DIRECT SOLUTION OF THE MANY-BODY SCHRODINGER-EQUATION IN THE HYPERSPHERICAL FORMALISM - APPLICATION OF THE CFHH-GLF METHOD TO A SET OF HE-LIKE SYSTEMS

We apply the CFHH-GLF method, a modified version of our HH-GLF method, to directly solve the three-body Schrodinger equation for a set of He -like systems, including H-, He, Li+, Be2+, and B3+. Correlation funct ions with no adjustable parameters are determined from the cusp condit ion of the wave function, Our calculational results exhibit very fast and good convergence with hyperspherical harmonics (HH) and a generali zed Laguerre function (GLF) and substantial improvement over the HH-GL F method. With only 36 HH and 6 GLF, we obtained the ground-state ener gy of -2.90371, -7.27988, -13.6555, and -22.0308 au for He, Li+, Be2+, and B3+, respectively. This compares with -2.89361, -7.26131, -13.625 3, and -21.9859 au, respectively, by the HH-GLF method and Pekeris' re sults of -2.90372, -7.27991, -13.6556, and -22.0310 au, respectively. So, the inclusion of 36 HH and 6 GLF has yielded the precision of a fe w parts in 10(6) for He, Li+, Be2+, and B3+. However, our calculationa l results for Hare not so good. We analyzed the cause of this kind of exception and improved our calculations in this respect by using a sli ghtly different correlation function. We finally obtained the ground-s tate energy of -0.527754 au for H- with 36 HH and 15 GLF, which is ver y near Pekeris' result of -0.527751 au and of the same order of precis ion as those achieved for other He-Like ions. (C) 1995 John Wiley and Sons, Inc.