Perturbation Theory of the Continuous Spectrum in the Theory of Nuclear Reactions

IF 1.7 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Few-Body Systems Pub Date : 2024-10-09 DOI:10.1007/s00601-024-01961-x

Brady J. Martin, W. N. Polyzou

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Abstract

Nuclear reactions are complex, with a large number of possible channels. Understanding how different channels contribute to a given reaction is investigated by perturbing the continuous spectrum. Tools are developed to investigate reaction mechanisms by identifying the contributions from each reaction channel. Cluster decomposition methods, along with the spectral theory of proper subsystem problems, is used to identify the part of the nuclear Hamiltonian responsible for scattering into each channel. The result is an expression of the nuclear Hamiltonian as a sum over all scattering channels of channel Hamiltonians. Each channel Hamiltonian is constructed from solutions of proper subsystem problems. Retaining any subset of channel Hamiltonians results in a truncated Hamiltonian where the scattering wave functions for the retained channels differ from the wave functions of the full Hamiltonian by N-body correlations. The scattering operator for the truncated Hamiltonian satisfies an optical theorem in the retained channels. Because different channel Hamiltonians do not commute, how they interact determines their contribution to the full dynamics.

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核反应理论中连续谱的扰动理论

核反应非常复杂，可能存在大量通道。通过扰动连续谱，可以了解不同通道对特定反应的贡献。通过确定每个反应通道的贡献，开发出了研究反应机理的工具。簇分解方法以及适当子系统问题的光谱理论被用来确定核哈密顿负责散射到每个通道的部分。其结果是将核哈密顿表达为所有散射通道的通道哈密顿之和。每个信道哈密顿都是由适当子系统问题的解构建而成的。保留通道哈密顿的任何子集都会产生一个截断哈密顿，其中保留通道的散射波函数与完整哈密顿的波函数之间存在 N 体相关性。截短哈密顿的散射算子满足保留通道的光学定理。由于不同通道的哈密顿不换算，它们之间的相互作用决定了它们对全动力学的贡献。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Few-Body Systems 物理-物理：综合

CiteScore

2.90

自引率

18.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Few-Body Systems presents original research work – experimental, theoretical and computational – investigating the behavior of any classical or quantum system consisting of a small number of well-defined constituent structures. The focus is on the research methods, properties, and results characteristic of few-body systems. Examples of few-body systems range from few-quark states, light nuclear and hadronic systems; few-electron atomic systems and small molecules; and specific systems in condensed matter and surface physics (such as quantum dots and highly correlated trapped systems), up to and including large-scale celestial structures. Systems for which an equivalent one-body description is available or can be designed, and large systems for which specific many-body methods are needed are outside the scope of the journal. The journal is devoted to the publication of all aspects of few-body systems research and applications. While concentrating on few-body systems well-suited to rigorous solutions, the journal also encourages interdisciplinary contributions that foster common approaches and insights, introduce and benchmark the use of novel tools (e.g. machine learning) and develop relevant applications (e.g. few-body aspects in quantum technologies).