Relativistic mean field theory in momentum representation and study of exotic nuclei

<p indent="0mm">In nuclear physics, weakly bound nuclei far from the stability line have attracted significant attention due to their exotic properties. The Fermi surface of these nuclei is close to the continuum threshold, making resonance states a focal point of research. This paper introduces the relativistic mean field in complex momentum representation (RMF-CMR), detailing its theoretical framework and numerical procedures. By employing RMF-CMR, neutron-rich and proton-rich nuclei are systematically studied, with ²⁵O serving as an example to illustrate its advantages over traditional methods. In conventional RMF calculations, the neutron density distribution rapidly decays near the boundary of the computational box. To depict diffuse matter density distributions, such as those found in halo nuclei, a larger box radius is required. However, RMF-CMR performs calculations in the momentum space, demonstrating that the diffusiveness of the neutron density distribution does not change with the box radius. This eliminates the inherent dependence on the box size and basis set size in RMF calculations. RMF-CMR can uniformly describe bound states, resonance states, and the continuum, making it suitable for both stable and exotic nuclei. The calculated single-neutron spectrum of ⁷⁸Ni spans three regions: Bound states located on the imaginary momentum axis, resonance states in the fourth quadrant, and the continuum along the integration path. Bound and resonance states are distinguished from the continuum. Compared with results from RMF-CSM, RSM, and ACCC, the energy and width parameters show consistency, confirming the reliability of resonance states derived from RMF-CMR calculations. Conventional techniques may struggle with very narrow or very broad resonance states, but CMR technology effectively captures these states, providing a powerful tool for studying long-lived nuclear decay processes. Additionally, RMF-CMR excels in handling the Coulomb long-range potential, crucial for exploring proton-rich nuclei. By carefully treating the Coulomb interaction, the RMF-CMR technique accurately describes proton-rich exotic nuclei; for instance, the calculated proton density distribution of ²⁶P is significantly diffuse, consistent with experimental speculation about a proton halo. RMF-CMR calculations yield not only the energies of resonance states but also their local wave functions. The momentum wave functions of a pair of pseudospin partner states, both major and minor components, exhibit localized characteristics in the momentum space. Notably, the small components of the real and imaginary parts of these partner state wave functions show striking similarities, revealing the pseudospin symmetry of resonance states. Through the systematic study of neutron- and proton-rich nuclei, we have a good description of experimentally observed neutron and proton halos, and predict the existence of undiscovered exotic neutron and proton halos. The calculated proton density distribution of ¹²⁴Zr is relatively compact, while the neutron density distribution is quite diffuse. This observation reinforces the classification of ¹²⁴Zr as a neutron halo nucleus. Overall, the RMF-CMR technique provides a unified description of bound states, resonance states, and the continuum, while adeptly addressing challenges posed by the Coulomb long-range potential. Its application scope extends beyond neutron-rich nuclei to include proton-rich nuclei, establishing a powerful research paradigm for exploring exotic nuclei far from the stability line. This advancement significantly broadens the field of nuclear physics research.