${\mathrm{\Sigma }}^{-}p$ emission rates in $K^{-}$ absorptions at rest on ${}^6\mathrm{Li},{}^7\mathrm{Li},{}^9\mathrm{Be},{}^{13}\mathrm{C}$, and ${}^{16}\mathrm{O}$

An experimental study of the $K_{\mathrm{stop}}^{-}A\to {\mathrm{\Sigma }}^{-}p{A}^{\prime }$ reaction on $A={}^6\mathrm{Li},{}^7\mathrm{Li},{}^9\mathrm{Be},{}^{13}\mathrm{C}$, and ${}^{16}\mathrm{O}p$-shell nuclei is presented. The data were collected by the FINUDA spectrometer operating at the $\mathrm{DA}\mathrm{\Phi }\mathrm{NE}\varphi$ factory (LNF-INFN, Italy). Emission rates for the reaction in the mentioned nuclei are measured and compared with the few existing data. The spectra of several observables are discussed; indications of quasifree absorptions by a $\left(np\right)$ pair embedded in the $A$ nucleus can be obtained from the study of the missing mass distributions.

Figure 1

(a) Missing mass of the $K_{\mathrm{stop}}^{-}{}^6\mathrm{Li}\to n{\pi }^{-}p{A}^{\prime }$ reaction: the vertical lines mark the ${}^4\mathrm{He}$ mass value (solid), and the lower limits set for the $K_{\mathrm{stop}}^{-}{}^6\mathrm{Li}\to {\left({\mathrm{\Sigma }}^{-}p\right)}^4\mathrm{He}$ and $K_{\mathrm{stop}}^{-}{}^6\mathrm{Li}\to {\left({\mathrm{\Sigma }}^{-}p{\pi }^0\right)}^4\mathrm{He}$ (dashed) reaction selection. The cross-hatched area (A) is filled by unphysical events, the grey one (B) by events from the QF $K_{\mathrm{stop}}^{-}{}^6\mathrm{Li}\to {\left(n{\pi }^{-}p\right)}^4\mathrm{He}$ reaction, the hatched one (D) by events compatible with the presence of at least one undetected ${\pi }^0$. (b) Invariant mass of the $\left(n{\pi }^{-}\right)$ system for the $K_{\mathrm{stop}}^{-}{}^6\mathrm{Li}\to n{\pi }^{-}p{A}^{\prime }$ reaction: in the inset events selected in the grey area (B) of (a) are selected. The grey-filled Gaussian areas correspond to the ${\mathrm{\Sigma }}^{-}$ signals; see text for details. The regions denoted as E and F and delimited by dashed vertical lines indicate, in the two plots, the chosen mass window for the evaluation of the ${\mathrm{\Sigma }}^{-}$ signal integral.

Figure 2

Two-dimensional projection of the acceptance multidimensional map for $n{\pi }^{-}p$ events emitted in $K^{-}$ induced reactions, integrated over the full FINUDA target volumes.

Figure 3

Acceptance corrected distributions of some observables measured in the $K_{\mathrm{stop}}^{-}{}^6\mathrm{Li}\to n{\pi }^{-}p{A}^{\prime }$ reaction, with the invariant mass of the $\left(n{\pi }^{-}\right)$ pair selected in a 12-$\mathrm{MeV}/c^2$ mass window centered on the ${\mathrm{\Sigma }}^{-}$ mass value. (a) Missing mass of the reaction, for events selected in the E region of the total missing mass plot of Fig. 1. The grey distribution corresponds to events belonging to region F only, the hatched one to events from region D of Fig. 1 after the selection in the ${\mathrm{\Sigma }}^{-}$ mass window (G). (b) Invariant mass distribution of the $\left(n{\pi }^{-}\right)p$ system, same selections. (c) Distribution of the angle between the $\left(n{\pi }^{-}\right)$ pair and the proton, same selections. (d), (e) Momentum distribution of the ${\pi }^{-}$ and the neutron, same selections. (f) Scatter plot of the $\left(n{\pi }^{-}\right)$ system vs proton momentum. Events belonging to region F (upper right part, plus markers) and to the G sample (lower left part, cross markers) are superimposed.

Figure 4

Upper row: acceptance corrected proton momentum spectrum for all targets, for events selected in the E region of Fig. 1. The events in the grey area come from region F only, those in the hatched area from region G (see text for description). Lower row: selections as described above, $\left(n{\pi }^{-}\right)$ momentum distribution in the ${\mathrm{\Sigma }}^{-}$ mass region for all the targets.

Figure 5

Emission rates of the $K^{-}A\to {\mathrm{\Sigma }}^{-}p[A-\left(np\right)]$ semi-inclusive and $K^{-}A\to {\mathrm{\Sigma }}^{-}pX{A}^{\prime }$ inclusive reactions for several nuclei. Measurements on ${}^4\mathrm{He}$ are from [1], measurements for $A\ge 6$ are by FINUDA ([18] and present work). For the measurements described in the present paper, the error bars report the statistical uncertainty, while the grey boxes show the statistical and systematic error added in quadrature; for the other measurements, the total error is reported.