The 4 He3 bound states and the scattering of a 4 He atom off a 4 He dimer at ultra-low energies are investigated using a hard-core version of the Faddeev differential equations. Various realistic 4 He-4 He interactions were employed, amomg them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. The ground state and the excited (Efimov) state obtained are compared with other results. The scattering lengths and the atom-diatom phase shifts were calculated for center of mass energies up to 2.45 mK. It was found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results.

We present a mathematically rigorous method suitable for solving three-body bound state and scattering problems when the inter-particle interaction is of a hard-core nature. The proposed method is a variant of the Boundary Condition Model and it has been employed to calculate the binding energies for a system consisting of three 4 He atoms. Two realistic He-He interactions of Aziz and collaborators, have been used for this purpose. The results obtained compare favorably with those previously obtained by other methods. We further used the model to calculate, for the first time, the ultra-low energy scattering phase shifts. This study revealed that our method is ideally suited for three-body molecular calculations where the practically hard-core of the inter-atomic potential gives rise to strong numerical inaccuracies that make calculations for these molecules cumbersome.LANL E-print physics/9612012.

Among the light nuclear clusters the α-particle is by far the strongest bound system and therefore expected to play a significant role in the dynamics of nuclei and the phases of nuclear matter. To systematically study the properties of the α-particle we have derived an effective four-body equation of the Alt-Grassberger-Sandhas (AGS) type that includes the dominant medium effects, i.e. self energy corrections and Pauli-blocking in a consistent way. The equation is solved utilizing the energy dependent pole expansion for the subsystem amplitudes. We find that the Mott transition of an α-particle at rest differs from that expected from perturbation theory and occurs at approximately 1/10 of nuclear matter densities.

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...

A complete derivation of a new two-variable integrodifferential equation valid for threeand many-boson systems is given here for the first time, and it is shown to be exact if all correlations higher than those of two-body type can be neglected. Its equivalence to the Faddeev equation for three bodies and its applicability to many-body systems are discussed in detail. Three-body forces are included. It is shown that the threeand four-body binding energies obtained by means of this equation are in good agreement with those obtained from the most sophisticated variational, Faddeev, and Faddeev-Yakubovsky calculations. This indicates that our new two-variable integrodifferential equation should also be useful for larger systems, in particular since unlike other methods it does not suffer from the disadvantage of rapidly increasing complexity with A. We also show that a simple adiabatic method for the solution of this equation {and hence also for the Faddeev equation) is quite sufficient, due to the closeness of the upper and lower bounds obtained in this way. Finally we apply the adiabatic method to nuclear three-body scattering and even include the effect of breakup for spin-dependent forces. It is found that asymptotic behavior is reached for a value of the hyperradius of the order of 3S fm.where

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.