Quasibound states ofη-nucleus systems

Abstract

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...

Search for quasi boundηmesons

“…[44], [45], [14] bound states in light nuclei were calculated by the finite rank approximation (FRA). Within this approximation the motion of the η and of the nucleons inside the nucleus are treated separately.…”

Low-energy ηd-resonance

“…Recently, in a number of theoretical investigations based on quite different approaches, such as the mean field approximation [5], the optical model [6], and few-body calculations [7,8], the idea of η-nuclei was given a rather firm ground. Experimentally, after the discouraging attempt of Ref.…”

“…A necessary condition for the existence of η-nuclei, hence, appears to be satisfied. A further indication is the observation of pionic nuclei (deeply bound pion states inside nuclei) [3], which were predicted theoretically in [4].Recently, in a number of theoretical investigations based on quite different approaches, such as the mean field approximation [5], the optical model [6], and few-body calculations [7,8], the idea of η-nuclei was given a rather firm ground. Experimentally, after the discouraging attempt of Ref.…”

“…[8]). The η-nucleon T -matrix is taken in the formconsisting of two vertex functions and the S 11 -propagator in between [7]. It corresponds to the process ηN → S 11 → ηN which at low energies is dominant.…”

Quasi-Bound3He −ηState and Spin-Observables of the Reactionpd→3Heη

“…Parameters of the quasi-bound state were estimated [4,5] from fit to the data. Microscopic four-body calculations support quasi-bound [7] or anti-bound (virtual) [8] states in the 3 He − η system within the existing uncertainties for the elementary ηN interaction. A special type of experiments is required to decide whether the pole in the 3 He − η system, if it really exists, corresponds to a quasi-bound (for strong enough ηN interaction) or anti-bound (for rather weak ηN interaction) state [9].…”