库仑相互作用的Fock表示。I. 两体问题
The Fock representation of the Coulomb interaction. I. Two-body problem
- National University of Uzbekistan（乌兹别克斯坦国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出库仑相互作用的Fock表示，在动量空间精确可分离，无需屏蔽或拟合，并与屏蔽-重整化方法在二体基准上比较，验证其有效性。
AI中文摘要：
未屏蔽的库仑相互作用在负能量下，通过Fock的球极投影，在动量空间中精确可分离，具有解析形状因子和强度。这里将其推导为势的算符恒等式，并作为可分离项块，无需屏蔽或拟合，添加到带电对的可分离核输入中。该表示与屏蔽-重整化方法及库仑畸变形状因子在二体基准上进行了比较：离壳t矩阵、αp泡利禁止态的库仑位移，以及pp、αp和αα对的库仑修正相移。Feshbach-Schur投影的泡利禁止态被证明需要库仑修饰的本征态，而Fock块在同一可分离问题中提供了该本征态。在正能量下，有限截断是一个具有解析、动量依赖半径的屏蔽库仑势。
英文摘要：
The unscreened Coulomb interaction is exactly separable in momentum space at negative energies, by the stereographic projection of Fock, with analytic form factors and strengths. It is derived here as an operator identity for the potential and added, without screening or fitting, as a block of separable terms to the separable nuclear input of a charged pair. The representation is compared with the screening--renormalization method and with Coulomb-distorted form factors on two-body benchmarks: the off-shell $t$~matrix, the Coulomb displacement of the $αp$ Pauli-forbidden state, and the Coulomb-modified phases of the $pp$, $αp$ and $αα$ pairs. The Feshbach--Schur projection of the Pauli-forbidden state is shown to require the Coulomb-dressed eigenstate, which the Fock block provides within the same separable problem. At positive energy a finite truncation is a screened Coulomb potential with an analytic, momentum-dependent radius.
