Properties of the drip‑line nucleus and mass relation of mirror nuclei

Researchers from Guangxi Normal University have observed that for heavy nuclei at the neutron drip line, the Coulomb energy heightened by an augmented charge could not be mitigated completely by symmetry energy because of isospin asymmetry saturation but is resisted complementally by strong nuclear deformation. The positions of saltation for the difference in proton numbers between two neighboring nuclei at the neutron drip line, and the isospin asymmetry of the neutron drip-line nucleus as a function of the neutron number distinctly correspond to the known magic numbers, which can serve as a reference to verify the undetermined neutron magic number. Through fitting of the binding energy difference between mirror nuclei (BEDbMN), a set of Coulomb energy coefficients with greater accuracy is obtained. A high-precision description of the BEDbMN is useful for accurately determining the experimentally unknown mass of the nucleus close to the proton drip line if the mass of its mirror nucleus is measured experimentally.

Properties of the drip‑line nucleus

The drip‑line nucleus exhibits extremely weak binding, resulting in a significantly more important proportion of coupling between nucleus-bound states and the continuum spectrum. This phenomenon causes many peculiarities among the nuclei near the drip line, such as the neutron skin and neutron halo, cluster structure, and the emergence and disappearance of traditional magic numbers. Therefore, the properties related to the drip line and drip-line nuclei serve as important standards for understanding nuclear theories.

Researchers observe that the isospin asymmetry of heavy nuclei on the neutron drip line tends toward a saturation value of 0.38, which is not dependent on models. An analysis of the nuclear quadrupole deformation value beta_2 and the deformation energy as a function of the neutron number suggests that in the heavy nuclei region, the strong Coulomb energy caused by the augmented proton is resisted by enormous deformation but not by the further addition of neutrons because of isospin asymmetry saturation.  This finding is benefit for understanding the competition between Coulomb energy, symmetry energy and deformation energy in nucleus.

Additionally, researchers also observe that the conventional magic number has a distinct correspondence with the saltation position of the isospin asymmetries of the most bound nucleus, the difference in proton numbers between two neighboring nuclei at the neutron drip line, and isospin asymmetry degree at the neutron drip-line nucleus as a function of the neutron number. Especially, the positions where differences in proton numbers between two neighboring nuclei at the neutron drip line with odd Z and even Z simultaneously undergo saltation nearby reproduce known magic numbers quite well. This indicates that the saltation without a known corresponding magic number can serve as a reference to verify the undetermined neutron magic number.

Coulomb parameters from mass relation of mirror nuclei

Based on the isospin symmetry of nuclear interactions, the binding energy difference between mirror nuclei (BEDbMN) results from the Coulomb energy and small mass difference between the neutron and proton. Precise measurement of the masses of mirror nuclei enables the study of isospin symmetry and the charge independence of the nuclear force and can be employed to test nuclear structure models. It is an effective approach for enhancing the precision of nuclear mass formulas by utilizing the mass relations of mirror nuclei to investigate the nuclear mass formula, particularly the reasonable correction of the Coulomb term.

By considering the mass relation of mirror nuclei, i.e., BEDbMN,  the researchers provided a set of Coulomb parameters with a stronger physical foundation and greater accuracy. This a set of Coulomb parameters can be used to accurately determine the mass of one of the mirror nuclei, which is experimentally unknown, by another whose mass is known. This is particularly useful for predicting the mass of isotopes that are difficult to synthesize or measure experimentally toward a proton drip line for N<50 where a mirror nuclei pair exists.  The complete study is accessible via DOI: 10.1007/s41365-024-01633-9