Statistical error propagation in ab initio no-core full configuration calculations of light nuclei

We propagate the statistical uncertainty of experimental $NN$ scattering data into the binding energy of ${}^3\text{H}$ and ${}^4\text{He}$. We also study the sensitivity of the magnetic moment and proton radius of the ${}^3\text{H}$ to changes in the $NN$ interaction. The calculations are made with the no-core full configuration method in a sufficiently large harmonic oscillator basis. For those light nuclei we obtain $\mathrm{\Delta }{E}^{\mathrm{stat}}\left({}^3\text{H}\right)=0.015\mathrm{MeV}$ and $\mathrm{\Delta }{E}^{\mathrm{stat}}\left({}^4\text{He}\right)=0.055\mathrm{MeV}$.

Figure 1

Deuteron momentum distribution for different local potentials. DS-OPE (blue band), DS-$\chi \mathrm{TPE}$ (red band), Gauss-OPE (green band), AV18 (yellow dashed line), Reid93 (red short-dashed line) and NijmII (light blue dotted line).

Figure 2

NCSM calculations of the deuteron binding energy (left panels) and root mean square radius (right panels) as a function of the basis truncation parameter $N_{\max }$ with different values of the harmonic oscillator parameter $\hslash \mathrm{\Omega }$ for the Gauss-OPE (top panels) and Reid93 (bottom panels) potentials. The Gauss-OPE potential shows a faster convergence rate in both quantities as evident from the smaller spread with respect to $\hslash \mathrm{\Omega }$ at fixed $N_{\max }$.

Figure 3

NCSM ground-state energy as a function of $N_{\max }$ for ${}^3\text{H}$ at $\hslash \mathrm{\Omega }=60$ MeV (left panel) and ${}^4\text{He}$ at $\hslash \mathrm{\Omega }=65$ MeV (right panel) with the Gauss-OPE potential. The red error bars indicate the mean and $3\sigma$ confidence interval of the 33 calculations with different potential parameters (see main text). The blue solid curves give the corresponding 33 extrapolations fitting the $a, c$, and $E_{\infty }$ of Eq. (12) to the calculated values of $E(N_{\max }=8,10,...,20)$. The panels at the top-right corners show the extrapolated value at $N_{\max }\to \infty$ from each fit with an error bar indicating the corresponding mean and $3\sigma$ confidence interval. The solid black indicates the experimental value.