{"title":"Rearrangement and breakup amplitudes from the solution of Faddeev-AGS equations by pseudo-state discretization of the two-particle continuum","authors":"Zeki C. Kuruoğlu","doi":"10.1016/j.nuclphysa.2024.122940","DOIUrl":null,"url":null,"abstract":"<div><p>The AGS equations for rearrangement transition operators in the three-particle problem are turned into a set of effective multi-channel two-body equations using the pseudo-state discretization of the two-particle resolvent. The resulting effective equations are LS-type integral equations in the spectator degrees of freedom, much like the LS equations of multichannel inelastic scattering. In particular, the effective potential matrix is real, energy-independent and non-singular, while the propagator matrix has only simple poles. Difficulties associated with the moving singularities of the effective potential matrix in the usual separable-T approach to AGS equations are avoided. After regularization of the kernel via subtraction procedures well known from two-particle scattering, the set of coupled LS-type equations in the spectator momenta are solved rather straightforwardly by the Nyström method. Solutions of effective two-body equations are then used to calculate the breakup amplitudes using the well-known relationship between rearrangement and breakup amplitudes. Calculations using a local momentum-space basis on a benchmark model of the n+d collision show that rather accurate results for elastic and breakup amplitudes can be obtained with rather small bases.</p></div>","PeriodicalId":19246,"journal":{"name":"Nuclear Physics A","volume":"1051 ","pages":"Article 122940"},"PeriodicalIF":1.7000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375947424001222","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
引用次数: 0
Abstract
The AGS equations for rearrangement transition operators in the three-particle problem are turned into a set of effective multi-channel two-body equations using the pseudo-state discretization of the two-particle resolvent. The resulting effective equations are LS-type integral equations in the spectator degrees of freedom, much like the LS equations of multichannel inelastic scattering. In particular, the effective potential matrix is real, energy-independent and non-singular, while the propagator matrix has only simple poles. Difficulties associated with the moving singularities of the effective potential matrix in the usual separable-T approach to AGS equations are avoided. After regularization of the kernel via subtraction procedures well known from two-particle scattering, the set of coupled LS-type equations in the spectator momenta are solved rather straightforwardly by the Nyström method. Solutions of effective two-body equations are then used to calculate the breakup amplitudes using the well-known relationship between rearrangement and breakup amplitudes. Calculations using a local momentum-space basis on a benchmark model of the n+d collision show that rather accurate results for elastic and breakup amplitudes can be obtained with rather small bases.
三粒子问题中重排转换算子的 AGS 方程通过双粒子解析的伪态离散化被转化为一组有效的多通道双体方程。由此得到的有效方程是旁观者自由度中的 LS 型积分方程,非常类似于多通道非弹性散射的 LS 方程。特别是,有效势矩阵是实数、与能量无关且非奇异的,而传播矩阵只有简单的极点。这就避免了在 AGS 方程的通常可分离 T 方法中与有效势矩阵移动奇点相关的困难。在通过双粒子散射中众所周知的减法程序对内核进行正则化之后,旁观者矩的耦合 LS 型方程组就可以通过 Nyström 方法直接求解了。然后利用有效二体方程的解,利用众所周知的重排与破裂振幅之间的关系计算破裂振幅。在 n+d 碰撞的基准模型上使用局部动量空间基础进行的计算表明,使用相当小的基础就可以获得相当精确的弹性和破裂振幅结果。
期刊介绍:
Nuclear Physics A focuses on the domain of nuclear and hadronic physics and includes the following subsections: Nuclear Structure and Dynamics; Intermediate and High Energy Heavy Ion Physics; Hadronic Physics; Electromagnetic and Weak Interactions; Nuclear Astrophysics. The emphasis is on original research papers. A number of carefully selected and reviewed conference proceedings are published as an integral part of the journal.