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, 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 Schrödinger 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 especially when the wave function has many oscillations. * Electronic address: hiyama@phys.kyushu-u.ac.jp † Electronic address: mkamimura@riken.jp C. Prediction of spin-orbit splitting in hypernuclei 15 D. Prediction of neutron-rich hypernuclei 16 E. Prediction of hypernuclear states with strangeness S = −2 17 F. Strategy of studying hypernuclei and Y N and Y Y interactions 18

S-shell $$\varLambda \varLambda $$ hypernuclei based on chiral interactions

“…In the present work, we utilize the Jacobi no-core shell model (J-NCSM) [6,7] to study double-strangeness hypernuclei. Historically, since the first observations of ΛΛ hypernuclei, 10 ΛΛ Be [8], 6 ΛΛ He [9] and especially after publication of the so-called Nagara event [10,11], various approaches have been employed to study doubly-strange hypernuclei [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For example, Nemura et al used the so-called stochastic variational method in combination with phenomenological effective central ΛN and ΛΛ potentials to investigate ΛΛ s-shell hypernuclei [12].…”

Restudy of the color-allowed two-body nonleptonic decay of bottom baryons ${Ξ_b}$ and ${Ω_b}$ supported by hadron spectroscopy

“…We adopt the three-body light-front quark model to calculate these form factors depicting these discussed bottom baryon to the charmed baryon transitions under the naïve factorization framework. We also improve the treatment of the spatial wave function of these involved heavy baryons in these decays, where the semirelativistic three-body potential model [30,36] is applied to calculate the numerical spatial wave function of these heavy baryons with the help of the GEM [37][38][39][40]. We call that the study of color-allowed twobody nonleptonic decay of bottom baryons Ξ b and Ω b is supported by hadron spectroscopy.…”

“…c denotes the ground state Ξ c or its first radial excited state Ξ c (2970), while Ω ( * ) c represents the ground state Ω c or its first radial excited state Ω c (2S ). In the realistic calculation, we take the numerical spatial wave functions of these involved bottom and charmed baryons as input, where the semirelativistic potential model [30,36] associated with the Gaussian expansion method (GEM) [37][38][39][40] is adopted. By fitting the mass spectrum of these observed bottom and charmed baryons, the parameters of the adopted semirelativistic potential model can be fixed.…”

Comprehensive study of nuclear reactions in muon catalyzed fusion: I. dt$μ$ system

“…to accurately solve the dtµ molecule [32]; one of the most precise values in the literature was obtained for the energy of the very shallow (dtµ) J=v=1 state. The method was then applied to the high accuracy calculation of the three-nucleon bound states [43] with a realistic NN force; numerous applications for various types of few-body systems have been summarized in review papers [44,[64][65][66].…”