Two dabs of green police paint mark the spot where Marta Russo fell. On a nearby wall hangs a marble remembrance plaque. Below it a cluster of grubby soft toys and some bouquets of wilted mimosa form an impromptu shrine. A note in childish handwriting reads: "Marta, we'll never forget you."

One sunny May morning in 1997, Marta and her fellow law student Jolanda Ricci were strolling along the broad alley that divides the Law and Political Science faculties at Rome's main university. Suddenly, Marta slumped to the ground.

At first Jolanda thought she had fainted. As she desperately tried to revive her friend, a passersby called for help. But Marta's skull had been pierced by a .22 calibre bullet. She died four days later without regaining consciousness. The 22-year-old was shot in broad daylight, at the centre of one of Italy's largest and most prestigious academic centres. The area was bustling with students, yet no one saw the assassin. Few even heard the fatal shot. Only later did some witnesses recalled a dull thud like the cracking of a plastic bottle.

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Marta Russo lived at home with her parents in a southern Rome suburb, was in her second year in law school at La Sapienza University, drove a second-hand Fiat, had a regular boyfriend, was sporty and social. As Marta's father Donato pleaded for anyone who knew anything to come forward, police tried desperately to understand why she had been killed. There was no history of drugs, no jilted lovers, no particular political or religious convictions. Everyone described Marta as terribly normal.

In a country accustomed to mafia slayings and terrorist murders the death of Marta Russo nevertheless struck a deep chord. Campus killings were associated with America, a firearms culture and the breakdown of social values. At La Sapienza panic set in. Could a serial killer be at large in a seat of learning frequented by more than 100,000 young people each day?

Left- and right-wing students abandoned their traditional antipathy, to protest together. Anxious parents urged their children to wear motorbike helmets until they were inside the lecture halls. Tens of thousands of students turned out for Marta's funeral, along with the Prime Minister and numerous dignitaries. Even the Pope sent a message of condolence. The authorities promised that justice would be done, the Rome police chief vowed that his men would find the killer, and pressure from the media was relentless.

Nearly two years on, the trial of Marta's alleged killers is drawing to a close in a high-security court near Rome's Olympic stadium. But rather than setting her ghost to rest, the trial is raising more questions than it solves.

Finding the killer was always going to be difficult. The Italian press indulged in theories that ran from a settling of scores between cocaine dealers to a new terrorist destabilisation strategy. All the police had to go on was the location of the killing - a walkway between two four- storey buildings - and its time: a passerby called an ambulance on his cellphone at 11.42am.

Initial suspicions focused on a cleaning company with offices just yards from the murder scene. Among the workers were several arms enthusiasts, and modified toy pistols were found on the premises. But none of the weapons were compatible.

Attention then shifted to the ground-floor bathrooms in line with where Marta fell. But searches there revealed no clues. Identifying who was there on a busy day was impossible. No ID cards are needed at the entrance to La Sapienza so a killer from outside could easily pass unnoticed among students or workmen. Then there was the hypothesis of mistaken identity. Police thought the real target might have been Marta's friend, Jolanda, whose father is a senior official in the prison service and had been in charge of Rome's maximum security Rebibbia prison. There was even a possible mafia connection. A young Sicilian woman, whose father had rebelled against mafia demands for protection money, said she believed mob hitmen had mistaken Marta for her. They were of similar height, and both were law students and blonde.

The breakthrough came on 19 May 1997, 10 days after the crime. Forensic tests revealed chemical components compatible with gunpowder on the window ledge of Room Six, a reading room in the Department of Legal Philosophy. An experiment with laser rays on the trajectory of the bullet also pointed to Room Six.

Around 25 people regularly went there to use the computers or consult weighty reference books. All department employees were brought in for questioning. The investigators were expecting full co-operation, given that the department was dedicated to the study of legal principles. They couldn't have been more wrong.

Rome's police chief spoke of a climate of "omerta", the term for mafia silence. Those questioned were reticent and appeared more worried about protecting their jobs and the department's reputation than helping find the killer. This was confirmed by a telephone tap on the department head, Bruno Romano, who was heard discouraging his staff from giving evidence. A respected and popular academic, Romano was briefly arrested for obstructing justice, charges that were later dropped. The impression arose that there was a collective desire to keep the spotlight off Italy's much criticised university system.

Despite the lack of co-operation, the police got lucky. Telecom records showed a phone call had been made in Room Six at 11.44am, just two minutes after Marta was shot. The caller was Maria Chiara Lipari, assistant to the head of department. A self-assured young woman, daughter of a former Christian Democrat senator, Maria Chiara was considered excellent witness material. At first she recalled "at a subliminal level" only that there were other colleagues in the room, but not who they were. After lengthy prodding she put names to faces. As she entered Room Six she saw the department secretary, Gabriella Alletto, and an assistant librarian, Francesco Liparota: two researchers, Giovanni Scattone and Salvatore Ferraro, were leaving in a great hurry. At first Gabriella Alletto denied she'd been near the reading room that morning. But eventually she signed a statement confirming Maria Chiara Lipari's account. And, in a sensational development, she claimed: "I saw Scattone half hidden behind the curtain with a black revolver in his hand and Ferraro alongside with his hands in his hair in a gesture of desperation." She hadn't disclosed these facts until a month after the crime, Alletto said, because she had been scared for herself and her two children.

Both women agreed that a third colleague, library assistant Francesco Liparota, was also present. He initially denied this but was arrested as an accomplice. Liparota was freed when he agreed to testify against Scattone and Ferraro.

On 14 June, just over a month after the killing, the police arrested the two researchers.

Giovanni Scattone is 31, baby-faced with large, startling blue eyes, an uncool Seventies haircut, and a shy manner; Salvatore Ferraro, 32, is his clean-cut, extroverted and preppy-looking friend. Both declared their innocence, come from stable middle-class homes, have no criminal records and were described as "exceptionally intelligent with brilliant career prospects". Scattone is accused of firing the fatal shot. His close friend Ferraro was allegedly his accomplice. Both are now on trial and face a possible 20 years in prison.

But this is a trial without a weapon and a motive. The gun has never been found and no amount of police delving has produced a reason for Marta's murder. For the public prosecutors, however, the motive is the very absence of a motive. They argue that Marta was killed as an intellectual dare by two clever young men convinced of their own superiority and invincibility. It was, they argue, an attempt by two apprentice legal philosophers to commit the perfect crime.

Newspapers reported that the pair were obsessed with firearms and had conducted a seminar for students on the difficulties of prosecuting a motiveless crime. Both reports proved to be false. Nevertheless, the no-motive motive was considered sufficiently convincing to keep Scattone and Ferraro in jail before the trial for 18 and 16 months respectively. Both used their time behind bars to study: Scattone completed his PhD with a thesis on "The legal rights of future generations".

"I saw my father cry for the first time when we saw on television that my brother had been arrested," recounts Giorgio Ferraro, Salvatore's older brother. "But we were sure it was just some terrible mistake that would quickly be ironed out." Ferraro's bank manager father and French teacher mother, who live in a small town in the southern region of Calabria, have followed their son's troubles from a distance, but Giorgio has given up his job as a lawyer and has moved to Rome to support his younger brother. "The case against him didn't stand up from the start, so the prosecutors, echoed by the press, tried to depict him as a psycho," says Giorgio.

Prosecutors presented notes from Salvatore's diary which supposedly show his obsession with violence and his sense of omnipotence. One entry read: "They have killed Sasa Ferraro who exalts the private war. They found him on the footpath, his eyes rolled back in fear. He no longer looked like a God." Says Giorgio: "Those scribblings dated back nine years to a brief period in which Salvatore used to write down the contents of his dreams. From about 90 entries, they highlighted the three that spoke of gruesome things."

Like the Ferraros, 72-year-old Giuseppe Scattone, a retired engineer with a passion for art and languages, is convinced of his son's innocence. He believes Giovanni was framed because of the immense public pressure to resolve the case. "They homed in on the Department, then on those who used the reading room. The police knew Giovanni knew how to shoot as he had done his military service in the Carabinieri corps," he says, showing me a photo of his youngest son smiling proudly in full military dress. "They also knew he could not prove beyond doubt where he was at the time of the shooting."

Giovanni Scattone told the police that at around 1pm he had left the family apartment in the leafy dormitory suburb of EUR. He went to the Literature Faculty, which is not on the main La Sapienza campus, where he consulted a timetable, chatted to a professor - who cannot confirm the visit - and picked up a certificate. Earlier, at the time of the shooting, he says he was on his way to the main campus.

"He could easily have confessed that he was playing with a gun that went off by accident. The police would then be able to say the case was closed. Having no criminal record, Giovanni would receive a limited sentence. But he is innocent and determined to prove it," says Scattone Snr, who has sold a family property to finance his son's defence.

Salvatore Ferraro, known to his friends as Sasa, can only claim that he was studying at home all morning. His lawyer sister, Teresa, confirms that. Telecom records show a phone call to the apartment at 11.30. But it takes only 12 minutes to walk from there to the Law Faculty.

On 20 April 1998 the trial for Marta Russo's murder began at a packed Corte d'Assise in Rome. "I just want the truth," commented Marta's father, a quietly spoken physical education teacher. Interest in the proceedings has been intense and TV specials dedicated to the Marta Russo case have topped the ratings.

In the absence of hard evidence, the trial has inevitably become a credibility contest between the defendants and their accusers. One of the most dramatic moments was a face-to-face encounter between Gabriella Alletto, the secretary, and Scattone - who she claims fired from the window. Though nervous, a well-groomed Alletto held her ground as Scattone accused her of making it all up. But Alletto's credibility took a nose dive in September last year with the screening in court of a secret police video taken during a lengthy night-time interrogation.

Alletto swears on her children's lives that she was never in Room Six and sobs as she is told that she risks a murder charge herself if she doesn't confirm who was in the room.

The inquisitorial video was criticised by media commentators and politicians, even by the then Prime Minister Romano Prodi, and triggered a formal inquiry into the two investigating magistrates, Carlo La Speranza and Italo Ormanni. They defended their strong-arm tactics with the assertion that: "A murder inquiry is not a tea party."

Another blow to the police's case was the testimony last month by the library assistant, Francesco Liparota. In a hesitant voice he told the court that he wasn't in Room Six at the time of the murder. He claimed that when he was in custody police had terrorised him with the idea that he would end up in jail unless he confirmed the magistrates' accusations against Scattone and Ferraro.

While their witnesses vacillated, the prosecution could at least count on some solid scientific evidence. That was until last month. In a bombshell report, three court-appointed experts said the initial forensic tests that indicated gunpowder on the window ledge of Room Six were inaccurate. The chemicals found were not necessarily indicative of gunpowder and only one of the particles found in the bags and on the clothes of Scattone and Ferraro could be traced to gunpowder.

The experts also criticised the ballistics report that indicated the bullet was fired from Room Six, saying the fatal shot could have been fired from six other locations and that the most likely were the two bathrooms on the ground floor.

In April, a jury comprising two magistrates and six members of the public will be called on to consider their verdict on a case that has intrigued the nation.

Was it an imperfect crime committed by two arrogant young intellectuals who took too seriously Nietzsche's concept of the superman? Or a perfect crime committed by someone who has yet to be traced?