Three-body models of the 6ΛΛHe and 9ΛBe hypernuclei with non-local interactions

Theeten, Marc; Baye, Daniel Jean; Descouvemont, Pierre

doi:10.1016/j.nuclphysa.2005.02.129

Cited by 7 publications

(3 citation statements)

References 29 publications

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“…Indeed, not only must these nonlocal potentials be derived but their use and evaluation of validity simultaneously require mastering accurate calculations of macroscopic three-body systems with nonlocal forces and of microscopic three-cluster systems for comparison. This knowhow has been developed in recent years by our groups [16,21,27,28,29,30,31]. The purpose of the present study is to clarify the role of nonlocality in the αα potential by comparing the results of its application to a three-cluster description of 12 C with those obtained with local potentials on one hand and with the fully microscopic 3α model on the other hand.…”

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confidence: 91%

Local versus nonlocal αα interactions in a 3α description of 12C

et al. 2008

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confidence: 91%

Local versus nonlocal αα interactions in a 3α description of 12C

et al. 2008

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“…It is valid with non-local interactions [16,17]. It also applies with a semi-relativistic kinetic energy [18] and for solving the time-dependent Schrödinger equation [19,20].…”

Section: Introductionmentioning

confidence: 99%

Lagrange‐mesh method for quantum‐mechanical problems

Baye

2006

Physica Status Solidi (b)

110

139

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The Lagrange-mesh method is an approximate variational calculation with the simplicity of a mesh calculation because of the use of a consistent Gauss quadrature. The method can be used for quantum-mechanical bound-state and scattering problems with local and non-local interactions or with a semi-relativistic kinetic energy, and for solving the time-dependent Schrödinger equation. No analytical evaluation of matrix elements is needed. The accuracy is exponential in the number of mesh points and is not significantly reduced with respect to the corresponding variational calculations. Lagrange functions can be based on classical or non-classical orthogonal polynomials as well as on trigonometric and sinc functions, as described in examples. Some singularities can be handled with a regularization technique. Applications to three-body systems are discussed for various choices of coordinate systems. The helium atom and hydrogen molecular ion are presented as examples.

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“…In this method, the trial eigenstates are developed in a basis of well-chosen functions, the Lagrange functions, and the Hamiltonian matrix elements are obtained with a Gauss quadrature. Moreover, the Lagrange mesh method can be extended to treat very accurately three-body problems, in nuclear or atomic physics [7,8].…”

Section: Introductionmentioning

confidence: 99%

Bound-state equivalent potentials with the Lagrange mesh method

Buisseret

Semay

2007

Phys. Rev. E

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The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be applied to solve the inverse problem, namely, to find the equivalent local potential starting from a particular bound state wave function and the corresponding energy. In order to check the method, we apply it to several cases which are analytically solvable: the nonrelativistic harmonic oscillator and Coulomb potential, the nonlocal Yamaguchi potential and the semirelativistic harmonic oscillator. The potential is accurately computed in each case. In particular, our procedure deals efficiently with both nonrelativistic and semirelativistic kinematics.

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Three-body models of the 6ΛΛHe and 9ΛBe hypernuclei with non-local interactions

Cited by 7 publications

References 29 publications

Local versus nonlocal αα interactions in a 3α description of 12C

Local versus nonlocal αα interactions in a 3α description of 12C

Lagrange‐mesh method for quantum‐mechanical problems

Bound-state equivalent potentials with the Lagrange mesh method

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