Resonating group Faddeev approach to deuteron-alpha scattering

Schmid, Erich W.; Doleschall, P.

doi:10.1103/physrevc.31.325

Cited by 14 publications

(8 citation statements)

References 21 publications

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“…Whenever effective two-cluster interactions are used in more complicated calculations, like a three-cluster bound state calculation, a cluster-transfer calculation [11] or a three-cluster Faddeev calculation [7,12], omission of a threebody potential will spoil the result unless it is negligibly small. In the present first approximation we can, in principle, determine the amount of effective three-body force arising from the Paul/principle and from hard core correlations.…”

Section: Three-body Forcesmentioning

confidence: 99%

The two- and three-cluster fish bone model with saturation

et al. 1985

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The two-and three-cluster fish bone optical model with hard core correlations is derived from the corresponding resonating group model. The nuclear saturation effect is represented by three different features of inter-cluster interactions: i) by the non-local exchange potential, ii) by a reduced attraction in the region of overlapping clusters, iii)by an effective three-cluster potential. Comparability of the microscopic theory with phenomenological models is established by two off-shell transformations which orthogonalize function bases and avoid appearance of artificial three-body forces.

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Section: Three-body Forcesmentioning

confidence: 99%

The two- and three-cluster fish bone model with saturation

et al. 1985

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“…[6]. For the local part of the potential, the authors adopted a Wood-Saxon shape with a spin-orbit term.…”

Section: Introductionmentioning

confidence: 99%

Refinement of then-αandp-αfish-bone potential

2012

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“…This term is a part of three-body type of interaction between clusters. The other parts of three-body type of interaction are connected with the kinetic energy operator, overlap and internal hamiltonians H (1) α . It means, as pointed out above, that three-body interaction originated from those terms of the total hamiltonian and overlap, where three-cluster exchange term A 123 is presented.…”

Section: Faddeev Equations For Three-cluster Systemsmentioning

confidence: 99%

“…a sum of three single-cluster hamiltonians H (1) α describing the internal structure of each cluster, and a term responsible for the inter-cluster dynamics. The latter consists of the kinetic energy operator for relative motion of clusters T r and the potential energy of interaction between clusters.…”

Section: Definitions and Notationsmentioning

confidence: 99%

“…It was also demonstrated repeatedly that the Faddeev approach is computationally more efficient. This led to numerous attempts to extend the Faddeev formalism to three-cluster systems (see for instance [1], [2], [2], [3], [4], [5], [3], [6], [7], [8], [9]). Because of complexity, which arise from the Pauli principle, many of these attempts were concentrated on simplified and approximate treatment of the Pauli principle.…”

Section: Introductionmentioning

confidence: 99%

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Faddeev type of equations for three-cluster systems with full treatment of the Pauli principle

Vasilevsky

Arickx

Broeckhove

2008

J. Phys.: Conf. Ser.

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Abstract. We analyze peculiarities of the Pauli principle in thrre-cluster system. We demonstrated that the antisymmetrization operator, being a source of the three-body interaction, can be decomposed into components involving either permutations between all three clusters, or permutations between two clusters only. Introducing this into the Faddeev equations, one obtains three alternative but equivalent formulations. These sets of equations are presented in operator form, for practical applications we will make use full set of the oscillator functions. IntroductionThe Resonating Group Method (RGM) is a well-established approach to three-cluster nuclear systems. It leads to both bound and scattering states using a coupled channels approach. It is a rigorous an self-consistent method for taking into account exactly the Pauli principle, but is computationally expensive and has slow convergence properties.The Faddeev formalism on the other hand has no problems dealing with the non-orthogonality of channels, and is much more suitable for implementing the boundary conditions for two-and three-cluster asymptotics. It was also demonstrated repeatedly that the Faddeev approach is computationally more efficient. This led to numerous attempts to extend the Faddeev formalism to three-cluster systems (see for instance). Because of complexity, which arise from the Pauli principle, many of these attempts were concentrated on simplified and approximate treatment of the Pauli principle.The key issue to extend the formalism to three-cluster systems is the correct and full treatment of the Pauli principle. It is well-known that full antisymmetrization leads to nonlocal, energy-dependent inter-cluster interaction. In addition, in a three-cluster system the antisymmetrization operator is a source of three-body interactions originating from the twobody nucleon-nucleon (NN) interaction, but also from the kinetic energy and overlap kernel.We want to address these difficulties by starting from the RGM wave function, and introduce it in the Faddeev equations. This wave function will then exhibit three Faddeev amplitudes, each with their appropriate set of boundary conditions. The antisymmetrization operator is then decomposed into components involving either permutations between all three clusters, or permutations between two clusters only. Introducing this into the Faddeev equations, one obtains three alternative but equivalent formulations.

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Resonating group Faddeev approach to deuteron-alpha scattering

Cited by 14 publications

References 21 publications

The two- and three-cluster fish bone model with saturation

The two- and three-cluster fish bone model with saturation

Refinement of then-αandp-αfish-bone potential

Faddeev type of equations for three-cluster systems with full treatment of the Pauli principle

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