Antiproton annihilation on light nuclei at very low energies

Recent experimental data obtained by the OBELIX collaboration on $\mathrm{\bar{p}}$D and $\mathrm{\bar{p}}$ $^4$He total annihilation cross sections are analyzed. The combined analysis of these data with existing antiprotonic atom data allows, for the first time, the imaginary parts of the S-wave scattering lengths for the two nuclei to be extracted. The obtained values are: $ {Im } a^{sc}_0 = [- 0.62 \pm 0.02 ({stat}) \pm 0.04 ({sys})] { fm}$ for $\mathrm{\bar{p}}$D and $ {Im } a^{sc}_0 = [- 0.36\pm 0.03({stat})^{+0.19}_{-0.11}({sys})] { fm}$ for $\bar{{p}}\:^4$He. This analysis indicates an unexpected behaviour of the imaginary part of the $\mathrm{\bar{p}}$-nucleus S-wave scattering length as a function of the atomic weight $A$: $| {Im } a^{sc}_0|$ ($\mathrm{\bar{p}}$p) $>$ $| {Im }~a^{sc}_0|$ ($\mathrm{\bar{p}}$D) $>$ $| {Im }~a^{sc}_0|$ ($\mathrm{\bar{p}}^4$He)