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We obtain good description of annihilation cross sections data of Barbina {\\it et al.} [Nucl.~Phys.~A {\\bf 612}, ~346~(1997)] and of Astrua {\\it et al.} [Nucl.~Phys.~A {\\bf 697},~209~(2002)] which exhibit an interesting dependence of the cross sections on the $p_{\\rm lab}$ as well as on the target atomic mass number $A$. 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