Nuclear charge radius predictions by kernel ridge regression with odd-even effects

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.

Investigation of Nuclear Binding Energy and Charge Radius Based on Random Forest Algorithm

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.

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

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

An improved effective liquid drop model for cluster radioactivity

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.

Charge radii of potassium isotopes in the RMF(BCS)^(*) approach

We apply the recently proposed RMF(BCS)*ansatz to study the charge radii of the potassium isotopic chain up to^(52)K.It is shown that the experimental data can be reproduced rather well,qualitatively similar to the Fayans nuclear density functional theory,but with a slightly better description of the odd-even staggerings(OES).Nonetheless,both methods fail for ^(50)K and to a lesser extent for ^(48,52)K.It is shown that if these nuclei are deformed with aβ_(20)≈−0.2,then one can obtain results consistent with experiments for both charge radii and spin-parities.We argue that beyond-mean-field studies are needed to properly describe the charge radii of these three nuclei,particularly for ^(50)K.

An analysis of nuclear charge radii based on the empirical formula

Several nuclear charge radii had been calculated based on the law of A1/3 and isospin dependence Z1/3 formula which had been used to describe the charge radii data. It is achieved that the isospin dependence Z1/3 formula is superior to the generally accepted A1/3 law through mean root square deviation analysis, that is, the Z1/3 formula is more effective to describe the charge radii data.

Constraining the relativistic mean-field models from PREX-2 data:effective forces revisited

Based on the current measurement of the neutron distribution radius(R_(n))of ^(208)Pb from the PREX-2 data,we revisited the recently developed G3 and IOPB-I force parameters by fine-tuning some specific couplings within the relativistic mean-field(RMF)model.Theω-ρ-mesons coupling and theρ-meson coupling are constrained to the experimental neutron radius of^(208)Pb without compromising the bulk properties of finite nuclei and infinite nuclear matter observables.The modified parameter sets are applied to calculate the gross properties of finite nuclei such as binding energies,charge distributions,nuclear radii,pairing gaps,and single-particle energies.The root-mean-square deviations in binding energy and charge radius are estimated with respect to the available experimental data for 195 even-even nuclei,and the results compare favourably with the well-calibrated effective interactions of Skyrme,Gogny and other relativistic mean-field parametrizations.The pairing gap estimations for modified G3 and IOPB-I for Sn isotopes are also compared with the Hartree-Fock-Bogoliubov calculation with the Gogny(D1S)interaction.The isotopic shift and single-particle energy spacing are also calculated and compared with the experimental data for both original and modified versions of the G3 and IOPB-I parameter sets.Subsequently,both the modified parameter sets are used to obtain the various infinite nuclear matter observables at saturation.In addition to these,the force parameters are adopted to calculate the properties of a high isospin asymmetry dense system such as neutron star matter and tested for validation using the constraint from GW170817 binary neutron star merger events.The tuned forces predict relatively good results for finite and infinite nuclear matter systems and the current limitation on the neutron radius from PREX-2.A systematic analysis using these two refitted parameter sets over the nuclear chart will be communicated shortly.