Triton binding energy with realistic statistical uncertainties

We compute the binding energy of triton with realistic statistical errors stemming from $NN$ scattering data uncertainties and the deuteron and obtain $E_t=-7.638\left(15\right)\mathrm{MeV}$. Setting the numerical precision as $\Delta E_t^{\mathrm{num}}\lesssim 1\mathrm{keV}$ we obtain the statistical error $\Delta E_t^{\mathrm{stat}}=15\left(1\right)\mathrm{keV}$ which is mainly determined by the channels involving relative $S$ waves. This figure reflects the uncertainty of the input $NN$ data, more than two orders of magnitude larger than the experimental precision $\Delta E_t^{\exp }=0.1\mathrm{keV}$, and sets a limit on the realistic precision that can be reached. This suggests an important reduction in the numerical precision and hence in the computational effort.

Figure 1

Normalized histograms representing the triton binding energy (in MeV) for a sample of 205 gaussian potential parameters. From left to right the normal density probability distribution functions $N(\mu ,\sigma )$ correspond to higher accuracy $E_t=-7.638\pm 0.0147$, intermediate accuracy $E_t=-7.596\pm 0.0178$, and lower accuracy $E_t=-7.575\pm 0.014$ (see main text).