Energy-dependent pole expansions for the effective potentials in the four-body integral equations

Sofianos, S. A.; McGurk, N.J.; Fiedeldey, H.

doi:10.1016/0375-9474(79)90650-x

Cited by 65 publications

(33 citation statements)

References 8 publications

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“…A numerical solution of this equation is rather complex. In order to reduce computational time, needed in particular to handle the dependence on the medium, we introduce an energy dependent pole expansion (EDPE) that has been proven useful in many applications involving the α-particle and is accurate enough for the present purpose [30]. However, we have to generalize the original version of the EDPE because of different right and left eigenvectors appearing for the three-body subsystem and given in Eq.…”

Section: In-medium Few-body Equationsmentioning

confidence: 99%

Light clusters in nuclear matter of finite temperature

et al. 2004

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Abstract. We investigate properties and the distribution of light nuclei (A ≤ 4) in symmetric nuclear matter of finite temperature within a microscopic framework. For this purpose we have solved few-body Alt-Grassberger-Sandhas type equations for quasi-nucleons that include self-energy corrections and Pauli blocking in a systematic way. In a statistical model we find a significant influence in the composition of nuclear matter if medium effects are included in the microscopic calculation of nuclei. If multiplicities are frozen out at a certain time (or volume), we expect significant consequences for the formation of light fragments in a heavy ion collision. As a consequence of the systematic inclusion of medium effects the ordering of multiplicities becomes opposite to the law of mass action of ideal components. This is necessary to explain the large abundance of α-particles in a heavy ion collision that are otherwise largely suppressed in an ideal equilibrium scenario. PACS

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Section: In-medium Few-body Equationsmentioning

confidence: 99%

Light clusters in nuclear matter of finite temperature

et al. 2004

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“…Using this method, we can find a separable representation for the subamplitudes in (3+1) and (2+2) partitions and one can reduce the three-and four-body problem to an effective quasi-particle two-body one, where one of the components appears as a quasi-particle. For making a separable representation of these subsystem amplitudes, one can use the energy dependent pole expansion (EDPE) [24] or the Hilbert-Schmidt expansion [23]. For this purpose, we will apply the Hilbert-Schmidt expansion.…”

Section: Introductionmentioning

confidence: 99%

Deeply quasi-bound state in single- and double- $\bar{K}$ K ¯ nuclear clusters

2016

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New calculations of the quasi-bound state positions in K − K − pp kaonic nuclear cluster are performed using non-relativistic four-body Faddeev-type equations in AGS form. The corresponding separable approximation for the integral kernels in the three-and four-body kaonic clusters is obtained by using the Hilbert-Schmidt expansion procedure. Different phenomenological models ofKN − πΣ potentials with one-and two-pole structure of Λ(1405) resonance and separable potential models forK-K and nucleonnucleon interactions, are used. The dependence of the resulting four-body binding energy on models of KN − πΣ interaction is investigated. We obtained the binding energy of the K − K − pp quasi-bound state ∼ 80-94 MeV with the phenomenologicalKN potentials. The width is about ∼ 5-8 MeV for the two-pole models of the interaction, while the one-pole potentials give ∼ 24-31 MeV width.

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“…The resulting three-body subamplitudes, denoted by their total spin S, total isospin I and total angular momentum L, are expanded in a separable form using the energy dependent pole expansion (EDPE) [7]. The relevant subamplitudes in spin-isospin space (S,/) are the spin doublet ( 89 ~), the spin quartet (~, 89 and the isoquartet ( 89 ~) which are included here in L = 0 and L = 1.…”

Section: Introductionmentioning

confidence: 99%

Contribution ofp-wave (3)+1 subamplitudes to4He binding energy and scattering observables below four-body breakup threshold

Fonseca

1986

Few-Body Systems

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Abstract. The four-body equations of Alt, Grassberger and Sandhas, in the form that the (2) + (2) subsystem amplitudes are treated by the convolution method, are solved for separable two-body interactions between nucleon pairs in the channels 3S1-3D 1 (too alone) and 1S 0. All L = 0 and L = 1 (3) + 1 subamplitudes are represented in a separable form using the energy dependent pole expansion. The contribution of p-wave (3)+ 1 subamplitudes to the 4He binding energy, threshold scattering observables and low energy cross sections for n3H ~ n3H, p3He ~ p3He, dd -+ dd and dd -+ pall reactions is studied for different two-body potentials.

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Energy-dependent pole expansions for the effective potentials in the four-body integral equations

Cited by 65 publications

References 8 publications

Light clusters in nuclear matter of finite temperature

Light clusters in nuclear matter of finite temperature

Deeply quasi-bound state in single- and double- $\bar{K}$ K ¯ nuclear clusters

Contribution ofp-wave (3)+1 subamplitudes to4He binding energy and scattering observables below four-body breakup threshold

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