Study of various few-body systems using Gaussian expansion method (GEM)

Abstract

We review our calculation method, Gaussian expansion method (GEM), and its applications to various few-body (3- to 5-body) systems such as 1) few-nucleon systems, 2) few-body structure of hypernuclei, 3) clustering structure of light nuclei and unstable nuclei, 4) exotic atoms/molecules, 5) cold atoms, 6) nuclear astrophysics and 7) structure of exotic hadrons. Showing examples in our published papers, we explain i) high accuracy of GEM calculations and its reason, ii) wide applicability of GEM and iii) successful predictions by GEM calculations before measurements. GEM was proposed 30 years ago and has been applied to a variety of subjects. To solve few-body Schroedinger equations accurately, use is made of the Rayleigh-Ritz variational method for bound states, the complex-scaling method for resonant states and the Kohn-type variational principle to S-matrix for scattering states. The total wave function is expanded in terms of few-body Gaussian basis functions spanned over all the sets of rearrangement Jacobi coordinates. Gaussians with ranges in geometric progression work very well both for short-range and long-range behavior of the few-body wave functions. Use of Gaussians with complex ranges gives much more accurate solution when the wave function has many oscillations.

30 pages, 46 figures, an invited review paper for the international symposium in honor of Prof. Akito Arima for his 88th birthday, to be published in Frontiers of Physics, Vol.13 (2018)

References in corpus (10)

• Primordial Nucleosynthesis: from precision cosmology to fundamental physics
• Stau-catalyzed ${}^6$Li Production in Big-Bang Nucleosynthesis
• Five-body cluster structure of double-$\Lambda$ hypernucleus ${}_{\Lambda \Lambda }^{11}$Be
• Gravitino Dark Matter and the Cosmic Lithium Abundances
• Description of ${}^4$He tetramer bound and scattering states
• Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials
• Big-Bang Nucleosynthesis Reactions Catalyzed by a Long-Lived Negatively Charged Leptonic Particle
• Universality in Efimov associated tetramers in 4He
• Resonant states of neutron-rich $\Lambda$ hypernucleus ${}_{\Lambda }^7$He
• Review on Effects of Long-lived Negatively Charged Massive Particles on Big Bang Nucleosynthesis

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