Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier

Static fission barriers for 95 even-even transuranium nuclei with charge number Z = 94-118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional(β_2, γ, β_4) deformation space. Taking the heavier (252)~Cf nucleus(with the available fission barrier from experiment) as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β_2 values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei(e.g., the Z =112-118 isotopes). Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications(e.g.,the strength of the spin-orbit coupling and the nuclear surface diffuseness) on the fission barrier are briefly discussed.     

Nuclear mass formula with a Yukawa-plus-exponential macroscopic model and a folded-Yukawa single-particle potential

We use a Yukawa-plus-exponential macroscopic model and a folded-Yukawa single-particle potential to systematically calculate the ground-state masses of 4023 nuclei ranging from ¹⁶O to {279}112. The method is also used to calculate the fission-barrier heights of 28 nuclei ranging from ¹⁰⁹Cd to ²⁵²Cf. We introduce several previously neglected physical effects, including a smaller nuclear radius constant, a proton form factor, an exact diffuseness correction, an A⁰ term, a chargeasymmetry term, and microscopic zero-point energies. The nuclear radius constant is determined from elastic electron scattering and microscopic calculations of nuclear density distributions, the range of the Yukawa-plus-exponential folding function is determined from heavy-ion elastic scattering, the surface-energy constant and surface-asymmetry constant are determined from the fission-barrier heights of the 28 nuclei that are considered, and the remaining constants are determined from the ground-state masses of 1323 nuclei ranging from ¹⁶O to ²⁵⁹No for which experimental values are known with experimental errors less than 1 MeV. For the final formula, the root-mean-square error in the ground-state masses is 0.835 MeV and the root-mean-square error in the fission-barrier heights is 1.331 MeV. Some of the remaining discrepancies in the groundstate masses can be understood in terms of instabilities with respect to ε₃ and ε₆ deformations.     

Core polarization effects and giant quadropole resonances in the A ≈ 90 region

The existence, in A ≈ 90 nuclei, of large E2 core polarization effects evident from experimental and shell model fits to decay rates is examined in two independent model calculations: a linearized Hartree-Fock calculation studying the nuclear response function and a macroscopic model involving excitations of giant quadrupole resonances. Both investigations confirm the need for large renormalization of proton and neutron E2 effective charges consistent with the recently discovered isoscalar and isovector giant quadrupole resonances.     

Microscopic quadrupole and hexadecapole moments of rare earth nuclei

The theoretical calculations of multipole moments of even-even rare earth nuclei are presented. The potential energy surface is evaluated by the shell correction method. The condition ensuring the equality of the density distribution of the macroscopic liquid droplet part of the potential energy and the density generated by the single particle potential is added. A single particle Nilsson potential is used. New, less stiff potential surfaces versusε ₄ are obtained while the multipole moments calculated at the equilibrium deformations agree well with experimental data.     

Anomaly in α-scattering from 6Li between 35 and 45 MeV

The elastic scattering of α-particles on ⁶Li nuclei has been measured from 20° to 170° (c.m.) and the inelastic scattering to the first excited state of ⁶Li has been measured for forward and backward angles. The elastic scattering angular distributions are calculated (i) in terms of pure potential scattering, (ii) in terms of potential scattering with an l-cut-off on the imaginary part of the potential and (iii) in terms of the coherent addition of the potential scattering amplitude and of the exchange amplitude. The third method gives the best fit to the data. The inelastic angular distributions are compatible with the macroscopic calculations, except in the very backward region where exchange phenomena are also shown to dominate.     

Calculations of the β-decay half-lives of neutron-deficient nuclei

In this work,β~+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation(QRPA),where neutron-neutron,proton-proton and neutron-proton(np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov(HFB) transformation.In addition to the pairing interaction,the Br¨uckner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions.Calculations are performed for even-even proton-rich isotopes ranging from Z =24 to Z =34.It is found that the np pairing interaction plays a significant role inβ-decay for some nuclei far from stability.Compared with other theoretical calculations,our calculations show good agreement with the available experimental data.Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.     

Spontaneous fission of isomeric states of actinide nuclei

Spontaneous fission half-lives of K-isomeric states are calculated on the basis of microscopic- macroscopic method. The isomeric state is assumed to be a 2-quasiparticle excited state with high angular momentum.The calculations were performed for nuclei with 96 < Z < 110 and 144 < N < 158. It was shown that in the case of K-isomeric states (if they exist) the spontaneous fission half-life time may be comparable to the spontaneous fission half-life time of the ground state. Therefore it was suggested that in measurements of fission half-lives it may be very important to distinguish between both possible components (or more) of the fission decay.     

Multi-nucleus IBA calculations in the NπNν scheme

IBA-1 calculations for ～ 100 nuclei in three mass regions from A = 100–200 are carried out according to a recently proposed N_πN_ν parametrization. The calculations use a total of only seven constants consisting of four parameters which are constant for all 100 nuclei and one parameter which takes on a separate value for each of the three regions. The changes in nuclear structure for each region are reproduced and the detailed values of individual energy levels and B(E2) values are reasonably well accounted for. The implications of the extreme economy in parameters are discussed and the usefulness of the present approach for other collective models is pointed out.     

Macroscopic-microscopic calculations of ground state properties of superheavy nuclei

We systematically calculate the ground state properties of superheavy even-even nuclei with proton number Z=94–118. The calculations are based on the liquid drop macroscopic model and the microscopic model with the modified single-particle oscillator potential. The calculated binding energies and α-decay energies agree well with the experimental data. The reliability of the macroscopic-microscopic(MM)model for superheavy nuclei is confirmed by the good agreement between calculated results and experimental ones. Detailed comparisons between our calculations and M?ller’s are made. It is found that the calculated results also agree with M?ller’s results and that the MM model is insensitive to the microscopic single-particle potential. Calculated results are also compared with results from relativistic mean-field (RMF) model and from Skyrme-Hatree-Fock(SHF) model. In addition, half-lives, deformations and shape coexistence are also investigated. The properties of some unknown nuclei are predicted and they will be useful for future experimental researches of superheavy nuclei.     

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.     

Study of pairing deformations by means of two-particle transfer reactions

The macroscopic approach for two-particle transfer reactions is applied in normal spherical nuclei and pairing deformation parameters β_p are estimated. For Ni isotopes the macroscopic approach works reasonably well while for the lead region strong energy dependence of theβ _p values has been observed. It is shown that alpha-transfer reactions can also be treated within this formalism as couplings of the two-neutron and two-proton channels.     

Systematic study of decay properties of heaviest elements

Decay properties and stability of heaviest nuclei with Z ?? 132 are studied within the macro-microscopical approach for nuclear ground-state masses. We use phenomenological relations for the half-lives with respect to ??-decay, ??-decay and spontaneous fission. Our calculations demonstrate that the ??-stable isotopes ²⁹¹Cn and ²⁹³Cn with a half-life of about 100 years are the longest-living superheavy nuclei located on the first island of stability. We found the second island of stability of superheavy nuclei in the region of Z ?? 124 and N ?? 198. It is separated from the ??continent?? by the ??gulf?? of short-living nuclei with half-lives shorted than 1 ??s.     

Microscopic calculation of pre-equilibrium emission

Previous TDHF calculations have shown that a pre-equilibrium emission of nucleons should be seen for asymmetric collisions of nuclei. Recent calculations indicate that the added effect of two-body collisions is to enhance this pre-equilibrium emission, it being seen also for symmetric collisions. More detailed calculations of this phenomenon are presenied here. The two-body collisions are treated by the time-relaxation method. This method is reviewed, and a revised formula for the relaxation time is introduced.Calculations are made in a slab geometry. For real nuclei, as much as 6% of all nucleons are estimated to be emitted at a beam energy of E_c.m. = 20 MeV/A. The energy distribution of the emitted nucleons relates to a temperature of 13 MeV at this energy. At 5 MeV/A, the emission is reduced to about 1 %.     

Effect of properties of superheavy nuclei on their production and decay

Properties and stability of superheavy nuclei resulting from hot fusion are discussed. It is shown that the microscopic–macroscopic approach allows obtaining the closed proton shell at Z ≥ 120. Isotopic trends of K-isomeric states in superheavy nuclei are predicted. Evaporation residue cross sections in hot fusion reactions are calculated using the predicted properties of superheavy nuclei. Interruption of α decay chains by spontaneous fission is analyzed. Alpha decay chains through isomeric states are considered. Internal level densities in superheavy nuclei are microscopically calculated.     

Systematics of spontaneous-fission barrier heights

Heights of (static) spontaneous-fission barriers of heaviest nuclei are calculated within a macroscopic—microscopic approach. Even—even nuclei with proton numbers Z = 96–120 are considered.     

Shell model approach to collectivity in pseudo spin-orbit coupling

A technique is described for shell model calculations in the newly suggested k-i representation of single particle states. The technique allows microscopic calculations for the structure of medium and heavy nuclei in spaces which are truncated in an analogy with the assumptions of the interacting boson model (IBM). The present technique incorporates all the power and generality of standard shell model calculations and provides a unified approach to even-even, even-odd and odd-odd nuclei.     

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model(GLDM), whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.     

The calculation of logft values and spectroscopic factors for nuclei in the mass range 10–15

Wave functions obtained in previous shell-model calculations [1, 2] for states of nuclei with massesA=10–15 are used to calculate logft values and spectroscopic factors. These wave functions, which were based on a modified surface delta two-body interaction, comprise the following active shell-model spaces: the 1p _3/2 and 1p _1/2 orbitals for mass 10–14 nuclei and restricted combinations of the 1p _1/2, 2s _1/2, 1d _5/2 and 1d _3/2 orbitals for mass 15 nuclei, leading to four different calculations in the latter case. The calculated results support evidence that the modified surface delta interaction is a valid approximation to the effective interaction in light nuclei.     

Particle-hole excitations in the208Pb mass region

Spectra, magnetic dipole moments and spectroscopic factors of a number ofA=205–209 nuclei as well asM1 transitions in²⁰⁸Pb are investigated in terms of large-scale shell-model calculations which include 1p ?1h excitations and for some nuclei 2p ?2h excitations. The calculated spectra agree well with the data. The calculatedg-factors are in fair agreement with the data in most cases. The predicted strength forM1 transitions to low-lying states in²⁰⁸Pb is less than that obtained from previous calculations. Spectroscopic factors forl=0 proton pick-up from²⁰⁸Pb and²⁰⁶Pb agree very well with recent experimental data from (e, e′p) reactions.     

Deformed Hartree-Fock calculation of proton-rich nuclei

We perform Hartree-Fock+BCS calculations for even-even nuclei with 2 ≤ Z ≤ 82 and N ranging from outside the proton drip line to the experimental frontier on the neutron-rich side. The ground state solutions are obtained for 737 nuclei, together with shape-coexistence solutions for 480 nuclei. Our method features the Cartesian-mesh representation of single-particle wavefunctions, which is advantageous in treating nucleon skins and exotic shapes. The results are compared with those of the finite-range droplet model of Møller et al. as well as the experimental values.