Using four representative nuclear mass models,namely,WS4,FRDM,DZ10,and KTUY,we perform a systematic investigation on how nuclear masses affect theα-decay properties of superheavy nuclei,including decay energies,α-cl...Using four representative nuclear mass models,namely,WS4,FRDM,DZ10,and KTUY,we perform a systematic investigation on how nuclear masses affect theα-decay properties of superheavy nuclei,including decay energies,α-cluster preformation factors,and corresponding half-lives.Theα-cluster preformation factors are obtained from two types of cluster-formation model(CFM)and extracted from experimental decay half-life.All mass models reproduce the knownα-decay energies with small root-mean-square errors,while WS4 and FRDM show the highest accuracy.Strong correlations among preformation factors from different mass models are identified in both CFM and extracted results,although the exponential dependence of half-lives on decay energy weakens correlations between the two approaches.For possibleα-decay chains of superheavy nuclei,the decay energy systematically decreases and the predicted half-life increases with decreasing proton number.This trend is also observed from the calculations for superheavy isotopes with same proton number.These results indicate that isotopes of superheavy elements with more neutrons are expected to exhibit enhanced stability,thus providing theoretical reference for future synthesis of elements with Z=119 and 120.展开更多
With experimental masses updated from AME11,the predictive power of relativistic mean-field(RMF) mass model is carefully examined and compared with HFB-17,FRDM,WS*,and DZ28 mass models.In the relativistic mean-field m...With experimental masses updated from AME11,the predictive power of relativistic mean-field(RMF) mass model is carefully examined and compared with HFB-17,FRDM,WS*,and DZ28 mass models.In the relativistic mean-field model,the calculation with the PC-PK1 has improved significantly in describing masses compared to the TMA,especially for the neutron-deficient nuclei.The corresponding rms deviation with respect to the known masses falls to 1.4 MeV.Furthermore,it is found that the RMF mass model better describes the nuclei with large deformations.The rms deviation for nuclei with the absolute value of quadrupole deformation parameter greater than 0.25 falls to 0.93,crossing the 1 MeV accuracy threshold for the PC-PK1,which may indicate the new model is more suitable for those largely-deformed nuclei.In addition,the necessity of new high-precision experimental data to evaluate and develop the nuclear mass models is emphasized as well.展开更多
Nuclear masses play a crucial role in both nuclear physics and astrophysics,driving sustained efforts toward precise experi-mental determination and reliable theoretical predictions.In this study,we compiled the newly...Nuclear masses play a crucial role in both nuclear physics and astrophysics,driving sustained efforts toward precise experi-mental determination and reliable theoretical predictions.In this study,we compiled the newly measured masses for 296 nuclides from 40 references published between 2021 and 2024,subsequent to the release of the latest atomic mass evalu-ation.These data were used to benchmark the performance of several relativistic and nonrelativistic density functionals,including PC-PK1,TMA,SLy4,SV-min,UNEDF1,and the recently proposed PC-L3R.The results for PC-PK1 and PC-L3R were obtained using the state-of-the-art deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc),whereas the others were adopted from the existing literature.It was found that the DRHBc calculations with PC-PK1 and PC-L3R achieved an accuracy better than 1.5 MeV,outperforming the other functionals,which all exhibited root-mean-square devia-tions exceeding 2 MeV.The odd-even effects and isospin dependence in these theoretical descriptions were examined.The PC-PK1 and PC-L3R descriptions were qualitatively similar,exhibiting robust isospin dependence along the isotopic chains.Finally,a quantitative comparison between the PC-PK1 and PC-L3R results is presented,with the largest discrepancies analyzed in terms of the potential energy curves from the constrained DRHBc calculations.展开更多
Nuclear mass is an important property in both nuclear and astrophysics.In this study,we explore an improved mass model that incorporates a higher-order term of symmetry energy using algorithms.The sequential least squ...Nuclear mass is an important property in both nuclear and astrophysics.In this study,we explore an improved mass model that incorporates a higher-order term of symmetry energy using algorithms.The sequential least squares programming(SLSQP)algorithm augments the precision of this multinomial mass model by reducing the error from 1.863 MeV to 1.631 MeV.These algorithms were further examined using 200 sample mass formulae derived from theδE term of the E_(isospin) mass model.The SLSQP method exhibited superior performance compared to the other algorithms in terms of errors and convergence speed.This algorithm is advantageous for handling large-scale multiparameter optimization tasks in nuclear physics.展开更多
Background:The masses of-2500 nuclei have been measured experimentally;however,>7000 isotopes are predicted to exist in the nuclear landscape from H(Z=1)to Og(Z=118)based on various theoretical calculations.Explori...Background:The masses of-2500 nuclei have been measured experimentally;however,>7000 isotopes are predicted to exist in the nuclear landscape from H(Z=1)to Og(Z=118)based on various theoretical calculations.Exploring the mass of the remaining isotopes is a popular topic in nuclear physics.Machine learning has served as a powerful tool for learning complex representations of big data in many fields.Purpose:We use Light Gradient Boosting Machine(LightGBM),which is a highly efficient machine learning algorithm,to predict the masses of unknown nuclei and to explore the nuclear landscape on the neutron-rich side from learning the measured nuclear masses.Methods:Several characteristic quantities(e.g.,mass number and proton number)are fed into the LightGBM algorithm to mimic the patterns of the residual δ(Z,A)between the experimental binding energy and the theoret-ical one given by the liquid-drop model(LDM),Duflo–Zucker(DZ,also dubbed DZ28)mass model,finite-range droplet model(FRDM,also dubbed FRDM2012),as well as the Weizsacker–Skyrme(WS4)model to refine these mass models.Results:By using the experimental data of 80%of known nuclei as the training dataset,the root mean square devia-tions(RMSDs)between the predicted and the experimental binding energy of the remaining 20%are approximately 0.234±0.022,0.213±0.018,0.170±0.011,and 0.222±0.016 MeV for the LightGBM-refined LDM,DZ model,WS4 model,and FRDM,respectively.These values are approximately 90%,65%,40%,and 60%smaller than those of the corresponding origin mass models.The RMSD for 66 newly measured nuclei that appeared in AME2020 was also significantly improved.The one-neutron and two-neutron separation energies predicted by these refined models are consistent with several theoretical predictions based on various physical models.In addition,the two-neutron separation energies of several newly measured nuclei(e.g.,some isotopes of Ca,Ti,Pm,and Sm)pre-dicted with LightGBM-refined mass models are also in good agreement with the latest experimental data.Conclusions:LightGBM can be used to refine theoretical nuclear mass models and predict the binding energy of unknown nuclei.Moreover,the correlation between the input characteristic quantities and the output can be inter-preted by SHapley additive exPlanations(a popular explainable artificial intelligence tool),which may provide new insights for developing theoretical nuclear mass models.展开更多
Nuclear mass is a fundamental property of nuclear physics and a necessary input in nuclear astrophysics.Owing to the complexity of atomic nuclei and nonperturbative strong interactions,conventional physical models can...Nuclear mass is a fundamental property of nuclear physics and a necessary input in nuclear astrophysics.Owing to the complexity of atomic nuclei and nonperturbative strong interactions,conventional physical models cannot completely describe nuclear binding energies.In this study,the mass formula was improved by considering an additional term from the Fermi gas model.All nuclear masses in the Atomic Mass Evaluation Database were reproduced with a root-mean-square deviation(RMSD)of -1.86 MeV(1.92 MeV).The new mass formula exhibits good performance in the neutron-rich nuclear region.The RMSD decreases to 0.393 MeV when the ratio of the neutron number to the proton number is≥1.6.展开更多
The ability of the radial basis function(RBF)approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31),Hartree–Fock-Bogoliubov(HFB27...The ability of the radial basis function(RBF)approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31),Hartree–Fock-Bogoliubov(HFB27),finite-range droplet model(FRDM12)and Weizsäcker-Skyrme(WS4)mass models.It is found that when the RBF approach is employed with a simple linear basis function,different mass models have different performances in extrapolating nuclear masses in the same region,and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions.The WS4 and FRDM12 models(two macroscopic–microscopic mass models),combined with the RBF approach,may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.展开更多
The validity of the isobaric multiplet mass equation(IMME)is of foundamental importance due to the basic concept of isospin.Recently,a serious breakdown was found in the A=54,T=3,isospin septet,the largest isospin sys...The validity of the isobaric multiplet mass equation(IMME)is of foundamental importance due to the basic concept of isospin.Recently,a serious breakdown was found in the A=54,T=3,isospin septet,the largest isospin system where the validity of IMME have been tested up to now.Inspired by this work,I revist the mass of some isobaric analogue states with the help of recent results from advanced mass measurement experiment.It is found that the IMME holds well in A=50 and 46 isospin septet and the coefficients of IMME also follow the systematic trends.Mass excess value for^(50)Ni and^(46)Fe,is predicted to be-3932(20)keV and 898(67)keV,respectively.展开更多
The isospin asymmetry and quadrupole deformation value of drip-line nuclei are investigated using the Weizsäcker-Skyrme nuclear mass formula.We observe that for heavy nuclei at the neutron drip line,the Coulomb e...The isospin asymmetry and quadrupole deformation value of drip-line nuclei are investigated using the Weizsäcker-Skyrme nuclear mass formula.We observe that for heavy nuclei at the neutron drip line,the Coulomb energy heightened by an aug-mented charge could not be mitigated completely by symmetry energy because of isospin asymmetry saturation but is resisted complementally by strong nuclear deformation.The positions of saltation for the difference in proton numbers between two neighboring nuclei at the neutron drip line,and the isospin asymmetry of the neutron drip-line nucleus as a function of the neutron number distinctly correspond to the known magic numbers,which can serve as a reference to verify the undeter-mined neutron magic number.Through fitting of the binding energy difference between mirror nuclei(BEDbMN),a set of Coulomb energy coefficients with greater accuracy is obtained.A high-precision description of the BEDbMN is useful for accurately determining the experimentally unknown mass of the nucleus close to the proton drip line if the mass of its mirror nucleus is measured experimentally.展开更多
This study performed a statistical analysis of the correlation and uncertainty of parameters in the classical liquid drop mass formula(namely BW3 type)via regression,along with the theoretical impact of error propagat...This study performed a statistical analysis of the correlation and uncertainty of parameters in the classical liquid drop mass formula(namely BW3 type)via regression,along with the theoretical impact of error propagation.Within the improved BW3 formula,the total deviation between evaluation and experiment can be reduced to 1.66 MeV,involving a reduction from 2.89(2.42)MeV to 1.92(1.89)MeV in the proton(neutron)-dripline region.Ridge regression validation verified this total deviation as the optimal point in the present mass model.Through trend coefficients and Pearson linear-correlation analysis,obvious collinearity was identified between volume,surface,Coulomb,and curvature terms,with notable correlation among high-order symmetry energy and surface symmetry terms.The theoretical derivation of the distribution of binding energy error was then achieved through error propagation analysis.Across the nuclide chart,the error uncertainty of mass predictions varies from 1.996 to 124.469 keV,demonstrating a convex trend of the initial decrease of evaluation error followed by an increase versus the neutron number.展开更多
Nuclear masses are investigated for the first time using the eXtreme Gradient Boosting(XGBoost)method.Nucleon numbers,valence nucleon numbers,and physical quantities related to the magic number are used as input featu...Nuclear masses are investigated for the first time using the eXtreme Gradient Boosting(XGBoost)method.Nucleon numbers,valence nucleon numbers,and physical quantities related to the magic number are used as input features for the decision tree,which learns the residuals of experimental binding energies with respect to the Bethe-Weizsäcker(BW2)formula predictions,and the XGBoost method can achieve high accuracy predictions of nuclear binding energy.For nuclear masses of magic number nuclei with prediction challenges,XGBoost can better capture the physical information associated with the magic number compared to that using BW2,and the root mean square deviation of its predicted nuclear mass ranges from 2.769 to 0.732 MeV.Comparing the results of BW2^(*)and XGBoost^(*) with the pseudo-experimental data of Finite-Range Droplet Model(FRDM12)suggests that the XGBoost^(*) method may have better extrapolation abilities.展开更多
With the development of radioactive-ion-beam facilities,many exotic phenomena have been discovered or predicted in the nuclei far from the stability line,including cluster structure,shell structure,deformed halo,and s...With the development of radioactive-ion-beam facilities,many exotic phenomena have been discovered or predicted in the nuclei far from the stability line,including cluster structure,shell structure,deformed halo,and shape decoupling effects.The study of exotic nuclear phenomena is at the frontier of nuclear physics nowadays.The covariant density functional theory(CDFT)is one of the most successful microscopic models in describing the structure of nuclei in almost the whole nuclear chart.Within the framework of CDFT,toward a proper treatment of deformation and weak binding,the deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc)has been developed.In this contribution,we review the applications and extensions of the DRHBc theory to the study of exotic nuclei.The DRHBc theory has been used to investigate the deformed halos in B,C,Ne,Na,and Mg isotopes and the theoretical descriptions are reasonably consistent with available data.A DRHBc Mass Table Collaboration has been founded,aiming at a high precision nuclear mass table with deformation and continuum effects included,which is underway.By implementing the angular momentum projection based on the DRHBc theory,the rotational excitations of deformed halos have been investigated and it is shown that the deformed halos and shape decoupling effects also exist in the low-lying rotational excitation states of deformed halo nuclei.展开更多
A novel technique of isochronous mass spectrometry(IMS),termed Bρ-defned IMS,was developed at the experimental cooler-storage ring CSRe in Lanzhou for the frst time.Two time-of-fight detectors were installed in a str...A novel technique of isochronous mass spectrometry(IMS),termed Bρ-defned IMS,was developed at the experimental cooler-storage ring CSRe in Lanzhou for the frst time.Two time-of-fight detectors were installed in a straight section of the CSRe,thereby enabling simultaneous measurements of the velocity and revolution time of each stored short-lived ion.This technique boosts the broadband precision,efciency,sensitivity,and accuracy of mass measurements of short-lived exotic nuclides.Using Bρ-defned IMS,the masses of^(22)Al,^(62)Ge,^(64)As,^(66)Se,and^(70)Kr were measured for the frst time,and the masses of^(65)As,^(67)Se,and other 21 nuclides were redetermined with improved accuracy.Mass data have been used in studies of relevant issues regarding nuclear structures and nuclear astrophysics.Herein,we review the development of experimental techniques and main physical results and outline plans for future experiments.展开更多
We examined the conditions of neutron density(n) and temperature(T9) required for the N = 50, 82,and 126 isotopes to be waiting points(WP) in the r-process. The nuclear mass based on experimental data presented in the...We examined the conditions of neutron density(n) and temperature(T9) required for the N = 50, 82,and 126 isotopes to be waiting points(WP) in the r-process. The nuclear mass based on experimental data presented in the AME2020 database(AME and AME ± Δ) and that predicted using FRDM,WS4, DZ10, and KTUY models were employed in our estimations. We found that the conditions required by the N = 50 WP significantly overlap with those required by the N = 82 ones, except for the WS4 model. In addition, the upper(or lower) bounds of the n-T9 conditions based on the models are different from each other due to the deviations in the two-neutron separation energies.The standard deviations in the nuclear mass of 108 isotopes in the three N = 50, 82, and 126 groups are about rms = 0.192 and 0.434 Me V for the pairs of KTUY-AME and WS4-KTUY models,respectively. We found that these mass uncertainties result in a large discrepancy in the nn-T_(9) conditions, leading to significant differences in the conditions for simultaneously appearing all the three peaks in the r-process abundance. The newly updated FRDM and WS4 calculations can give the overall conditions for the appearance of all the peaks but vice versa for their old versions in a previous study. The change in the final r-process isotopic abundance due to the mass uncertainty is from a few factors to three orders of magnitude. Therefore, accurate nuclear masses of the r-process key nuclei, especially for 76 Fe,81Cu,127Rh,132Cd,192Dy, and 197Tm, are highly recommended to be measured in radioactive-ion beam facilities for a better understanding of the r-process evolution.展开更多
In conventional isochronous mass spectrometry(IMS)performed on a storage ring,the precision of mass measurements for short-lived nuclei depends on the accurate determination of the revolution times(T)of stored ions.Ho...In conventional isochronous mass spectrometry(IMS)performed on a storage ring,the precision of mass measurements for short-lived nuclei depends on the accurate determination of the revolution times(T)of stored ions.However,the resolution of T inevitably deteriorates due to the magnetic rigidity spread of the ions,limiting the mass-resolving power.In this study,we used the betatron tunes Q(the number of betatron oscillations per revolution)of the ions and established a correlation between T and Q.From this correlation,T was transformed to correspond to a fixed Q with higher resolution.Using these transformed T values,the masses of ^(63)Ge,^(65)As,^(67)Se,and ^(71)Kr agreed well with the mass values measured using the newly developed IMS(Bρ-IMS).We also studied the systematics of Coulomb displacement energies(CDEs)and found that anomalous staggering in CDEs was eliminated using new mass values.This method of T transformation is highly effective for conventional IMS equipped with a single time-of-flight detector.展开更多
In this study,we revisit the previous mass relations of mirror nuclei by considering 1/N-and 1/Z-dependent terms and the shell effect across a shell.The root-mean-squared deviation is 66 keV for 116 nuclei with neutro...In this study,we revisit the previous mass relations of mirror nuclei by considering 1/N-and 1/Z-dependent terms and the shell effect across a shell.The root-mean-squared deviation is 66 keV for 116 nuclei with neutron number N≥10,as com-pared with experimental data compiled in the AME2020 database.The predicted mass excesses of 173 proton-rich nuclei,including 98 unknown nuclei,are tabulated in the Supplemental Material herein with competitive accuracy.展开更多
This paper was published online on 28 June 2025,and there is a numerical error in Fig.1 of the published version.This correction only resulted in minor changes to the last decimal places of the root mean square(rms)de...This paper was published online on 28 June 2025,and there is a numerical error in Fig.1 of the published version.This correction only resulted in minor changes to the last decimal places of the root mean square(rms)deviation of the BWK formula,and through rigorous verification,such discrepancies will not have any impact on the key conclusions of the paper.The Fig.1 in the published version is corrected as Fig.1 in this erratum.Fig.1.Differences between the experimental binding energies and predictions calculated using the BWK*and BWK formulas,respectively.The dashed lines denote the traditional magic numbers.展开更多
Shell effect plays an important role in nuclear mass predictions,especially for the nuclei around the magic numbers.In this study,a new semi-empirical shell correction term is constructed to improve the mass descripti...Shell effect plays an important role in nuclear mass predictions,especially for the nuclei around the magic numbers.In this study,a new semi-empirical shell correction term is constructed to improve the mass description of the Bethe-Weizsäcker(BW)formula.For nuclei withZ,N≥8,the root mean square(rms)deviation of the newly proposed formula with respect to the latest nuclear mass evaluation dataset AME2020 is 0.887 MeV,inducing a 72.23%reduction compared to the rms deviation of 3.194 MeV for the BW formula.The deviations between the theoretical predictions and experimental data are within 1.5 MeV for 91.90%of the nuclei.In addition,the new mass formula significantly improves the predictions of the binding energies for magic nuclei.The rms deviation of our formula for the binding energy of magic nuclei is only 1.065 MeV,which is a 80.80 reduction compared with that of the BW formula.展开更多
The Bayesian neural network(BNN)has been widely used to study nuclear physics in recent years.In this study,a BNN was applied to optimize seven theoretical nuclear mass models,namely,six global models and one local mo...The Bayesian neural network(BNN)has been widely used to study nuclear physics in recent years.In this study,a BNN was applied to optimize seven theoretical nuclear mass models,namely,six global models and one local model.The accuracy of these models in describing and predicting masses of nuclei with both the proton number and the neutron number greater than or equal to eight was improved effectively for two types of numerical experiments,particularly for the liquid drop model and the relativistic mean-field theory,whose root mean square deviations(RMSDs)for describing(predicting)nuclear masses were reduced by 81.5%-90.6%(66.9%-84.2%).Additionally,the relatively stable RMSDs as nuclei move away from theβ-stability line and the good agreement with experimental single-neutron separation energies further confirm the reliability of the BNN.展开更多
Mass is a fundamental property and an important fingerprint of atomic nucleus.It provides an extremely useful test ground for nuclear models and is crucial to understand energy generation in stars as well as the heavy...Mass is a fundamental property and an important fingerprint of atomic nucleus.It provides an extremely useful test ground for nuclear models and is crucial to understand energy generation in stars as well as the heavy elements synthesized in stellar explosions.Nuclear physicists have been attempting at developing a precise,reliable,and predictive nuclear model that is suitable for the whole nuclear chart,while this still remains a great challenge even in recent days.Here we employ the Fourier spectral analysis to examine the deviations of nuclear mass predictions to the experimental data and to present a novel way for accurate nuclear mass predictions.In this analysis,we map the mass deviations from the space of nucleon number to its conjugate space of frequency,and are able to pin down the main contributions to the model deficiencies.By using the radial basis function approach we can further isolate and quantify the sources.Taking a pedagogical mass model as an example,we examine explicitly the correlation between nuclear effective interactions and the distributions of mass deviations in the frequency domain.The method presented in this work,therefore,opens up a new way for improving the nuclear mass predictions towards a hundred kilo-electron-volt accuracy,which is argued to be the chaos-related limit for the nuclear mass predictions.展开更多
基金Supported by the National Natural Science Foundation of China(12205105,12311540139)by the Fundamental Research Funds for the Central Universities(2024ZYGXZR058)the startup funding of South China University of Technology。
文摘Using four representative nuclear mass models,namely,WS4,FRDM,DZ10,and KTUY,we perform a systematic investigation on how nuclear masses affect theα-decay properties of superheavy nuclei,including decay energies,α-cluster preformation factors,and corresponding half-lives.Theα-cluster preformation factors are obtained from two types of cluster-formation model(CFM)and extracted from experimental decay half-life.All mass models reproduce the knownα-decay energies with small root-mean-square errors,while WS4 and FRDM show the highest accuracy.Strong correlations among preformation factors from different mass models are identified in both CFM and extracted results,although the exponential dependence of half-lives on decay energy weakens correlations between the two approaches.For possibleα-decay chains of superheavy nuclei,the decay energy systematically decreases and the predicted half-life increases with decreasing proton number.This trend is also observed from the calculations for superheavy isotopes with same proton number.These results indicate that isotopes of superheavy elements with more neutrons are expected to exhibit enhanced stability,thus providing theoretical reference for future synthesis of elements with Z=119 and 120.
基金supported by the 211 Project of Anhui University (Grant No.02303319-33190135)the Key Research Foundation of Education Ministry of Anhui Province of China(Grant No.KJ2012A021)+1 种基金the Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No.NCET-09-0031)the National Natural Science Foundation of China(Grant Nos.10975008,11105010,11035007, 11128510,11175001 and 11205004)
文摘With experimental masses updated from AME11,the predictive power of relativistic mean-field(RMF) mass model is carefully examined and compared with HFB-17,FRDM,WS*,and DZ28 mass models.In the relativistic mean-field model,the calculation with the PC-PK1 has improved significantly in describing masses compared to the TMA,especially for the neutron-deficient nuclei.The corresponding rms deviation with respect to the known masses falls to 1.4 MeV.Furthermore,it is found that the RMF mass model better describes the nuclei with large deformations.The rms deviation for nuclei with the absolute value of quadrupole deformation parameter greater than 0.25 falls to 0.93,crossing the 1 MeV accuracy threshold for the PC-PK1,which may indicate the new model is more suitable for those largely-deformed nuclei.In addition,the necessity of new high-precision experimental data to evaluate and develop the nuclear mass models is emphasized as well.
基金supported by the National Natural Science Foundation of China(Nos.12265012 and 12305125)Guizhou Provincial Science and Technology Projects(No.ZK[2022]203)+2 种基金PhD fund of Guizhou Minzu University(No.GZMUZK[2024]QD76)the National Key Laboratory of Neutron Science and Technology(No.NST202401016)the Sichuan Science and Technology Program(No.2024NSFSC1356).
文摘Nuclear masses play a crucial role in both nuclear physics and astrophysics,driving sustained efforts toward precise experi-mental determination and reliable theoretical predictions.In this study,we compiled the newly measured masses for 296 nuclides from 40 references published between 2021 and 2024,subsequent to the release of the latest atomic mass evalu-ation.These data were used to benchmark the performance of several relativistic and nonrelativistic density functionals,including PC-PK1,TMA,SLy4,SV-min,UNEDF1,and the recently proposed PC-L3R.The results for PC-PK1 and PC-L3R were obtained using the state-of-the-art deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc),whereas the others were adopted from the existing literature.It was found that the DRHBc calculations with PC-PK1 and PC-L3R achieved an accuracy better than 1.5 MeV,outperforming the other functionals,which all exhibited root-mean-square devia-tions exceeding 2 MeV.The odd-even effects and isospin dependence in these theoretical descriptions were examined.The PC-PK1 and PC-L3R descriptions were qualitatively similar,exhibiting robust isospin dependence along the isotopic chains.Finally,a quantitative comparison between the PC-PK1 and PC-L3R results is presented,with the largest discrepancies analyzed in terms of the potential energy curves from the constrained DRHBc calculations.
基金supported by the National Natural Science Foundation of China(Nos.U2267205 and 12475124)a ZSTU intramural grant(22062267-Y)Excellent Graduate Thesis Cultivation Fund(LW-YP2024011).
文摘Nuclear mass is an important property in both nuclear and astrophysics.In this study,we explore an improved mass model that incorporates a higher-order term of symmetry energy using algorithms.The sequential least squares programming(SLSQP)algorithm augments the precision of this multinomial mass model by reducing the error from 1.863 MeV to 1.631 MeV.These algorithms were further examined using 200 sample mass formulae derived from theδE term of the E_(isospin) mass model.The SLSQP method exhibited superior performance compared to the other algorithms in terms of errors and convergence speed.This algorithm is advantageous for handling large-scale multiparameter optimization tasks in nuclear physics.
基金This work was supported in part by the National Science Foundation of China(Nos.U2032145,11875125,12047568,11790323,11790325,and 12075085)the National Key Research and Development Program of China(No.2020YFE0202002)the"Ten Thousand Talent Program"of Zhejiang Province(No.2018R52017).
文摘Background:The masses of-2500 nuclei have been measured experimentally;however,>7000 isotopes are predicted to exist in the nuclear landscape from H(Z=1)to Og(Z=118)based on various theoretical calculations.Exploring the mass of the remaining isotopes is a popular topic in nuclear physics.Machine learning has served as a powerful tool for learning complex representations of big data in many fields.Purpose:We use Light Gradient Boosting Machine(LightGBM),which is a highly efficient machine learning algorithm,to predict the masses of unknown nuclei and to explore the nuclear landscape on the neutron-rich side from learning the measured nuclear masses.Methods:Several characteristic quantities(e.g.,mass number and proton number)are fed into the LightGBM algorithm to mimic the patterns of the residual δ(Z,A)between the experimental binding energy and the theoret-ical one given by the liquid-drop model(LDM),Duflo–Zucker(DZ,also dubbed DZ28)mass model,finite-range droplet model(FRDM,also dubbed FRDM2012),as well as the Weizsacker–Skyrme(WS4)model to refine these mass models.Results:By using the experimental data of 80%of known nuclei as the training dataset,the root mean square devia-tions(RMSDs)between the predicted and the experimental binding energy of the remaining 20%are approximately 0.234±0.022,0.213±0.018,0.170±0.011,and 0.222±0.016 MeV for the LightGBM-refined LDM,DZ model,WS4 model,and FRDM,respectively.These values are approximately 90%,65%,40%,and 60%smaller than those of the corresponding origin mass models.The RMSD for 66 newly measured nuclei that appeared in AME2020 was also significantly improved.The one-neutron and two-neutron separation energies predicted by these refined models are consistent with several theoretical predictions based on various physical models.In addition,the two-neutron separation energies of several newly measured nuclei(e.g.,some isotopes of Ca,Ti,Pm,and Sm)pre-dicted with LightGBM-refined mass models are also in good agreement with the latest experimental data.Conclusions:LightGBM can be used to refine theoretical nuclear mass models and predict the binding energy of unknown nuclei.Moreover,the correlation between the input characteristic quantities and the output can be inter-preted by SHapley additive exPlanations(a popular explainable artificial intelligence tool),which may provide new insights for developing theoretical nuclear mass models.
基金supported by the National Natural Science Foundation of China(Nos.12175199 and U2267205)a ZSTU intramural grant(No.22062267-Y).
文摘Nuclear mass is a fundamental property of nuclear physics and a necessary input in nuclear astrophysics.Owing to the complexity of atomic nuclei and nonperturbative strong interactions,conventional physical models cannot completely describe nuclear binding energies.In this study,the mass formula was improved by considering an additional term from the Fermi gas model.All nuclear masses in the Atomic Mass Evaluation Database were reproduced with a root-mean-square deviation(RMSD)of -1.86 MeV(1.92 MeV).The new mass formula exhibits good performance in the neutron-rich nuclear region.The RMSD decreases to 0.393 MeV when the ratio of the neutron number to the proton number is≥1.6.
基金supported by the National Natural Science Foundation of China(Grant No.U1867212,12047567)the Natural Science Foundation of Guangxi(Grant NO.2017GXNSFGA198001)the Middle-aged and Young Teachers’Basic Ability Promotion Project of Guangxi(CN)(Grant No.2019KY0061)。
文摘The ability of the radial basis function(RBF)approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31),Hartree–Fock-Bogoliubov(HFB27),finite-range droplet model(FRDM12)and Weizsäcker-Skyrme(WS4)mass models.It is found that when the RBF approach is employed with a simple linear basis function,different mass models have different performances in extrapolating nuclear masses in the same region,and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions.The WS4 and FRDM12 models(two macroscopic–microscopic mass models),combined with the RBF approach,may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.
文摘The validity of the isobaric multiplet mass equation(IMME)is of foundamental importance due to the basic concept of isospin.Recently,a serious breakdown was found in the A=54,T=3,isospin septet,the largest isospin system where the validity of IMME have been tested up to now.Inspired by this work,I revist the mass of some isobaric analogue states with the help of recent results from advanced mass measurement experiment.It is found that the IMME holds well in A=50 and 46 isospin septet and the coefficients of IMME also follow the systematic trends.Mass excess value for^(50)Ni and^(46)Fe,is predicted to be-3932(20)keV and 898(67)keV,respectively.
基金supported by the Ministry of Science and Technology of China(No.2022YFE0103400)Natural Science Foundation of Guangxi Province(No.2021GXNSFAA196052)National Natural Science Foundation of China(No.11965004).
文摘The isospin asymmetry and quadrupole deformation value of drip-line nuclei are investigated using the Weizsäcker-Skyrme nuclear mass formula.We observe that for heavy nuclei at the neutron drip line,the Coulomb energy heightened by an aug-mented charge could not be mitigated completely by symmetry energy because of isospin asymmetry saturation but is resisted complementally by strong nuclear deformation.The positions of saltation for the difference in proton numbers between two neighboring nuclei at the neutron drip line,and the isospin asymmetry of the neutron drip-line nucleus as a function of the neutron number distinctly correspond to the known magic numbers,which can serve as a reference to verify the undeter-mined neutron magic number.Through fitting of the binding energy difference between mirror nuclei(BEDbMN),a set of Coulomb energy coefficients with greater accuracy is obtained.A high-precision description of the BEDbMN is useful for accurately determining the experimentally unknown mass of the nucleus close to the proton drip line if the mass of its mirror nucleus is measured experimentally.
基金Research at ZSTU was supported by the National Natural Science Foundation of China(Grants No.U2267205,No.12475124)ZSTU intramural grant(22062267-Y)+2 种基金supported by the National Natural Science Foundation of China(Grant No.12075121)the Natural Science Foundation of Jiangsu Province(Grant No.BK20190067)the Fundamental Research Funds for the Central Universities(Grant No.30922010312)。
文摘This study performed a statistical analysis of the correlation and uncertainty of parameters in the classical liquid drop mass formula(namely BW3 type)via regression,along with the theoretical impact of error propagation.Within the improved BW3 formula,the total deviation between evaluation and experiment can be reduced to 1.66 MeV,involving a reduction from 2.89(2.42)MeV to 1.92(1.89)MeV in the proton(neutron)-dripline region.Ridge regression validation verified this total deviation as the optimal point in the present mass model.Through trend coefficients and Pearson linear-correlation analysis,obvious collinearity was identified between volume,surface,Coulomb,and curvature terms,with notable correlation among high-order symmetry energy and surface symmetry terms.The theoretical derivation of the distribution of binding energy error was then achieved through error propagation analysis.Across the nuclide chart,the error uncertainty of mass predictions varies from 1.996 to 124.469 keV,demonstrating a convex trend of the initial decrease of evaluation error followed by an increase versus the neutron number.
基金supported by the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology(2023yjrc107)。
文摘Nuclear masses are investigated for the first time using the eXtreme Gradient Boosting(XGBoost)method.Nucleon numbers,valence nucleon numbers,and physical quantities related to the magic number are used as input features for the decision tree,which learns the residuals of experimental binding energies with respect to the Bethe-Weizsäcker(BW2)formula predictions,and the XGBoost method can achieve high accuracy predictions of nuclear binding energy.For nuclear masses of magic number nuclei with prediction challenges,XGBoost can better capture the physical information associated with the magic number compared to that using BW2,and the root mean square deviation of its predicted nuclear mass ranges from 2.769 to 0.732 MeV.Comparing the results of BW2^(*)and XGBoost^(*) with the pseudo-experimental data of Finite-Range Droplet Model(FRDM12)suggests that the XGBoost^(*) method may have better extrapolation abilities.
文摘With the development of radioactive-ion-beam facilities,many exotic phenomena have been discovered or predicted in the nuclei far from the stability line,including cluster structure,shell structure,deformed halo,and shape decoupling effects.The study of exotic nuclear phenomena is at the frontier of nuclear physics nowadays.The covariant density functional theory(CDFT)is one of the most successful microscopic models in describing the structure of nuclei in almost the whole nuclear chart.Within the framework of CDFT,toward a proper treatment of deformation and weak binding,the deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc)has been developed.In this contribution,we review the applications and extensions of the DRHBc theory to the study of exotic nuclei.The DRHBc theory has been used to investigate the deformed halos in B,C,Ne,Na,and Mg isotopes and the theoretical descriptions are reasonably consistent with available data.A DRHBc Mass Table Collaboration has been founded,aiming at a high precision nuclear mass table with deformation and continuum effects included,which is underway.By implementing the angular momentum projection based on the DRHBc theory,the rotational excitations of deformed halos have been investigated and it is shown that the deformed halos and shape decoupling effects also exist in the low-lying rotational excitation states of deformed halo nuclei.
基金National Key R&D Program of China(Grant No.2023YFA1606401)CAS Project for Young Scientists in Basic Research(Grant No.YSBR-002)+1 种基金Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB34000000)NSFC(Grant No.12305126)。
文摘A novel technique of isochronous mass spectrometry(IMS),termed Bρ-defned IMS,was developed at the experimental cooler-storage ring CSRe in Lanzhou for the frst time.Two time-of-fight detectors were installed in a straight section of the CSRe,thereby enabling simultaneous measurements of the velocity and revolution time of each stored short-lived ion.This technique boosts the broadband precision,efciency,sensitivity,and accuracy of mass measurements of short-lived exotic nuclides.Using Bρ-defned IMS,the masses of^(22)Al,^(62)Ge,^(64)As,^(66)Se,and^(70)Kr were measured for the frst time,and the masses of^(65)As,^(67)Se,and other 21 nuclides were redetermined with improved accuracy.Mass data have been used in studies of relevant issues regarding nuclear structures and nuclear astrophysics.Herein,we review the development of experimental techniques and main physical results and outline plans for future experiments.
基金supported by the National Research Foundation of Korea(NRF)Grant funded by the Korean Ministry of Education,Science,and Technology(No.NRF2020R1C1C1006029)。
文摘We examined the conditions of neutron density(n) and temperature(T9) required for the N = 50, 82,and 126 isotopes to be waiting points(WP) in the r-process. The nuclear mass based on experimental data presented in the AME2020 database(AME and AME ± Δ) and that predicted using FRDM,WS4, DZ10, and KTUY models were employed in our estimations. We found that the conditions required by the N = 50 WP significantly overlap with those required by the N = 82 ones, except for the WS4 model. In addition, the upper(or lower) bounds of the n-T9 conditions based on the models are different from each other due to the deviations in the two-neutron separation energies.The standard deviations in the nuclear mass of 108 isotopes in the three N = 50, 82, and 126 groups are about rms = 0.192 and 0.434 Me V for the pairs of KTUY-AME and WS4-KTUY models,respectively. We found that these mass uncertainties result in a large discrepancy in the nn-T_(9) conditions, leading to significant differences in the conditions for simultaneously appearing all the three peaks in the r-process abundance. The newly updated FRDM and WS4 calculations can give the overall conditions for the appearance of all the peaks but vice versa for their old versions in a previous study. The change in the final r-process isotopic abundance due to the mass uncertainty is from a few factors to three orders of magnitude. Therefore, accurate nuclear masses of the r-process key nuclei, especially for 76 Fe,81Cu,127Rh,132Cd,192Dy, and 197Tm, are highly recommended to be measured in radioactive-ion beam facilities for a better understanding of the r-process evolution.
基金supported in part by the National Key R&D Program of China (No. 2023YFA1606401)CAS Project for Young Scientists in Basic Research (No. YSBR-002)+3 种基金Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB34000000)the NSFC (Nos. 12305126, 12135017, 12121005)the support from the Youth Innovation Promotion Association of the Chinese Academy of Sciences (No. 2021419)the support from the Yong Scholar of Regional Development,CAS (No.[2023]15)
文摘In conventional isochronous mass spectrometry(IMS)performed on a storage ring,the precision of mass measurements for short-lived nuclei depends on the accurate determination of the revolution times(T)of stored ions.However,the resolution of T inevitably deteriorates due to the magnetic rigidity spread of the ions,limiting the mass-resolving power.In this study,we used the betatron tunes Q(the number of betatron oscillations per revolution)of the ions and established a correlation between T and Q.From this correlation,T was transformed to correspond to a fixed Q with higher resolution.Using these transformed T values,the masses of ^(63)Ge,^(65)As,^(67)Se,and ^(71)Kr agreed well with the mass values measured using the newly developed IMS(Bρ-IMS).We also studied the systematics of Coulomb displacement energies(CDEs)and found that anomalous staggering in CDEs was eliminated using new mass values.This method of T transformation is highly effective for conventional IMS equipped with a single time-of-flight detector.
基金supported by the National Natural Science Foundation of China(No.11905130).
文摘In this study,we revisit the previous mass relations of mirror nuclei by considering 1/N-and 1/Z-dependent terms and the shell effect across a shell.The root-mean-squared deviation is 66 keV for 116 nuclei with neutron number N≥10,as com-pared with experimental data compiled in the AME2020 database.The predicted mass excesses of 173 proton-rich nuclei,including 98 unknown nuclei,are tabulated in the Supplemental Material herein with competitive accuracy.
基金National Natural Science Foundation of China(12375109,11875070,11935001)the Anhui project(Z010118169)+2 种基金the Key Research Foundation of Education Ministry of Anhui Province(2023AH050095)University Synergy Innovation Program of Anhui Province(GXXT-2023-007)the University Natural Science Outstanding Youth Research Projects of Anhui Province(2022AH030039)。
文摘This paper was published online on 28 June 2025,and there is a numerical error in Fig.1 of the published version.This correction only resulted in minor changes to the last decimal places of the root mean square(rms)deviation of the BWK formula,and through rigorous verification,such discrepancies will not have any impact on the key conclusions of the paper.The Fig.1 in the published version is corrected as Fig.1 in this erratum.Fig.1.Differences between the experimental binding energies and predictions calculated using the BWK*and BWK formulas,respectively.The dashed lines denote the traditional magic numbers.
基金supported by the National Natural Science Foundation of China(12375109,11875070,11935001)the Anhui project(Z010118169)+2 种基金the Key Research Foundation of Education Ministry of Anhui Province(2023AH050095)the University Synergy Innovation Program of Anhui Province(GXXT-2023-007)the University Natural Science Outstanding Youth Research Projects of Anhui Province(2022AH030039)。
文摘Shell effect plays an important role in nuclear mass predictions,especially for the nuclei around the magic numbers.In this study,a new semi-empirical shell correction term is constructed to improve the mass description of the Bethe-Weizsäcker(BW)formula.For nuclei withZ,N≥8,the root mean square(rms)deviation of the newly proposed formula with respect to the latest nuclear mass evaluation dataset AME2020 is 0.887 MeV,inducing a 72.23%reduction compared to the rms deviation of 3.194 MeV for the BW formula.The deviations between the theoretical predictions and experimental data are within 1.5 MeV for 91.90%of the nuclei.In addition,the new mass formula significantly improves the predictions of the binding energies for magic nuclei.The rms deviation of our formula for the binding energy of magic nuclei is only 1.065 MeV,which is a 80.80 reduction compared with that of the BW formula.
文摘The Bayesian neural network(BNN)has been widely used to study nuclear physics in recent years.In this study,a BNN was applied to optimize seven theoretical nuclear mass models,namely,six global models and one local model.The accuracy of these models in describing and predicting masses of nuclei with both the proton number and the neutron number greater than or equal to eight was improved effectively for two types of numerical experiments,particularly for the liquid drop model and the relativistic mean-field theory,whose root mean square deviations(RMSDs)for describing(predicting)nuclear masses were reduced by 81.5%-90.6%(66.9%-84.2%).Additionally,the relatively stable RMSDs as nuclei move away from theβ-stability line and the good agreement with experimental single-neutron separation energies further confirm the reliability of the BNN.
基金supported by the National Program on Key Basic Research Project of China(2013CB834400)the National Natural Science Foundation of China(11205004,11305161,11335002,11475014,11575002,and 11411130147)+2 种基金the Natural Science Foundation of Anhui Province(1708085QA10)the RIKEN iTHES ProjectiTHEMS Program
文摘Mass is a fundamental property and an important fingerprint of atomic nucleus.It provides an extremely useful test ground for nuclear models and is crucial to understand energy generation in stars as well as the heavy elements synthesized in stellar explosions.Nuclear physicists have been attempting at developing a precise,reliable,and predictive nuclear model that is suitable for the whole nuclear chart,while this still remains a great challenge even in recent days.Here we employ the Fourier spectral analysis to examine the deviations of nuclear mass predictions to the experimental data and to present a novel way for accurate nuclear mass predictions.In this analysis,we map the mass deviations from the space of nucleon number to its conjugate space of frequency,and are able to pin down the main contributions to the model deficiencies.By using the radial basis function approach we can further isolate and quantify the sources.Taking a pedagogical mass model as an example,we examine explicitly the correlation between nuclear effective interactions and the distributions of mass deviations in the frequency domain.The method presented in this work,therefore,opens up a new way for improving the nuclear mass predictions towards a hundred kilo-electron-volt accuracy,which is argued to be the chaos-related limit for the nuclear mass predictions.
