Coupled rearrangement channel calculations of muonic molecules and A =3 nuclei

Benchmark test calculation of a four-nucleon bound state

“…In order to solve the bound four-nucleon system we employ the Faddeev-Yakubovsky equations(FY) [20][21][22][23], the Coupled-Rearrangement-Channel Gaussian-Basis Variational Method (CRCGV) [24][25][26][27][28][29][30][31], the Stochastic Variational Method(SVM) with correlated Gaussians [32][33][34][35], the Hyperspherical Harmonic Variational Method(HH) [36][37][38][39][40][41], the Green's function Monte Carlo(GFMC) [42,43,19,44] method, the No-Core Shell Model(NCSM) [45][46][47], and the effective interaction hyperspherical harmonic method(EIHH) [48]. The various procedures are briefly described below.…”

“…Use of basis functions that spanned all the three rearrangement Jacobian coordinates was essential to the high-precision calculation. The method was also applied to three-nucleon bound states [25,26] and was found to accomplish a much more rapid convergence in the binding energy with respect to the number of the three-body angular momentum channels (see Fig. 5 of [26]).…”

Precise solution of few-body problems with the stochastic variational method on a correlated Gaussian basis

“…Considerable effort has been exerted to obtain accurate groundstate properties of the few-nucleon systems with Faddeev-Yakubovsky (FY) [1][2][3], variational [4][5][6], variational Monte Carlo (VMC) [7,8] and Green's function Monte Carlo (GFMC) methods [9,10]. Most of these approaches has focused on three-or four-body problems.…”

“…For example, conventional methods [6,15] for the choice of the Gaussian parameters lead to prohibitively large bases for more than 3 or 4 particles, which has limited the applicability of the Gaussian basis to few-body problems.…”

“…One repeats this "trial and error" procedure until the basis set up leads to convergence. The original procedure of the SVM, proposed in [12], has recently been developed further and successfully applied to multicluster descriptions of light exotic nuclei, such as 6 He=α +n+n, 8 He=α + n + n + n + n, 9 Li=α + t + n + n, and 9 C=α+ 3 He+p + p [13,17]. Learning from these applications, we have now generalized and refined the method further to encompass diverse systems emerging in nuclear and atomic physics.…”