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We study the dependence of the cooling of isolated neutron stars on themagnitude of the $3P_2$ neutron gap. It is demonstrated that our ``nuclearmedium cooling'' scenario is in favor of a suppressed value of the $3P_2$neutron gap.Comment: 18 p., 12 figs., extended version of astro-ph/0501678, accepted in  A&

Medium effects in cooling of neutron stars and the 3P$_\mathsf{2}$ neutron gap