STURMIAN FUNCTION-APPROACH AND (N)OVER-BARN BOUND-STATES

A suitable numerical approach based on Sturmian functions is employed to solve the (N) over bar N bound state problem for local and nonlocal potentials. The approach accounts for both the strong short-range nuc lear potential and the long-range Coulomb force and provides directly the wave function of protonium and (N) over bar N deep bound states wi th complex eigenvalues E = E-R-i(Gamma/2). The spectrum of (N) over ba r N bound states has two parts, the atomic states bound by several keV , and the deep bound stares which are bound by several hundred MeV. Th e observed very small hyperfine splitting of the 1s level and the 1s a nd 2p decay widths are reasonably well reproduced by both the Paris an d Bonn potentials (supplemented with a microscopically derived quark a nnihilation potential), although there are differences in magnitude la nd level ordering. We present further arguments for the identification of the (PF2)-P-13 deep bound state with the exotic tensor meson f(2)( 1520). Both investigated models can accommodate the f(2)(1520) but dif fer greatly in the total number of levels and in their ordering. The m odel based on the Paris potential predicts the P-13(0) level slightly below 1.1 GeV while the model based on the Bonn potential puts this st ate below 0.8 GeV. It remains to be seen if this state can be identifi ed with a scalar partner of the f(2)(1520).