Bayesian predictions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:math> nuclei using eigenvector continuation emulators
T. Djärv, A. Ekström, C. Forssén, H. Johansson
Abstract
We make ab initio predictions for the $A=6$ nuclear level scheme based on two- and three-nucleon interactions up to next-to-next-to-leading order in chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$). We utilize eigenvector continuation and Bayesian methods to quantify uncertainties stemming from the many-body method, the $\ensuremath{\chi}\mathrm{EFT}$ truncation, and the low-energy constants of the nuclear interaction. The construction and validation of emulators is made possible via the development of jupiterncsm---a new $M$-scheme no-core shell model code that uses on-the-fly Hamiltonian matrix construction for efficient, single-node computations up to ${N}_{\text{max}}=10$ for $^{6}\mathrm{Li}$. We find a slight underbinding of $^{6}\mathrm{He}$ and $^{6}\mathrm{Li}$, although consistent with experimental data given our theoretical error bars. As a result of incorporating correlated $\ensuremath{\chi}\mathrm{EFT}$-truncation errors we find more precise predictions (smaller error bars) for separation energies: ${S}_{d}(^{6}\mathrm{Li})=0.89\ifmmode\pm\else\textpm\fi{}0.44\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}, {S}_{2n}(^{6}\mathrm{He})=0.20\ifmmode\pm\else\textpm\fi{}0.60\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, and for the beta decay $Q$ value: ${Q}_{{\ensuremath{\beta}}^{\ensuremath{-}}}(^{6}\mathrm{He})=3.71\ifmmode\pm\else\textpm\fi{}0.65\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. We conclude that our error bars can potentially be reduced further by extending the model space used by jupiterncsm.