Even as Israel and the Palestine Liberation Organization (PLO) continue to trade blows across the Lebanese border, the question of how deeply Israel should be involved in the Lebanese conflict is being debated within the Israeli government and media.
The debate has arisen against a background of a month of hostilities in northern and southern Lebanon -- the most dangerous time, according to observers here, since Israel moved thousands of troops into Lebanon in 1978.
So far, two themes have emerged:
* While some generals and members of the Israeli government would like Israel to intervene military on behalf of the Lebanese Christians who are fighting Syrian troops in northern Lebanon, such aid seems unlikely at present because of the dangers of an escalated war.
* But Israel intends to continue and perhaps even expand its policy of attacking PLO bases in south Lebanon at will, and of full backing for the anti-PLO Christian militia of Lebanese Maj. Saad Haddad along the Lebanese Israeli border.
Debate was sparked not by Israeli policy in south Lebanon -- which has wide public backing because it appears to have checked almost all PLO terrorist attacks across the Lebanon-Israel border -- but by Syria's massive shelling of the Christian Lebanese town of Zahle since early April.
Prime Minister Menachem Begin repeated Israel's "moral commitment" to the Lebanese Christian, Extending it to the whole country. Senior Israel military sources told the press that Israel could not afford destruction of Lebanese Christian forces, lest this give the Syrians and PLO total freedom of movement up to Israel's border.
Israel's role in aiding the Christians in the north is not completely clear. The london Daily Telegraph reported on April 13 that Israeli chief of staff Rafael Eitan had visited the headquarters of the Christian militias in Juniye in northern Lebanon at the beginning of April, just before the Syrian shelling of Zahle began. Senior Israeli military sources then admitted for the first time that Israel was supplying equipment to the Christians of Lebanon in the north, while denying that they had sent military advisers or ran training bases there.
However, the most controversy was stirred by an interview in the Israeli press last week with Maj. Gen. A. Bengal, chief of the Israeli northern command. Bengal asserted that Israel should help the Christians in the north take over the whole of Lebanon.
This interview was cleared by the Army and has not been disavowed by any government official, nor by the Israeli chief of staff, who himself expressed hawkish, though more restrained, views of Lebanon in an interview the same day.
The pro-Labor Party daily, the Jerusalem Post, complained that this silence would "reenforce suspicion . . . that some government leaders are intent on involving Israel in a fine little war in Lebanon on the eve of the knesset [ parliament] elections."
Hawkish Knesset Foreign Affairs and Defense Committee chairman Moshe Arens gave an interview warning that Israel would take direct military action against Syria if it did not stop attacking Lebanon's Christians. Israeli analysts wrote that the aim of such a war would be to destroy the PLO infranstructure in Lebanon and damage Syrian forces.
But analysts here believe that, for the time being, the Israeli government will not intervene directly in the north. They say that, while Syria is isolated in the Arab world, Israeli military intervention would reunite the fragmented Arab world around Syria.
Moreover -- and they say this is critical -- while the Reagan administration has no sympathy to the pro-Soviet PLO and Syrian leadership, it would not welcome a war that might involve the Soviets. Such a war might also threaten Israeli-Egyptian relations on which American hopes for a new Mid east strategic realignment rest.