We propose an exact method for locating the zeros of the Jost function for analytic potentials in the complex momentum-plane. We further extend the method to the complex angular-momentum plane to provide the Regge trajectories. It is shown, by using several examples, that highly accurate results for extremely wide as well as for extremely narrow resonances with or without the presence of the Coulomb interaction can be obtained.

The position and movement of poles of the amplitude for elastic -meson scattering off the light nuclei 2 H, 3 H, 3 He, and 4 He are studied. It is found that, within the existing uncertainties for the elementary N interaction, all these nuclei can support a quasibound state. The values of the -nucleus scattering lengths corresponding to the critical N interaction that produces a quasibound state are given. ͓S0556- 2813͑96͒50305-5͔PACS number͑s͒: 25.80. Ϫe, 21.45.ϩv, 25.10.ϩs Since meson factories cannot produce -meson beams, these particles are available for experimental investigations only as products of certain nuclear reactions where they appear as final-state particles. Therefore, final-state interaction effects are the only source of information about the -meson interaction with nucleons. In this connection, -nucleus systems can play an important role in investigating the N dynamics, especially if they can form quasibound states. In this case, the final-state mesons can be trapped for a relatively long time, and thus the properties of the N interaction can be studied.Estimations, obtained in the framework of the optical model approach ͓1,2͔, put a lower bound on the atomic number A for which an -nucleus bound state could exist, namely Aу12. In Ref. ͓3͔, the formation of -nucleus states has been investigated, using the standard Green's function method of many-body problems. There it was found that an 16 O bound state should be possible. Experimentally the cross sections of pion collisions with lithium, carbon, oxygen, and aluminum, however, gave no evidence for the existence of bound states with these nuclei ͓4͔.A new theoretical analysis of the problem ͓5͔ predicted a binding of the meson to 12 C and heavier nuclei, however, with rather large widths. The formation of an 4 He bound state was studied in a more recent work by Wycech et al. ͓6͔, using a modified multiple scattering theory. These authors obtained a comparatively large negative value for the real part of the -nucleus scattering length, which was interpreted as an indication that an -nucleus bound state could exist. We note that previous results of ours, concering the scattering lengths with ligh nulcei ͓7-9͔, showed that the -4 He scattering length can have an even larger ͑negative͒ real part than that of Ref. ͓6͔.In Ref. ͓10͔, a preliminary investigation on the possibility of -meson binding in the d, t, 3 He, and 4 He systems was made within the framework of the finite-rank approximation ͑FRA͒ of the nuclear Hamiltonian ͓11,12͔. The FRA approach treats the motion of the projectile ( meson͒ and of the nucleons inside the nucleus separately. As a result the internal dynamics of the nucleus enters the theory only via the nuclear wave function. In ͓10͔, these wave functions were approximated by simple Gaussian forms, which repro-duce the nuclear sizes only. In the present work, we perform calculations with more realistic nuclear wave functions, obtained via the so-called integro-differential equation approach ͑IDEA͒ ͓13-17͔. We study, in particula...

Three-and four-neutron systems are studied within the framework of the hyperspherical approach with a local S-wave nn-potential. Possible bound and resonant states of these systems are sought as zeros of three-and fourbody Jost functions in the complex momentum plane. It is found that zeros closest to the origin correspond to sub-threshold (nnn) 1 2 − and (nnnn) 0 + resonant states. The positions of these zeros turned out to be sensitive to the choice of the nn-potential. For the Malfliet-Tjon potential they are E 0 ( 3 n) = −4.9 − i6.9 (MeV) and E 0 ( 4 n) = −2.6 − i9.0 (MeV). Movement of the zeros with an artificial increase of the potential strength also shows an extreme sensitivity to the choice of potential. Thus, to generate 3 n and 4 n bound states, the Yukawa potential needs to be multiplied by 2.67 and 2.32 respectively, while for the Malfliet-Tjon potential the required multiplicative factors are 4.04 and 3.59.

A combination of the variable-constant and complex coordinate rotation methods is used to solve the two-body Schrödinger equation. The latter is replaced by a system of linear first-order differential equations, which enables one to perform direct calculation of the Jost function for all complex momenta of physical interest, including the spectral points corresponding to bound and resonance states. Explicit forms of the equations, appropriate for central, noncentral, and Coulomb-tailed potentials are given. Within the proposed method, the scattering, bound, virtual, and resonance state problems can be treated in a unified way. The effectiveness of the method is demonstrated by a numerical example.