原子核量子相变及对关联问题的新探索

Quantum phase transition and paring interaction is of great interest in many areas of physics, and their manifestations vary significantly in different systems. In this project, we will perform new exploration theoretically related to nuclear quantum phase transition and nuclear paring interaction. On the one hand, the new high-order interaction in the interacting boson model will be explored, such as O(6) cubic interaction replacing the SU(3) quadrupole-quadrupole interaction to describe the spherical to axially deformed shape-phase transition and its application to nuclei with X(5) critical point symmetry to find the new physical significance. We will also extend this to the whole Caston triangle with the three dynamical symmetry to investigate the phase transitional behavior of nuclei across the whole transitional region with a schematic Hamiltonian. Also another two kinds of new high-order interactions will be investigated, respectively, seeking how the concept of dynamical symmetry will be enriched by increasing the order of the interaction and obtain new characterization and new physics. The low-lying energy levels, isomer shifts, E2 transition rates, quarupole moment and expectation values of shape variables across the entire transitional region will be investigated. On the other hand, pairing force is of great interest and an important residual interaction in nuclei. It is also challenging problem, since the approximations are usually adopted in which serious problems exist, such as the nonconservation of the number of particles which can lead to spurious states, nonorthogonal solutions. The exactly solvable models, such as mean-field plus nearest-orbit pairing model and the mean-field plus the extended pairing model, will be explored for the unified description of well-deformed nuclei. The binding energies,pairing excitation energies and even-odd mass differences, moment of inertia, and the occupation probability of valence nucleon pairs will be investigated systematically. It may be helpful in understanding the pair correlation and the possible new magic number, which could provide significant information to new elements.

原子核的量子相变和对关联问题是实验和理论都感兴趣的研究方向，是目前原子核物理的研究前沿。群论方法可以求出某些物理问题的精确解并有助于寻找新的物理，本项目将应用与群论方法相关的两个代数模型:1)引入高阶项的相互作用玻色子模型;2)平均场加对力的严格解模型，分别研究与原子核形状量子相变相关的新物理对称性和原子核中的对关联问题。一是在相互作用玻色子模型基础上，进一步引入与四极形变相关的各种不同高阶项相互作用，计算能谱和波函数并以此研究其他的电磁性质和与形状相关的感兴趣物理量，从而研究原子核过渡区可能出现的新量子相变行为，深入认识原子核量子相变及临界点对称性。二是在平均场加对力的严格解模型下，计算激发能谱和波函数，并以此研究结合能、奇偶能差、对激发能、转动惯量及其他电磁性质，深刻理解原子核中的对关联效应并预言可能出现的新幻数原子核，为发现可能的原子核新核素提供有意义的信息。

本项目应用与群论方法相关的两个代数模型即平均场加对力严格解模型和相互作用玻色子模型分别研究了与原子核中对关联和形状量子相变相关的一些有趣物理现象。原子核的平均场加对力模型的严格求解并不容易，极具挑战性，所以如何从理论上解决量子多体问题的计算问题，如何得到精确解，就变得尤为重要，因为精确解对于研究对关联、特别是丰质子或丰中子滴线核的多粒子关联至关重要。 本项目利用代数方法对一些感兴趣的量子多体系统的哈密顿量, 通过群代数的特殊对称性和引入推广Heine-Stieltjes多项式方法，对球形或形变平均场加依赖轨道对力模型进行了精确求解。从微观上提出几何四极-四极相互作用并对球形平均场加四极-四极相互作用加对力模型进行了严格求解及应用于原子核类转动相到对凝聚相的crossover区相变研究。在相互作用玻色子模型(IBM)中提出一种描述准转相变区原子核的新方案；建立了IBM对三轴转子的描述；提出描述原子核从振动到伽马不稳定运动E(5)临界点新模型等。本项目拓展的部分内容是围绕目前国际最新实验开展了多夸克奇特态和新强子共振态性质的理论探索。