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arXiv 1206.3791nucl-th
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含靶激发和库仑相互作用的AGS形式的广义Faddeev氘核剥离方程

Generalized Faddeev equations in the AGS form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction

A. M. Mukhamedzhanov, V. Eremenko, A. I. Sattarov

摘要:

一般反应的理论描述,特别是$(d,p)$反应的理论,需要进入新的世纪。本文在少体积分方程理论的框架内讨论了氘从由${A}$核子组成的靶核上剥离的过程。广义Faddeev方程的AGS形式,考虑到目标的激发,与现实的光学势提供了最先进和完整的描述的氘核剥离。这类方程在实际应用中的主要问题是库仑势的屏蔽,它只适用于轻核。在本文中,我们提出了一个新的制定的Faddeev方程的AGS形式考虑到目标激发明确包括库仑相互作用。通过将$(A+2)$ -体算符投影到靶态上,导出了考虑靶核子激发态的矩阵三体积分方程。利用动量空间中部分库仑散射波函数的显式方程,我们给出了库仑扭曲波表象中的AGS方程,而不需要屏蔽过程。我们还使用显式表达式的离壳两体库仑散射$T$ -矩阵,这是需要计算的AGS方程中的有效势。对包含离壳库仑T矩阵的积分进行正则化,使所得方程适合于计算。对于$NN$和核子-靶核相互作用,我们假定可分离势,这大大简化了AGS方程的求解。

英文摘要:

Theoretical description of reactions in general, and the theory for $(d,p)$ reactions, in particular, needs to advance into the new century. Here deuteron stripping processes off a target nucleus consisting of ${A}$ nucleons are treated within the framework of the few-body integral equations theory. The generalized Faddeev equations in the AGS form, which take into account the target excitations, with realistic optical potentials provide the most advanced and complete description of the deuteron stripping. The main problem in practical application of such equations is the screening of the Coulomb potential, which works only for light nuclei. In this paper we present a new formulation of the Faddeev equations in the AGS form taking into account the target excitations with explicit inclusion of the Coulomb interaction. By projecting the $(A+2)$-body operators onto target states, matrix three-body integral equations are derived which allow for the incorporation of the excited states of the target nucleons. Using the explicit equations for the partial Coulomb scattering wave functions in the momentum space we present the AGS equations in the Coulomb distorted wave representation without screening procedure. We also use the explicit expression for the off-shell two-body Coulomb scattering $T$-matrix which is needed to calculate the effective potentials in the AGS equations. The integrals containing the off-shell Coulomb T-matrix are regularized to make the obtained equations suitable for calculations. For $NN$ and nucleon-target nuclear interactions we assume the separable potentials what significantly simplifies solution of the AGS equations.

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