It’s the multibillion dollar conundrum facing private equity firms trying to snap up Toshiba Corp.: what to do about the troubled conglomerate’s sensitive nuclear power business.

Toshiba, which had originally opposed a buyout, now plans to solicit proposals from potential investors in a drastic change in stance. The nuclear unit, which is deemed important to Japan’s national security, could be the biggest obstacle to any deal.

As PE giants including Bain Capital, CVC Capital Partners and KKR & Co. consider bids for the company, one of their biggest challenges will be devising a plan that wins government approval. According to experts, they have no easy choices.

“If a foreign fund were to buy Toshiba, it would be subject to examination by the government under the Foreign Exchange and Foreign Trade Control Law,” said Mitsuhito Taki, a lawyer specializing in corporate legal affairs at Yanagida & Partners in Tokyo. “It would be difficult to allow a foreign fund to acquire the company given Toshiba’s current business profile.”

Representatives for CVC and KKR declined to comment. Bain didn’t comment.

Toshiba’s nuclear business is involved in decommissioning Japan’s wrecked Fukushima Dai-Ichi nuclear power plant, making it hard for the government to accept a transfer of ownership to an overseas firm. The company also retrofits existing nuclear plants across the country to meet post-Fukushima safety standards and resume operations.

One solution for global PE firms would be to allow a Japanese partner take a majority stake in Toshiba, according to Taki. That would make it easier for the government approve a deal, and also reduce the potential liability for any foreign buyer.

But given that Toshiba has a market value of about $18 billion, it would also mean a Japanese buyer would have to put up at least $9 billion, an amount that would be difficult for any Japanese fund or company that might be interested, Taki said.

Another approach would be to keep the business and attempt to satisfy the requirements of the Japanese government. That, according to Seki Obata, an associate professor at Keio Business School in Tokyo, is unlikely to happen.

“I don’t think funds want that kind of trouble,” he said. “Besides, running the business while negotiating the sensitive subject with the government would be too difficult for them.”

Yet another option would be to sell the nuclear unit, either before or shortly after a PE deal. However, finding a buyer wouldn’t be easy, according to Ryuzo Yamamoto, a professor emeritus specializing in energy policy at Tokoha University in Japan’s Shizuoka prefecture.

Toshiba’s nuclear technology has fallen behind trends outside Japan, Yamamoto said. The firm lags behind overseas rivals in developing small and advanced modular reactors. And Toshiba’s boiling water reactors aren’t being considered for use in future projects.

According to Obata, compatriot Hitachi Ltd., which also has a nuclear power business, would be the only realistic buyer. Still, he argued it’s doubtful Hitachi would raise its hand because it’s also drastically reviewing its portfolio, including selling non-core operations.

Buying Toshiba’s nuclear business would “slow the speed of its own reforms,” he said.

Keiji Kojima, Hitachi’s president, was asked whether he was interested in acquiring Toshiba’s nuclear business at a press conference on April 28.

“I have almost no such thoughts about it,” he said.