Asymptotic boundary conditions for three-body breakup: Probable nonutility of the standard approach

Kuruoglu, Zeki C.; Levin, F. S.

doi:10.1103/physrevc.36.49

Cited by 10 publications

(10 citation statements)

References 8 publications

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“…This is in strong contrast to the (erroneous) conclusion drawn in Ref. [1], which unfortunately overlooked the important end-point contribu-was introduced, which vanishes at a=0 but diverges at a =+n. In Ref.…”

Section: The Saddle-point Approximationcontrasting

confidence: 96%

“…(28) is the one which was used in Ref. [1]. Note that we have absorbed the factor of -2/~into the definition of T(q).…”

Section: The Saddle-point Approximationmentioning

confidence: 99%

“…In Ref. [1] the question was raised for which values of p does the asymptotic form given in Eqs. (23) and (24}provide an accurate approximation for Eq.…”

mentioning

confidence: 99%

“…In order to match the notation of Ref. [1], we replace (19) by +4/3ko lib", «, (x,y) = f dq f&(x)»n(qy) T(q» 0 where fI, (x) is the irregular solution to the interacting two-body problem which is normalized at infinity to be…”

mentioning

confidence: 99%

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Boundary conditions for three-body scattering in configuration space

Glöckle

Payne

1992

Phys. Rev. C

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where we investigate the free three-body propagation from sources with different spatial extents. In a forthcoming article this study will be improved by considering the three-body propagation including one pairwise finalstate interaction and finally the full treatment of the Faddeev equations. We summarize our results in Sec. V.Aside from the interest of gaining insight into these equations from the point of view of general scattering theory, the solution of this problem is also of practical interest. The possibility of solving the three-nucleon scattering equations in configuration space has important applications for nucleon-deuteron scattering and for the proper treatment of the final-state interaction of three nucleons in the disintegration of He caused by real or virtual photons. These processes provide very useful insights into the nuclear dynamics of few-body systems. In recent years the three-nucleon scattering problem has 1992 The American Physical Society 45 BOUNDARY CONDITIONS FOR THREE-BODY SCATTERING IN. . . 975 been solved in momentum space [3] and applied to elastic n-d scattering and n-d breakup processes; it is important to check these calculations by an independent method, which would be a configuration-space treatment.

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Section: The Saddle-point Approximationcontrasting

confidence: 96%

“…(28) is the one which was used in Ref. [1]. Note that we have absorbed the factor of -2/~into the definition of T(q).…”

Section: The Saddle-point Approximationmentioning

confidence: 99%

“…In Ref. [1] the question was raised for which values of p does the asymptotic form given in Eqs. (23) and (24}provide an accurate approximation for Eq.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Boundary conditions for three-body scattering in configuration space

Glöckle

Payne

1992

Phys. Rev. C

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“…In the momentum space approach, for example, the effects appear as logarithmic singularities and discontinuities by a step function in the integral kernels of the equations so that we need to perform the integration very carefully [8]. In the differential equation approach, due to the breakup effects one needs to set boundary conditions at very long distance, the order of tens or hundreds times larger than the range of interaction potentials [9,10,11,12]. Since we treat the wave functions as solutions of the Faddeev integral equations, the long-range behavior should appear in the integral kernel.…”

Section: Introductionmentioning

confidence: 99%

Operation of the Faddeev Kernel in Configuration Space

Ishikawa

2007

Few-Body Systems

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Abstract. We present a practical method to solve Faddeev three-body equations at energies above three-body breakup threshold as integral equations in coordinate space. This is an extension of previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions.

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Scattering Models in Nuclear Systems

Tjon

1989

New Aspects of Nuclear Dynamics

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Asymptotic boundary conditions for three-body breakup: Probable nonutility of the standard approach

Cited by 10 publications

References 8 publications

Boundary conditions for three-body scattering in configuration space

Boundary conditions for three-body scattering in configuration space

Operation of the Faddeev Kernel in Configuration Space

Scattering Models in Nuclear Systems

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