Further ROSAT measurements of the period of 4U 1820-30

We have made two new observations of 4U 1820-30 with the ROSAT position sensitive proportional counter (PSPC). The measurements do not provide further evidence for a secular period decrease of this source. Instead, after inclusion of our new arrival time measurements the significance of the orbital period derivative drops (from 5.5 to 4.6 sigma), its best-fit value decreases (to P-dot/P =(-5.3 +/- 1.1) x 10(exp -8)/yr) and the formal probability that statistical fluctuations have caused the observed P-dot increases to 0.5% (from 0.003%). We detect light curve changes that are large enough to be the cause of some (or all) of the period changes seen in 4U 1820-30, but not large enough to explain the discrepancy of the observed period derivative with that theoretically predicted. We explore the possibility that the secular period change observed during 1976-1991 could have been dominated by random or systematic changes in the position and shape of an occulting bulge on the disk rim and conclude that phase shifts caused by this mechanism could in principle explain the discrepancy entirely.