原子核单粒子共振态的研究进展

共振是自然界普遍存在的有趣现象。在核物理领域,存在许多奇特现象,共振在其中扮演着重要角色。介绍了近期发展的RMF-CSM、RMF-CGF和RMF-CMR方法及其对原子核单粒子共振态的研究。给出了120Sn,31Ne等核的单粒子共振态的能量和宽度及其随质量数、形变的变化规律,分析了19C,31Ne和39Mg等核的晕形成的物理机制和在N=20附近能级反转的原因。特别是新发展的RMF-CMR方法,在描述稳定核和奇特核方面都取得了成功,支持Zr同位素存在巨晕的预言。Resonance is an interesting phenomenon in nature. In nuclear physics, resonance plays an important role in the formation of many exotic phenomena. This paper introduces the recently developed RMF-CSM, RMFCGF, and RMF-CMR methods and their researches on nuclear single-particle resonances. The energies and widths of the single-particle resonant states in 120Sn and 31Ne and their evolution to mass number and deformation are given. In addition, the physical mechanism of the halo formation in 19C, 31Ne and 39Mg and the cause of energy level inversion near N=20 are analyzed. In particular, the newly developed RMF-CMR approach has been successful in describing stable and exotic nuclei and supports the prediction that Zr isotopes exist in a giant halo.     

复动量表象方法对丰中子Cr同位素奇特结构的研究

奇特核的研究是核物理中最有趣的前沿课题之一。中等质量核中是否存在晕现象,目前的研究相对较少。复动量表象(CMR)方法可以用来探索原子核中的奇特结构。连续谱阈值附近的共振态在奇特现象的形成中起着重要的作用。利用相对论点耦合框架下的复动量表象(RMFPC-CMR)方法研究了丰中子Cr同位素中的奇特结构,得到的非常接近于零的双中子分离能和迅速增大的中子均方根半径表明在靠近中子滴线的Cr同位素中存在晕结构。从获得的单粒子能级、费米面附近价核子占据几率、中子和质子密度分布以及各能级对原子核密度的贡献可以发现3s_1/2和2d_3/2能级的占据有利于中子晕的形成。研究发现,低角动量弱束缚能级对异常增大的半径和弥散密度分布有显著的贡献,这导致靠近中子滴线的^76-82Cr是中子晕核。这一预测结果对在实验中探索中等质量区的晕核具有一定的参考价值。     

А∧Ca和А∧∧Ca超核中的巨中子晕现象

利用密度相关零程对力的相对论连续谱Hartree—Bogolubov方法，对偶中子数的Ca同位素从质子滴线到中子滴线范围内的单∧超核和双∧超核基态性质进行了系统研究。与通常的原子核相比，单∧超核和双∧超核中起子提供的吸引力会相应地降低中子费米面。所预言的中子滴线超核分别为А∧Ca和А∧∧Ca，比原来预测的通常滴线核^74Ca多两个中子。基于对双中子分离能、中子密度分布、半径、单粒子能谱、轨道占据数和连续谱贡献的分析，预言了超核中的巨中子晕现象。     

奇特核和超核中的晕现象

讨论奇特核和超核中的各种晕现象. 根据密度相关零程对力的相对论连续谱Hartree Bogoliubov理论给出的计算结果， 预言了中子滴线附近的Ca原子核中可能存在着巨晕， 并简要介绍了O， Ni， Zr， Sn和Pb等一些质子幻数核从质子滴线到中子滴线之间的原子核基态性质. 随后给出超核内的晕现象研究， 如Ca超核内的中子晕和153ΛC内的单Λ超子晕. Halos in the relativistic continuum Hartree Bogoliubov (RCHB) theory are investigated，including giant halo in the even N Ca isotope near neutron drip line，halos in hypernuclei and the hyperon halos in 153ΛC.     

AΛCa和 AΛΛCa超核中的巨中子晕现象

利用密度相关零程对力的相对论连续谱Hartree-Bogoliubov方法,对偶中子数的Ca同位素从质子滴线到中子滴线范围内的单Λ超核和双Λ超核基态性质进行了系统研究. 与通常的原子核相比,单Λ超核和双Λ超核中超子提供的吸引力会相应地降低中子费米面. 所预言的中子滴线超核分别为77ΛCa和78ΛΛCa,比原来预测的通常滴线核74Ca多两个中子. 基于对双中子分离能、中子密度分布、半径、单粒子能谱、轨道占据数和连续谱贡献的分析,预言了超核中的巨中子晕现象.     

Λ ACa和ΛΛ ACa超核中的巨中子晕现象

利用密度相关零程对力的相对论连续谱Hartree-Bogoliubov方法,对偶中子数的Ca同位素从质子滴线到中子滴线范围内的单Λ超核和双Λ超核基态性质进行了系统研究.与通常的原子核相比,单Λ超核和双Λ超核中超子提供的吸引力会相应地降低中子费米面.所预言的中子滴线超核分别为77ΛCa和78ΛΛCa,比原来预测的通常滴线核⁷⁴Ca多两个中子.基于对双中子分离能、中子密度分布、半径、单粒子能谱、轨道占据数和连续谱贡献的分析,预言了超核中的巨中子晕现象.     

复动量格林函数方法对n-α散射研究

在复动量表象下引入格林函数,建立了复动量格林函数方法.把这种方法应用于n-α散射系统,计算其散射相移.提取n-α系统的共振态并研究共振态对能级密度、相移和散射截面的贡献.在不引入任何非物理参数的前提下,离散化薛定谔积分方程得到束缚态、共振态和连续谱.通过分析散射态物理量可以更好地理解共振态以及非共振连续谱态.在n-α系统中的成功应用,证明了该方法的正确性.     

实验粒子方法应用于核11Li四级软巨共振态的研究

由试验粒子方法求解相空间Vlasov方程,得到核单粒子几率密度分布函数f(r,p,t).基于此研究了核¹¹Li的四极巨共振激发.结果表明,在低激发能区2MeV左右核¹¹Li存在四极软巨共振态,它的强度占E2跃迁能量权重求和(EWSR)的百分比敏感地依赖于¹¹Li核的中子晕分布,而能量中心位于29MeV左右的正常四极巨共振,则与中子晕分布无关.最后对结果作了简要的讨论.     

自相似结构壳模型

为了扩展以简谐振子为基矢的常规壳模型（ＳＭ）计算到晕核，提出了自相似结构壳模型（ＳＳＭ）．通过对简谐振子动能项和势能项的重度规以及单粒子平均场模拟，可以得到ＳＳＭ中的单粒子轨道有态相关的圆频率，在ＳＳＭ中，晕核大的均方根半径、厚的中子皮以及Ｂｏｒｒｏｍｅａｎ晕核和的束缚态性质能够再现出来。     

相对论连续谱Hartree-Bogoliubov理论对滴线原子核结构的研究

回顾了相对论连续谱Hartree-Bogoliubov理论对奇特核结构的描述.包括对¹¹Li晕核的微观描述,并发现了其形成机制是由于Cooper对从1p_1/2轨道被散射到2s_1/2轨道;预言了滴线核的新现象——由6个中子组成的巨晕,给出了形成晕现象的条件为弱束缚与低离心位垒;解释了实际核中的赝自旋对称性;自旋轨道分裂与势能位垒弥散的关系;经典禁区内粒子对晕的影响;超重元素的结构研究等.     

β delayed emission of a proton by a one-neutron halo nucleus

Some one-neutron halo nuclei can emit a proton in a β decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core + neutron bound state and final core + proton scattering states. The decay probability per second is evaluated for the ¹¹Be, ¹⁹C and ³¹Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.     

球形Dirac方程的空间格点求解及假态问题

本文在空间格点上利用虚时间步长方法求解了球形Dirac方程, 着重研究了出现的假态问题. 利用三点数值导数公式离散方程中一阶导数项, 可以证明对于量子数为 κ 和 -κ的单粒子能级能量是完全相同的, 其中一个为物理解, 另一个为假态. 通过在径向Dirac方程中引入Wilson 项, 可以解决假态问题, 得到全部物理解. 文章以 Woods-Saxon 势为例, 考虑 Wilson 项后, 得到与打靶法一致的结果.     

Momentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei

Recently the research on the halo structure of drip-line nuclei has shown some interesting properties of the existence of one or more halo nucleons. In the framework of few-body Glauber model, the momentum distribution of a fragment and nucleon removal cross section in the reaction of halo nuclei is presented and extended to nuclei having more than one halo nucleons. The reaction mechanism is treated with and without taking account of the final-state interaction. The wave function of removal halo nucleons in the continuum state is modified by imposing an orthogonal condition to the bound state. An analytical expression of the longitudinal momentum distribution of the fragment is derived when the bound state wave function of halo nucleons is taken as a Gaussian-type function. This is useful in the further investigation on the structure of halo nuclei.     

Momentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei

Recently the research on the halo structure of drip-line nuclei has shown some interesting properties of the existence of one or more halo nucleons. In the framework of few-body Glauber model, the momentum distribution of a fragment and nucleon removal cross section in the reaction of halo nuclei is presented and extended to nuclei having more than one halo nucleons. The reaction mechanism is treated with and without taking account of the final-state interaction. The wave function of removal halo nucleons in the continuum state is modified by imposing an orthogonal condition to the bound state. An analytical expression of the longitudinal momentum distribution of the fragment is derived when the bound state wave function of halo nucleons is taken as a Gaussian-type function. This is useful in the further investigation on the structure of halo nuclei.     

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.     

Breakup reactions of two-neutron halo nuclei

Investigation of reactions initiated in collisions of beams of unstable nuclei with nuclear targets has resulted in the discovery of a new type of nuclear structure, the halo, in some light nuclei at the boundary of nucleon stability. A survey of different reactions with two-neutron halo nuclei and their use for gaining information on the structure of exotic nuclei is presented. Kinematically complete breakup reactions, which provide the possibility of obtaining quite reliable information on the structure of the ground state and the continuum of nuclei, are considered in detail. The microscopic four-body model of breakup reactions for two-neutron halo nuclei with account of characteristic specific features of their structure is formulated. The model is based on the distorted wave approximation and is applicable for analysis of low excitations of the continuum near the breakup threshold, the region most sensitive to manifestation of specific features of the halo structure. The described approach enables the calculation of all observables of kinematically complete experiments in nucleus-nucleus collisions at intermediate energies for which one-step processes dominate, and creates the basis for the spectroscopy of continua via successive analysis of various correlation cross sections available in kinematically complete experiments.     

Constraints on two-neutron separation energy in the Borromean C nucleus

The recently extracted matter radius of carbon isotope ²²C allows us to estimate the mean-square distance of a halo neutron with respect to the center-of-mass of this nucleus. By considering this information, we suggest an energy region for an experimental investigation of the unbound ²¹C virtual state. Our analysis, in a renormalized zero-ranged three-body model, also indicates that the two-neutron separation energy in ²²C is expected to be found below ∼0.4 MeV$\sim 0.4\text{MeV}$, where the ²²C is approximated by a Borromean configuration with a pointlike ²⁰C and two s-wave halo neutrons. A virtual-state energy of ²¹C close to zero, would make the ²²C, within Borromean nuclei configurations, the most promising candidate to present an excited bound Efimov state or a continuum three-body resonance.     

双中子集团结构研究进展

回顾了晕核发现以来双中子集团结构的研究进展,分析了可能的发展方向。系统的理论研究表明, 在原子核的表面和低密度核物质中, 空间紧密关联的2n集团的出现是一个普遍的现象。 但在较重原子核表面出现2n集团的机制与核物质或轻晕核中的机制很不一样, 前者是由有限核的平均场造成的尺度效应（size effect）,而后者主要是由低密度下对相互作用（或对能隙）的增强造成的。另外,在轻晕核或有限核表面,2n集团的均方根半径与它们到核芯的距离（或背景密度）有关,最小值普遍可以达到2～3 fm,然而在核物质中2n集团最小只能到～5 fm。 实验方面,在重靶上的库仑激发强度, 能够比较准确地给出2n系统到核芯的平均距离。 但到目前为止尚没有有效的实验方法给出基态中两个中子之间的间距, 主要原因是中子发射过程中末态相互作用（共振态或虚粒子态）造成的两步过程的干扰, 这个问题在库仑激发破碎（重靶）或核作用破碎（轻靶）中都出现。“拖出”反应和敲出核芯反应是下一步可以考虑的路径。 双中子的关联测量通常效率比较低,尤其是需要有效排除中子串扰(CT)事件。为此, 需要发展特殊设计的中子关联测量装置, 在提高探测效率的同时,能够通过运动学关系以及其他方法有效排除中子CT信号。 在数据处理阶段,通过反复迭代给出的双中子关联函数, 经验证明是比较有效的关联状态表达方式, 从中可以直接提取出双中子分布均方根半径。 This article outlines the progress in the study of the di neutron structure in various systems. Systematic theoretical investigations reveal that di neutron structure is a general phenomenon appeared at nucleus surface and in low density nuclear matter. But the underline mechanism of forming di neutron clusters at the surface of heavier nuclei is quite different to that for light halo nuclei or at the low density nuclear matter, with the former being basically due to the so called “size effect” and the latter due to the enhanced pairing interaction. It is also realized that the RMS radii of the di neutron cluster at the surface of light halo nuclei or heavier finite nuclei varies with the distance from the center of nuclei (or background density) and may attain a minimum of about 2～3 fm, whereas that in the low density nuclear matter may only attain about 5 fm. From experimental side, Coulomb excitation caused by heavy targets provides a good way to extract the mean distance from the center of the neutron pair to the center of nucleus. But up to now it is still difficult to experimentally determine the distance between the two valence neutrons, due primarily to the final state interactions which lead to two step emission of neutrons via resonances or virtual intermediate states. This problem happens in both Coulomb and nuclear breakup processes. Possible ways to avoid this problem might come from experiments based on “towing mode” or core knockout reactions. Detection of two neutrons in coincidence often suffers from low efficiencies and the need to reject the cross talk events. Therefore it is important to develop specially designed multi neutron detection array to achieve high efficiency as well as good cross talk rejection performance using kinematics conditions. For data analysis, it was found that two neutron correlation function generated by iteration method is a good expression of the correlation situation, from which the RMS radii of the two neutron distribution may be deduced.