Peninsulas of the neutron stability of nuclei in the vicinity of neutron magic numbers

On the basis of the Hartree-Fock method as implemented with Skyrme forces (Ska, SkM*, Sly4, and SkI2) and with allowance for an axial deformation and nucleon pairing in the Bardeen-Cooper-Schrieffer approximation, the properties of extremely neutron-rich even-even nuclei were calculated beyond the neutron drip line known earlier from theoretical calculations. It was shown that the chains of isotopes beyond the neutron drip line that contain N = 32, 58, 82, 126, and 184 neutrons form peninsulas of nuclei stable against the emission of one neutron and, in some cases, peninsulas of nuclei stable against the emission of two neutrons. The neutron- and proton-density distributions in nuclei forming stability peninsulas were found to be spherically symmetric. A mechanism via which the stability of nuclei might be restored beyond the neutron drip line was discussed. A comparison with the results of calculations by the Hartree-Fock-Bogolyubov method was performed for long chains of sulfur and gadolinium isotopes up to the neutron drip line.     

Ground-state properties of neutron magic nuclei

A systematic study of the ground-state properties of the entire chains of even–even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82, and 126 has been carried out using relativistic mean-field plus Bardeen–Cooper–Schrieffer approach. Our present investigation includes deformation, binding energy, two-proton separation energy, single-particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using nonrelativistic approach (Skyrme–Hartree–Fock method) along with available experimental data and indeed they are found with excellent agreement. In addition, the possible locations of the proton and neutron drip-lines, the (Z, N) values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail.     

传统中子幻数稳定性的研究

在考虑了BCS理论的相对论平均场模型框架内,通过系统研究N=8,20,28,50,82和126六条同中子素链中每个元素费米面附近的单粒子能级间隔、粒子数占有概率比以及原子核体系的粒子数偏离随质子数的变化规律,讨论了传统中子幻数的壳结构在从中子滴线区到质子滴线区整个核谱上的稳定性,预言只有在轻核的丰中子区域,传统的中子幻数效应才可能消失,并把计算结果和最近的文献报道作了比较. 关键词： 相对论平均场模型 能级间隔 占有概率 粒子数偏离     

A new mass formula and new neutron and proton magic numbers in light nuclei

This mass formula explains gross features of the binding energy curves for all the elements from Li to Bi. It has no shell effects incorporated. Comparisons of separation energies computed from this formula and measured masses show extra-stability at N=6 (Z=3?8), Z=6 (N=6?9), N=14 (Z=7?10), Z=14 (N=14?19), N=16 (Z=7?8), Z=16 (N=24?26), loss of magicity at N=8 (Z=4), N=20 (Z=12?15) and quenching of N=50, 82, 126, Z=50 near driplines. Z=82 magicity rises at N=104 after strong quenching near N=107.     

A relativistic mean-field study of magic numbers in light nuclei from neutron to proton drip-lines

In an axially deformed relativistic mean-field calculation of single-particle energy spectra ofN = 8 (Li-Mg) andN = 14,16 (C-Mg) isotonic chain and the one- and two-neutron separation energies of various isotopes of Li-Mg, new magic numbers are found to exist atN = 6 andN = 16 and/orN = 14, which are in addition to theN = 8 andN = 20 magic numbers. In neutron-rich nuclei, the shell gap atN = 6 is larger than atN = 8 and a large gap is observed forN = 16 or 14 for the neutron-rich andN = 14 for proton-rich nuclei. Large shell gaps are also found to exist atN = 14 and 16 orN = 16 alone for nuclei near theβ-stability line. The above results are independent of the parameter sets TM2, NL3 and NL-SH used here. Similarly, new large shell gaps are predicted atZ = 616 and/or 14 for protons.     

Doubly magic properties in superheavy nuclei

A systematic study of global properties of superheavy nuclei in the framework of the Liquid Drop Model and the Strutinsky shell correction method is performed. The evolution equilibrium deformations, TRS graphs and α-decay energies are calculated using the TRS model. The analysis covers a wide range of even-even superheavy nuclei from Z =102 to 122. Magic numbers and their observable influence occurring in this region have been investigated. Shell closures appear at proton number Z =114 and at neutron number N =184.     

Doubly magic properties in superheavy nuclei

A systematic study of global properties of superheavy nuclei in the framework of the Liquid Drop Model and the Strutinsky shell correction method is performed. The evolution equilibrium deformations, TRS graphs and α-decay energies are calculated using the TRS model. The analysis covers a wide range of even-even superheavy nuclei from Z=102 to 122. Magic numbers and their observable influence occurring in this region have been investigated. Shell closures appear at proton number Z=114 and at neutron number N=184.     

Peninsula of neutron stability of nuclei in the neighborhood of neutron magic number N = 126

The properties of the ground state of even-even nuclei with extreme neutron excess that are remote from the known neutron drip line (NDL) are calculated. The calculations are based on the Hartree-Fock method with Skyrme forces SkM*, SkI2, Sly4, Ska) with allowance for axial deformation and the BCS pairing approximation. It is shown that the isotone chain at the neutron number N = 126 beyond the NDL forms a peninsula of nuclei that are stable with respect to the emission of one neutron (PNS). The neutron and proton density distributions of the PNS nuclei have spherical symmetry. A mechanism for restoring the stability of nuclei beyond the NDL is discussed. The obtained results are compared with those from Hartree-Fock-Bogoliubov calculations for long isotope chains of Zr and Pd up to the NDL.     

Proton and neutron occupation numbers forfp-shell nuclei

Spectroscopic factors for single-particle transfer are calculated from many-particle shell-model wave functions for 23 different transfer reactions onfp-shell nuclei. A comparison of the present theory with the available experimental data is very successful. Subshell occupation numbers of target ground states are studied in detail. Some systematic deficiencies for low seniority shell-model wave functions are revealed. In several cases the experimental information appears to be rather incomplete.     

A personal view of some issues involved in the structure of nuclei with large neutron excess

Large neutron excess poses new issues concerning the competition of deformation and pairing as well as changes in nuclear shell structure. To cite this article: I. Hamamoto, B.R. Mottelson, C. R. Physique 4 (2003).     

Nuclear masses and properties of nuclei in the vicinity of the remote magic nucleus <Superscript>100</Superscript>Sn

Results are presented that were obtained by calculating various properties of nuclei occurring in the vicinity of the doubly magic neutron-deficient nuclide ¹⁰⁰Sn, which are being intensively studied at present. The calculated features include the masses of 25 nuclei and the properties of excited states of the magic nuclide and of nuclei belonging to the magic core plus two quasiparticles type. The problems of effective quadrupole charges and of the renormalization of the weak axial constant in nuclei lying in the vicinity of ¹⁰⁰Sn are considered.     

Observation of abnormally large radii of nuclei in excited states in the vicinity of neutron thresholds

Differential cross sections for inelastic scattering leading to the excitation of some nuclear states situated near neutron-emission thresholds were analyzed. With the aid of a modified diffraction model, abnormally large radii were found for the 1/2₁⁺ state of the ¹³C nucleus at 3.09 MeV, for the first levels of positive-parity rotational bands in the ⁹Be (1/2⁺ level at 1.68 MeV and 5/2⁺ level at 3.05 MeV) and ¹¹Be (5/2⁺ level at 1.78 MeV and 3/2⁺ level at 3.41 MeV) nuclei, and for the 2₁⁺ state of the ¹⁴Be nucleus at 1.54 MeV and 1₁⁻ state of the ¹²Be nucleus at 2.7 MeV. All of these states possess signatures typical of neutron halos.     

Mapping the magic numbers in binary Lennard-Jones clusters

Using a global optimization approach that directly searches for the composition of greatest stability, we have been able to find the particularly stable structures for binary Lennard-Jones clusters with up to 100 atoms for a range of Lennard-Jones parameters. In particular, we have shown that just having atoms of different sizes leads to a remarkable stabilization of polytetrahedral structures, including both polyicosahedral clusters and at larger sizes structures with disclination lines.     

Magic numbers in exotic nuclei and spin-isospin properties of the NN interaction

The magic numbers in exotic nuclei are discussed, and their novel origin is shown to be the spin-isospin dependent part of the nucleon-nucleon interaction in nuclei. The importance and robustness of this mechanism is shown in terms of meson exchange, G-matrix, and QCD theories. In neutron-rich exotic nuclei, magic numbers such as N = 8, 20, etc. can disappear, while N = 6, 16, etc. arise, affecting the structure of the lightest exotic nuclei to nucleosynthesis of heavy elements.     

Slow neutron scattering parameters for stable nuclei with nucleon numbers betweenA=79 andA=96

The relation between the method of coupled channels for rearrangement reactions (CRC) and the bound state approximation to the channel coupling array formalism (BSCCA), advocated in recent years, is investigated in detail for a simple 3-body system expressed in terms of truncated component wavefunctions of Faddeev type. The system is described by coupled differential or integral equations that are truncated into a model space of strongly-coupled channels. It is shown that CRC can be derived from the truncated coupled equations, either in differential or integral form, provided care is taken to use the entire model space. The corresponding BSCCA in this model space can be obtained from a restrictive condition on the integral from of the coupled equations, while it cannot be obtained consistently from the differential form of the coupled equations. The boundary conditions for the component functions are discussed in detail.     

M1 resonances in unstable magic nuclei

Within a microscopic approach which takes into account RPA configurations, the single-particle continuum and more complex 1p 1 h?phonon configurations isoscalar and isovector M1 excitations for the unstable nuclei^56,78Ni and^100,132Sn are calculated. For comparison, the experimentally known Ml excitations in⁴⁰Ca and²⁰⁸Pb have also been calculated. In the latter nuclei good agreement in the centroid energy, the total transition strength and the resonance width is obtained. With the same parameters we predict the magnetic excitations for the unstable nuclei. The strength is sufficiently concentrated to be measurable in radioactive beam experiments. New features are found for the very neutron rich nucleus⁷⁸Ni and the neutron deficient nucleus¹⁰⁰Sn.     

Investigation of neutron deficient Zr and Nb nuclei with heavy ion induced compound reactions

³²S and¹²C induced compound reactions on Fe, Ni and Se targets have been used to produce neutron deficient nuclei in the mass region 84≦A ≦87. In-beamγ-ray spectroscopy consisting of the measurement of excitation functions,γγ coincidences andγ-ray angular distributions has been performed. The following level energies and spin-parity values have been deduced:⁸⁴Zr: 540 keV, 2⁺; 1262.8, (4⁺); 2137.2, (6⁺); 3089.2⁸⁶Zr: 751.9, 2⁺; 1666.6, (4⁺); 2670.0, (6⁺); 2705.5, (5); 3271.3; 3298.5, (8⁺); 3423.5, (7); 3531.5, (10⁺); 3645.9; 4326.1; 4417.3 Half-lives and energies ofγ-rays from the residual activities have been measured. The existence of three new isotopes could be established by their radioactive decay:⁸⁴Nb(12±3 s)→⁸⁴Zr⁸⁶Nb(80±12 s)→⁸⁶Zr⁸⁷Mo(14.6±1.5 s)→⁸⁷Nb→⁸⁷Zr     

Evidence for magic numbers of free lead-clusters

Microclusters Pb_n have been generated by condensation of lead atoms in cold He-gas. Electronic time-of-flight mass spectra show resolved peaks up to n ≈ 110 with pronounced size dependent structure up to n = 20. The magic numbers $\text{n}{}^1\text{= 7, 10, 13, 17}\text{and}\text{19}$ are deduced from the spectra.     

Statistical measures and magic numbers in metal clusters

In this work, a shell model for metal clusters up to 220 valence electrons is used to obtain the fractional occupation probabilities of the electronic orbitals. Then, the calculation of a statistical measure of complexity and the Fisher-Shannon information is carried out. An increase of both magnitudes with the number of valence electrons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are indicated by the Fisher-Shannon information. So, as in the case of atomic nuclei, the study of statistical indicators also unveil the existence of magic numbers in metal clusters.