晕核散射Glauber理论研究

【作者】 赵耀林；

【导师】 马中玉；

【作者基本信息】 中国原子能科学研究院 ， 粒子物理与原子核物理， 2003， 博士

【摘要】 晕核是弱束缚系统，具有非常特殊的性质，最外层的价核子具有非常弥散的空间分布，通常采用核芯加晕核子的少体结构近似。Glauber理论是当前分析晕核反应得到晕核结构和密度分布信息的主要理论工具之一，并且广为使用。其中光学极限近似的Glauber模型能很好地描述高能小角度的稳定核散射，进一步推广应用于研究中低能稳定核散射时，需要考虑库仑相互作用对有效碰撞参数的修正和核子—核子两体散射在朝前方向的弥散。通过稳定核，从轻核到重核中低能散射反应截面和弹性角分布的系统计算，分析显示在Glauber理论计算中库仑场和核子—核子两体相互作用有限力程修正对于正确描述中低能稳定核散射有着重要作用。库仑场的排斥效应使得核—核反应有效的碰撞参数增大，使计算的反应截面减小，同时这种修正的效应随能量增大而减小。考虑了低动量转移的核子—核子两体散射在朝前方向上的弥散，使计算得到的反应截面增大，而且我们从弹性角分布的分析中得到考虑了有限力程修正的效应无论是在峰的位置还是角分布的绝对值都能更好地符合实验。 研究晕核反应时需要考虑晕核各个组成部分之间的空间关联，对此我们应用将晕核核芯和晕核子分开处理的少体近似Glauber模型，并且将其推广到了含有多个晕核子的晕核散射。讨论了有和无介子产生两种情况下的晕核散射反应截面和核子逃逸截面，给出了相应的计算公式。进一步还详细推导了晕核散射的碎片动量分布(包括纵向、横向动量分布)，得到了考虑末态相互作用的弹性分离过程和不考虑末态相互作用非弹性分离过程的晕核散射碎片动量分布。特别是在晕核子的纵向和横向密度分布可分离的情况下，如高斯密度分布，进一步求解了纵向动量分布宽度的解析形式，建立了分布宽度与晕核子束缚态波函数之间的直接联系。 由于在少体近似Glauber模型中晕核被分成核芯和晕核子来处理，所以得到的晕 中国原子能科学研究院博士学位论文核散射反应截面、核子逃逸截面以及动量分布的计算公式均包含高重积分。为使理论计算变得可行，我们在核芯和靶核密度采用多个高斯分布拟合的情况下，解析求解了各个散射矩阵元中的光学相移函数及交叉项含有的与晕核核芯、靶核密度分布有关的积分;同时对与碰撞参数和晕核子坐标有关的积分(八重以上，并且积分维数随晕核子数很快增加)采用蒙特卡洛方法计算。通过上述方法我们可以对具有任意形式密度分布的晕核散射反应截面、核子逃逸截面以及动量分布等进行计算。 论文中对光学极限近似Glauber模型和少体近似Glauber理论计算的反应截面进行了比较，得到对密度分布比较紧密的核散射用两种方法计算的结果基本相同，而对具有很大空间弥散分布的晕核散射两种模型计算的结果差别较大，并且晕核子的空间分布越弥散，空间关联效应越显著，这种差别也就越大。因此在讨论晕核散射时需要考虑晕核子、核芯和靶核之间的空间关联，采用少体近似Glauber模型。 利用考虑空间关联的少体近似Glauber理论我们采用多种形式的密度分布(分别由谐振子势、Wbods一Saxon势或相对论平均场理论给出)对最新实验测量的丰中子核，4Be、’”e和丰质子核23AI、27P、28P的反应截面进行了分析。对于’4Be+’Ze反应，当’4Be采用具有两个处于251/2态晕中子结构的弥散密度分布时，理论计算能够很好地描述实验。对于’”c分析了其基态四种可能组态及各种组态混合对于反应截面的贡献，分析表明要同时解释’”C的反应截面和碎片动量分布，需要考虑核芯‘”c的增大和组态混合。采用相同的方法对于23AI反应截面的研究显示，由于coulomb位垒的阻碍作用，其处于251/2或ld5/2态质子的均方根半径都比较小，同时考虑核芯“ZMg增大和251/;态质子的空间弥散分布才能解释其截面的异常增大。进一步对27P、28P反应截面的研究分析表明，考虑核芯2751的增大可以很好解释实验测量得到28P反应截面的增大，而要解释27P反应截面的异常增大，需要同时考虑核芯2“Si增大和具有非常弥散空间分布的2s，，:态晕核子。更多还原

【Abstract】 The investigation on the halo structure of drip-line nuclei is one of the most important subjects and has attracted much attention both experimentally and theoretically. The halo nucleus is a weakly bound system, which has very peculiar properties. Usually it is considered to have a few-body structure, which is composed of a core and valence nucleons with a large diffused density distribution. It is well know that the Glauber theory is one of the most popular approaches for analyzing the experimental data of halo nucleus scatterings, which directly connects the matter radius and density distribution of the halo nucleus to the reaction cross section. The optical-limit Glauber theory has been of great success in describing the stable nucleus scattering at high energies. As it is extended to the nucleus scattering at low and intermediate energies, the modification of the Coulomb field to the effective impact parameter and the diffuseness of the nucleon-nucleon (N-N) scattering in the forward direction has to be taken into account. Through a systematic study on reaction cross sections and the angular distribution of the stable nucleus scatterings, we find that the inclusion of the N-N finite range interaction and Coulomb modification in the Glauber theory plays very important role in reproducing the experiment data at these energy regions. Due to the repulsive Coulomb field, the effective impact parameter increases, and therefore the calculated reaction cross section decreases. Considering the diffuseness of the N-N scattering in the forward direction results in an increased reaction cross section. And also the angular distributions calculated in the Glauber theory including these two corrections are in good agreement with the experiment data.In the investigation of the halo nucleus reaction with a loosely bound structure, one has to consider the strong spatial correlations among its constituents. Recently a few-body Glauber theory has been proposed, where the core and halo nucleons are treated separately. We apply the few-body Glauber theory to halo nucleus reactions and extend it to the halo nucleus with more than one or two halo nucleons. Both the reaction and nucleon removal cross section are derived with or without considering the meson production, and the relevant expressions are given. We further formulate the momentum distribution of a fragment in the halo nucleus scattering. Itsdetailed expressions in the elastic dissociation process with considering the final-state interaction and the inelastic dissociation process without considering the final-state interaction are obtained, respectively. Particularly an analytical expression for the longitudinal momentum distribution is derived if the density distribution of halo nucleons is assumed as a Gaussian type function. A direct connection of the width of the momentum distribution to the bound state wave function of halo nucleons is established.Since in the few-body Glauber theory the core and valence nucleons of a halo nucleus are treated separately, the obtained expressions of the reaction cross section, the nucleon removal cross section and the momentum distribution are all involved in multidimensional integrations. In order to make the theoretical calculation feasible, we first obtain an analytical formalism of partial integrals with respect to the coordinates of the core and target in the phase-shift functions and their cross terms of scattering matrix elements, if the density distributions of the core and target are fitted to a few Gaussian forms. Then the rest multidimensional integrals with respect to the impact parameter and coordinates of halo nucleons are performed by a Monte Carlo method. Therefore we could carry out numerical calculations and obtain the reaction cross section, the nucleon removal cross section and the momentum distribution in the scattering of a halo nucleus with any types of density distributions.We compare the reaction cross sections calculated in the few-body Glauber theory and the optical-limit Glauber theory更多还原