Microscopic Nuclear Structure Theory

从自由核子-核子相互作用出发，在微观上计算原子核的性质，近十年来取得了巨大的进展。在这方面，最成功的理论方法之一是无核壳模型（NCSM）。我们不采用标准的壳模型假设，即大多数核子都占据一个惰性核，而是把所有A核子都看作是活跃的。通过这种方式，人们能够制定一个系统的程序，从现实的微观相互作用出发，得出有效的相互作用。这一过程利用了在所有原子核中，二体和三体团簇所具有的相似结构。结果表明，这些有效相互作用极大地加快了收敛速度，使收敛解成为可能，现在已经很明显，现有的理论技术能够精确地计算轻核的性质，使用NN相互作用作为输入。因为结果显示了相当大的欠结合，很明显，一些额外的成分是必要的，如三核子相互作用。因此，NCSM将被扩展到包括三体集团（ore.ective相互作用），不仅基于两体微观力，而且基于现实的三核子（3 N）裸相互作用。这样做很重要，因为，例如，轻核的光谱预计对3 N相互作用的自旋结构敏感。有了这些高体相互作用，人们也将能够在更小的基空间中对更重的核子进行NCSM计算，并获得更好的收敛性，从而得到更精确的结果。这种三体团簇方法的发展是一个重大的进步，因为它将使人们能够研究目前的3 N相互作用模型和基于手征微扰理论的模型对光谱的影响。因此，它将成为探测这些相互作用的重要工具。通过发展一种精确计算三体团簇的技术，人们还可以研究它的结构，这取决于所研究的核素中核子的数量和模型空间的大小。所有核结构计算的目标之一是基于微观计算的集体结构的理解。12 C的结构是一个有趣的例子。第一激发态0+被认为具有3a结构。这个问题的融合解决方案是一个挑战，但在NCSM计算范围内。一旦得到它们，人们就可以详细地研究基态和激发态结构之间的差别.当前研究的另一个重要方面是将NCSM方法推广到任意算符. NCSM是建立在集团哈密顿量的么正变换的基础上的，当人们能够将这种变换推广到跃迁算符或电流算符时，就有可能从NCSM波函数中提取有意义的物理观测值，预测轻核的电弱性质将是这一新技术的一个重要应用。

Tremendous progress has been made in the last ten years in calculating the properties of atomicnuclei microscopically starting with the free nucleon-nucleon (NN) interaction. One of the mostsuccessful theoretical approaches in this regard is the No Core Shell Model(NCSM). Insteadof invoking the standard shell-model assumption, that most of the nucleons occupy an inertcore, one treats all A nucleons as being active. In this way one is able to formulate a systematicprocedure to derive e.ective interactions starting from realistic microscopic ones. This proceduremakes use of the similar structures that two- and three-body clusters are expected to have in allnuclei. It was shown that these e.ective interactions speed up convergence tremendously andmake converged solutions possible.It has now become apparent that present theoretical techniques are able to accurately calculatethe properties of light nuclei using the NN interaction as input. Because the results showa considerable underbinding, it is clear that some extra ingredient is necessary, such as threenucleoninteractions. Hence, the NCSM will be expanded to include the three-body cluster (ore.ective interaction) based not only on the two-body microscopic forces, but also on realisticthree-nucleon (3N) bare interactions. It is important do this, because, for example, the spectraof light nuclei are expected to be sensitive to the spin structure of the 3N interaction. With thesehigher-body interactions one will also be able to perform NCSM calculations for heavier nucleiin smaller basis spaces and obtain better convergence and, hence, more accurate results. Thedevelopment of this three-body cluster approach is an major step forward, as it will enable oneto study the e.ects of current 3N interaction models and models based on chiral perturbationtheory on the spectra. Consequently, it will become an important tool to probe these interactions.By developing a technique for computing the three-body cluster exactly, one can alsoinvestigate its structure, depending upon the number of nucleons in the nuclide being studiedand upon the size of the model space.One of the goals of all nuclear structure calculations is the understanding of collective structuresbased on microscopic calculations. The structure of 12C is an interesting example. The.rst excited 0+ state is believed to have a 3a structure. Converged solutions for this problemare a challenge, but are within the reach of NCSM calculations. Once they can be obtained,one can study in detail the di.erence between the ground state and excited state structures.Another important aspect of the current investigations is the extension of the NCSM methods toarbitary operators. The NCSM is based on a unitary transformation of the cluster Hamiltonian.When one is able to extend this transformation to transition or current operators, it becomespossible to extract meaningful values for physical observables from the NCSM wave functions.The prediction of electroweak properties of light nuclei will be an important application of thisnew technique.