Phase and density dependence of the delayed annihilation of metastable antiprotonic helium atoms in gas, liquid, and solid helium

Systematic studies of the phase and density dependence of the delayed annihilation time spectra of antiprotons (DATS) in gaseous, liquid, and solid helium have been performed using the low energy antiproton ring at CERN. The results show a small but significant dependence of DATS on the phase and density of the helium medium. The average lifetime of antiprotons (Tₐᵥ) in gas at 10--30 K was found to be 4.03±{}0.02 {μ}s. In liquid helium Tₐᵥ decreases with density from 3.0 {μ}s at 1 bar to 2.5 {μ}s at 60 bars, while in solid helium its value is 2.14±{}0.03 {μ}s, 20% shorter than that in liquid helium of the same density. There is no change of DATS betweeen normal 1-bar liquid and superfluid helium. An isotope effect between ⁴He and ³He similar to the one previously observed in the gas phase has also been found for liquid helium. All the data can be fitted fairly well with a simple three-level chain decay model with describes the general structure of DATS, characterized by downaward curving behavior on a logarithmic scale at later times and by the presence of a short-lived component. No delayed annihilation was observed in lithium.