considering the relationship between the nuclear radius and the average bindingenergy of nucleons,a simple semi-empirical formula for the nuclear rms charge radii is suggest-ed together with the formula for light neutron-rich nuclear rms neutron radii.These formulascan well fit the new experimental values.

Predictions of nuclear charge radii

In this study,we improve the relations of the charge-radius difference of two isotopes by considering a term that relates to the proton number and the parity of the neutron number.The correction reduces the root-mean-squared deviation to 0.0041 fm for 651 nuclei with a neutron number larger than 20,in comparison with experiment-al data compiled in the CR2013 database.The improved relations are combined with local relations consisting of the charge radii of four neighboring nuclei.These combinations also prove to be efficient in describing and predicting nuclear charge radii and can reflect the structure evolutions of nuclei.Our predictions of 2467 unknown nuclear charge radii at competitive accuracy,which are calculated using these two types of relations,are tabulated in the Supplemental Material.

STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION

Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.

Solution of the Nucleon Structure Problem from a Field Theory of Fermions and Bosons and the Origin of the Proton Stability

A bound state formalism derived from a fermion-boson symmetric Lagrangian has been used to calculate the nucleon masses, the charge neutrality of the neutron, the magnetic moments and the electromagnetic form factor ratios μpGEp/GMpand μnGEn/GMn. A quantitative description is obtained, assuming a mixing of a scalar bound state of 3(f f¯)fstructure with its corresponding vector (f f¯)fstate (f indicating massless elementary fermions). Only a few parameters are needed, mainly fixed by energy and momentum conservation. The nucleon stability is explained by an extra binding in the confinement potential, negative for electric and positive for magnetic binding of the proton, and opposite for the neutron. The stronger electric extra binding of the proton allows a decay of the neutron to proton and electron.

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.

Real stability radii and quadratic matrix inequality

In the sequel,we suppose system （2） to be Cg-stable,i.e.Cg is a given open set in thecomplex plane and all the eigenvalues of A are in Cg.Both B∈Rn×m and C∈Rp×n are giv-en.Δ∈Rm×p is an unknown perturbation matrix.In the following,σ（·）is used to de-scribe the maximum singular value of the matrix;R（·） and N（·） are the column spaceand null space of matrix respectively.

Ionic effective radii under high-temperatures state

REFERENCES [1, 2] prove that ionic radii will increase or decrease with temperature rising orlowering. If the ionic radii at room temperature are known, many phenomena of the ioniccompounds occurring at room temperature can be explained. Also if the ionic radii at high tem-perature are known, many phenomena of the ionic compounds occurring at high temperaturecan also be explained. Therefore, to calculate the effective radii of ions at high temperature isconsidered of great significance. For example, the 'investigation of KIO3-CsIO3

A GENERAL EQUATION FOR CALCULATING THE SINGLE BOND RADII R(1)OF ACTINIDES

Ⅰ. INTRODUCTION The valence state changes of actinides are complicated by their electron structures, because the valence electron structures of an element are different in different compounds. For this reason, study on the electron structures of metals and compounds of actinides is of important theoretical significance. The equation for calculating the single bond radii R(1) and the hybrid levels of valence 3 actinides have been established by Chen et al.,

EFFECT OF IONIC RADII ON UNIT-CELL VOLUMES OF ISOSTRUCTURAL COMPOUNDS

The relation between cell-edges or unit-cell volumes of isostructural compounds and theionic radii has wide applications in crystal chemistry. The authors have proved: (1) For a series of multiple isostructural compounds such as A_mB_n…X_p, when the anionand other cations are fixed, there exists the following relation between the unit-cell volume Vand the radius r_A of a certain cation such as A: V = (a + br_A)(r_X + r_A)~3 (a and b are constants). (2) For binary isostructural compounds A_mX_p, the above relation is reduced to V = k(r_X + r_A)~3 (k is a constant). (3) For binary isostructural compounds the relation between V and r_A^3 is approximatelylinear, and for multiple compounds, it is often curvilinear but still approximately linear whenthe variation of r_A is slight. As another approximation, a linear relation also exists betweenV and r_A for isostructural compounds. (4) The relation of ce1l-edge a vs. r_A is linear for binary isostructural compounds. Butno such a good linear relation exists for multiple isostructural compounds.

Theoretical study on characteristic ionic radii

The characteristic radii for univalent cations and anions were defined by the classical turning point of the electron movement in an ion. The numerical results of the elements from first- to third-rows in the periodic table were obtained using %ab initio% method. The results correlate quite well with Pauling ionic radii and Shannon and Prewitt ionic radii.

变基圆涡旋式压缩机多刚柔耦合动力学特性分析

为阐明汽车空调涡旋压缩机转子系统摩擦副非稳态动态激励机理,建立变基圆涡旋式压缩机多刚柔耦合动力学模型,以变基圆涡旋压缩机气体力为边界条件,研究轴系摩擦副动态接触激励;而后,基于变基圆涡旋式压缩机多刚柔耦合动力学模型,对动态接触激励进行影响因素分析。结果表明,动态接触激励力的频率响应峰值主要出现在100Hz、200Hz、700Hz与2300Hz及其边频处,为转频的整数倍次与动涡盘的1/2倍频处;为降低变基圆涡旋式压缩机轴系摩擦损耗,应合理设置防自转机构间隙及个数。

两异径湿球颗粒间静态液桥力的近似解析公式及数值评测

针对异径球形湿颗粒间液桥力,以Young-Laplace公式为基础,结合环形近似法并引入等效半径,在宽松设定的条件下推导出了简化的近似解析公式。此公式形式简洁,且当两球半径相等时,可回归到Pitois等提出的径球液桥力公式。本文对此近似解析公式进行参数敏感度分析,发现随着颗粒间距的增大,液桥力对颗粒半径的敏感度降低。此外,本文近似解析公式与其他实验和理论结果进行对比发现,该近似解析公式与上述实验和数值结果相当吻合,表明该近似解析公式可以较准确地计算接触角较小时的异径球颗粒间的液桥力,因而适于湿颗粒系统的数值模拟。