what is the goldilocks range from a neutron star?
Welcome to the PF.
Google is your friend. I Googled your thread title and got lots of hits:
I don't think life would be easy if the local source of energy is X-rays.
The title question is not the same as the question you posted.
The goldilocks zone or "circumstellar habitable zone" is defined by the irradiance that allows liquid surface water on a planet similar to earth. Irradiance is proportional to distance squared.
The closest neutron star PSR_J0108-1431 has a spin down energy release of 5.8 x 1023 W. Which corresponds to 1.5 x 10-3 solar luminosity. You can stick that number into the equation and calculate the CHZ: √(1.5x 10-3) = 0.039 astronomical units is the same range as earth. The CHZ is not an exact distance.
A "safe distance" is quite a different matter. Much of the irradiance comes in the form of x-rays and high energy particles. The surface temperature may be between 0 and 100C but the atmosphere would be ripped away if the planet is similar to earth.
Higher mass planets might hold on to an atmosphere for awhile longer. The bottom of a deep sea trench would not receive high energy radiation. There is discussion about the possibility of life on Europa or Titan.
Neutron stars tend to be rather hostile to life. Not just because of their excessive high energy radiation and particle emissions, but, also due to their lineage. It is fairly well established they would wreak havoc upon planetary atmospheres. Only a super earth would be able to retain enough of an atmosphere to sustain biologic processes. Also consider that the typical neutron star progenitor is a supernova - an event that does not bode well for complex molecules, much less any preexisting life forms. Significant time would be needed for a newborn neutron star to settle down sufficient to permit biogenesis to reboot on any surviving planets..
Separate names with a comma.