Treatment of the Three- and Four-Nucleon Systems by a Generalized Separable-Potential Model

Alt, E. O.; Grassberger, Peter; Sandhas, W.

doi:10.1103/physrevc.1.85

Cited by 96 publications

(34 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While in the continuum theories, the four-body problem can be reduced to an "effective," rather complex three-body problem (Grassberger and Sandhas, 1967;Alt, Grassberger, and Sandhas, 1970;Kroger and Sandhas, 1977), in the lattice theory there is at present no simple integral equation with which to formulate explicitly such problems in the manner of the n = 3 body problem treated above. Just having such an equation would be of great benefit, because in many instances the strong coupling expansion [see the development surrounding Eq.…”

Section: Discussionmentioning

confidence: 99%

The few-body problem on a lattice

1986

View full text Add to dashboard Cite

The author explores some of the inherent simplifications of "quantum lattice physics." He distinguishes between fermions and bosons and analyzes the n-body problem for each, with n = 1,2,3... typically a small number. With delta-function (zero-range) interactions, the three-body problem on a lattice is manageable, and some results can even be extrapolated to n > 4. Such calculations are not limited to one dimension (where the well-known Bethe ansatz solves a number of n-body problems). On the contrary, studies cited are mainly in three dimensions and actually simplify with increasing dimensionality. For example, it is found that bound states of n > 3 particles in d > 3 dimensions are formed discontinuously as the strength of two-body attractive forces is increased, and are therefore always in the easily analyzed "strong coupling limit." In the Appendix, an exactly solved example from the theory of itinerant-electron magnetism illustrates how a rigorous solution to the few-body problem is capable of yielding information concerning the iV-body problem.

show abstract

Section: Discussionmentioning

confidence: 99%

The few-body problem on a lattice

1986

View full text Add to dashboard Cite

show abstract

“…Although a variety of methods for studying the four-body systems has been proposed in the literature, the Faddeev AGS method [22,28] and Faddeev-Yakubovsky approach [29,30] are more preferable to other methods. Using the separable approximation for the two-body potentials and for Faddeev amplitudes appearing in different K-type and H-type partitions of the four-body system, the both Faddeev approaches will produce the same set of effective two-body equations [22,23,31].…”

Section: B Four-body Equationsmentioning

confidence: 99%

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

2016

View full text Add to dashboard Cite

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.

show abstract

“…Three-body systems may be modeled with the Faddeev equations [6][7][8], and four-body systems may by modeled with the Yakubovsky equations [9]. Furthermore, the Alt-Grassburger-Sandhas (AGS) [10] equations have been used for N-body amplitudes and are found from the (N − 1)-body and lower amplitudes. Although extremely * Corresponding author.…”

mentioning

confidence: 99%

Relativistic elastic differential cross sections for equal mass nuclei

2015

View full text Add to dashboard Cite

The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann-Schwinger equation with the first order optical potential that was employed in the calculation.Published by Elsevier B.V. This is an open access article under the CC BY license

show abstract

Treatment of the Three- and Four-Nucleon Systems by a Generalized Separable-Potential Model

Cited by 96 publications

References 48 publications

The few-body problem on a lattice

The few-body problem on a lattice

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

Relativistic elastic differential cross sections for equal mass nuclei

Contact Info

Product

Resources

About