Influence of binding energies of electrons on nuclear mass predictions

Nuclear mass contains a wealth of nuclear structure information, and has been widely employed to extract the nuclear effective interactions. The known nuclear mass is usually extracted from the experimental atomic mass by subtracting the masses of electrons and adding the binding energy of electrons in the atom. However,the binding energies of electrons are sometimes neglected in extracting the known nuclear masses. The influence of binding energies of electrons on nuclear mass predictions are carefully investigated in this work. If the binding energies of electrons are directly subtracted from the theoretical mass predictions, the rms deviations of nuclear mass predictions with respect to the known data are increased by about 200 ke V for nuclei with Z, N 8. Furthermore, by using the Coulomb energies between protons to absorb the binding energies of electrons, their influence on the rms deviations is significantly reduced to only about 10 ke V for nuclei with Z, N 8. However, the binding energies of electrons are still important for the heavy nuclei, about 150 ke V for nuclei around Z = 100 and up to about 500 ke V for nuclei around Z = 120. Therefore, it is necessary to consider the binding energies of electrons to reliably predict the masses of heavy nuclei at an accuracy of hundreds of ke V.     

Extending the nuclear chart by continuum: From oxygen to titanium

Nuclear masses ranging from O to Ti isotopes are systematically investigated with relativistic continuum Hartree-Bogoliubov (RCHB) theory, which can provide a proper treatment of pairing correlations in the presence of the continuum. From O to Ti isotopes, there are 402 nuclei predicted to be bound by the density functional PC-PK1. For the 234 nuclei with mass measured, the root mean square (rms) deviation is 2.23 MeV. It is found that the proton drip-lines predicted with various mass models are roughly the same and basically agree with the observation. The neutron drip-lines predicted, however, are quite different. Due to the continuum couplings, the neutron drip-line nuclei predicted are extended further neutron-rich than other mass models. By comparison with finite-range droplet model (FRDM), the neutron drip-line nucleus predicted by RCHB theory has respectively 2(O), 10(Ne), 10(Na), 6(Mg), 8(Al), 6(Si), 8(P), 6(S), 14(K), 10(Ca), 10(Sc), and 12(Ti) more neutrons.     

THE SYSTEMATIC CALCULATIONS OF (n,2n) AND (n,3n) REACTION CROSS SECTIONS FOR MEDIUM-HEAVY NUCLEI AT 14.5MeV

The (n,2n) and (n,3n) reaction processes have been studied by mechanism analysis of the neutron-induced nuclear reactions,formulae for evaluating the reduced cross section have been given.The cross sections of 14.5MeV (n,2n),(n,3n) reactions have been calculated according to the systematic method for Z=58—83 about 53 nuclei.A good agreement between the results of the systematic calculations and the experimental data has been reached.     

Phonon–particle coupling effects in odd–even mass differences of semi-magic nuclei

A method to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on a direct solving the Dyson equation with PC corrected mass operator, is used for finding the odd–even mass difference between 18 even Pb isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather high accuracy of the predictions for these mass differences already on the mean-field level, with the average deviation from the existing experimental data equal to 0.389 MeV. It is only a bit worse than the corresponding value of 0.333 MeV for the Skyrme EDF HFB-17, which belongs to a family of Skyrme EDFs with the highest overall accuracy in describing the nuclear masses. Account for the PC corrections induced by the low-laying phonons 2 ₁ ⁺ and 3 ₁ ^- significantly diminishes the deviation of the theory from the data till 0.218 MeV.     

Two-body and three-body halo nuclei

We have extracted the nuclear asymptotic normalization coefficients (ANC) for the virtual transitions B→A+N via some transfer reactions and the radioactive nuclear beam experiments. With these coefficients, root-mean-square (rms) radii for the valence particle in some possible halo nuclei have been calculated. The values of rms radii extracted with ANC approach are nearly model-independent, hence are a good quantity for the investigation of nuclear halo. In addition, we have also calculated the rms radii for the two valence neutrons in some three-body systems in terms of the relationship between the radii of valence particle, core nucleus and nuclear matter. With two conditions for nuclear halo formation, we have examined these extracted rms radii. The results show that 11Be(1/2+, g.s), 12B(1-, 2.621 MeV), 13C(1/2+, 3.089 MeV), 14C(0-, 6.903 MeV), 14C(1-, 6.094 MeV), 15C(1/2+, g.s) and 19C(1/2+, g.s) with the valence particle in the 2s ground or excited state are the neutron halo nuclei, whereas 17F(1/2+, 0.495 MeV) and 21Na(1/2+, 2.423 MeV) are the proton halo nuclei in the excited state. For three-body systems, except the well-established two-neutron halo nuclei 6He and 11Li, 14Be and 17B might be the two-neutron halo nuclei as well.     

Application of kernel ridge regression in predicting neutron-capture reaction cross-sections

This article provides the first application of the machine-learning approach in the study of the cross-sections for neutron-capture reactions with the kernel ridge regression (KRR) approach. It is found that the KRR approach can reduce the root-mean-square (rms) deviation of the relative errors between the experimental data of the Maxwellian-averaged $(n,\gamma )$ cross-sections and the corresponding theoretical predictions from 69.8% to 35.4%. By including the data with different temperatures in the training set, the rms deviation can be further significantly reduced to 2.0%. Moreover, the extrapolation performance of the KRR approach along different temperatures is found to be effective and reliable.     

Properties of A = 7-9 Drip-Line Nuclei in RMF Theory

The relativistic mean-field （RMF） theory is used to calculate the properties of A =7-9 drip-line nuclei ^7Li, ^7;9Be, ^8;9B, and ^9C. Systematic deviations between experimental and theoretical binding energies are found. Possible reasons of these systematic deviations are discussed in terms of pairing energy. The root-mean-square （rms） radii of matter distributions for these nuclei agree with the experimental data quite well. The one-proton halo structure in ^8B is reproduced well, and the two-proton halo in ^9C is predicted. The calculations show that the RMF theory is valid in studying the properties of light drip-line nuclei.     

在超重核区应用Viola-Seaborg公式研究α衰变寿命

在超重核区(Z≥104)使用文献[7—9]给出的3组参数应用Viola-Seaborg公式计算了α衰变寿命,所得结果与实验值进行比较,发现其结果与实验值相差较大。为此,利用最小二乘法分别在重核区和超重核区重新对参数进行了拟合,得到的计算结果与实验值相比符合得较理想,尤其是由超重核得到的参数的结果非常理想。     

Search for supersymmetry in light nuclei

The supersymmetry assumption based on a system of valence interacting bosons and odd nucleons has been checked in the second half of the nuclear sd-shell. The dynamical supersymmetric hamiltonian restricted to the linear combination of chosen second-order Casimir invariants has been applied to energy levels of several nuclei organized in supermultiplets. The supersymmetry predictions for nine nuclei are in accord, to a good approximation, with experimental energy levels up to 4–7 MeV.     

Ground-state properties of neutron magic nuclei

A systematic study of the ground-state properties of the entire chains of even–even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82, and 126 has been carried out using relativistic mean-field plus Bardeen–Cooper–Schrieffer approach. Our present investigation includes deformation, binding energy, two-proton separation energy, single-particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using nonrelativistic approach (Skyrme–Hartree–Fock method) along with available experimental data and indeed they are found with excellent agreement. In addition, the possible locations of the proton and neutron drip-lines, the (Z, N) values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail.     

Nuclear Masses and Nuclear Shape Transitions in Z=50—71

Some parameters and the β equation of Johansson mass formula were modified.In the fit to the experimental masses and two-neutron separation energies (S_2n) of 640 nuclides in the region of 50≤Z≤71,four free parameters are presented.The root-mean-square deviation of the mass values and S_2n are 0.827MeV and 0.406MeV respectively.The characters of transition from spherical to deformed shapes (N>90) are also reproduced by the curves of S_2n.     

A Bayesian-neural-network prediction for fragment production in proton induced spallation reaction

Fragment production in spallation reactions yields key infrastructure data for various applications. Based on the empirical SPACS parameterizations, a Bayesian-neural-network (BNN) approach is established to predict the fragment cross sections in proton-induced spallation reactions. A systematic investigation has been performed for the measured proton-induced spallation reactions of systems ranging from intermediate to heavy nuclei systems and incident energies ranging from 168 MeV/u to 1500 MeV/u. By learning the residuals between the experimental measurements and SPACS predictions, it is found that the BNN-predicted results are in good agreement with the measured results. The established method is suggested to benefit the related research on nuclear astrophysics, nuclear radioactive beam sources, accelerator driven systems, proton therapy, etc.     

宏观微观模型对重核区原子核基态性质的研究

利用连续介质模型并基于Nilsson模型考虑微观修正, 研究了重核区原子核( Z≥82)基态性质, 得到了较好的结果。 通过拟合 Z≥82原子核的结合能实验数据, 得到了两组连续介质模型的新参数。 利用这两组参数计算的重核结合能与实验值的均方根偏差约为0.8 MeV, 电荷半径的均方根偏差约为0.07 fm。 The continuous medium model with shell correction from Nilsson model is used to study the ground state properties of heavy nuclei (Z≥82). New parameters are obtained for the continuous medium model by fitting the experimental binding energies. The theoretical calculations for the masses and radii are in good agreements with experimental values, and the root mean square deviations are about 0.8 MeV for the masses, and about 0.07 fm for the radii.     

A Mass Formula with a Few Free Parameters and Nuclear Mass Calculations

A mass formula with deformation and shell corrections for a few free parameters was described.By means of the formula the calculations of 1440 nuclear masses and 1250 two neutron separation energies s_2n in the region of 28≤Z≤81 were performed.The root-mean-square deviations are respectively 1.01MeV for nuclear masses and 0.57MeV for s_2n.The results of the theory could also reproduce the characters of the closure shell,the subshell and the deformation of the nuclei.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

A new macroscopic-microscopic description of the double-humped fission barriers

The new mass relation based on the generalised Hugenholtz-Van Hove theorem has been used to obtain a relation for the fission barriers of three nuclei. This relation has been found satisfactory to describe the data. Further a general expression has been given describing satisfactorily the inner barrier height, the second minimum and the second barrier height for all actinides with an rms deviation of 0.32, 0.32 and 0.33 MeV respectively. The estimated shell energies agree reasonably well with those of Brack et al. In addition the barriers for thorium isotopes have been described well.     

Measurements of the spin correlation parameters Axx and Ayy for p-p scattering at 46.9 MeV

The A_xx and A_yy spin correlation coefficients of proton-proton scattering have been measured at E_lab = 46.9 MeV and θ_c.m. = 90° with the same experimental techniques already used at Saclay from 11 to 26 MeV and at Grenoble at 37.2 MeV. For A_xx the deviation from the predictions of the energy-dependent phase-shifts analysis of Livermore is significant (≈ 3.7 standard deviations) but not as large as for the 47.5 MeV Tokyo measurement. For A_yy the agreement is very good.