Isotopic dependence of the yield ratios of light fragments from different projectiles and their unified neutron skin thicknesses

The yield ratios of neutron-proton(R(n/p))and^(3)H-^(3)He(R(^(3)H∕^(3)He))with reduced rapidity from 0 to 0.5 were simulated at 50 MeV/u even-even ^(36−56)Ca+^(40)Ca,even-even ^(48−78)Ni+^(58)Ni,and ^(100−139)Sn(every third isotopes)+112 Sn for full reduced impact parameters using the isospin-dependent quantum molecular dynamics(IQMD)model.The neutron and proton density distributions and root-mean-square radii of the reaction systems were obtained using the Skyrme-Hartree-Fock model,which was used for the phase space initialization of the projectile and target in IQMD.We defined the unified neutron skin thickness asΔRnp=<r^(2)>^(1∕2) n−<r^(2)>^(1∕2)p,which was negative for neutron-deficient nuclei.The unifiedΔRnp values for nuclei with the same relative neutron excess from different isotopic chains were nearly equal,except for extreme neutron-rich isotopes,which is a type of scaling behavior.The yield ratios of the three isotopic chain-induced reactions,which depended on the reduced impact parameter and unified neutron skin thickness,were studied.The results showed that both R(n/p)and R(^(3)H∕^(3)He)decreased with a reduced impact parameter for extreme neutron-deficient isotopes;however,they increased with reduced impact parameters for extreme neutron-rich isotopes,and increased with theΔRnp of the projectiles for all reduced impact parameters.In addition,a scaling phenomenon was observed betweenΔR np and the yield ratios in peripheral colli-sions from different isotopic chain projectiles(except for extreme neutron-rich isotopes).Thus,R(n/p)and R(^(3)H∕^(3)He)from peripheral collisions were suggested as experimental probes for extracting the neutron or proton skin thicknesses of non-extreme neutron-rich nuclei from different isotopic chains.

Configurational information entropy analysis of fragment mass cross distributions to determine the neutron skin thickness of projectile nuclei

Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.The BNN+FRACS machine learning model was adopted to predict the fragment mass cross-sections(σ_(A))of the projectile fragmentation reactions induced by calcium isotopes from ^(36)Ca to ^(56)Ca on a ^(9)Be target at 140MeV/u.The fast Fourier transform was adopted to decompose the possible information compositions inσA distributions and determine the quantity of CIE(S_(A)[f]).It was found that the range of fragments significantly influences the quantity of S_(A)[f],which results in different trends of S_(A)[f]~δnp correlation.The linear S_(A)[f]~δnp correlation in a previous study[Nucl.Sci.Tech.33,6(2022)]could be reproduced using fragments with relatively large mass fragments,which verifies that S_(A)[f]determined from fragmentσAis sensitive to the neutron skin thickness of neutron-rich isotopes.

A possible experimental observable for the determination of neutron skin thickness

The dependence between neutron skin thickness and neutron abrasion cross section （σnabr） for neutron-rich nuclei is investigated within the framework of the statistical abrasion ablation model. Assuming that the density distributions for proton and neutron are of Fermi-type, and adjusting the diffuseness parameter of neutron density distribution in the droplet model, we find out the good linear correlation between the neutron skin thickness and the abrasion cross section σnabr for neutron-rich nuclei. The uncertainty of neutron skin thickness determined from σnabr is very small. It is suggested that σnabr can be used as a new experimental observable to extract the neutron skin thickness for neutronrich nucleus. The scaling behaviours between neutron skin thickness and σnabr, separately, for isotopes of ^26-35Na, ^44-56Ar, ^48-60Ca, ^67-78Ni are also investigated.

The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin

The equation of state for nuclear matter is presented within the Brueckner Hartree-Fock （BHF） scheme, by using the realistic Argonne VI8 or Bonn B two-nucleon potentials plus their corresponding microscopic three-nucleon forces. It is then applied to calculate the properties of finite nuclei within a simple liquid-drop model, and we compare the calculated volume, surface, and Coulomb parameters with the empirical ones from the liquid drop model. Nuclear density distributions and charge radii in good agreement with the experimental data are obtained~ and we predict the neutron skin thickness of various nuclei.

Impact parameter dependence of the yield ratios of light particles as a probe of neutron skin

The yield ratios of neutron/proton(R(n/p)) and ~3H=~3He(R(t/~3He)) with reduced rapidity from 0 to 0.5 are investigated for 50 MeV/u ^(42;44;46;48;50;52;54;56)Ca+^(40)Ca.This was conducted at whole reduced impact parameters using the isospin-dependent quantum-molecular-dynamics model in which the initial neutron and proton densities are sampled within the Skyrme–Hartree–Fock model, using which the neutron skin thickness(△R_(np)) is determined for different neutron-rich Ca isotopes. The results show that both R(n/p) and R(t/~3He) have strong linear correlations with △R_(np) of different Ca isotopic projectiles from five different centralities. It is suggested that R(n/p) and R(t/~3He), from the same centrality, could be treated as possible experimental observables to extract the neutron skin or halo thickness for neutron-rich isotopic nuclei,including the nuclei near the neutron drip line.

Exploring the sensitivity of α-decay half-life to neutron skin thickness for nuclei around ^(208)Pb

Based on the newest experimentally extracted nuclear density distributions for double-magic nucleus208Pb(Tarbert et al. in Phys Rev Lett 112:242502, 2014),the sensitivity of α-decay half-life to nuclear skin thickness is explored in the vicinity of the shell closure region around208 Pb, i.e., isotopes of Z ? 82 and isotones of N ? 126.With the two-parameter Fermi(2PF) density distributions and an analytically derived formula, the α-decay half-life is found to be closely related to the magnitude of nuclear skin thickness. For a decays to the Z ? 82 isotopes, the α-decay half-life is found to decrease with the increasing neutron skin thickness, while the opposite behavior is found for a decays to the N ? 126 isotones. Therefore, it could be a possible way to extract the nuclear skin thickness from measured α-decay half-lives.

Determination of the neutron skin thickness from interaction cross section and charge-changing cross section for B,C,N,O,F isotopes

The effective neutron and proton root-meansquare radius of stable and unstable nuclei(^(12-15,17)B,^(12-20)C,^(14-21)N,^(16-24)O and ^(18-21,23-26)F) were deduced from the charge-changing cross section,σ_(cc),and the interaction cross sections,σ_I,by using a statistical abrasion-ablation model calculation.The extracted proton radii are in good agreement with the data from the Atomic Data and Nuclear Data Tables within the errors.Furthermore,we can observe that the neutron skin thickness increases monotonously with the increasing neutron number in these isotopes,which is consistent with the systematical trend of theoretical calculations.

Neutron skin thickness of ^(90)Zr and symmetry energy constrained by charge exchange spin-dipole excitations

The charge exchange spin-dipole(SD) excitations of ^(90)Zr are studied using the Skyrme Hartee-Fock plus proton-neutron random phase approximation with SAMi-J interactions.The experimental value of the model-independent sum rule obtained from the SD strength distributions of ^(90)Zr(p,n) ^(90)Nb and ^(90)Zr(n,p) ^(90)Y is used to deduce the neutron skin thickness.The neutron skin thickness Δr_(np) of ^(90)Zr is extracted as 0.083±0.032 fm,which is similar to the results of other studies.Based on the correlation analysis of the neutron skin thickness Δr_(np) and the nuclear symmetry energy J as well as its slope parameter L,a constraint from the extracted Δr_(np) leads to the limitation of J to 29.2±2.6 MeV and L to 53.3±28.2 MeV.

Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei

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.

A revisit to the neutron skin thickness of neutron-rich nuclei in the statistical abrasion ablation model

The cross sections of the fragments produced in the projectile fragmentation reactions of the even calcium isotopes from A=36 to A=52 are calculated using the statistical abrasion ablation model.The neutron skin thickness are studied by investigating the fragments isotopic cross section distributions.The neutron-skin thicknesses of the calcium isotopes have a good linear correlation to the peak positions of their fragment isotopic cross section distributions.The correlation between the neutron skin thickness and the neutron density distributions of 48 Ca is investigated by introducing a parameter to adjust the diffuseness parameter in the fermi-type density distribution.

A new probe of neutron skin thickness

The correlation between neutron-to-proton yield ratio （Rnp） and neutron skin thickness （δnp） in neutron-rich projectile induced reactions is investigated within the framework of the Isospin-Dependent Quantum Molecular Dynamics （IQMD） model. The density distribution of the Droplet model is embedded in the initialization of the neutron and proton densities in the present IQMD model. By adjusting the diffuseness parameter of neutron density in the Droplet model for the projectile, the relationship between the neutron skin thickness and the corresponding Rnp is obtained. The results show strong linear correlation between Rnp and δnp for neutron-rich Ca and Ni isotopes. It is suggested that Rnp may be used as an experimental observable to extract δnp for neutron-rich nuclei, which is very interesting in the study of the nuclear structure of exotic nuclei, the equation of state （EOS） of asymmetric nuclear matter and neutron-rich matter in astrophysics, etc.

Symmetry energy at subsaturation densities and the neutron skin thickness of ^(208)Pb

The mass-dependent symmetry energy coefficients asym(A) has been extracted by analysing the heavy nuclear mass differences reducing the uncertainties as far as possible in our previous work.Taking advantage of the obtained symmetry energy coefficient asym(A) and the density profiles obtained by switching off the Coulomb interaction in208 Pb,we calculated the slope parameter L0.11 of the symmetry energy at the density of 0.11 fm-3.The calculated L0.11 ranges from 40.5 Me V to 60.3 Me V.The slope parameter L0.11 of the symmetry energy at the density of 0.11 fm-3is also calculated directly with Skyrme interactions for nuclear matter and is found to have a fine linear relation with the neutron skin thickness of208 Pb,which is the difference of the neutron and proton rms radii of the nucleus.With the linear relation the neutron skin thickness Rn pof208 Pb is predicted to be 0.15–0.21 fm.

中子皮厚度与中子星半径

在相对论平均场理论框架下在拉氏量密度中引入同位旋相关的高阶修正项, 研究了中子皮厚度和中子星半径的关系. 利用有效相互作用PK1得到208Pb的中子皮厚度最小可达 0. 17fm, 这与近期Skyrme HF模型得到的结果一致. 随着同位旋相关的高阶修正项系数的变化, 208Pb的中子皮厚度和中子星半径的变化趋势相同.

原子核的中子皮厚度与非对称核物质态方程

挑选47组常用的Skyrme参数，采用Skyrme能量密度泛函结合拓展的Thomas-Fermi展开，用约束的密度变分法，我们计算了208^Pb、112-124^Sn、48^Ca、96^Zr、18^O等丰中子核的中子皮厚度并与实验数据分析抽取的中子皮厚度比较，研究了中子皮厚度与非对称核物质态方程中同位旋相关的对称能项之间的关系．我们发现中子皮厚度随对称能系数α,以及对称能在饱和密度附近的斜率L、曲率Ksym的增大呈现近似的线性增大的趋势，对称能越硬的核势确定的中子皮越厚．以反质子湮灭法拟合的参考实验值作为标准，我们给出对称能系数，对称能在饱和密度附近的斜率和曲率的参考范围分别为：αs=30～35MeV，L=20-100MeV，Ksym=256-70MeV。满足这个条件的Skyrme参数有：SLy0-SLy10、SkM^＊、SkP、SLy230a、SkMP、SKT1—3、Ski3、MSk1-2、SⅡ．

放射性核引起的反应

评述了放射性核自身的特征和它引起的反应机制研究．论述了晕核、中子皮核、电磁断裂和软偶极共振以及放射性核所引起的弹性散射。

零温度和有限温度下原子核的中子皮厚度

中子皮厚度是研究原子核内质子和中子性质差异，尤其是分布差异的重要物理量，一直受到人们的重视，在零温度情况下(原子校为“冷核”)，实验上通过分析质子弹性散射和α散射数据。来确定中子皮厚度，但中子分布是很难精确测定的。由此得到的中子皮厚度的差别很大，在有限温度情况下(原子校为“热核”)，由于热核的亚稳定性，在实验上很难通过分析实验数据来确定中子皮厚度，因此。迫切需要从理论上来预言零温度和有限温度下原子核的中子皮厚度。

核物质的对称能与中子皮厚度(英文)

在现有的平均场模型中引入同位旋相关的高阶修正项, 研究了核物质对称能的密度依赖性和208Pb的中子皮厚度。采用新提出的PK1相互作用以及NL3, S271和Z271相互作用, 得到核物质饱和点对称能的范围为 29—38MeV以及相应的208Pb中子皮厚度为 0. 17— 0. 28fm. 在所有相互作用中, 核物质饱和点的对称能与208Pb的中子皮厚度近似呈线性关系.

在相对论平均场框架下研究同位旋依赖的高阶核子-ω-ρ介子耦合(英文)

在相对论平均场的框架下,对208Pb中子皮对新的同位旋依赖的高阶核子-ω-ρ介子耦合项的敏感性进行了研究。计算表明,高阶同位旋依赖的核子-ω-ρ介子耦合能够进一步软化对称能,因而能够在不影响其它基态可观测量的情况下,进一步减小208Pb的中子半径。

热核中子皮厚度的微观研究

本文从扩展Skyrme相互作用出发,利用有限温度自洽半经典(FTSCSC)方法,确定热核核子密度ρ_q.(q=n、p),微观地研究了热核^(40)Ca、^(90)Zr、^(120)Sn在不同温度下的中子皮厚度.

原子核集体激发性质约束对称能的密度依赖性

通过实验测得^(90)Zr、^(144)Sm和^(208)Pb的同位旋矢量巨偶极共振能量,^(68)Ni、^(132)Sn的矮共振强度以及其占能量权重求和规则的百分比,^(208)Pb的anti-analog巨偶极共振及同质异位相似态的能量;基于相对论和非相对论平均场理论,采用不同的有效相互作用计算了原子核的集体激发性质,并通过理论结果和实验数据的对比约束对称能的密度依赖性.