Overview of K̄-Nuclear Quasi-Bound States

The K̄-nucleus interaction near threshold is strongly attractive and absorptive as suggested by fits to the strong-interaction shifts and widths of K−-atom levels [1]. Global fits yield ‘deep’ optical potentials with Re VK̄(ρ0) ∼ −(150 − 200) MeV [2–5], whereas more theoretically inclined studies that fit the low-energy K−p reaction data, including the I = 0 quasi-bound state Λ(1405) as input for constructing density dependent optical potentials, suggest relatively ‘shallow’ potentials with Re VK̄(ρ0) ∼ −(40−60) MeV [6–8]. The issue of depth of the attractive K̄-nucleus potential is discussed in Section 2. Paradoxically, due to the strong (absorptive) Im VK̄ , relatively narrowK − deeply bound atomic states are expected to exist [9], independently of the size of Re VK̄ . Figure 1 from Ref. [10] shows on the left-hand side a calculated spectrum of K− atomic states in Pb where, in particular, all the circular states below the 7i (l = 6) state are not populated by X-ray transitions due to the strong K−-nuclear absorption, and on the right-hand side it demonstrates saturation of the 2p atomic-state width as a function of the absorptivity parameter Im b0 of VK̄ . The physics behind is that a strong Im VK̄ acts repulsively, suppressing the atomic wavefunction in the region of overlap with Im VK̄ . The calculated width of the ‘deeply bound’ atomic 1s and 2p is less than 2 MeV, also confirmed by the calculation of Ref. [11], calling for experimental ingenuity how to form these levels selectively by a non-radiative process [12]. This saturation mechanism does not hold for K̄-nuclear states which retain very good overlap with the potential. Hence, the questions to ask are (i) whether it is possible at all to bind strongly K̄ mesons in nuclei, and (ii) are such quasi-bound states sufficiently narrow to allow observation and identification? The first question was answered favorably by Nogami [13] as early as 1963 arguing that the K−pp system could acquire about 10 MeV binding in its I = 1/2 state. Yamazaki and Akaishi, within a single-channel K−pp calculation [14], reported a binding energy B ∼ 50 MeV and width Γ ∼ 60 MeV; however,