By Paul Rincon
Science reporter, BBC News
Mr Litvinenko was a former KGB agent
The poisoning of the former Russian spy Alexander Litvinenko would have required considerable scientific know-how, according to experts.
Mr Litvinenko's death on 23 November was linked to a "major dose" of radioactive polonium-210 found in his body.
Traces of radiation have since been found at five locations around London, including a sushi restaurant and hotel visited by the Russian.
But the radioactive substance implicated is as difficult to obtain as it can be to detect.
Polonium-210 occurs naturally in the environment and in people at low concentrations. But acquiring enough of it to kill would require individuals with expertise and connections.
Experts estimate that less than a microgram (one millionth of a gram) of the radioactive substance could have been responsible for Mr Litvinenko's death.
Higher doses than that would have killed the former KGB officer more quickly.
Polonium-210 emits intense radiation in the form of alpha particles, but these are unable to travel very far.
Professor Nick Priest, one of the few UK scientists to have worked with polonium-210, told BBC News that these particles penetrate about 60 micrometres through biological tissue - equivalent to the thickness of a few cells.
But because alpha particles deposit their energy in a rush, they can cause terrible damage to those cells if they get inside the body through swallowing or inhalation.
Polonium is also particularly harmful because it is taken up by a broad spread of the body's tissues, whereas other radioactive elements might bind to certain tissues - such as bone - preferentially.
"If you had it in a glass or tin vessel, you wouldn't be able to detect it outside. Which makes it rather ideal as a poison," said Dr Frank Barnaby, a nuclear consultant to the Oxford Research Group.
But once that container is open, polonium-210 particles have a tendency to creep out and contaminate the surrounding environment.
Professor Priest, now at Middlesex University, said the polonium could, in theory, have been dissolved in a liquid: "It could have been any volume from a litre down to a few drops," he said. Equally, it could have been bound to another material such as chalk.
The amount of polonium thought to have been used was hardly enough to see with the naked eye.
Radiation has been found at several sites around London
There are at least three ways to make polonium-210. It can either be extracted from rocks containing radioactive uranium, produced in a nuclear research reactor, or separated chemically from the substance radium-226.
The element was discovered in 1897 using the extraction method. Marie Curie isolated polonium from the uranium-rich mineral pitchblende, later naming it after her native country of Poland.
But according to Nick Priest, this method could not have produced enough of the material to kill Alexander Litvinenko.
"To produce the amounts required you would need to use a nuclear reactor," he told BBC News.
Nuclear research reactors are used primarily for the production of radioisotopes (the radioactive forms of elements in the periodic table) and differ from the power reactors used to generate electricity.
Professor Priest has worked for the UK's National Radiological Protection Board - now part of the Health Protection Agency - and the United Kingdom Atomic Energy Authority (UKAEA) at Harwell.
He says the most likely way of producing the required polonium-210 is to bombard the element bismuth in a reactor with neutron particles in order to change it into a radioactive form called bismuth-210.
Contact with carrier's sweat or urine could lead to exposure
But polonium-210 must be ingested to cause damage
Radiation has very short range and cannot pass through skin
Washing eliminates traces
This undergoes radioactive decay, yielding polonium-210 and a smaller amount of radioactive thallium-206 as "daughter products".
The polonium then needs to be chemically separated from bismuth.
Klaus Luetzenkirchen, director of nuclear chemistry at the Institute for Transuranium Elements in Karlsruhe, Germany, said polonium could be chemically separated from radium-226. But he added that this would need sophisticated lab facilities because the latter substance produces dangerous levels of penetrating radiation.
Some experts estimate the number of reactor facilities around the world capable of producing polonium-210 is in the region of 40-50. But others think the number could be much lower.
The available evidence points to a source for the poison outside the UK.
These include several facilities throughout the former Soviet Union, along with other countries such as Australia and Germany.
Alpha particles are stopped by a sheet of paper and cannot pass through unbroken skin
Beta particles are stopped by an aluminium sheet
Gamma rays are stopped by thick lead
"There is only one reactor in the United Kingdom that could produce it, and I'm pretty sure they didn't," said Nick Priest. He explained that it was unlikely that polonium-210 could be produced in a reactor without administrators knowing about it.
Alternatively, the radioactive substance could have been purchased from a commercial supplier. Chris Lloyd, a radiation protection adviser, said polonium-210 was used commercially in devices that control static electricity.
The polonium in anti-static devices is not in a form that can be readily administered as a poison. It would be difficult - though not impossible - to retrieve.
Polonium, along with the element beryllium, was once used as a neutron trigger in atomic bombs produced by the US, the UK and Russia. It was also used as a heat source in the Soviet Lunokhod Moon rovers during the 1970s.
The Litvinenko affair also placed the black market trade in radioactive materials under renewed scrutiny.
Since 1995, the UN's nuclear watchdog, the International Atomic Energy Agency (IAEA), has maintained a database on the illicit trafficking of nuclear and radioactive materials.
As of last year, the database contained 827 confirmed incidents. Of these, 224 incidents involved nuclear materials and 516 involved radioactive materials.
The IAEA said it had not received confirmation of polonium finding its way into this underground market, but there have been a number of unconfirmed reports.
On Tuesday, Russia's nuclear chief rejected suggestions that the polonium-210 linked to Mr Litvinenko's death could have been stolen from the country.
Sergei Kiriyenko said Russia exports 8g of polonium-210 each month, all of it to the US. Exports to Britain ended about five years ago.
While he stressed the tough export controls on polonium-210, the nuclear chief said the final products in which polonium was used worldwide were outside official controls.
In theory, it might be possible for investigators in the Litvinenko case to trace the origin of the polonium-210. But this would probably depend on finding trace amounts of other substances.
"In general, different types of [radioactive] materials pick up characteristics during their production," said Ian Hutcheon, an expert in nuclear forensics at the Lawrence Livermore National Laboratory in Livermore, California.
"If you have samples of the material, you can gather information about where they were or were not produced by analysing trace constituents."
He told BBC News: "There aren't many places around the world that make polonium. I was able to find only two or three, so I don't think we are looking at 50 different places."
Klaus Luetzenkirchen said: "If there was only polonium-210 and nothing else then I presume it would be extremely difficult - if not impossible - to trace it back.
"All you have is a certain kind of element or isotope, which, in principle, could come from anywhere."
Even if the origin of the polonium could be tracked down, commentators point out that there was no guarantee it would lead to a suspect, especially if the material was stolen.
Professor Alistair Hay, from the University of Leeds, told BBC News 24 that those responsible had carefully chosen polonium-210 for its toxicity and difficulty of detection.
"Where the substance has come from is highly important, of course, and that's now the job of Scotland Yard," he said.