Western Europe's Communist showcase is showing cracks, a result of the party's effort to broaden its base toward the Catholic center. This is happening as U.S.-Soviet detente has soured and Italy's working class has turned militant.

"Carter's human-rights talk isn't helping Soviet dissidents," a non-Communist leader told us, "but it surely is making life hell for the Communists here."

As long as the U.S.-Soviet dialogue was progressing smoothly, as during the Nixon-Ford-Kissinger years the Italian Communist Party (PCI) basked in the warmth of detent. But today it is a posture of embarrassed ambiguity, compelled to make odious choices that expose and widen contradictions between a "democratic" Western party (governed internally by authoritarian centralism) and one tied to the Communist center in the Kremlin.

An equally insoluble problem afflicting the PCI is the due bills to its working-class base. These IOUs stem from the PCI's courtship of the Catholic center and its self-portrait as the salvation of an Italy torn by violence in the streets, raging inflation, massive deficit spending and group hatred. That self-portrait is the PCI's pass into the "historic compromise" of coalition government with the ruling Christian Democrats.

With a steely eye on that still-distant goal, PCI leaders have opened a widening gap, between themselves and the 1,712,084 card-carrying party members (down by 6,000 from a year ago) "who want to behave like Communists," in the words of a political operative.

This explains the phenomenon of violence against PCI leaders by university students (radicalized by the incredibly inept education policies of the Christian Democrats) and by workers infuriated at the PCI's tentative bourgeois approach to curing inflation.

If the Christian Democrats succeed in gaining formal support of the PCI for a "common program" - limited to public order, education and the economy - these contradictions between the PCI leadership and its ranked-and-file may enlarge, further postponing the party's payment of those IOUs to its natural working-class and student constituency.

"The universities are a disaster," Benedetto Craxi, head of the Socialist Party, told us. "They have become a farm for the unemployed, tens of thousands of them, creating an intellectual proletariat with revolutionary visions. Not only does the PCI not speak for them, they are badly hurting the PCI."

As for the party's working-class base, Giorgi Benevnuto, head of the third-largest union, told us that "disillusioned workers are paying too high a price for the historic compromise. No PCI leader could risk making a speech at the Alfa-Romeo auto factory today. He would be driven off."

Some politicians here are convinced that internal debate over the party's predicament extends deep into its 36-member directorate, perhaps endangering Secretary General Enrico Berlinguer, sponsor of the party's courtship of the Catholic center and the man held accountable for the present dilemma.

Berlinguer recently made four speeches in little more than two weeks - far more than usual. One was in an industrial suburb of working-class Naples, but it failed to stop the flood of defections in last month's municipal election, which defeated the Communist incumbent and cost the PCI a 12-point drop in its vote from 1976.

Likewise, the unusually precise pro-Soviet speech of Armando Cossuta, a leader of the PCI left wing, sounded like a complaint and a call to greater militancy. While proclaiming "complete autonomy" from Moscow, Cossutta said that "it is unthinkable . . . for a party of workers, a party like ours, to break its ties of solidarity with the Communist Party of the Soviet Union and to go in for anti-Sovietism."

It would be a mistake to make too much of still-slender evidence of trouble in Western Europe's most successful Communist Party, but the agony of pleasing two souls at the same time could mark a turning point. One soul is rooted in Moscow, the order is striving for credibility within the free political traditions of the West.

Compounding the agony is the descent of detente into a twilight zone. the PCI's future, however, may depend not so much on resolving its split personality, however debilitating, as on the economic and political chaos of Western Europe - particularly France and Italy herself.