When Pieter Botha emerged from the double doors of the parliamentary building as the new chief of the ruling National Party and therefore South Africa's new prime minister, no one was surprised.

But clearly, not everyone was satisfied.

"We want Pik We want Pik!" sections of the crowd began to chant, referring to the unsuccessful candidate for party leader, Foreign Minister Roelof "Pik" Botha.

For a new South African leader to be greeted by demands for one of his rival candidates is nothing short of remarkable in white politics here. It was one more indication of the public interest in this premiership race unseen in the past 30 years of continuous rule by the Afrikaner-dominated National Party.

According to most accounts, tha choice occasioned by the resignation of John Vorster also provoked the most venomous power struggle in the National Party's recent history.

"Unually the Afrikans newspapers just list the candidates and say nothing more: They never admit there's any political infighting going on during the race," said one Afrikaner observer. "But this time, they are openly talking about the competition and the back-stabbing."

One of the losers, Black Affairs Minister Connie Mulder admitted publicly yesterday that he had been hurt by the disclosure of mismanagement in the Information Department he used to head.

"I have no doubt about that," he said. Rumors were rife before the election that there would be more revelations in the future.

Both the public interest in this election and the party in fighting appear to indicate that the top job in this country has become more critical as South Africa experiences increased stresses. The black riots and the growing ostracization of South Africa from the world community seem to have convinced many whites that fundamental and faster changes must come.

Many of them were hoping that the National Party would break with its traditional pattern of choosing its most conservative man to lead it. They especially feared Defense Minister Pieter Botha whose impulsiveness and propensity for military solutions earned him the sobriquet of Piet Wapen - "Pete the Weapon."

Pik Botha, who once said he was not prepared to die for a discriminatory sign in an elevator, appeared to be the popular choice of the white man in the street - both English and Afrikaner. But his popularity was translated into party caucus votes and Pik Botha mustered only 22 "ayes" in the 172-member body.

For the National Party, choosing a leader is an internal affair and the causus members, as one of them put it to a local newspaper, "will not be influenced by public opinion." Rather, the selection depends on who knows the party machinery and who will keep the party united.

Pieter Botha, who has devoted the past 42 years to National Party politics, was the natural choice.

Initial reaction to Pieter Botha was summed up in the headline of the Cape Times newspaper - "Toughness But No Change Yet."

It was the Johannesburg Star however, that raised an interesting point about the new prime minister. "What is not so well-known is that he has forged a defense force led by a cadre of young officers whose stated, collective view is that South Africa's problems cannot be solved militarily. Instead, they should be solved by political solutions acceptable to all the country's people . . . It . . . does the minister of defense credit."

It is generally believed that the South African defense force holds more moderate views than the overall political establishment, but whether that is to the credit of Pieter Botha or despite him, remains to be seen.