Anybody could pass into Ukraine, one of the fighters said, but guards on the Russian side were not letting weapons through because that would be “an act of war.”

Carol Saivetz, a Russian specialist for the Security Studies Program at the Massachusetts Institute of Technology, said the switch from reliance on local eastern Ukrainian men to a force with more Russians started last month. It is almost certainly proceeding with the blessing and backing of the Kremlin, she said, “even if the Russians are indeed volunteers rather than serving military men.”

She added, “Putin has so stirred up Russian nationalism, and with the propaganda barrage that there are fascists in Kiev, it’s not inconceivable that some lost souls will sign up to serve.

“It’s also clear that Russia has been assisting them in their efforts,” she said, “and now, as it becomes an increasingly professionalized force, there have to be questions about how much support Russia is giving. My bet is a lot.”

Not everything, certainly not everyone, coming into Ukraine has to cross at a checkpoint. Outside the official crossing areas, the borderlands are a porous landscape of wheat fields, oak forests and innumerable ravines and country roads, crisscrossed by militants who can easily escape detection.

The route to the frontier from the Russian side leads across the Don Steppe, an area known in czarist times as the “Wild Field.” It is a rural and agricultural panorama, where ripe winter wheat blows in the breezes, interspersed with dense forests and tiny villages.