That doesn’t mean a deal on Iran’s nuclear ambitions is imminent. A new United Nations report yesterday listed three new incidents of deviousness when Iran had said its research was less advanced than it was.

Neither Rafsanjani nor anyone else is going to freeze this work lightly — and probably none will agree to do so permanently. But the longing for contact with the West suggests a deal may not be quite dead.

The funniest part of BBC Newsnight’s interview with Rafsanjani on Wednesday night was when he was asked if he thought the US was still the “Great Satan” and Britain the “Small Satan”, those iconic terms of the 1979 revolution.

The answer: “If they decide to behave in a just manner, then no, they’re no longer satans”. Nice to know; and delivered with all the authority of a cleric to determine how many devils are at large.

But his remark that he did, indeed, see signs of such “just” behaviour marks a real shift. That has been matched by most candidates, although all insist that the US must treat Iran with “dignity” and “fairness”, not words yet leaping from the lips of Washington’s conservatives.

The interest in better relations with the West is just one of the new, pragmatic themes of this campaign. Previous ones have been preoccupied with philosophy and religion, but this one has focussed on “delivery”, in new Labour’s phrase.

The decision by the Grand Ayatollah Ali Khamanei, the Supreme Leader, to allow Mustafa Moin, 54, the former Higher Education Minister, to enter the race, has magnified this change. Moin’s entry triggered a competition for the huge youth vote (71 per cent of Iranians are above the voting age of 15) and pulled conservatives towards the centre, at least in their talk.

There has been huge emphasis on job creation, and on keeping the more relaxed social rules of the past eight years. There has been very little talk about religion, to the point where some have quipped that there was more in November’s US presidential election.

Rafsanjani, a pragmatic conservative, has not criticised the religious establishment’s supremacy over secular institutions, as Moin has done. But he has been pushing privatisation, economic liberalisation and a greater role for non-governmental groups, all things likely to challenge religious control.

But Rafsanjani would hardly offer an easy resolution to the nuclear stalemate, in which Britain, France and Germany have been trying to persuade Iran to freeze its research.

Rafsanjani has stuck to the official position that Iran should continue the work for purely peaceful purposes — a line that appears generally popular with Iranians. But that may lay the ground for a clash with Europe and the US this summer.

In a tough report yesterday, the International Atomic Energy Agency listed three counts on which Iran’s work was more advanced than it had revealed.

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