Background: Nuclear masses are of fundamental importance in both nuclear physics and astrophysics, and the masses for most neutron-rich exotic nuclei are still beyond the experimental capability. The relativistic continuum Hartree-Bogoliubov (RCHB) theory has achieved great successes in the studies of both stable and exotic nuclei. The mass table based on the RCHB theory has been constructed with the assumption of spherical symmetry [Xia et al., At. Data Nucl. Data Tables 121, 1 (2018)]. The upgraded version including deformation effects based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) is under construction, and the part for even-even nuclei has been finished [Zhang et al., At. Data Nucl. Data Tables 144, 101488 (2022)]. The kernel ridge regression (KRR) approach is a useful machine-learning approach in refining nuclear mass prediction, and is found to be reliable in avoiding the risk of worsening predictions at large extrapolation distance [Wu and Zhao, Phys. Rev. C 101, 051301(R) (2020)].

Purpose: The aim of this work is to combine the RCHB mass model and the KRR approach to construct a high-precision and reliable nuclear mass model describing both stable and weakly bound neutron-rich exotic nuclei. Another purpose is to utilize the masses of even-even nuclei from the DRHBc theory to validate the performance of the KRR approach.

Method: The KRR approach is employed to refine the RCHB mass model by learning and representing the mass residual of the RCHB mass model with the experimental data. The leave-one-out cross-validation is applied to determine the hyperparameters in the KRR approach. The DRHBc mass model for even-even nuclei is employed to help to analyze the physical effects included in the KRR corrections and examine the KRR extrapolations.

Results: The refined RCHB mass model with KRR corrections can achieve an accuracy of root-mean-square deviation 385 keV from the experimental masses. The major contributions contained in the KRR corrections are found to be the deformation effects. The KRR corrections also contain some residual deformation effects and some other effects beyond the scope of the DRHBc theory. The extrapolation of the KRR approach in refining the RCHB predictions is found to be very reliable.

Conclusions: A mass model benefiting from the RCHB model with continuum effects properly treated and the KRR approach is constructed. This model is demonstrated to be accurate in reproducing the masses of experimentally known nuclei and reliable in extrapolating to the experimentally unknown neutron-rich regions.

• Received 10 November 2023
• Accepted 23 January 2024

DOI:https://doi.org/10.1103/PhysRevC.109.024310