Investigation of halo structure of 6 He by hyperspherical three-body method
TL;DR: In this article, a repulsive part is introduced in the interaction between the core and the extra-core neutron, to simulate Pauli principle, and two neutron separation energy, r.m.s. radii, correlation factor and probability density distributions have been calculated.
Abstract: Hyperspherical harmonics expansion method is applied to a three-body model of two neutron halo nuclei. Convergence of the expansion has been ensured. A repulsive part is introduced in the interaction between the core and the extra-core neutron, to simulate Pauli principle. Two neutron separation energy, r.m.s. radii, correlation factor and probability density distributions have been calculated for 6He. It is found that the convergence of the two neutron separation energy is relatively slow, while other quantities reach convergence quickly.
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TL;DR: In this article, the 2+ resonance state of 6He in a three-body model (4He + n + n) was calculated by adopting a novel theoretical technique, where hyperspherical harmonics were used to obtain a shallow well followed by a low and wide barrier, which effectively traps the system in a sharp resonant state and facilitates calculation of the resonance energy accurately.
Abstract: Calculation of the 2+ resonance state of 6He in a three-body model (4He + n + n) is done by adopting a novel theoretical technique. The effective three-body potential for the 2+ state of 6He is obtained using hyperspherical harmonics and it presents a shallow well followed by a low and wide barrier. Numerical diffculties present in the calculation of the resonance energy of such a shallow well–barrier combination are overcome by the construction of a one-parameter (λ) isospectral potential having a bound state in the continuum. This potential develops a deep well followed by a high barrier for small positive values of λ. This effectively traps the system in a sharp resonant state and facilitates calculation of the resonance energy accurately. We obtain the first 2+ resonance at 1.814 MeV with a width of 135 keV. We also get a second 2+ resonance at 4.9 MeV.
14 citations
TL;DR: In this paper, the ground state energies of exotic three-body atomic systems consisting two muons and a positively charged nucleus have been calculated using hyperspherical harmonics expansion (HHE) method.
Abstract: Ground state energies of exotic three-body atomic systems consisting two muons and a positively charged nucleus like: 1H+μ−μ−, 4He2+μ−μ−, 3He2+μ−μ−, 7Li3+μ−μ−, 6Li3+μ−μ−, 9Be4+μ−μ−, 12C6+μ−μ−, 16O8+μ−μ−, 20Ne10+μ−μ−, 28Si14+μ−μ− and 40Ar18+μ−μ− have been calculated using hyperspherical harmonics expansion (HHE) method. Calculation of matrix elements of two body interactions involved in the HHE method for a three body system is greatly simplified by expanding the bra- and ket- vector states in the hyperspherical harmonics basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal-Revai coefficients (RRC), which are the transformation coefficients between the hyperspherical harmonics bases corresponding to the two partitions. Use of these coefficients found to be very useful for the numerical solution of three-body Schrodinger equation where the two-body potentials are other than Coulomb or harmonic oscillator type. However, in this work the interaction potentials involved are purely Coulomb. The calculated energies have been compared with (i) those obtained by straight forward manner; and (ii) with those found in the literature (wherever available). The calculated binding energies agree within the computational error.
12 citations
TL;DR: In this paper, a new technique to calculate the position and width of weak resonant states in weakly bound systems, using isospectral potentials, was proposed, which has desirable properties which make the calculation of the resonance simpler and more accurate.
Abstract: We propose a new technique to calculate the position and width of weak resonant states in weakly bound systems, using isospectral potentials. A new potential is constructed which is strictly isospectral with the original one but has desirable properties which make the calculation of the resonance simpler and more accurate. The usefulness of the method is demonstrated by calculating the first 1+ resonance in 6Li, using a three-body cluster model for the latter.
8 citations
TL;DR: In this paper, ground state energies of atomic three-body systems like negatively charged hydrogen, normal helium, positively charged-lithium, beryllium, carbon, oxygen, neon and negatively charged exotic muonium and positronium atoms have been calculated adopting hyperspherical harmonics expansion method.
Abstract: Ground state energies of atomic three-body systems like negatively charged hydrogen, normal helium, positively charged-lithium, beryllium, carbon, oxygen, neon and negatively charged exotic- muonium and positronium atoms have been calculated adopting hyperspherical harmonics expansion method. Calculation of matrix elements of two body interactions needed in the hyperspherical harmonics expansion method for a three body system is greatly simplified by expanding the bra- and ket-vector states in the hyperspherical harmonics (HH) basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal–Revai coefficients (RRC), which are the transformation coefficients between the HH bases corresponding to the two partitions. Use of RRC become particularly essential for the numerical solution of three-body Schrődinger equation where the two-body potentials are other than Coulomb or harmonic. However in the present work the technique is used for two electron atoms 1H−(p
+
e
−
e
−), D−(d
+
e
−
e
−), Mu−(μ
+
e
−
e
−),4He(4
He
2+
e
−
e
−),6Li(6
Li
3+
e
−
e
−),10Be(10
Be
4+
e
−
e
−),12C(12
C
6+
e
−
e
−),16O(16
O
8+
e
−
e
−) etc. and the exotic positronium negative ion Ps
−(e
+
e
−
e
−) where the interactions are purely Coulomb. The relative convergence in ground state binding energy with increasing K
max
for 20Ne has been demonstrated as a representative case. The calculated energies at K
max
= 28 using RRC’s have been compared with those obtained by a straight forward manner in some representative cases to demonstrate the appropriateness of the use of RRC. The extrapolated energies have also been compared with those found in the literature. The calculated binding energies agree within the computational error.
5 citations
TL;DR: In this article, hyperspherical harmonics expansion method has been applied for two-electron ions 1H− (Z = 1) to 40Ar16+ (Z= 18), negatively charged-muonium Mu− and exotic positronium ion Ps−(e+e−e−) considering purely Coulomb interaction.
Abstract: The energies of the low-lying bound S-states of some two-electron systems (treating them as three-body systems) like negatively charged hydrogen, neutral helium, positively charged-lithium, beryllium, carbon, oxygen, neon, argon and negatively charged muonium and exotic positronium ions have been calculated employing hyperspherical harmonics expansion method. The matrix elements of two-body interactions involve Raynal–Revai coefficients which are particularly essential for the numerical solution of three-body Schrődinger equation when the two-body potentials are other from Coulomb or harmonic. The technique has been applied for to two-electron ions 1H− (Z = 1) to 40Ar16+ (Z = 18), negatively charged-muonium Mu− and exotic positronium ion Ps−(e+e−e−) considering purely Coulomb interaction. The available computer facility restricted reliable calculations up to 28 partial waves (i.e. Km = 28) and energies for higher Km have been obtained by applying an extrapolation scheme suggested by Schneider.
5 citations
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46,339 citations
TL;DR: In this article, a detailed review of bound state properties of loosely bound nuclei is presented, with emphasis on genuine three-body features, and a number of plausible model interactions, including treatments of the Pauli principle, are presented.
723 citations
TL;DR: In this paper, it was shown that low binding of these nuclei will lead to a neutronization of the nuclear surface and possibly to large cross-sections for Coulomb dissociation, which then offers a new way to study clusters and their binding energies.
Abstract: Empirical evidence suggests that neutron pairing plays an important role for the stability of nuclei near the neutron drip line. It is shown that the low binding of these nuclei will lead to a neutronization of the nuclear surface and possibly to large cross-sections for Coulomb dissociation, which then offers a new way to study clusters and their binding energies.
620 citations
TL;DR: In this article, the interaction cross sections (σI) of all He isotopes of 790 MeV/nucleon on Be, C, and Al targets were measured by a transmission-type experiment.
479 citations
TL;DR: In this article, the renormalized numerov method has been generalized to bound states of the coupled-channel Schroedinger equation and a method for detecting wave function nodes is presented.
Abstract: The renormalized Numerov method, which was recently developed and applied to the one‐dimensional bound state problem [B. R. Johnson, J. Chem. Phys. 67, 4086 (1977)], has been generalized to compute bound states of the coupled‐channel Schroedinger equation. Included in this presentation is a generalization of the concept of a wavefunction node and a method for detecting these nodes. By utilizing node count information it is possible to converge to any specific eigenvalue without the need of an initial close guess and also to calculate degenerate eigenvalues and determine their degree of degeneracy. A useful interpolation formula for calculating the eigenfunctions at nongrid points is also given. Results of example calculations are presented and discussed. One of the example problems is the single center expansion calculation of the 1sσg and 2sσg states of H+2.
382 citations