谐振子有效理论中有效相互作用的形式
The Form of the Effective Interaction in Harmonic-Oscillator-Based Effective Theory
摘要：
我探索的形式的有效相互作用的谐振子为基础的有效理论（HOBET）在次-领先的顺序（N3 LO）。由于HOBET中的包含空间（如壳模型中）由振子能量定义，因此长距离（低动量）和短距离（高动量）自由度都位于高能排除空间中。一个HOBET有效的相互作用，其中短程接触梯度膨胀相结合的精确总和的相对动能。通过这种方法，消除了包含空间（P）和排除空间（Q）通过动能的非常强的耦合。人们发现QT和QV的相互作用由一个单一的参数kappa决定，kappa是一个可观测的结合能|E|与有效理论中的一个参数振子能量的比值。一旦确定了对kappa的函数依赖性，则驻留在Q中的短程物理的剩余逐阶减法变得系统化并迅速收敛。数值计算是用来证明如何以及由此产生的扩展再现运行的赫夫从高尺度到一个典型的壳模型规模的8毫巴Ω。在N3 LO的各种全球性能的Heff再现到一个典型的精度为0.01%，或约1千电子伏。有效相互作用的态依赖性一直是核物理中的一个难题，在Bloch-Horowitz形式中体现为Heff的能量依赖性（|E|）。它表明，几乎所有的这种状态依赖也提取在这里遵循的程序，孤立在分析依赖Heff对卡帕。因此，存在一个简单的厄米赫夫，可以用于光谱计算。
英文摘要：
I explore the form of the effective interaction in harmonic-oscillator-based effective theory (HOBET) in next-to-next-to-next-to-leading order (N3LO). As the included space in a HOBET (as in the shell model) is defined by the oscillator energy, both long-distance (low-momentum) and short-distance (high-momentum) degrees of freedom reside in the high-energy excluded space. A HOBET effective interaction is developed in which a short-range contact-gradient expansion is combined with an exact summation of the relative kinetic energy. By this means the very strong coupling of the included (P) and excluded (Q) spaces by the kinetic energy is removed. One finds that the interplay of QT and QV is governed by a single parameter kappa, the ratio of an observable, the binding energy |E|, to a parameter in the effective theory, the oscillator energy. Once the functional dependence on kappa is identified, the remaining order-by-order subtraction of the short-range physics residing in Q becomes systematic and rapidly converging. Numerical calculations are used to demonstrate how well the resulting expansion reproduces the running of Heff from high scales to a typical shell-model scale of 8 hbar omega. At N3LO various global properties of Heff are reproduced to a typical accuracy of 0.01%, or about 1 keV. The state-dependence of the effective interaction has been a troubling problem in nuclear physics, and is embodied in the energy dependence of Heff(|E|) in the Bloch-Horowitz formalism. It is shown that almost all of this state dependence is also extracted in the procedures followed here, isolated in the analytic dependence of Heff on kappa. Thus there exists a simple, Hermitian Heff that can be use in spectral calculations.
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