Properties of lead isotopes in the vicinity of the neutron drip line

On the basis of the Hartree-Fock method with Skyrme forces of the Ska, SkM*, and Sly4 type, the position of the neutron drip line and the properties of neutron-rich lead isotopes are studied with allowance for deformations. It is shown that, in extremely neutron-rich nuclei, the neutron and proton density distributions are characterized by an anomalously large deformation parameter of β ～ 0.6. Also, nuclei of superdeformed lead isotopes have anomalously large root-mean-square radii. The existence of the isotopes ^266–288Pb, which are stable to the emission of one neutron, is predicted.     

Spherical nuclei near the stability line and far from it

Results of microscopic and semiphenomenological calculations of features of spherical nuclei lying near the stability line and far from it are presented. The reason why the nuclei being considered are spherical is that they are magic at least in one nucleon sort. The present analysis is performed for Z = 50 and Z = 28 isotopes and for N = 50 isotones, the region extending from neutron-rich to neutron-deficient nuclei being covered. The isotopic dependence of the mean-field spin–orbit nuclear potential is revealed; systematics of energies of levels and probabilities for electromagnetic transitions is examined; and root-mean-square radii of nuclei are calculated, along with the proton- and neutron-density distributions in them. Nuclei in the vicinity of closed shells are considered in detail, and the axial-vector weak coupling constant in nuclei is evaluated. A systematic comparison of the results of calculations with experimental data is performed.     

Beyond mean field approach to the beta decay of medium mass nuclei relevant for nuclear astrophysics

The Gamow-Teller strength distributions for the β decay of the ground state as well as the lowest excited states of the rp-process waiting point nuclei ⁶⁸Se and ⁷²Kr are obtained within the complex Excited Vampir variational approach using realistic effective interactions and a rather large model space. The shape mixing is consistently described for both the states in the even-even parent and the states in the odd-odd daugther nucleus. The influence of the shape mixing accounted by the different effective interactions used and comparison with the available data are presented. The possible influence of the decay of the lowest excited states of the parent nuclei in the astrophysical environment of X-ray bursts is discussed.Gamow-Teller strength distributions, β-decay half-lives, and β-delayed neutron emission probabilities for neutron-rich Zr nuclei are investigated for the first time within the complex Excited Vampir approach using a large model space. Comparison with available data and predictions relevant for the astrophysical r process are presented.     

The structure of11Be

More than twenty experimental level data of nuclei far from β-stability are selected to determine new effective parameters for the Modified Surface Delta Interaction and for the single particle energies. With these parameters used in the calculation for 1p-shell nuclei far from β-stability, the agreement between computed results and experimental data becomes fair, and the parity inversion for the 1/2⁺ ground state in¹¹Be is correctly reproduced. The structure of¹¹Be is discussed in some detail.     

Structural properties of the 10Be and 10C four-cluster nuclei

The structure functions for the ¹⁰Be and ¹⁰C nuclei are studied in a four-particle approximation (two alpha-particle clusters plus two nucleons). New versions of the αα interaction potential are constructed. Together with the nα, pα, and NN potentials proposed previously, they make it possible to describe the binding energies and radii of the nuclei being considered, along with the S-wave twocluster phase shifts at low energies. General properties of four-particle wave functions are studied, and two basic configurations of the cross and tetrahedron types are revealed in the ¹⁰Be and ¹⁰C nuclei. A detailed analysis of the behavior of the structure functions is performed for these nuclei. The density distributions, form factors, and pair correlation functions are considered. The momentum distributions are obtained for the alpha particles and extra nucleons. The structure functions for the ¹⁰Be and ¹⁰C four-cluster nuclei are compared with those for the ⁶He three-cluster nucleus. The bound states of the nuclei are studied within a high-precision variational approach by using Gaussian bases.     

16O nucleus in the 4α cluster model

The ¹⁶O nucleus is treated as a bound state of the four-alpha-particle system showing 3α + α clustering. The pair interaction of the alpha particles involved is simulated by a phenomenological potential. Additional three-particle potentials are introduced in order that the entire system and its three-particle subsystems be bound. The parameters of these potentials are determined by fitting the experimental values of the binding energies and the root-mean-square radii of the ¹²C and ¹⁶O nuclei. The calculations are performed on the basis of the s-wave differential equations for the Faddeev and Yakubovsky components. The ground and the first excited state of the ¹⁶O nucleus are investigated. The most probable spatial arrangement of the alpha-particle clusters in the system is determined. The charge form factors are calculated for the ¹²C and ¹⁶O nuclei. The results of our model calculations comply well with experimental data.     

Calculation of nucleon densities in calcium,nickel, and molybdenum isotopes on the basis of the dispersive optical model

The radial distributions of proton and neutron densities in the even–even isotopes ^40?70Cа and ^48?78Ni and the analogous distributions of neutron densities in the even–even isotopes ^92?138Mo were calculated on the basis of the mean-fieldmodel involving a dispersive optical potential. The respective root-mean-square radii and neutron-skin thicknesses were determined for the nuclei under study. In N > 40 calcium isotopes, the calculated neutron root-mean-square radius exhibits a fast growth with increasing N, and this is consistent with the prediction of the neutron-halo structure in calcium isotopes near the neutron drip line.     

Electron charge form factors and static properties of extremely light 1p-shell nuclei within the anisotropic-oscillator model involving projections

The mirror odd nuclei ⁷Li and ⁷Be and the neutron-rich nucleus ⁶He are considered within a microscopic approach relying on the variational principle. The binding energies of the nuclei, their root-mean-square radii, and the electron charge C0 and C2 form factors are calculated. The resulting form factors are compared with the predictions of the independent-particle model that assumes intermediate coupling. The sensitivity of the nuclear properties obtained here to the choice of nucleon-nucleon potential, to deviations of the nuclear deformation from that which follows from a variation of the total-energy functionals, and to taking projections onto states characterized by definite values of the total angular momentum and its projection is analyzed. A comparison with experimental data is performed.     

Binding energies and radii of α-cluster-type nuclei from calculations based on the strictly restricted dynamics model

The properties of α-cluster-type nuclei with 4≤A≤80 are studied by employing the microscopic strictly restricted dynamics model (SRDM). The SRDM parameter set found via a fit to the experimental and theoretical values of nuclear binding and excited-level energies, classified according to the ground-state SU ₃ configurations, includes a nuclear-radius parameter r ₀ entering into the expression R=r ₀ A ^1/3 [fm], as well as the parameters of the effective central NN-interaction potential. The use of the microscopic SRDM allows one to obtain additional information about nuclei along the Z=N line, including binding energies, radii, and spectra of low-lying levels. The calculated nuclear binding energies and nuclear root-mean-square radii 〈r ²〉^1/2 are in reasonable agreement with their experimental counterparts.     

Quantitative conditions for the formation of p-wave neutron halos

With the experimental binding energies and configurations, the root-mean-square radii of p-wave valence neutron distributions for nuclei up to the second p-shell have been calculated in the framework of the single-particle potential model. By analyzing the relations between the radii and the binding energies, the scaling laws of p-wave valence neutron distributions are obtained. The quantitative conditions for the formation of p-wave neutron halos are deduced from these scaling laws. Based on the investigation on the probability of finding the valence nucleon outside the range of the interaction potential, a 2p_3/2 halo state in ⁴⁷S is anticipated for the first time. These obtained results might provide reference for searching for p-wave neutron halos in nuclei up to the second p-shell.     

Quantitative conditions for the formation of p-wave neutron halos

With the experimental binding energies and configurations, the root-mean-square radii of p-wave valence neutron distributions for nuclei up to the second p-shell have been calculated in the framework of the single-particle potential model. By analyzing the relations between the radii and the binding energies, the scaling laws of p-wave valence neutron distributions are obtained. The quantitative conditions for the formation of p-wave neutron halos are deduced from these scaling laws. Based on the investigation on the probability of finding the valence nucleon outside the range of the interaction potential, a 2p3/2 halo state in 47S is anticipated for the first time. These obtained results might provide reference for searching for p-wave neutron halos in nuclei up to the second p-shell.     

Deformed relativistic mean-field calculations on nuclei near Z = 50 with FSUGold

The ground-state properties of Sn, Te, Xe, and Ba isotopes have been systematically investigated in the framework of the deformed relativistic mean-field theory with the new parameter set FSUGold. The results show that FSUGold is as successful as NL3 ^* in reproducing the ground-state binding energies of the nuclei. The calculated two-neutron separation energies, quadrupole deformations, and root-mean-square (rms) charge radii are in good agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 82 . Detailed discussions on the binding energies, two-neutron separation energies, quadrupole deformations, rms charge radii and “binding energies” of the last neutrons are given.     

Neutron Halos in the Excited States of Spherical Nuclei Near the β-Stable Line

The newly discovered neutron halos in the excited states of nuclei 12B, 13C, and 209pb are studied by therelativistic mean-field theory. The calculated binding energies are very close to the experimental ones. The experimentally extracted root-mean-square radii of the last neutron with different occupations in nuclei are well reproduced bycalculations. New candidates for the neutron halos in excited states are predicted and are useful for further search ofneutron halos in the excited states of stable nuclei.     

Hartree-Fock and Hartree-Bogolyubov calculations inp shell nuclei

Hartree-Fock (HF) and Hartree-Fock-Bogolyubov (HFB) calculations have been performed for the 1p shell nuclei. Nuclear deformations are assumed to be at most axially symmetric. The HFB transformation is restricted to allow forp-p andn-n pairing only.Volkov's force, a soft-core, two-body interaction of semi-realistic nature, is used which does not produce any single-particle spin-orbit splittings. Coulomb force and the usual correction for centre-of-mass motion are taken into account. The calculations are carried out in a single-particle basis including all states up to principle oscillator quantum numberN=3 (in some cases,N=4). Binding energies, rms radii, density distributions, and quadrupole moments are calculated and found to be in reasonable agreement with experiment. Large Hartree-Fock energy gaps are obtained. They prevent the pairing correlations considered from becoming effective in an HFB approach and from changing the HF ground-state properties appreciably. In non-selfconjugate nuclei, the Pauli principle, rather than the Coulomb interaction, yields large differences between the charge and mass distributions. A theorem on selfconsistent symmetries is proved. The coefficients of the HFB transformation turn out to be real, if time-reversal and angular momentum projection flip are selfconsistent symmetries.     

Nuclear radius systematics of Kr isotopes studied via their interaction cross-sections at relativistic energies

The interaction cross-sections of neutron-deficient ^72,76,80Kr isotopes have been measured by use of the transmission method at relativistic energies. Based on the Glauber model analysis effective root-mean-square matter radii of these nuclei have been determined for the first time. A systematic evolution of the matter radii in the mass A ∼70 region is discussed and compared with that of light nuclei.     

High spin states in48Cr

The self-consistent finite Fermi-system theory with three different parameter sets is used to calculate decay energies and Gamow-Teller strength distributions of neutronrich short-lived nuclides near shell closures Z=50, N=82. Among the parameters, the role of a strong surface neutron-proton attraction and an isovector spin-orbit force is discussed. The obtainedβ-decay half-lives are compared with large-scale calculation results and with available experimental data. Some predictions for the ground state properties of other unstable closed-shell nuclei are presented.     

致密天体中电子气体对原子核结构的影响

运用相对论平均场理论结合Wigner-Seitz近似,研究了致密物质中电子气体对⁵⁶Fe和¹²⁰Sr结构的影响,对关联的处理采用Bardeen-Cooper-Schrieffer方法.结果表明电子气体对单粒子能级、核子密度分布、核子分布均方根半径、原子核均方根半径等性质都有影响,并且对质子的影响大于对中子的影响. 关键词： 相对论平均场理论 Wigner-Seitz近似 单粒子能级 均方根半径     

Global dynamical correlation energies in covariant density functional theory: Cranking approximation

The global dynamical correlation energies for 575 even-even nuclei with proton numbers ranging from Z = 8 to Z = 108 calculated with the covariant density functional theory using the PC-PK1 parametrization are presented. The dynamical correlation energies include the rotational correction energies obtained with the cranking approximation and the quadrupole vibrational correction energies. The systematic behavior of the present correlation energies is in good agreement with that obtained from the projected generator coordinate method using the SLy4 Skyrme force although our values are systematically smaller. After including the dynamical correlation energies, the root-mean-square deviation predicted by the PC-PK1 for the 575 even-even nuclei masses is reduced from 2.58 MeV to 1.24 MeV.     

Charge radii and quadrupole-deformation parameters of high-spin isomers

Experimental data on the differences of charge radii of nuclei in the ground and high-spin isomeric states are surveyed. High-resolution laser-spectroscopy methods were used for measurements. The results obtained for the differences of these radii by two methods—from measurements of isomeric shifts of the levels of atoms containing the nuclei being studied and from measurements of their quadrupole moments in both states under the assumption that the differences of the radii are determined by the difference in their quadrupole deformations—were compared. Two-particle isomers in odd—odd nuclei, isomers formed upon the break of one or several nucleon pairs, and isomers featuring the 1i _13/2 configuration of the odd neutron in mercury nuclei were considered. The observed distinctions between the aforementioned differences of charged radii are discussed for isomeric states of different nature.     

Skyrme-Hartree-Fock Description of the Nuclear Structure in Ca Isotopes (Ⅰ)Binding Energy and Shell Effects,Radii and Density Distributions

The ground state properties of Ca isotopes far from stability line were systematically studied using the Skyrme Hartree Fock model.The shell effects on the binding energy and two neutron separation energy are discussed.The isospin dependency of the unclear radii and nucleon density distributions and the shell effects on these properties are also studied.It is shown that the neutron magic number affests the width of nuclear surface and the nucleon density distributions beyond the nuclear surface.The change of proton rms radii R_rms with neutron number excess I=(N-Z)/A follows R_rms=3/5(1+αI+βI²)r_pZ^1/3.The effect of the centrifugal potential on the nuclear density in the outer trach of nuclear surface is clearly shown.