Bound on Time-Reversal Noninvariance in the Nuclear Hamiltonian

Energy-level fluctuations are calculated by random-matrix methods, for time-reversal noninvariant (TRNI) Hamiltonians. The theory, applied to the data, shows that in the neutron and proton resonance regions (i.e., for heavy and intermediate nuclei, respectively), the local rms off-diagonal multiparticle $H\left(\mathrm{TRNI}\right)$ matrix element $\lesssim \frac{D}{10}$, with $D$ the level spacing. Spectral averaging methods reduce this to a bound on the nucleon-nucleon TRNI vs TRI interactions. First calculations, for ${}_{}{}^{169}{}_{}{}^{}\mathrm{Er}$, give a 1% upper bound.