Studying the Nuclear Structure of Some Target Nuclei Used for Radiotherapy Nuclei Production by Using Skyrme-Hartree-Fock Method

The nuclear structure for some target nuclei namely: 32S, 58Ni, 89Y, 90Zr, 100Mo and 197Au used for production of the therapeutic radionuclides;32P, 58Co, 89Sr, 90Y, 99Mo, 100Tc, 197Pt and 197Hg has been investigated using Skyrme-Hartree-Fock method based on Skyrme effective two-body interaction. For these purpose, we have calculated the various nuclear densities, the corresponding root mean square radii and nuclear binding energies. The density dependent initial neutron and proton exciton numbers have been also calculated which give the ability to investigate the neutron and proton induced reaction cross-sections for these target nuclei using hybrid model for pre-equilibrium nuclear reactions. The calculated results are compared with available experimental data.

Skyrme-Hartree-Fock方法对Ca同位素基态性质的研究 (Ⅰ)结合能、壳结构、半径与密度分布

用Skyrme Hartree Fock模型系统地研究了40 Ca到70 Ca到Ca同位素偶偶核的基态性质及其同位旋依赖性 .讨论了结合能、均方根半径、密度分布随同位旋的变化 ,研究了壳效应对结合能、双中子分离能S2n及和表面弥散厚度的影响 .结果表明壳效应在S2n、表面弥散厚度中表现得非常明显 .质子均方根半径Rrms随相对中子数I=(N -Z) /A的变化满足Rrms=35(1 +αI + βI2 )rpZ1/ 3.离心位垒对核表面以外的密度分布有很大影响 .

Skyrme-Hartree-Fock方法对Ca同位素基态性质的研究(Ⅱ)中子晕、中子皮与经典禁区内粒子

用Skyrme Hartree Fock模型研究了Ca同位素的纯中子物质的厚度和经典禁区内粒子数随同位旋的变化 .定义了零粒子半径和单粒子半径 ,并用这两种半径定义方法研究纯中子物质厚度后发现 :纯中子物质的厚度明显地受到壳结构的影响 ,零粒子半径和单粒子半径是探讨中子晕比较合适的物理量 .经典禁区内质子数和中子数的差别可以作为定义中子晕或中子皮的指标 .

Beyond-mean-field study of^(37)_(Λ)Ar based on the Skyrme-Hartree-Fock model

We present the hypernuclear states of^(37)_ΛAr obtained using the Skyrme-Hartree-Fock(SHF)model and a beyond-mean-field approach,including angular momentum projection(AMP)and the generator coordinate method(GCM).A comprehensive energy spectrum is given,which includes normally deformed(ND)and super deformed(SD)hypernuclear states with positive or negative parities.Energy levels corresponding to the configurations in which aΛhyperon occupies the s-,p-,or sd-shell orbitals are discussed.For the s-shellΛ,we pay special attention to the ND and SD states corresponding to the configurations^(36)Ar^(N)\otimes s_Λand^(36)Ar^(S)otimes s_Λ,where^(36)Ar^(N)and^(36)Ar^(S)denote the ND and SD nuclear cores,respectively.The disagreements between different models over theΛseparation energy of the SD state in previous studies are revisited.For the p-shellΛ,four rotational bands are predicted,and the impurity effects are shown.Furthermore,two energy levels corresponding to the configurations^(36)Ar^otimesΛ[101](3)(2)^(-)and^(36)Ar^(S)otimesΛ[101](1)(2)^(-)are obtained below the separation threshold of^(36)Ar+Λwithin 0.5 MeV.For the sd-shellΛ,three bound states are found near the separation threshold,and the mechanism behind these states are discussed.

Systematic study of two-proton radioactivity half-lives using the two-potential and Skyrme-Hartree-Fock approaches

In this work,we systematically study the two-proton(2_(p))radioactivity half-lives using the two-potential approach,and the nuclear potential is obtained using the Skyrme-Hartree-Fock approach and the Skyrme effective interaction of SLy8.For true 2_(p) radioactivity(Q2_(p)>0 and Q_(p)<0,where Q_(p) and Q2_(p) are the released energies of the one-proton and two-proton radioactivity,respectively),the standard deviation between the experimental half-lives and our theoretical calculations is 0.701.In addition,we extend this model to predict the half-lives of 15 possible 2_(p) radioactivity candidates with Q2_(p)>0 obtained from the evaluated atomic mass table AME2016.The calcu-lated results indicate a clear linear relationship between the logarithmic 2_(p) radioactivity half-lives(logio10T_(1/2))and coulomb parameters[(Z_(d)^(0.8)+l^(0.25))Q_(2_(p))^(-1/2)]considering the effect of orbital angular momentum proposed by Liu et al.[Chin.Phys.C 45,024108(2021)].For comparison,the generalized liquid drop model(GLDM),effective liquid drop model(ELDM),and Gamow-like model are also used.Our predicted results are consistent with those obtained using other relevant models.

超重核的基态性质

用Skyrme Hartree Fock+BCS方法计算了超重核的基态性质,讨论了结合能、α衰变、形变、壳结构和自发裂变等问题.计算得到的结合能较好地反映了实验测量值,α衰变能与实验值符合很好.发现基本上有两种类型的超重核形变:在270108核附近的β2≈0.2的长椭球形变和在298114核附近的近球形形变.单粒子能级分布计算表明:在质子Z=108和中子N=162存在变形壳,在质子Z=114和中子N=184存在球形壳.用得到的α衰变能和Viola Seaborg公式估算了α衰变半寿命,能合理地符合实验测量值.

超重核密度的计算

用Skyrme-Hartree-Fock模型计算了超重核的密度分布,并讨论了其形状和同位旋相关性。以292120核为例,计算表明形变对密度分布有相当大的影响。

Skyrme—Hartree—Fock Calculation on Exotic Light Nuclei

The ground state properties of ligtht nuclei are investigated by the Skyrme-Hartree-Fock approaclh with three sets ofnew force parameters SKI2,SKI3 and SKI4 [P.G.Reinhard and H.Flocard,Nucl.Phys.A584 (1995)467].Calculations show that the Skyrme-Hartree-Fock theory with above force parameters provides a good descriptionon the light isotopes except for some neutron-halo nuclei 11Li,14Be and 17B.Among the three sets of force parameters,SKI4,which has taken into consideration of the isospin dependence of the spin-orbit force,is the best one.Detailed comparison and analysis on the results are given.

Self-Consistent Calculation With Density-Dependent Pairing Forces for O Isotopes

The ground state properties of 0 isotopes are investigated by the Skyrme-Hartree-Fock(SHF)approach plus density-dependent pairing correlations.In comparison with the results of SHF calculationsusing the constant-gap approach,our calculations using the density-dependent pairing correlations providea good description of the O isotopes.Detailed comparison and analysis are given.

Ξ超子-核子有效相互作用Skyrme力参数的初步研究

在SkyrmeHartreeFock理论框架下,根据已有实验数据首次对ΞN有效相互作用进行了研究,初步确定了ΞN的Skyrme有效力参数,并由此计算了几种Ξ超核的势阱深度和相应的Ξ超子单粒子能级,以及Ξ超子在核中的均方根半径和相应超核的电荷分布半径,在较大的范围内得到了合理的结果.

丰中子核中的中子势能特性

利用Skyrme Hartree Fock势和Woods Saxon势 ,选取稳定核4 8Ca和丰中子核60 Ca ,对中子平均场势能进行了研究 ,并给出了其特性 .发现丰中子核60 Ca的SHF势与Woods Saxon势在核表面区域相当符合 ,但在核表面以外有相当大的差距 .SHF势在表面以外部分比表面区域呈现出更大的弥散度 ,而原有的Woods Saxon势不能描述这一特征 .为此 ,对Woods Saxon势形式进行了修正 ,经过验证 ,修正的Woods Saxon势能正确地描述丰中子核的中子晕特性 .

Tensor force effect on proton shell structure in neutron-rich Ca isotopes

In the framework of the Skyrme-Hartree-Fock approach with 36 sets of the TI J parameterizations,the tensor force effect on the evolution of the single-proton states in the calcium isotopes is systematically investigated.It is shown that the single-proton states with higher angular momenta are influenced significantly by the tensor force and the trend in the evolution of somesingle-particle energy differences with the mass number of the isotopes depends sensitively on a parameter βT associated with the intensity of the tensor force.To understand this phenomenon,we analyze the spin-orbit potentials and the radial wave functions of relevant single-proton orbits in detail.In addition,it is found that some TI J interactions could cause the 2s1/21d3/2 energy level inversion in 48Ca.

Expanding proton dripline by employing a number of muons

Through mean-field calculations,we demonstrate that,in a large Z nucleus binding multiple muons,these heavy leptons localize within a few dozen femtometers of the nucleus.The mutual Coulomb interactions between the muons and protons can lead to a substantial decrease in proton chemical potential,surpassing 1 MeV.These findings imply that,in principle,the proton-dripline can be expanded on the nuclear chart,suggesting the possible production of nuclei with Z around 120.

Properties of Zr hypernuclei in deformed Skyrme Hartree-Fock approach

Properties of the even-N Zr isotopes and their corresponding single-Λ and double-Λ hypernuclei are studied in the deformed Skyrme-Hartree-Fock approach. Binding energy, the two-neutron separation energies, radii are studied from beta-stable zone to the neutron drip line in this paper. The neutron drip line nuclei predicted with SLy4 and SkI4 interactions are 122Zr and 138Zr, respectively. The neutron drip line of single-Λ and double-Λ hypernuclei are Λ139Zr and 2Λ142 Zr with SkI4 interaction, respectively. The predicted hyperon drip line hypernuclei with 80Zr and 138Zr cores are 20Λ100Zr and 50Λ188Zr, respectively.

Impurity effects of theΛhyperon in the hypernuclear systems^(25)ΛMg and(29)ΛSi

Based on the beyond-mean-field Skyrme-Hartree-Fock model,impurity effects of theΛhyperon in the hypernuclear systems^(25)ΛMg and^(29)ΛSi are investigated,respectively.Four cases,in which theΛhyperon occupies the single-particle orbitals L[000]1+/2,L[110]1-/2,L[101]3-/2 and L[101]1-/2,are focused.In each case,the potential energy surface and the energy curves projected on certain angular momenta are employed to show the influence of theΛhyperon on the nuclear core.Beside the shrinkage effect that is induced by theΛhyperon occupying the sΛorbital,it is found that theΛhyperon on the pΛorbital,L[110]1-/2,drives the nuclear core toward a prolate shape,while the ones on the other two pΛorbitals,L[101]3-/2 and L[101]1-/2,drive the nuclear core toward an oblate shape.The energy spectra and the corresponding intra-band E2 transition rates for the rotational bands are given as a prediction for future experiments.

Investigation of the relationship between mirror proton radii and neutron-skin thickness

Through systematic investigations using the axially deformed solutions of the Skyrme-Hartree-Fock-Bogoliubov equations with 132 sets of Skyrme interaction parameters,it is confirmed that the neutron-skin thickness(Sn)of a neutron-rich nucleus is proportional to the difference between the proton radii of mirror nuclei(R_(p)^(mir)).This indicates that Sn may be deduced from R_(p)^(mir).Compared with the results of the Skyrme-Hartree-Fock model,pairing effects are found to enhance the correlation for most mirror pairs,whereas deformation effects may weaken the correlation.Furthermore,the correlation between Sn and R_(p)^(mir) is studied for isotones with N=20 and N=28,which reveals a stronger linear correlation with increasing|N−Z|.This result demonstrates that it is possible to extract the neutron-skin thickness of an unstable nucleus from the proton radii difference of the mirror nuclei of its isotones.

Efect of Tensor Force on the Halo Structure of ^(29)Ne and ^(31)Ne

The structure of Ne isotopes has been investigated by using deformed Skyrme-Hartree-Fock （SHF） method and BCS approximation. Especially the effect of tensor force on the halo structure of 29Ne and 31Ne is discussed. To this end, the tensor contributions are considered to the energy density function and the single particle potential in SHF theory. For comparison, four Skyrme interactions are used： SLy5 and SGII without tensor force, and SLy5＋T and SGII＋ T with tensor force. The results indicate that the inclusion of tensor force shows a more pronounced halo structure for 31Ne.

Effects of a kaonic meson on the ground-state properties of nuclei

The effects of an additional K-meson on the ground-state properties of nuclei are investigated within an axially-deformed Skyrme-Hartree-Fock approach combined with a Skyrme-type kaon-nucleon interaction.The K-meson increases the binding energies of all nuclei,whereas it affects deformations only for light nuclei without shell closure.The nucleon drip lines are modified due to the strongly attractive K-N interaction.This is attributed to the behavior of the highest-occupied nucleon single-particle levels near the drip lines,which is analyzed in detail.

Skyrme型NΛ相互作用下超越平均场模型的Λ超核研究

使用超越平均场Skyrme-Hartree-Fock(SHF)模型对_Λ~9Be,_(ΛΛ)^(10)Be,_Λ^(13)C和_Λ^(21)Ne进行计算,采用SLy4参数组的Skyrme力作为NN相互作用力,采用最近提出的SLL4参数组的Skyrme力作为NΛ相互作用。计算中包含了超子的自旋-轨道力以再现单粒子态的自旋-轨道能级分裂和不交叉效应,并采用BCS方法处理对力。讨论了不同组态超核的相关性质,包含^(12)C?Λ[000]1/2^+,^(12)C?Λ[110]1/2^-,^(12)C?Λ[101]3/2^-和^(12)C?Λ[101]1/2^-及~8Be?Λ[000]1/2^+,~8Be?Λ[110]1/2^-,~8Be?Λ[101]3/2^-和~8Be?Λ[101]1/2^-。计算了_Λ~9Be,_Λ^(13)C的低激发能谱并与实验值进行了比较。结果表明,采用的超越平均场SHF模型能很好地再现Λ超子占据sΛ轨道的正宇称能级。对8Be的计算结果表明该模型可以很好地再现8Be的集团结构,可以得出_Λ~9Be的真实超核态能级和9Be类似态。对_Λ~9Be及13ΛC的计算均再现了自旋双重态(3/2+,5/2+),但是得到的双重态能级差依然与实验值有出入。此外,对于上述超核体系均在Λ超子占据Λ[000]1/2^+轨道时产生了收缩效应。还对_Λ^(21)Ne进行了计算并和超越平均场RMF模型计算结果进行比较,发现两者计算结果虽有细节上的出入,但是结果基本一致。