There is a rhapsodic moment in Pulitzer Prize-winner Richard Rhodes’s new play, “Reykjavik,” when, after days of negotiations over nuclear weapons between then-U.S. President Ronald Reagan and Soviet Union President Mikhail Gorbachev, Reagan suddenly drops a bomb of his own.

“Why don’t we get rid of them all?” Reagan asks. “Can we agree, at the end of ten years, to nuclear abolition?”

For a moment, the two men come together, shoulder to shoulder, at the front of the stage. They look up and out into the audience, as Reagan envisions the two of them meeting again as old men, drinking champagne as they watch the world’s last two nuclear missiles being ground into scrap.

But in the play, as in 1986, when the Reykjavik Summit actually occurred in the capital city of Iceland, talks between Reagan and Gorbachev ultimately collapse.

Those few minutes, however, represent the feelings of both hope and regret that characterize “Reykjavik,” which was presented Tuesday night at Cemex Auditorium.

The hour-long production — featuring just Reagan, played by Drama and Classics Professor Rush Rehm, and Gorbachev — is notable for staying close to the transcripts of the famous event. Rhodes, who is affiliated with Stanford’s Center for International Security and Cooperation (CISAC), previously won a Pulitzer Prize for his 1987 book, “The Making of the Atomic Bomb.”

“I was going through the transcripts of the Reykjavik summit in 2006, and it was intriguing to see [the Soviet and American transcripts] side by side and see what the American side left out,” Rhodes said after the performance. “Particularly, Reagan’s move to eliminate everything [all nuclear weapons] was excised.”

The play seeks to show a fuller picture of both leaders. Reagan is shown to be charismatic and good-hearted, but forgetful. For much of the summit, he reads his arguments off note cards and repeatedly mentions how, in the aftermath of World War I, Europe’s great powers agreed to ban chemical weapons, but “held onto their gas masks.”

Gorbachev is depicted as the more intelligent and focused of the two, but also spends time talking about his youth, which was spent working on a collective farm.

Both he and Reagan find common ground in having “come from nothing.” Such conversations take place when the negotiations have grown too tense. Reagan describes his years as a lifeguard or taking care of his alcoholic father as a child.

“Something that gets lost in reading history texts is the feeling and emotion of the event,” said Ravi Patel ’13, an international relations minor who attended after learning about the summit in some of his classes. “All I really knew was what was accomplished during the meeting. I didn’t know the tensions involved in the negotiating process,” Patel added.

The play demonstrates some of those tensions. For all the friendly feeling generated by swapping childhood stories, the two leaders cannot bring themselves to trust one another.

In the performance, the heart of the disagreement between the two men is Reagan’s Strategic Defense Initiative (SDI), dubbed “Star Wars” by the media. The initiative would have established an American space-based missile shield to prevent against nuclear attack.

“Damn it, Mikhail, SDI is for defense,” Reagan says. “Why do I have to keep saying that? And we’ll share it. You have my word.”

“You don’t even share your milk machines with us!” Gorbachev retorts.

The play suggests Reagan’s famous stubbornness, something which Tom Woosnam, a high school physics teacher and member of the audience, said he both admired and disliked.

“I was not convinced that Reagan’s stubbornness was based in rationality,” Woosnam said. “[But his] motivation was to protect his country.”

Everything in Rhodes’s play — moments of levity included — points to this fundamental mistrust in both leaders. When negotiations have failed at the end of the play, each character blames the other.

“You just don’t get it,” Reagan says. “How am I supposed to trust you?”

“I don’t know what else I could have done!” Gorbachev replies.

“Well, I do” Reagan says. “You should have said ‘yes.’”

“Reykjavik” will be performed again tonight at 7 p.m. in Cemex Auditorium.