Triton asymptotic normalization constants by the hyperspherical harmonics expansion method

1990 ◽  
Vol 42 (4) ◽  
pp. 1249-1253 ◽  
Author(s):  
Apurba Kumar Ghosh ◽  
Tapan Kumar Das
Keyword(s):  
Expansion Method ◽  
Asymptotic Normalization ◽  
Hyperspherical Harmonics ◽  
Hyperspherical Harmonics Expansion

scholarly journals Implementation of Local Chiral Interactions in the Hyperspherical Harmonics Formalism

2021 ◽  
Vol 9 ◽  
Author(s):  
Simone Salvatore Li Muli ◽  
Sonia Bacca ◽  
Nir Barnea
Keyword(s):  
Truncation Error ◽  
Expansion Method ◽  
Muonic Atom ◽  
Light Nuclei ◽  
Hyperspherical Harmonics ◽  
Irreducible Tensors ◽  
Nuclear Systems ◽  
Chiral Interactions ◽  
Three Body ◽  
Hyperspherical Harmonics Expansion

With the goal of using chiral interactions at various orders to explore the properties of the few-body nuclear systems, we write the recently developed local chiral interactions as spherical irreducible tensors and implement them in the hyperspherical harmonics expansion method. We devote particular attention to three-body forces at next-to-next-to leading order, which play an important role in reproducing experimental data. We check our implementation by benchmarking the ground-state properties of 3H, 3He, and 4He against the available Monte Carlo calculations. We then confirm their order-by-order truncation error estimates and further investigate uncertainties in the charge radii obtained by using the precise muonic atom data for single-nucleon radii. Having local chiral Hamiltonians at various orders implemented in our hyperspherical harmonics suites of codes opens up the possibility to test such interactions on other light-nuclei properties, such as electromagnetic reactions.

scholarly journals Solution of Faddeev integral equations in configuration space using the hyperspherical harmonics expansion method

2014 ◽  
Vol 23 (11) ◽  
pp. 1450069
Author(s):  
Valery I. Kovalchuk
Keyword(s):  
Configuration Space ◽  
Magnetic Moments ◽  
Expansion Method ◽  
Bound State ◽  
Binding Energies ◽  
Hyperspherical Harmonics ◽  
Faddeev Equations ◽  
Charge Radii ◽  
Mixed Symmetry ◽  
Hyperspherical Harmonics Expansion

In this paper, a method has been developed to solve three-particle Faddeev equations in the configuration space making use of a series expansion in hyperspherical harmonics. The following parameters of the bound state of triton and helium-3 nuclei have been calculated: the binding energies, the weights of symmetric and mixed-symmetry components of the wave function, the magnetic moments, and the charge radii.

scholarly journals Application of hyperspherical harmonics expansion method to the low-lying bound S-states of exotic two-muon three-body systems

2014 ◽  
Vol 23 (10) ◽  
pp. 1450055 ◽  
Author(s):  
Md. Abdul Khan
Keyword(s):  
Nuclear Charge ◽  
Expansion Method ◽  
Bound State ◽  
Hyperspherical Harmonics ◽  
Nuclear Core ◽  
Partial Waves ◽  
Extrapolation Scheme ◽  
Three Body ◽  
S States ◽  
Hyperspherical Harmonics Expansion

In this paper, energies of the low-lying bound S-states (L = 0) of exotic three-body systems, consisting a nuclear core of charge +Ze (Z being atomic number of the core) and two negatively charged valence muons, have been calculated by hyperspherical harmonics expansion method (HHEM). The three-body Schrödinger equation is solved assuming purely Coulomb interaction among the binary pairs of the three-body systems X Z+μ-μ- for Z = 1 to 54. Convergence pattern of the energies have been checked with respect to the increasing number of partial waves Λmax. For available computer facilities, calculations are feasible up to Λmax = 28 partial waves, however, calculation for still higher partial waves have been achieved through an appropriate extrapolation scheme. The dependence of bound state energies has been checked against increasing nuclear charge Z and finally, the calculated energies have been compared with the ones of the literature.

Hyperspherical harmonics expansion of the ground state of the Ps−ion

1996 ◽  
Vol 54 (6) ◽  
pp. 601-603 ◽  
Author(s):  
Rakhi Chattopadhyay ◽  
Tapan Kumar Das ◽  
Prasanta Kumar Mukherjee
Keyword(s):  
Ground State ◽  
Hyperspherical Harmonics ◽  
Hyperspherical Harmonics Expansion
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