Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of a-decay is extended to the regions around doubly magic spherical nucleus ^208Pb and around deformed shell closure ^270Hs, respectively. The effects of spherical shell closures (N=126 and Z=82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical a-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus ^208Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of α-decays from the ground state of a parent nucleus to the ground state (0^ ) of its deformed daughter nucleus and to the first excited state (2^ ) are calculated in the framework of the cluster model. The results indicate that a measurement of α spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus ^270Hs.     

Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of α-decay is extended to the regions around doubly magic spherical nucleus 208pb and around deformed shell closure 270Hs, respectively. The effects of spherical shell closures (N = 126 and Z = 82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical α-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus 208 Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of a-decays from the ground state of a parent nucleus to the ground state (0 ) of its deformed daughter nucleus and to the first excited state (2 ) are .calculated in the framework of the cluster model. The results indicate that a measurement of c spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus 270 Hs.     

Ground state properties and potential energy surfaces of ~(270)Hs from multidimensionally-constrained relativistic mean field model

We study the ground state properties,potential energy curves and potential energy surfaces of the superheavy nucleus 270Hs by using the multidimensionally-constrained relativistic mean-field model with the efFective interaction PC-PK1.The binding energy,size and shape as well as single particle shell structure corresponding to the ground state of this nucleus are obtained.270Hs is well deformed and exhibits deformed doubly magic feature in the single neutron and proton level schemes.One-dimensional potential energy curves and two-dimensional potential energy surfaces are calculated for 270Hs with various spatial symmetries imposed.We investigate in detail the effects of the reflection asymmetric and tri axial distortions on the fission barrier and fission path of 270Hs.When the axial symmetry is imposed,the reflection symmetric and reflection asymmetric fission barriers both show a double-hump structure and the former is highe匚However,when tri axial shapes are allowed the reflection symmetric barrier is lowered very much and then the reflection symmetric fission path becomes favorable.     

α结团模型在形变核区域的推广

将α结团模型推广至形变核,计算偶偶形变母核α衰变基态到子核基态和子核第一激发态的分支比,显示出α衰变精细结构的测量是提取核形变信息的有效手段.The cluster model of α-decay is extended to deformed nuclei. The branching ratios of α-decays from the ground state of a parent nucleus to the ground state 0~(+) of its deformed daughter nucleus and to the first excited state 2~(+) are calculated in the framework of the cluster model. The results indicate that a measurement of α spectroscopy is a feasible method to extract the information of nuclear deformation.     

Fusion Barrier of Super-heavy Elements in a Generalized Liquid Drop Model

The macroscopic deformed potential energies for super-heavy elements Z = 110,112,114,116,118 arc determined within a generalized liquid drop model (GLDM). A quasi-molecular mechanism is introduced to describe the deformation of a nucleus in the GLDM and the shell model simultaneously. The macroscopic energy of a twocenter nuclear system in the GLDM includes the volume-, surface-, and Coulomb-energies, the proximity effect at each mass asymmetry, and accurate nuclear radius. The shell correction is calculated by the Strutinsky method and the microscopic single particle energies are derived from a shell model in an axially deformed Woods-Saxon potential with the quasi-molecular shape. The total potential energy of a nucleus can be calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is applied to predict the fusion barriers of the cold reactions ^64Ni ^208 spb → ^272 110*, ^70Zn ^208pb → ^278 112*, ^76Ge ^208seb → ^284 114*,^82Se ^208pb → ^29 116*, ^86Kr ^208pb → ^294 118*. It is found that the neck in the quasi-molecular shape is responsible for the deep valley of the fusion barrier. In the cold fusion path, double-hump fusion barriers could be predicted by the shell corrections and complete fusion events may occur.     

Deformed Potential Energy of ^263Db in a Generalized Liquid Drop Model

The macroscopic deformed potential energy for super-heavy nuclei ^263 Db, which governs the entrance and alphadecay channels, is determined within a generalized liquid drop model (GLDM). A quasi-molecular shape is as-sumed in the GLDM, which includes volume-, surface-, and Coulomb-energies, proximity effects, mass asymmetry,and an accurate nuclear radius. The microscopic single particle energies are derived from a shell model in anaxially deformed Woods-Saxon potential with a quasi-molecular shape. The shell correction is calculated by theStrutinsky method. The total deformed potential energy of a nucleus can be calculated by the macro-microscopicmethod as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is appliedto predict the deformed potential energy of the experiment ^22Ne ^241Am→^263Db^*→^259Db 4n, which wasperformed on the Heavy Ion Accelerator in Lanzhou. It is found that the neck in the quasi-molecular shape isresponsible for the deep valley of the fusion barrier due to the shell corrections. In the cold fusion path, thedouble-hump fusion barrier is predicted by the shell correction and complete fusion events may occur.     

Deformed Potential Energy of Super Heavy Element Z = 120 in a Generalized Liquid Drop Model

The macroscopic deformed potential energy for super-heavy elements Z=120 is determined within a generalized liquid drop model (GLDM). The shell correction is calculated with the Strutinsky method and the microscopic single particle energies are derived from the shell model in an axially deformed Woods-Saxon potential with the same quasi-molecular shape. The total potential energy of a nucleus is calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is adopted to describe the deformed potential energies in a set of cold reactions. The neck in the quasi-molecular shape is responsible to the deep valley of the fusion barrier due to shell corrections. In the cold fusion path, the double-hump fusion barrier is predicted by the shell correction and complete fusion events may occur. The results show that some of projectile-target combinations in the entrance channel, such as ^50Ca ^252Fm→120 and 58Fe 244 pu→^302 120 , favour the fusion reaction, which can be considered as candidates for the synthesis of super heavy nuclei Z=120 and the former might be the best cold fusion reaction to produce the nucleus ^302 120among them.     

Description of ^178Hf^m2 in the Constrained Relativistic Mean Field Theory

Properties of the ground state of ^178Hf and the isomeric state ^178Hf^m2 are studied within the adiabatic and diabatie constrained relativistic mean field （RMF） approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of ^178Hf. Using the ground state single-particle eigenvalues obtained in the present eaiculation, the lowest excitation configuration with K^π = 16^＋ is found to be v（7/2^-[514]）^-1（9/2^＋ [624]）^1 π（7/2^＋ [404]）^-1 （9/2^-[514]）^1. Its excitation energy caiculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the ^178Hf^m2 experimentai excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.     

Clustering Structure of 10Be Studied with the Deformed RMF＋BCS Method

We investigate the nucleus 10Be using the deformed relativistic mean field （RMF） model and BCS theory. The calculated density distribution suggests two α clusters in the nucleus 10Be. According to BCS theory, the two valence neutrons transit to the first excited state 02＋ in a pair and form a 2-n cluster. By comparing the two neutron separation energy （S2n） with the single neutron separation energy （Sn）, and analyzing the difference between the neutron and proton rms radii （Rn-Rp） calculated by the deformed RMF, we suggest that 10Be is the best candidate for a two-neutron skin. The two-neutron skin clings to the 2α clusters closely and makes the two α clusters have cross and chain distribution.     

Oscillation of Hot Fissioning Nuclei around a Saddle Point

Three time scales of a fissioning nucleus starting from the ground state to the scission point are defined and calculated by the Monte Carlo method. The result shows that the time of oscillating around the saddle point is longer than both the mean first passage time from the ground state to the saddle point and the time of descent from the saddle to scission points. Thus it is suggested that more neutrons could be emitted from a hot heavy fissioning nucleus during the period of the stretching and contracting of the deformation process.     

△-Resonances in Ground State Properties of ^40 20Ca Spherical Cold Finite Nucleus at Equilibrium and under Compression

The ground state properties of the spherical nucleus ^40Ca have been investigated by using constrained spherical Hartree Fock （CSHF） approximation at equilibrium and under high radial compression in a six major shells. The effective baryon-baryon interaction that includes the △（1236） resonance freedom degrees to calculate nuclear properties is used. The nucleon-nucleon （N-N） interaction is based on Reid soft core （RSC） potential. The results of calculations show that much of increase in the nuclear energy generated under compression is used to create the massive △ particles. The number of △ ＇s can be increased to about 2.1% of constituents of nucleus when nuclear density reaches about 1.34 times of normal density. The single particle energy levels are calculated and their behavior under compression is also examined. △ good agreement has been found between current calculations and phenomenological shell model for low lying single-particle spectra. The gap between shells is very clear and L-S coupling become stronger as increasing the static load on the nucleus. The results show a considerable reduction in compressibility when freedom degrees of △＇s are taken into account. It has been found that the total nuclear radial density becomes denser in the interior and less dense in the exterior region of nucleus. The surface of nucleus becomes more and more responsive to compression than outer region.     

Mixed symmetry states and electromagnetic transition in the N=Z nucleus ^28Si

The interacting boson model with isospin （IBM-3） has been used to study mixed symmetry states and electromagnetic transitions at low-lying states for a ^28Si nucleus. The theoretical calculations show that the 24^＋ state is the lowest mixed symmetry state in ^28Si and the 43＋ state is also a mixed symmetry state.     

Gound State Properties of Nuclei in ^295118 α-Decay Chain

The properties of nuclei belonging to the α-decay chain of superheavy element ^295118 have been studied in the framework of axially deformed relativistic mean field （RMF） theory with the parameter set of NL-Z2 in the blocked BCS approximation. Some ground state properties such as binding energies, deformations, and α-decay energies Qα have been obtained and agree well with those from finite-range droplet model （FRDM）. The single-particle spectra of nuclei in ^295118 α-decay chain show that the shell gaps present obviously nucleon number dependence. The root-mean-square （rms） radii of proton, neutron and matter distributions change slowly from ^283112 to ^295118 but dramatically from ^279110 to ^283112, which may be due to the subshell closure at Z = 110 in ^279110. The α-decay half-lives in 295118 decay chain are evaluated by employing the cluster model and the generalized liquid drop model （GLDM）, and the overall agreement is found when they are compared with the known experimental data. The α-decay lifetimes obtained from the cluster model are slightly larger than those of GLDM ones. Finally, we predict the α-decay half-lives of Z=118, 116, 114, 112 isotopes using the cluster model and GLDM, which also indicate these two models can corroborate each other in studies on superheavy nuclei. The results from GLDM are always lower than those obtained from the cluster model.     

Microwave-Optical Double-Resonance Spectroscopy Experiment of 199Hg＋ Ground State Hyperfine Splitting in a Linear Ion Trap

We report a spectroscopy experiment of the ^199Hg＋ ions are optically pumped by a discharge lamp and splitting is measured to be 40507347996.8（0.1）Hz by line width as 30mHz is also observed. This progress ion frequency standards. ground state hyperfine splitting in a linear ion trap. The cooled by helium buffer gas. The ground state hyperfine the mierowave-optical double-resonance method. A nsrrow builds the foundation for the realization of trapped ^199Hg＋     

Spin polarization effect for Os2 molecule

Density functional Theory （DFT） （B3p86） of Gaussian03 has been used to optimize the structure of Os2 molecule. The result shows that the ground state for Os2 molecule is 9-multiple state and its electronic configuration is ^9∑^＋g, which shows spin polarization effect of Os2 molecule of transition metal elements for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions with higher energy states. So, the fact that the ground state for Os2 molecule is a 9-multiple state is indicative of spin polarization effect of Os2 molecule of transition metal elements. That is, there exist 8 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Os2 molecule is minimized. It can be concluded that the effect of parallel spin of Os2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters for the ground state ^9∑^＋g and other states of Os2 molecule are derived. Dissociation energy De for the ground state of Os2 molecule is 3.3971eV, equilibrium bond length Re is 0.2403nm, vibration frequency ωe is 235.32cm^-1. Its force constants f2, f3, and f4 are 3.1032×10^2aJ·nm^-2, -14.3425×10^3aJ·nm^-3 and 50.5792×10^4aJ·nm^-4 respectively. The other spectroscopic data for the ground state of Os2 molecule ωexe, Be and ae are 0.4277cm^- 1, 0.0307cm^- 1 and 0.6491 × 10^-4cm^-1 respectively.     

Spin polarization effect for molecule Ta2

Density functional theory （DFT） （B3p86） has been used to optimize the structure of the molecule Ta2. The result shows that the ground state of molecule Ta2 is a 7-multiple state and its electronic configuration is ^7∑u^＋, which shows the spin polarization effect for molecule Ta2 of transition metal elements for the first time. Meanwhile, spin pollution has not been found because the wavefunction of the ground state does not mix with those of higher states. So, the fact that the ground state of molecule Ta2 is a 7-multiple state indicates a spin polarization effect of molecule Ta2 of the transition metal elements, i.e. there exist 6 parallel spin electrons and the non-conjugated electrons are greatest in number. These electrons occupy different space orbitals so that the energy of molecule Ta2 is minimized. It can be concluded that the effect of parallel spin of the molecule Ta2 is larger than the effect of the conjugated molecule, which is obviously related to the effect of d-electron delocalization. In addition, the Murrell-Sorbie potential functions with parameters for the ground state ^7∑u^＋ and other states of the molecule Ta2 are derived. The dissociation energy De, equilibrium bond length Re and vibration frequency we for the ground state of molecule Ta2 are 4.5513eV, 0.2433nm and 173.06cm^-1, respectively. Its force constants f2, f3 and f4 are 1.5965×10^2aJ.nm^-2, -6.4722×10^3aJ·nm^-3 and 29.4851×10^4aJ·nm^-4, respectively. Other spectroscopic data we xe, Be and αe for the ground state of Ta2 are 0.2078cm^-1, 0.0315 cm^-1 and 0.7858×10^-4 cm^-1, respectively.     

Theoretical Investigation of the Exotic Structure of the Mirror Nuclei ^17Ne and ^17N

The exotic structures of the ground state of the mirror nuclei ^17Ne and ^17N are investigated by means of the asymptotic normalization coefficient （ANC） method to explore the role of the Coulomb interaction, The probebilities of a valence nucleon outside the binding-potential are P = 56.69±2.98/7.46% for ^17Ne and P = 45.51±2.32/5.81% for ^17N. The rms radii are （r^2）^1/2 = 5.06±0.11/0.30 fm and （r^2）^1/2=4.24±0.06/0.16 fm, respectively. The results obtained are nearly independent of the potential parameters. According to the halo occurrence conditions, it is suggested that ^17Ne is a two-proton halo and ^17N is a two-neutron skin. Moreover, two effects of the Coulomb interact-ion on the exotic structure are analysed. From the present results, the exotic structure of the nucleus in the proton-rich side is more obvious than that of its mirror nucleus because of the Coulomb interaction.     

Isotope Dependence of Superheavy Nucleus Formation Cross Section

The dynamical process in the superheavy nucleus synthesis is studied on the basis of the two-dimensional Smoluchowski equation. Special attention is paid to the isotope dependence of the cross section for the superheavy nucleus formation by means of making a comparison among the reaction systems of ^54Re＋204pb, ^56Re ＋206Pb, and ^58Fe＋^208Pb. It is found by this comparison that the formation cross section is very sensitive to the conditional saddle-point height and the neutron separation energy of the compound nucleus. Reaction systems with lower height of conditional saddle-point and smaller neutron separation energy are more favourable for the synthesis of the superheavy nucleus.     

Properties of the β-Delayed Proton Decay of 147Er

The β-delayed proton decay of 147Er is studied experimentally using the 58 Ni＋92Mo reaction at a beam energy of 383 MeV. Based on a He-jet apparatus coupled with a tape transport system, the β-delayed proton radioactivities both from the vδl/2 ground state and the vh11/2 isomer in 147 Er are identified by proton-7 coincidence measurements. By analyzing the time distribution of the 4＋ → 2＋-γ transition in the grand-daughter nucleus 146Dy, a half-life of 1.6 ± 0.2s is determined for the Vh11/2 isomer in 147 Er. The half-life for the ground state of 147Er is estimated to be 3.2±1.2 s.     

Calculation of Energy and Other Properties of Muonic Helium Atom Using Boundary Conditions of Wave Function

The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary conditions. It is shown that the obtained energy are very close to the values calculated by others. But the small differences of the expectation values of r^2n are due to the incorporated boundary conditions in proposed wave function and are expected.