A theoretical treatment of four-body resonances by using the complex scaling method

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A theoretical treatment of four-body resonances by using the complex scaling method is discussed. In order to reduce the dimension of the Hamiltonian matrix, the stochastic variational method is applied for the subsystems of the four-body system. Furthermore, to investigate the resonant solutions embedded in the continuum states we employ the complex-range Gaussian basis function, and two comments in applying the complex-range basis function to the complex scaling method are given. We also introduce the additional four-body pseudo potential to clarify whether the obtained solution is a true resonance or not. As a numerical example, we investigate the applicability of the present method to the 0± states of 4He, which is a four-nucleon resonant system. ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .