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1.Variation After Projection of HFB

Variation After Projection (VAP) combined with the Hartree-Fock-Bogoliubov (HFB) theory is a powerful method in nuclear physics, particularly for describing nuclear structure and the interplay between pairing correlations and deformation effects in atomic nuclei.

Background and Motivation:(1)The Hartree-Fock-Bogoliubov (HFB) theory is a cornerstone of nuclear structure calculations. It effectively incorporates both mean-field effects and pairing correlations, allowing for the description of phenomena like superfluidity in nuclei. (2)However, the HFB wavefunction typically breaks certain symmetries of the nuclear Hamiltonian, such as particle number, angular momentum, and parity, to simplify calculations. This symmetry breaking introduces artifacts that can obscure physical insights. (3)The Variation After Projection (VAP) method addresses this issue by projecting the symmetry-restored wavefunction onto states with definite quantum numbers (e.g., particle number or angular momentum) before optimizing the wavefunction. This is more accurate than the simpler Projection After Variation (PAV) approach, where symmetry projection is performed only after the variational minimization.

Applications in Nuclear Physics: (1)VAP-HFB is widely applied to study nuclear clustering phenomena, pairing correlations, and shape coexistence. (2)It is particularly useful in describing light nuclei, where clustering effects are pronounced (e.g., alpha clustering in 12𝐶). (3)In heavy nuclei, VAP-HFB helps investigate deformation, rotational bands, and pairing gaps.

2. Ab initio method of Nucleus Clustering Phenomena

Nuclear clustering phenomena refer to the formation of substructures, or clusters, within atomic nuclei, where groups of nucleons (such as alpha particles 𝛼) behave as coherent units. Understanding clustering is critical for explaining nuclear structure and reactions, especially in light nuclei like 12C and 8Be. An ab initio approach aims to describe such phenomena starting directly from the fundamental interactions between nucleons, without empirical fitting to specific nuclear properties. These methods strive to solve the nuclear many-body problem using realistic nuclear forces derived from quantum chromodynamics (QCD) or nucleon-nucleon interaction models.