Sturmian function approach andN¯Nbound states

Abstract

A suitable numerical approach based on Sturmian functions is employed to solve the {bar N}N bound state problem for local and nonlocal potentials. The approach accounts for both the strong short-range nuclear potential and the long-range Coulomb force and provides directly the wave function of protonium and {bar N}N deep bound states with complex eigenvalues E=E{sub R}{minus}i({Gamma}/2). The spectrum of {bar N}N bound states has two parts, the atomic states bound by several keV, and the deep bound states which are bound by several hundred MeV. The observed very small hyperfine splitting of the 1s level and the 1s and 2p decay widths are reasonably well reproduced by both the Paris and Bonn potentials (supplemented with a microscopically derived quark annihilation potential), although there are differences in magnitude and level ordering. We present further arguments for the identification of the {sup 13}PF{sub 2} deep bound state with the exotic tensor meson f{sub 2}(1520). Both investigated models can accommodate the f{sub 2}(1520) but differ greatly in the total number of levels and in their ordering. The model based on the Paris potential predicts the {sup 13}P{sub 0} level slightly below 1.1 GeV while the model based on the Bonn potential putsmore » this state below 0.8 GeV. It remains to be seen if this state can be identified with a scalar partner of the f{sub 2}(1520). {copyright} {ital 1997} {ital The American Physical Society}« less