Chiral nuclear forces and <italic>ab initio</italic> nuclear structure calculations

Understanding the microscopic interaction between nucleons is one of the primary goals of nuclear physics, connecting the phenomena of the atomic nucleus with the fundamental theory of the strong interaction, quantum chromodynamics (QCD). In recent decades, chiral effective field theory (χEFT) has established itself as the theoretical foundation for this endeavor, providing a systematic and improvable framework to derive nuclear forces consistent with the symmetries of QCD. Coupled with advances in ab initio quantum many-body methods and computational power, this approach has extended its predictive capabilities far beyond the few-body systems to medium-mass and even heavy nuclei, covering both stable isotopes and exotic, weakly-bound nuclides near the drip lines.This paper provides a systematic review of our recent progress in ab initio nuclear structure calculations driven by χEFT, with a particular emphasis on theoretical developments tailored for nuclei where continuum effects are important. Traditional methods like the no-core shell model (NCSM) and the in-medium similarity renormalization group (IMSRG) often use a harmonic oscillator basis, which is fundamentally limited in describing the spatial extension and decay properties of weakly-bound and unbound systems. Our team has pioneered a series of potent quantum many-body methods utilizing the complex-momentum Berggren basis, which naturally incorporates continuum and resonance states through a generalized completeness relation. These include the no-core Gamow shell model (NCGSM) and the Gamow-IMSRG (G-IMSRG), successfully extending the ab initio map into regions where continuum effects are crucial.A major achievement using NCGSM with the high-precision N3LOEM interaction was the theoretical prediction of the elusive tetraneutron resonance, an unbound system composed purely of neutrons, which was subsequently confirmed by experimental observation. Furthermore, NCGSM was successfully applied to A=4, T=1 isospin triplet, correctly describing their wide-resonance characteristics and the effects of isospin symmetry breaking.For medium-mass nuclei, we introduced the deformed-IMSRG (D-IMSRG), employing a deformed Hartree-Fock basis to effectively capture static shape correlations, which is essential for studying the N=20 “island of inversion” region. Utilizing optimized chiral forces like N2LOopt and N2LOsat, our calculations accurately reproduce the ground-state energies of Be, C, O, Ne, and Mg isotopes. However, a persistent challenge remains the systemic underprediction of charge radii across various ab initio methods and chiral forces—the “radius puzzle”. We demonstrated that the inclusion of three-nucleon forces (3NFs), as in the N2LOsat interaction, yields a more spatially extended density distribution for halo nuclei like 22C when properly treated with G-IMSRG, offering a better agreement with experimental radii and underscoring the vital role of 3NFs and the underlying fitting strategy. The importance of 3NFs was further confirmed in the description of high-spin isomerism, where the presence of a three-nucleon component was shown to be indispensable for correctly reproducing the spectra of nuclei like 53Co and 53Fe.Looking ahead, the development of χEFT and quantum many-body methods remains a highly active frontier. Future efforts include pushing the chiral expansion to higher orders (e.g., N4LO) to reduce systematic errors and rigorously test convergence, refining global fitting strategies to better constrain 3NFs, and further investigating electroweak current operators to resolve issues like the radius puzzle. Crucially, while most current many-body calculations non-perturbatively solve the Schrödinger equation, an exciting and highly challenging frontier involves employing perturbative many-body methods with chiral forces. This alternative approach holds the promise of providing fresh insights into the long-standing discrepancies of non-perturbative frameworks and serves as an independent, valuable avenue for rigorously testing the consistency and predictive power of χEFT itself. The synergy between advancing χEFT, robust quantum many-body methods, and refined structural observables will continue to deepen our fundamental understanding of nuclear interaction.