Threshold scattering of the η-meson off light nuclei

Abstract

The scattering lengths of η-meson collisions with light nuclei 2 H, 3 H, 3 He, and 4 He are calculated on the basis of few-body equations in coherent approximation. It is found that the η-nucleus scattering length depends strongly on the number of nucleons and the potential-range parameter. By taking into account the off-shell behavior of the ηN amplitude, the ηα scattering length increases considerably.In η-nucleus collisions at threshold energies, a large Final State Interaction (FSI) is expected due to the N * (1535) S 11 -resonance. This resonance, which is strongly coupled to the ηN and πN channels, lies only ∼ 50 MeV above the ηN threshold and has a very broad width of Γ ≈ 150 MeV [1]. The η-nucleus dynamics, thus, is of interest from the point of view of both few-body and meson-nucleon physics.In the energy region covering the S 11 -resonance, the πN and ηN scattering processes are to be considered as a coupled-channel problem [2][3][4]. The first of these channels has a long record of theoretical and experimental investigations, while the second one is understood only in a rudimentary way. The πN and ηN channels are connected to each other primarily via the N * (1535) resonance. In fact, the ηNN coupling constant was shown to be negligible [5][6][7] as compared to the one of the ηNN * vertex. This latter vertex constant, being hence crucial for determining the ηN interaction, is known only with a large uncertainty, so that the ηN scattering length inferred from it varies from (0.27 + i 0.22)fm [2] to (0.55 + i 0.30)fm [8]. The ηN near-threshold interaction, therefore, remains an interesting field of investigation. Of particular relevance in this context is the possibility of η-nucleus bound states [9,10]. Their existence would provide us with an excellent opportunity to answer the above-mentioned questions in a reliable manner.

Faddeev-type calculation ofηdthreshold scattering

“…As it should be, the AGS and FSA results converge to each other when the target particles become much heavier than the incident one (see Table 1.) .In Table 2 we compare the present AGS calculations with our previous results obtained by means of the FRA [11]. In Table 3 we present A ηd calculated with α = 3.316 fm −1 for various values of a ηN given in the literature.…”

“…Another reason comes from the differences among the employed approximations some of which might be detrimental in view of the resonant character of the ηN dynamics and the delicacy of the quasi-bound state problem. As was shown in Ref.[10] this problem cannot be adequately addressed by a meson-nucleus optical model or any low-order perturbation theory.Among the approximate approaches the few-body dynamics of the η-nucleus systems was most explicitly treated in our previous calculations [11][12][13][14][15] based on the finite-rank approximation (FRA) of the nuclear Hamiltonians. The shortcoming of these calculations is the neglect of excitations of the nuclear ground states.…”

“…Among the approximate approaches the few-body dynamics of the η-nucleus systems was most explicitly treated in our previous calculations [11][12][13][14][15] based on the finite-rank approximation (FRA) of the nuclear Hamiltonians. The shortcoming of these calculations is the neglect of excitations of the nuclear ground states.…”

Extraction of scattering lengths from final-state interactions

“…Here especially the isoscalar component is significant because of its close link to the term of the nucleon [4]. On a more phenomenological level the ηN scattering length is interesting because the magnitude of its real part is directly linked with speculations about the existence of η-mesonic hadronic bound states such as η 3 He [5][6][7][8][9][10][11] or η 4 He [12]. Unfortunately, a direct determination of the scattering length is only feasible in a few cases.…”

η-PHOTOPRODUCTION OFF 3He: SEARCH FOR η-MESIC NUCLEI

“…Subsequently, the formation of light η -mesic nuclei including 3 H, 3 He, 4 He was discussed in the framework of dierent models ( [32], [37]). Experimental search for such states was for example done via the study of the threshold behavior of η -production reactions in hadron and photon induced reactions.…”