A poll of southern voters shows Jesse L. Jackson leading his five Democratic presidential rivals but trailing "don't know," while Vice President Bush holds a fat lead on the Republican side.

The Atlanta Journal and Constitution conducted their second Southern Primary Poll of voters in 12 states last month.

Jackson leads with the support of 27 percent of the Democratic respondents. But 6 percent chose none of the six candidates and 29 percent said "don't know" or did not answer, the papers report in today's combined editions.

Trailing Jackson are Sen. Albert Gore Jr. (Tenn.), with 13 percent; Massachusetts Gov. Michael S. Dukakis, 9 percent; Rep. Richard A. Gephardt (Mo.) and Sen. Paul Simon (Ill.), 5 percent each; and former Arizona governor Bruce Babbitt, 3 percent.

Sen. Joseph R. Biden Jr. (Del.), who withdrew while the poll was being taken, was at 3 percent before his name was dropped.

On the GOP side, Bush leads with the support of 46 percent of Republican respondents. Trailing him are Sen. Robert J. Dole (Kan.), 19 percent; former television evangelist Marion G. (Pat) Robertson, 10 percent; Rep. Jack Kemp (N.Y.), 7 percent; former secretary of state Alexander M. Haig Jr., 6 percent, and former Delaware governor Pierre S. (Pete) du Pont IV, 2 percent.

Nine percent of the Republican respondents said "don't know" or did not answer; 2 percent chose none of the six candidates.

The poll was conducted Sept. 18-28 for the newspapers by the Roper Organization among 6,452 potential voters in Virginia, North Carolina, South Carolina, Florida, Georgia, Tennessee, Kentucky, Alabama, Mississippi, Louisiana, Arkansas and Texas.

Results were statistically weighted to conform to age, sex, state and other factors; the margin of error is 2 percent.

Pollsters also asked Democratic respondents their choices if five other candidates were in the party's field: Biden, former senator Gary Hart (Colo.), New York Gov. Mario M. Cuomo, Sen. Sam Nunn of Georgia and Rep. Patricia Schroeder (Colo.). The latter three have said they will not run.

Hart led with 27 percent despite his withdrawal amid allegations of an affair with a Miami model. Next were Cuomo, at 17 percent; Nunn, 14 percent; Jackson, 11 percent; Gore, 5 percent; Dukakis, 3 percent; Gephardt and Schroeder, 2 percent each, and Simon, Babbitt and Biden, one percent each.