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arXiv 1012.5406nucl-th
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核子-核子散射理论中的么正服装变换方法

Method of unitary clothing transformations in the theory of nucleon-nucleon scattering

I. Dubovyk, O. Shebeko

摘要:

应用Greenberg和Schweber在量子场论中提出的服装过程描述核子-核子(N-N)散射。我们考虑赝标、矢量和标量介子场通过Yukawa型耦合与费米子场相互作用,在“裸”粒子之间引入试探相互作用。随后的幺正服装变换(UCT)被发现通过新的相互作用算子表示总的哈密顿量,这些相互作用算子指的是具有物理(可观察)性质的粒子,即所谓的服装粒子。在这项工作中,我们集中在埃尔米特和能量无关的运营商的衣服核子,建立在二阶的耦合常数。将相应的动量空间解析表达式与核力介子理论中单个介子对单玻色子交换势的贡献进行了比较。为了计算N-N散射的T矩阵,我们使用了一个等价定理,使我们能够在衣服粒子表示(CPR)中操作,而不是裸粒子表示(BPR),其大量的虚拟过程。在强子态希尔伯特空间的双核子扇区中,我们导出了T矩阵的CPR元的Lippmann-Schwinger型方程。

英文摘要:

The clothing procedure, put forward in quantum field theory (QFT) by Greenberg and Schweber, is applied for the description of nucleon-nucleon (N-N) scattering. We consider pseudoscalar, vector and scalar meson fields interacting with fermion ones via the Yukawa-type couplings to introduce trial interactions between "bare" particles. The subsequent unitary clothing transformations (UCTs) are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T-matrix of the N-N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation (BPR) with its large amount of virtual processes. We have derived the Lippmann-Schwinger type equation for the CPR elements of the T-matrix for a given collision energy in the two-nucleon sector of the Hilbert space of hadronic states.

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