Resonant States in Few-Body Systems: An Introduction to the Special Issue

Resonant states are a focal point across numerous branches of physics, encompassing reactions and unbound systems.Theoretically, these states correspond to the complex energy poles of the Hamiltonian matrix.While several methods exist to determine their positions, distinguishing the contribution of resonant states from non-resonant background processes, comparing theoretical predictions with experimental data remains challenging.This issue features several original contributions showcasing cutting-edge research into the dynamics of resonant states.Among the contributions, a concise review of prevalent numerical techniques used to ascertain resonant state properties such as energy and width is included 1.Emphasis is placed on the ambiguities encountered when comparing theoretical predictions with experimental findings.Expanding into the realm of relativistic problems, the issue discusses a computational approach proposed for calculating bound and resonant states by solving Klein-Gordon and Dirac equations for real and complex energies, with the potential represented in a Coulomb-Sturmian basis 2.From an experimental standpoint, neutron-induced resonances hold particular significance in nuclear system studies.The issue presents a straightforward derivation of these states, particularly in neutron-rich nuclei, and extends the discussion to "N-body" resonances 3.From a theoretical point of view, the R-matrix method, widely utilized for describing scattering processes 4.It is demonstrated how this method can be extended to assess the energy and width of a resonance by computing eigenvalues of a complex symmetric matrix.Resonances may manifest as bound states embedded in the continuum, with migration from bound to resonant states possibly catalyzed by specific terms in the Hamiltonian.One such case discussed in the issue pertains to the excited 0 + state of the α-particle, illustrating how the Coulomb force between two protons drives the migration of this state to a resonance state, with connections drawn to Efimov physics 5.Resonant states often play a pivotal role in catalyzing specific reactions, profoundly altering reaction rates.Consequently, investigating particular resonant states holds significance across various contexts, such as fusion rates.One contribution in the issue delves into discussions surrounding ultra-low-energy nuclear synthesis via a three-body molecular resonance 6.Hadronic physics is replete with structures appearing as resonant states, including tetra and pentaquark configurations observed in recent years by various experimental collaborations, notably the LHCb collaboration.These observations fostered fruitful exchanges between experimental and theoretical groups, with the issue exploring specific pentaquark structures within the constituent quark model 7.Additionally, the mass and magnetic moments of light and heavy baryons are described using the quark-diquark model in another