We introduce a unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model (NCSM), a bound-state technique, with the no-core shell model/resonating group method (NCSM/RGM), a nuclear scattering technique. This new ab initio method, no-core shell model with continuum (NCSMC), leads to convergence properties superior to either NCSM or NCSM/RGM while providing a balanced approach to different classes of states. In the NCSMC, the ansatz for the many-nucleon wave function includes (i) a square-integrable $A$-nucleon component expanded in a complete harmonic oscillator basis and (ii) a binary-cluster component with asymptotic boundary conditions that can properly describe weakly bound states, resonances, and scattering. The Schrödinger equation is transformed into a system of coupled-channel integral-differential equations that we solve using a modified microscopic $R$-matrix formalism within a Lagrange mesh basis. We demonstrate the usefulness of the approach by investigating the unbound ${}^7$He nucleus.

The neutron-rich unbound $^{7}\mathrm{He}$ nucleus has been the subject of many experimental investigations. While the ground-state $3/{2}^{-}$ resonance is well established, there is a controversy concerning the excited $1/{2}^{-}$ resonance reported in some experiments as low lying and narrow (${E}_{R}$\sim${}1\text{ }\text{ }\mathrm{MeV}$, $$\Gamma${}$\le${}1\text{ }\text{ }\mathrm{MeV}$) while in others as very broad and located at a higher energy. This issue cannot be addressed by ab initio theoretical calculations based on traditional bound-state methods. We introduce a new unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model, a bound-state technique, with the no-core shell model combined with the resonating-group method, a nuclear scattering technique. Our calculations describe the ground-state resonance in agreement with experiment and, at the same time, predict a broad $1/{2}^{-}$ resonance above 2 MeV.

We apply the ab initio no-core shell model combined with the resonating-group method approach to calculate the cross sections of the ${}^3\mathrm{H}(d,n){}^4\mathrm{He}$ and ${}^3\mathrm{He}(d,p){}^4\mathrm{He}$ fusion reactions. These are important reactions for the big bang nucleosynthesis and the future of energy generation on Earth. Starting from a selected similarity-transformed chiral nucleon-nucleon interaction that accurately describes two-nucleon data, we performed many-body calculations that predict the $S$ factor of both reactions. Virtual three-body breakup effects are obtained by including excited pseudostates of the deuteron in the calculation. Our results are in satisfactory agreement with experimental data and pave the way for microscopic investigations of polarization and electron-screening effects, of the ${}^3\mathrm{H}(d,\gamma n){}^4\mathrm{He}$ bremsstrahlung and other reactions relevant to fusion research.

We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-$\beta$ decay of ${}^{48}\mathrm{Ca}$. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For ${}^{48}\mathrm{Ca}$ we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-$\beta$ decay of ${}^{48}\mathrm{Ca}$ with a quenching factor deduced from two-body currents in recent ab initio calculation of the Ikeda sum rule in ${}^{48}\mathrm{Ca}$ [Gysbers et al., Nat. Phys. 15, 428 (2019)].

The fusion of deuterium (D) with tritium (T) is the most promising of the reactions that could power thermonuclear reactors of the future. It may lead to even more efficient energy generation if obtained in a polarized state, that is with the spin of the reactants aligned. Here, we report first-principles predictions of the polarized DT fusion using nuclear forces from effective field theory. By employing the ab initio no-core shell model with continuum reaction method to solve the quantum mechanical five-nucleon problem, we accurately determine the enhanced fusion rate and angular distribution of the emitted neutron and ⁴He. Our calculations demonstrate in detail the small contribution of anisotropies, placing on a firmer footing the understanding of the rate of DT fusion in a polarized plasma. In the future, analogous calculations could be used to obtain accurate values for other, more uncertain thermonuclear reaction data critical to nuclear science applications.