The Mandelbaum Gate by Muriel Spark

When Barbara Vaughan's fiancé joins an archaeological excursion to the Dead Sea Scrolls, she takes the opportunity to explore the Holy Land. It is 1961, and the nation of Israel is still in its infancy. For Barbara, a half-Jewish Catholic convert, this is a journey of faith, and she ignores warnings not to cross the Mandelbaum Gate from Israel into Jordan.