Nuclear mass contains a wealth of nuclear structure information, and has been widely employed to extract the nuclear effective interactions. The known nuclear mass is usually extracted from the experimental atomic mass by subtracting the masses of electrons and adding the binding energy of electrons in the atom. However, the binding energies of electrons are sometimes neglected in extracting the known nuclear masses. The influence of binding energies of electrons on nuclear mass predictions are carefully investigated in this work. If the binding energies of electrons are directly subtracted from the theoretical mass predictions, the rms deviations of nuclear mass predictions with respect to the known data are increased by about 200 keV for nuclei with Z, N ~〉 8. Furthermore, by using the Coulomb energies between protons to absorb the binding energies of electrons, their influence on the rms deviations is significantly reduced to only about 10 keV for nuclei with Z, N ≥ 8. However, the binding energies of electrons are still important for the heavy nuclei, about 150 keV for nuclei around Z = 100 and up to about 500 keV for nuclei around Z = 120. Therefore, it is necessary to consider the binding energies of electrons to reliably predict the masses of heavy nuclei at an accuracy of hundreds of keV.
Nuclear single-proton resonances are sensitive to the Coulomb field,while the exchange term of Coulomb field is usually neglected due to its nonlocality.By combining the complex scaling method with the relativistic mean-field model,the influence of the Coulomb exchange term on the single-proton resonances is investigated by taking Sn isotopes and N=82 isotones as examples.It is found that the Coulomb exchange term reduces the singleproton resonance energy within the range of 0.4-0.6 MeV and leads to similar isotopic and isotonic trends of the resonance energy as those without the Coulomb exchange term.Moreover,the single-proton resonance width is also reduced by the Coulomb exchange term,whose influence generally decreases with the increasing neutron number and increases with the increasing proton number.However,the influence of the Coulomb exchange term cannot change the trend of the resonance width with respect to the neutron number and proton number.Furthermore,the influence of the Coulomb exchange term on the resonance width is investigated for the doubly magic nuclei ^(40)Ca,^(56,78)Ni,^(100,132)Sn,and ^(208)Pb.It is found that the Coulomb exchange term reduces the proton resonance width within 0.2 MeV,whose magnitude depends on the specific nucleus and the quantum numbers of resonant states.
With experimental masses updated from AME11,the predictive power of relativistic mean-field(RMF) mass model is carefully examined and compared with HFB-17,FRDM,WS*,and DZ28 mass models.In the relativistic mean-field model,the calculation with the PC-PK1 has improved significantly in describing masses compared to the TMA,especially for the neutron-deficient nuclei.The corresponding rms deviation with respect to the known masses falls to 1.4 MeV.Furthermore,it is found that the RMF mass model better describes the nuclei with large deformations.The rms deviation for nuclei with the absolute value of quadrupole deformation parameter greater than 0.25 falls to 0.93,crossing the 1 MeV accuracy threshold for the PC-PK1,which may indicate the new model is more suitable for those largely-deformed nuclei.In addition,the necessity of new high-precision experimental data to evaluate and develop the nuclear mass models is emphasized as well.
The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian.Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying(improving) the spin(pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the(pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.
Resonance research is a hot topic in nuclear physics,and many methods have been developed for resonances.In this paper,we explore resonances by solving the Schrodinger equation in complex momentum representation,in which the bound states and resonant states are separated completely from the continuum and exposed clearly in the complex momentum plane.We have checked the convergence of the calculations on the grid numbers of the Gauss-Hermite quadrature and the Gauss-Legendre quadrature,and the dependence on the contour of momentum integration.Satisfactory results are obtained.^17O is chosen as an example,and we have calculated the bound and resonant states to be in excellent agreement with those calculated in the coordinate representation.
Mass is a fundamental property and an important fingerprint of atomic nucleus.It provides an extremely useful test ground for nuclear models and is crucial to understand energy generation in stars as well as the heavy elements synthesized in stellar explosions.Nuclear physicists have been attempting at developing a precise,reliable,and predictive nuclear model that is suitable for the whole nuclear chart,while this still remains a great challenge even in recent days.Here we employ the Fourier spectral analysis to examine the deviations of nuclear mass predictions to the experimental data and to present a novel way for accurate nuclear mass predictions.In this analysis,we map the mass deviations from the space of nucleon number to its conjugate space of frequency,and are able to pin down the main contributions to the model deficiencies.By using the radial basis function approach we can further isolate and quantify the sources.Taking a pedagogical mass model as an example,we examine explicitly the correlation between nuclear effective interactions and the distributions of mass deviations in the frequency domain.The method presented in this work,therefore,opens up a new way for improving the nuclear mass predictions towards a hundred kilo-electron-volt accuracy,which is argued to be the chaos-related limit for the nuclear mass predictions.
