Energy Density in Pulsed Spallation Neutron Source Targets Against the Density Ceiling

This paper computes the characteristic densities of the target of a pulsed spallation neutron source from published operating parameters and compares them, quantity by quantity, with the Aldred density ceiling of 9.72e+57 kilograms per cubic metre, the neutron-branch bound at prescription coefficient one eighth. The headline comparison gives a margin of 67.2 orders of magnitude between the operating point and the ceiling: each pulse deposits an energy density whose mass equivalent is 67.2 orders of magnitude below the ceiling, while the solid target itself, tungsten at full material density, sits about 53.7 orders below; target lifetime is set by radiation damage, thermal shock and cavitation, none of which involves the ceiling. Every number is obtained from the deposited calculation, which uses only published device parameters, internationally tabulated constants, and algebra stated in full. The result is negative in the useful sense: it shows that the ceiling imposes no constraint on the system as designed or operated, identifies the empirical and engineering limits that act instead, and states precisely what change in operating parameters would be required before the ceiling could matter. The study is a computation from stated assumptions; nothing in it is a measurement.