Gaussian expansion method for few-body systems

We review our method of calculation, Gaussian Expansion Method (GEM), for bound and scattering states of few-body systems. The method was proposed in 1988 and has been applied to a variety of few-body systems. The understanding on the structure and the mechanisms of reactions of those systems obtained from such applications is discussed together with some useful techniques for the calculations. A well-chosen set of Gaussian basis functions forms an approximate complete set in a finite coordinate space so that it can describe accurately short-range correlations and long-range asymptotic behavior as well as highly oscillatory character of wave functions in the bound and the scattering states of the systems. Examples of applications of GEM include i) the latest determination of antiproton mass by the analysis of laser spectroscopic data for antiprotonic helium atoms, ii) predictions and experimental verifications on the structure of hypernuclei and hyperon-nucleon interactions, iii) Coulomb three-body calculations of bound and resonant states of muonic molecules as well as muon transfer reactions in muon catalyzed fusion cycles, iv) a new treatment of CDCC (continuum-discretized coupled channels) method for three- and four-body breakup processes, and v) benchmark test calculations for three- and four-nucleon bound states using realistic interactions.