THE declared purpose of the attack on Libya was to punish Col. Muammar Qaddafi for his past terrorist deeds and deter him from doing more of the same. Whether he has been ``punished'' is doubtful. Most reports from inside Libya suggest that his popularlity at home, which had been sinking steadily, has now been restored. His critics at home have been silenced. In the Arab world, all have sent to him their sympathy and to Washington their disapproval. Saudi Arabia, America'a closest friend and supporter among the Arabs, was firm in its expression of disapproval.
Lisa Anderson, a Columbia University expert on Libya and Tunisia, thinks that without the attack, Colonel Qaddafi would probably have been overthrown within a few months. With the attack, she thinks his tenure is extended, opposition elements friendly to the United States have been humiliated, and those unfriendly have been strengthened.
If Professor Anderson is correct, Colonel Qaddafi is a gainer, not a loser, from the American strike.
The second purpose was to deter further acts of terrorism. So far, one American and two Britons have been ``executed'' in Lebanon in declared ``reprisal.''
An attempt to sabotage an El Al Israeli airliner at Heathrow Airport, London, has been foiled, but the attempt was made. An American embassy staff technician in Khartoum, Sudan, was wounded. All nonessential United States embassy people have been evacuated out of the Sudan. American embassies and American business offices and personnel throughout the Arab world, and beyond, have been put on the alert.
Terrorism aimed at the US has not been ended by the strike on Libya. More has occurred, and more is expected.
This leaves President Reagan with a new problem. He has declared that if terrorism does not end, he will take further punitive action.
What else is to be done? To repeat what happened a week ago would only intensify the results of that operation. It would mean more rallying of Arabs to Colonel Qaddafi and arouse more resentment against the US throughout Western Europe.
The neoconservatives in the Reagan political surroundings are urging him to bomb the oil docks from which Libyan oil flows to Western Europe. That would impose an economic hardship on Libya, but also on Western Europe, and would merely intensify the wave of disapproval that has swept through the allied countries in the wake of the raid on Libya.
British Prime Minister Margaret Thatcher supported the original raid of last week by allowing the use of British airfields. It is doubtful that she would dare allow any British military base to be used in a second strike. The popular and political reaction in Britain to her action of last week has been almost entirely negative.
This particular round in the story of US relations with Colonel Qaddafi began with the sortie of the US Sixth Fleet into the Gulf of Sidra. The colonel sent out two patrol boats to a challenge. They were sunk. Qaddafi retaliated with a bomb in a discoth`eque in West Berlin. One American was killed. President Reagan responded with the attack on Libya. Arab ire is resounding in many places. This can go on, and on.
But we come back to the question of what President Reagan can do next. He has promised further action if there are further acts of terrorism, but if it is military it will only add to the estrangement of Western Europe, the radicalization of the Arab community, and benefit to Moscow.
Largely unnoticed so far is that the real, long-term net gainer from any American attack on any Arab is -- Moscow.
All Arab countries are anticommunist and deeply suspicous of Moscow. But all now find themselves looking toward Moscow for protection against the US. Syria, probably the main source of action by Palestinian ``terrorists,'' is safe. Russia's protective arm is on its shoulder.