Astronomers work in "Julian days" (a date is 'Julian day +23143214' not 'March 22nd, 11 CE') but I do not know why historians don't convert to Gregorian for events far too early to have been dated according to the Roman calendar. But the following article explains early on that it uses Julian days:
Leo Depuydt, 'The Time of Death of Alexander the Great: 11 June 323 B.C. (–322), ca. 4:00–5:00 PM.' Die Welt des Orients, Bd. 28 (1997), p. 124 n. 23 wrote:
In a discussion of the date of the Battle of Gaugamela (1 October 331 B.C.), in which Alexander defeated Darius III, Hauben (CdE 67, 149 [see note 2]) notes the difficulty of referring to 13 Ululu, with Bernard (BCH 114, 516 [see note 1]), as the "expected" Babylonian date of the lunar eclipse of the evening of 20 September 331.
As Hauben rightly notes, one expects 14 Ululu. In fact, the cuneiform Diaries do give 14 Ululu. Lines 1' and 2' and the beginning of line 3' of tablet BM 36761 + 36390 are as follows (Sachs/Hunger, Astronomical Diaries ..., p. 177):
2' The 13th, moonset to sunrise: 8?...[...]
3' [... lunar] eclipse, in its totality covered, (etc.)
Only illegible traces remain of line 1'. "The 13th" in line 2' must mean "daytime of the 13th." The observation in line 3' must therefore pertain to a night following day time of 13 Ululu, because lunar eclipses are visible only at night. This following night cannot be that of 13 Ululu, because night always precedes daytime in the astronomical Diaries. That the night in question is that of 14 Ululu, and not a later night, is certain because the night of 15 Ululu is described from line 5' onward
(So an evening eclipse would be on the same Julian day as the 13th, but the next Babylonian day).
Leo Depuydt, 'The Time of Death of Alexander the Great: 11 June 323 B.C. (–322), ca. 4:00–5:00 PM.' Die Welt des Orients, Bd. 28 (1997), pp. 126, 127 wrote:
According to Plutarch's Life of Alexander (75.6), Aristoboulos reports that Alexander died on Day "30" of the month of Daisios. It has long been known that the last day of Greek lunar months is always called Day 30, whether the month has 29 days or 30 days. In 29-day months, number 29 is skipped; Day 30 follows Day 28 and is in effect the 29th of the month. However, it is not certain whether Daisios had 29 or 30 days in 323 B.C. It is not because the parallel Babylonian month Aiaru had 29 days (see section 1) that Daisios should too. Daisios belongs to a different lunar calendar. It is therefore difficult to derive anything definite from Aristoboulos's date. It can only be interpreted in light of the Babylonian date. It has no independent value as proof.
Daisios is the name of a Greek-Macedonian lunar month. In recent years, there has been a major paradigm shift in the theory of the beginning of the Greek month and day. There used to be no doubt that the Greek month began with first crescent visibility, like the Babylonian lunar month. But it seems now much more likely that it began earlier, with last crescent visibility. In fact, according to this new paradigm, it is altogether statistically typical for a Greek lunar month and a corresponding Babylonian month to begin in the morning and the evening respectively of the same day. Accordingly, the day number of an event that occurred during
daytime would be typically one higher in the Macedonian calendar than in the Babylonian calendar. Since a new Babylonian lunar month, Simanu, began in the evening Alexander died, it would be statistically normal for his death to have occurred on Day 1 of the Greek lunar month.