The present system, which grants convicted murderers like Yigal Amir some rights, looks to me like broken one. In principle, the proper punishment for murderers (especially those, who deny you your franchise right by voting for you by means of a pistol rather than by ballot) is death. However, in practice they should be sentenced to life term. This is because of the possibility that the convicted person was framed – a possibility which is too real when police forces do not have adequate budgets or professionalism.
This is in contrast to people, who committed less serious crimes and do not deserve to be executed because of those crimes. While they are imprisoned, they are entitled to some rights, which will allow them to return to society in more or less sane frame of mind and become contributing members of society.
What rights should convicted and imprisoned murderers have?
My position is that they should be granted the right to run their own investigations and evidence collection, which can lead to their exoneration. They should have unlimited access to lawyers and to law libraries. They should have access to forensic textbooks and other sources of information. After all, the reason they were kept alive is to allow for the possibility that they were wrongfully convicted and imprisoned. Except for the right to collect evidence of their innocence and appeal their conviction, they should have no rights.
This applies, in principle, even to Yigal Amir. This covers the hypothetical case, in which he was framed AND hypnotized (brainwashed) to believe that Itzhak Rabin had to be murdered.