Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator ...Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator and Bayesian model averaging(BMA)to optimize the predictions of RCfrom sophisticated theoretical models.The CBP estimator treats the residual between the theoretical and experimental values of RCas a continuous variable and derives its posterior probability density function(PDF)from Bayesian theory.The BMA method assigns weights to models based on their predictive performance for benchmark nuclei,thereby accounting for the unique strengths of each model.In global optimization,the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%.The extrapolation analyses consistently achieved an improvement rate of approximately 45%,demonstrating the robustness of the CBP estimator.Furthermore,the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm,effectively reproducing the pronounced shell effects on RCof the Ca and Sr isotope chains.The studies in this paper propose an efficient method to accurately describe RCof unknown nuclei,with potential applications in research on other nuclear properties.展开更多
The α-nucleus interaction is crucial in the description of α decay. Recently, we developed a pocket-type dynamical doublefolding potential(DDFP) that effectively incorporates both the surface-medium effect and inter...The α-nucleus interaction is crucial in the description of α decay. Recently, we developed a pocket-type dynamical doublefolding potential(DDFP) that effectively incorporates both the surface-medium effect and interior Pauli repulsion in α decay [H. Zheng et al., Phys. Rev. C 109, L011301(2024)]. This potential results in a pocket geometry within the nuclear surface region, which is consistent with the α-clustering characteristics predicted by microscopic calculations. In this study, the accuracy of the pocket-type DDFP was validated via systematic calculations of α-decay half-lives and an extended evaluation of the nuclear charge radii of the daughter nuclei. The results demonstrate good agreement with the experimental data for both quantities, thereby confirming the reliability of the DDFP model. Compared with calculations that use α-nucleus interactions derived from conventional double-folding procedures, DDFP employs fewer adjustable parameters to achieve a more accurate description of the charge radii based on the experimental α-decay energies.展开更多
An improved Z^1/3 law of nuclear charge radius is presented. The comparison between the calculated and experimental nuclear charge radii now available shows that this new formula is better than the other conventional ...An improved Z^1/3 law of nuclear charge radius is presented. The comparison between the calculated and experimental nuclear charge radii now available shows that this new formula is better than the other conventional formulae.展开更多
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....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.展开更多
The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(...The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.展开更多
The geometric structure parameters and radial density distribution of 1s2s1S excited state of the two-electron atomic system near the critical nuclear charge Z_(c)were calculated in detail under tripled Hylleraas basi...The geometric structure parameters and radial density distribution of 1s2s1S excited state of the two-electron atomic system near the critical nuclear charge Z_(c)were calculated in detail under tripled Hylleraas basis set.Contrary to the localized behavior observed in the ground and the doubly excited 2p^(23)Pe states,for this state our results identify that while the behavior of the inner electron increasingly resembles that of a hydrogen-like atomic system,the outer electron in the excited state exhibits diffused hydrogen-like character and becomes perpendicular to the inner electron as nuclear charge Z approaches Z_(c).This study provides insights into the electronic structure and stability of the two-electron system in the vicinity of the critical nuclear charge.展开更多
Nuclear binding energies, charge radii and the charge distributions of even-even tin （Sn） isotopes are calculated using relativistic mean field theory, and the theoretical results are found to be in accordance with ...Nuclear binding energies, charge radii and the charge distributions of even-even tin （Sn） isotopes are calculated using relativistic mean field theory, and the theoretical results are found to be in accordance with the experimental data. The nuclear charge form factors for Sn isotopes are calculated using the phase-shift analysis method. It is shown that the minima of the charge form factors shift upward and inward with an increase in the neutron number of the Sn isotopes.展开更多
The random forest algorithm was applied to study the nuclear binding energy and charge radius.The regularized root-mean-square of error(RMSE)was proposed to avoid overfitting during the training of random forest.RMSE ...The random forest algorithm was applied to study the nuclear binding energy and charge radius.The regularized root-mean-square of error(RMSE)was proposed to avoid overfitting during the training of random forest.RMSE for nuclides with Z,N>7 is reduced to 0.816 MeV and 0.0200 fm compared with the six-term liquid drop model and a three-term nuclear charge radius formula,respectively.Specific interest is in the possible(sub)shells among the superheavy region,which is important for searching for new elements and the island of stability.The significance of shell features estimated by the so-called shapely additive explanation method suggests(Z,N)=(92,142)and(98,156)as possible subshells indicated by the binding energy.Because the present observed data is far from the N=184 shell,which is suggested by mean-field investigations,its shell effect is not predicted based on present training.The significance analysis of the nuclear charge radius suggests Z=92 and N=136 as possible subshells.The effect is verified by the shell-corrected nuclear charge radius model.展开更多
In this work, the total energies of doubly excited states (<em>ns</em><sup>2</sup>) <sup>1</sup>S<sup>e</sup>, (<em>np</em><sup>2</sup>) <sup&...In this work, the total energies of doubly excited states (<em>ns</em><sup>2</sup>) <sup>1</sup>S<sup>e</sup>, (<em>np</em><sup>2</sup>) <sup>1</sup>D<sup>e</sup>, (<em>nd</em><sup>2</sup>) <sup>1</sup>G<sup>e</sup>, (<em>nf</em><sup>2</sup>) <sup>1</sup>I<sup>e</sup>, (<em>ng</em><sup>2</sup>) <sup>1</sup>K<sup>e</sup>, and (<em>nh</em><sup>2</sup>) <sup>1</sup>M<sup>e</sup> of the helium isoelectronic sequence with Z ≤ 10 are calculated in the framework of the variational method of the Screening Constant by Unit Nuclear Charge (SCUNC). These calculations are performed using a new wavefunction correlated to Hylleraas-type. The possibility of using the SCUNC method in the investigation of high-lying Doubly Excited States(DES) in two-electron systems is demonstrated in the present work in the case of the (<em>nl</em><sup>2</sup>) <sup>1</sup><em>L</em><sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><em>π</em></span></span></span></sup> doubly excited states, where accurate total energies are tabulated up to <em>n</em> = 20. All the results obtained in this paper are in agreement with the values of the available literature and may be useful for future experimental and theoretical studies on the doubly excited (<em>nl</em><sup>2</sup>) <sup>1</sup><em>L</em><sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><em>π</em></span></span></sup> states of two-electron systems.展开更多
Standard perturbation theory is employed to calculate the mass shifts of the 2^(1)S_(0)-^(3)S_(1)and 2^(3)S_(1)-2^(3)P_(J)transitions for^(4,6,8)He.High-precision results are obtained for the mass shifts in the isotop...Standard perturbation theory is employed to calculate the mass shifts of the 2^(1)S_(0)-^(3)S_(1)and 2^(3)S_(1)-2^(3)P_(J)transitions for^(4,6,8)He.High-precision results are obtained for the mass shifts in the isotope pairs 6He-4He and 8He-4He,with uncertainties below 1 part per million(ppm).Our analysis provides a complete set of isotope-shift results and systematically examines their sensitivity to nuclear charge-radius differences.Once experimental measurements reach a precision comparable to that of the calculated mass shifts,the squared differences of nuclear charge radii can be determined with an accuracy of approximately 0.4%-0.6%,representing an order-of-magnitude improvement over current values.展开更多
When discussing atomic nuclei,deformation is one of the most common topics.However,when we connect the con-cept of shape with high-precision experimental measure-ments,sometimes the explanation may not be as simple as...When discussing atomic nuclei,deformation is one of the most common topics.However,when we connect the con-cept of shape with high-precision experimental measure-ments,sometimes the explanation may not be as simple as we think.A recent measurement of nuclear charge radii(Phys.Rev.Lett.134,182501(2025))challenges current nuclear ab initio models.展开更多
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...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.展开更多
We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlat...We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.展开更多
In this paper, resonance energies and excitation energies of doubly 2<em>sns</em> <sup>1,3</sup><em>S</em><sup>e</sup>, 2<em>snp</em> <sup>1,3</sup&...In this paper, resonance energies and excitation energies of doubly 2<em>sns</em> <sup>1,3</sup><em>S</em><sup>e</sup>, 2<em>snp</em> <sup>1,3</sup><em>P</em><sup>0</sup>, 2<em>pnp</em> <sup>1,3</sup><em>D</em><sup>e</sup>, 2<em>pnd</em> <sup>1,3</sup><em>F</em><sup>0</sup> and 2<em>pnf</em> <sup>1,3</sup><em>G</em><sup>e</sup> excited states of the helium isoelectronic sequence with <em>Z</em> <span style="white-space:nowrap;">≤</span> 10 are calculated. Calculations are carried out in the framework of the variational procedure of the formalism of the Screening Constant per Unit Nuclear Charge (SCUNC). New correlated wave function of Hylleraas type is used. Precise resonance and excitation energies are tabulated and good agreement is obtained when a comparison is made with available literature values.展开更多
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...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.展开更多
We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge wit...We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z2/3. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV 〈～ L 〈～ 82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.展开更多
Theoretical modeling of nucleus-nucleus collisions is often based on the nucleus-nucleus potential.One of the advanced methods for constructing this potential is the semi-microscopical double-folding model with M3 YPa...Theoretical modeling of nucleus-nucleus collisions is often based on the nucleus-nucleus potential.One of the advanced methods for constructing this potential is the semi-microscopical double-folding model with M3 YParis NN-forces.Proton and neutron densities are significant components of this model.The correct nucleon density(ND) must reproduce the experimental nuclear charge density(NCD).However,those who deal with modeling the fusion process typically disregard this circumstance.We aim to achieve a good description of both the nuclear charge density and above-barrier fusion cross sections of even-even light nuclei with Z=N.We consider several versions of NDs available in literature and construct our own approximation for the ND of the even-even spherical nuclei^(12)C,^(16)O,and^(40)Ca,abbreviated as FE-density(Fermi+exponential).We carefully compare the NCDs resulting from different versions of NDs with the experimental NCDs.After finding the nucleus-nucleus potential using the double-folding model with the density dependent M3 Y-Paris NN-forces and FE densities,we evaluate the abovebarrier fusion cross sections for five reactions,^(12)C+^(12)C,^(12)C+^(16)O,^(16)O+^(16)O,^(16)O+^(40)Ca,and^(40)Ca+^(40)Ca,and40Ca+40Ca,for which experimental data are available.The cross sections are calculated using two approaches:a) the barrier penetration model and b) the trajectory model with surface friction(TM).To find the transmission coefficients for the TM,the Langevin equations are employed.For all considered reactions,our TM typically reproduces the above-barrier experimental cross sections within 10-15%.The only adjustable parameter of the model,the optimal friction strength KRm,is found to be approximately 90 zs·GeV-1for the light reactions12C+12C,12C+16O,and16O+16O and approximately 15zs·GeV-1for the heavy reactions16O+40Ca and40Ca+40Ca.The latter findings are in reasonable agreement with the systematics found previously.Thus,the FE-recipe allows highly accurate and simultaneous reproduction of both the nuclear charge density and above-barrier fusion cross sections of five reactions involving12C,160,and40Ca nuclei.展开更多
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-...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.展开更多
Using two nuclear models,i)the relativistic continuum Hartree-Bogoliubov(RCHB)theory and ii)the Weizsäcker-Skyrme(WS)model WS*,the performances of nine kinds of kernel functions in the kernel ridge regression(KRR...Using two nuclear models,i)the relativistic continuum Hartree-Bogoliubov(RCHB)theory and ii)the Weizsäcker-Skyrme(WS)model WS*,the performances of nine kinds of kernel functions in the kernel ridge regression(KRR)method are investigated by comparing the accuracies of describing the experimental nuclear charge radii and the extrapolation abilities.It is found that,except the inverse power kernel,all other kernels can reach the same level around 0.015~0.016 fm for these two models with KRR method.The extrapolation ability for the neutron rich region of each kernel depends on the trainning data.Our investigation shows that the performances of the power kernel and Multiquadric kernel are better in the RCHB+KRR calculation,and the Gaussian kernel is better in the WS*+KRR calculation.In addition,the performance of different basis functions in the radial basis function method is also investigated for comparison.The results are similar to the KRR method.The influence of different kernels on the KRR reconstruct function is discussed by investigating the whole nuclear chart.At last,the charge radii of some specific isotopic chains have been investigated by the RCHB+KRR with power kernel and the WS*+KRR with Gaussian kernel.The charge radii and most of the specific features in these isotopic chains can be reproduced after considering the KRR method.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12475135,12035011,and 12475119)the Shandong Provincial Natural Science Foundation,China(No.ZR2020MA096)the Fundamental Research Funds for the Central Universities(No.22CX03017A)。
文摘Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator and Bayesian model averaging(BMA)to optimize the predictions of RCfrom sophisticated theoretical models.The CBP estimator treats the residual between the theoretical and experimental values of RCas a continuous variable and derives its posterior probability density function(PDF)from Bayesian theory.The BMA method assigns weights to models based on their predictive performance for benchmark nuclei,thereby accounting for the unique strengths of each model.In global optimization,the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%.The extrapolation analyses consistently achieved an improvement rate of approximately 45%,demonstrating the robustness of the CBP estimator.Furthermore,the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm,effectively reproducing the pronounced shell effects on RCof the Ca and Sr isotope chains.The studies in this paper propose an efficient method to accurately describe RCof unknown nuclei,with potential applications in research on other nuclear properties.
基金supported by the National Natural Science Foundation of China(Nos.12035011,11975167,12175151,12005139,11947123)the Guangdong Major Project of Basic and Applied Basic Research(No.2021B0301030006)the Steady Support Program for Higher Education Institutions of Shenzhen(Nos.20200810163629001,20200817005440001).
文摘The α-nucleus interaction is crucial in the description of α decay. Recently, we developed a pocket-type dynamical doublefolding potential(DDFP) that effectively incorporates both the surface-medium effect and interior Pauli repulsion in α decay [H. Zheng et al., Phys. Rev. C 109, L011301(2024)]. This potential results in a pocket geometry within the nuclear surface region, which is consistent with the α-clustering characteristics predicted by microscopic calculations. In this study, the accuracy of the pocket-type DDFP was validated via systematic calculations of α-decay half-lives and an extended evaluation of the nuclear charge radii of the daughter nuclei. The results demonstrate good agreement with the experimental data for both quantities, thereby confirming the reliability of the DDFP model. Compared with calculations that use α-nucleus interactions derived from conventional double-folding procedures, DDFP employs fewer adjustable parameters to achieve a more accurate description of the charge radii based on the experimental α-decay energies.
基金supported the National Natural Science Foundation of China under Grant Nos. 10435010, 10675006, and 10675007
文摘An improved Z^1/3 law of nuclear charge radius is presented. The comparison between the calculated and experimental nuclear charge radii now available shows that this new formula is better than the other conventional formulae.
基金supported by Shanghai “Science and Technology Innovation Action Plan” Project (No. 21ZR140950)。
文摘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.
基金This work was supported by the National Natural Science Foundation of China(Nos.11875027,11975096).
文摘The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.
基金supported by the National Natural Science Foundation of China(Grant Nos.12074295,12304271,and 12104420).
文摘The geometric structure parameters and radial density distribution of 1s2s1S excited state of the two-electron atomic system near the critical nuclear charge Z_(c)were calculated in detail under tripled Hylleraas basis set.Contrary to the localized behavior observed in the ground and the doubly excited 2p^(23)Pe states,for this state our results identify that while the behavior of the inner electron increasingly resembles that of a hydrogen-like atomic system,the outer electron in the excited state exhibits diffused hydrogen-like character and becomes perpendicular to the inner electron as nuclear charge Z approaches Z_(c).This study provides insights into the electronic structure and stability of the two-electron system in the vicinity of the critical nuclear charge.
基金supported by National Natural Science Foundation of China(Nos.10535010,10675090,10775068,10735010,10975072and11035001)the 973 National Major State Basic Research and Development of China(2007CB815004)+1 种基金CAS Knowledge Innovation Project(KJCX2-SW-N02)the Research Fund of Doctoral Point(RFDP)(Nos.20070284016,20100091110028)
文摘Nuclear binding energies, charge radii and the charge distributions of even-even tin （Sn） isotopes are calculated using relativistic mean field theory, and the theoretical results are found to be in accordance with the experimental data. The nuclear charge form factors for Sn isotopes are calculated using the phase-shift analysis method. It is shown that the minima of the charge form factors shift upward and inward with an increase in the neutron number of the Sn isotopes.
基金Supported by Basic and Applied Basic Research Project of Guangdong Province(2021B0301030006)。
文摘The random forest algorithm was applied to study the nuclear binding energy and charge radius.The regularized root-mean-square of error(RMSE)was proposed to avoid overfitting during the training of random forest.RMSE for nuclides with Z,N>7 is reduced to 0.816 MeV and 0.0200 fm compared with the six-term liquid drop model and a three-term nuclear charge radius formula,respectively.Specific interest is in the possible(sub)shells among the superheavy region,which is important for searching for new elements and the island of stability.The significance of shell features estimated by the so-called shapely additive explanation method suggests(Z,N)=(92,142)and(98,156)as possible subshells indicated by the binding energy.Because the present observed data is far from the N=184 shell,which is suggested by mean-field investigations,its shell effect is not predicted based on present training.The significance analysis of the nuclear charge radius suggests Z=92 and N=136 as possible subshells.The effect is verified by the shell-corrected nuclear charge radius model.
文摘In this work, the total energies of doubly excited states (<em>ns</em><sup>2</sup>) <sup>1</sup>S<sup>e</sup>, (<em>np</em><sup>2</sup>) <sup>1</sup>D<sup>e</sup>, (<em>nd</em><sup>2</sup>) <sup>1</sup>G<sup>e</sup>, (<em>nf</em><sup>2</sup>) <sup>1</sup>I<sup>e</sup>, (<em>ng</em><sup>2</sup>) <sup>1</sup>K<sup>e</sup>, and (<em>nh</em><sup>2</sup>) <sup>1</sup>M<sup>e</sup> of the helium isoelectronic sequence with Z ≤ 10 are calculated in the framework of the variational method of the Screening Constant by Unit Nuclear Charge (SCUNC). These calculations are performed using a new wavefunction correlated to Hylleraas-type. The possibility of using the SCUNC method in the investigation of high-lying Doubly Excited States(DES) in two-electron systems is demonstrated in the present work in the case of the (<em>nl</em><sup>2</sup>) <sup>1</sup><em>L</em><sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><em>π</em></span></span></span></sup> doubly excited states, where accurate total energies are tabulated up to <em>n</em> = 20. All the results obtained in this paper are in agreement with the values of the available literature and may be useful for future experimental and theoretical studies on the doubly excited (<em>nl</em><sup>2</sup>) <sup>1</sup><em>L</em><sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><em>π</em></span></span></sup> states of two-electron systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.12204412,12274423,12174402,12393821,and 12004124)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant Nos.XDB0920100 and XDB0920101)support from the Natural Sciences and Engineering Research Council of Canada.All calculations were performed on the APM-Theoretical Computing Cluster(APM-TCC).
文摘Standard perturbation theory is employed to calculate the mass shifts of the 2^(1)S_(0)-^(3)S_(1)and 2^(3)S_(1)-2^(3)P_(J)transitions for^(4,6,8)He.High-precision results are obtained for the mass shifts in the isotope pairs 6He-4He and 8He-4He,with uncertainties below 1 part per million(ppm).Our analysis provides a complete set of isotope-shift results and systematically examines their sensitivity to nuclear charge-radius differences.Once experimental measurements reach a precision comparable to that of the calculated mass shifts,the squared differences of nuclear charge radii can be determined with an accuracy of approximately 0.4%-0.6%,representing an order-of-magnitude improvement over current values.
基金supported by the National Natural Science Foundation of China(No.12235003).
文摘When discussing atomic nuclei,deformation is one of the most common topics.However,when we connect the con-cept of shape with high-precision experimental measure-ments,sometimes the explanation may not be as simple as we think.A recent measurement of nuclear charge radii(Phys.Rev.Lett.134,182501(2025))challenges current nuclear ab initio models.
基金supported by the National Natural Science Foundation of China(Grant Nos.U1832120 and 11675265)S&T Program of Hebei(Grant No.236Z4601G)+4 种基金Scientific Research Foundation for the Introducing Returned Overseas Chinese Scholars of Hebei Province(Grant No.C20230360)Natural Science Foundation for Outstanding Young Scholars of Hebei Province(Grant No.A2020210012)Natural Science Foundation of Hebei Province(Grant No.A2021210010)Key Laboratory of High Precision Nuclear Spectroscopy,Institute of Modern Physics,Chinese Academy of Sciences(Grant No.IMPKFKT2021002)Key Project of Natural Science Foundation for Basic Discipline Research of Hebei Province(Grant No.A2023210064)。
文摘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.
文摘We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.
文摘In this paper, resonance energies and excitation energies of doubly 2<em>sns</em> <sup>1,3</sup><em>S</em><sup>e</sup>, 2<em>snp</em> <sup>1,3</sup><em>P</em><sup>0</sup>, 2<em>pnp</em> <sup>1,3</sup><em>D</em><sup>e</sup>, 2<em>pnd</em> <sup>1,3</sup><em>F</em><sup>0</sup> and 2<em>pnf</em> <sup>1,3</sup><em>G</em><sup>e</sup> excited states of the helium isoelectronic sequence with <em>Z</em> <span style="white-space:nowrap;">≤</span> 10 are calculated. Calculations are carried out in the framework of the variational procedure of the formalism of the Screening Constant per Unit Nuclear Charge (SCUNC). New correlated wave function of Hylleraas type is used. Precise resonance and excitation energies are tabulated and good agreement is obtained when a comparison is made with available literature values.
基金Supported by the Reform and Development Project of Beijing Academy of Science and Technology(13001-2110)Supported in part by the National Natural Science Foundation of China(12135004,11635003,11961141004,12047513)+2 种基金the support of the National Natural Science Foundation of China(11705118)the support of the National Natural Science Foundation of China(11975096)the Fundamental Research Funds for the Central Universities(2020NTST06)。
文摘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.
基金Supported by National Natural Science Foundation of China (10875031, 10847004, 10675172)Doctoral Station Foundation ofMinistry of Education of China (200800270017)National Basic Research Program of China (2007CB209900, 2010CB832903)
文摘We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z2/3. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV 〈～ L 〈～ 82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.
基金Supported by the Foundation for the Advancement of Theoretical Physics and Mathematics“BASIS.”。
文摘Theoretical modeling of nucleus-nucleus collisions is often based on the nucleus-nucleus potential.One of the advanced methods for constructing this potential is the semi-microscopical double-folding model with M3 YParis NN-forces.Proton and neutron densities are significant components of this model.The correct nucleon density(ND) must reproduce the experimental nuclear charge density(NCD).However,those who deal with modeling the fusion process typically disregard this circumstance.We aim to achieve a good description of both the nuclear charge density and above-barrier fusion cross sections of even-even light nuclei with Z=N.We consider several versions of NDs available in literature and construct our own approximation for the ND of the even-even spherical nuclei^(12)C,^(16)O,and^(40)Ca,abbreviated as FE-density(Fermi+exponential).We carefully compare the NCDs resulting from different versions of NDs with the experimental NCDs.After finding the nucleus-nucleus potential using the double-folding model with the density dependent M3 Y-Paris NN-forces and FE densities,we evaluate the abovebarrier fusion cross sections for five reactions,^(12)C+^(12)C,^(12)C+^(16)O,^(16)O+^(16)O,^(16)O+^(40)Ca,and^(40)Ca+^(40)Ca,and40Ca+40Ca,for which experimental data are available.The cross sections are calculated using two approaches:a) the barrier penetration model and b) the trajectory model with surface friction(TM).To find the transmission coefficients for the TM,the Langevin equations are employed.For all considered reactions,our TM typically reproduces the above-barrier experimental cross sections within 10-15%.The only adjustable parameter of the model,the optimal friction strength KRm,is found to be approximately 90 zs·GeV-1for the light reactions12C+12C,12C+16O,and16O+16O and approximately 15zs·GeV-1for the heavy reactions16O+40Ca and40Ca+40Ca.The latter findings are in reasonable agreement with the systematics found previously.Thus,the FE-recipe allows highly accurate and simultaneous reproduction of both the nuclear charge density and above-barrier fusion cross sections of five reactions involving12C,160,and40Ca nuclei.
基金Supported by National Natural Science Foundation of China(11905130)。
文摘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.
文摘Using two nuclear models,i)the relativistic continuum Hartree-Bogoliubov(RCHB)theory and ii)the Weizsäcker-Skyrme(WS)model WS*,the performances of nine kinds of kernel functions in the kernel ridge regression(KRR)method are investigated by comparing the accuracies of describing the experimental nuclear charge radii and the extrapolation abilities.It is found that,except the inverse power kernel,all other kernels can reach the same level around 0.015~0.016 fm for these two models with KRR method.The extrapolation ability for the neutron rich region of each kernel depends on the trainning data.Our investigation shows that the performances of the power kernel and Multiquadric kernel are better in the RCHB+KRR calculation,and the Gaussian kernel is better in the WS*+KRR calculation.In addition,the performance of different basis functions in the radial basis function method is also investigated for comparison.The results are similar to the KRR method.The influence of different kernels on the KRR reconstruct function is discussed by investigating the whole nuclear chart.At last,the charge radii of some specific isotopic chains have been investigated by the RCHB+KRR with power kernel and the WS*+KRR with Gaussian kernel.The charge radii and most of the specific features in these isotopic chains can be reproduced after considering the KRR method.
