Macroscopic-microscopic Approach Research Articles

SADDLE-POINT SHAPES OF HEAVY AND SUPERHEAVY NUCLEI

The potential energy of the heaviest nuclei is analyzed in a large deformation space. The main attention is given to shapes of these nuclei at their saddle point and to the comparison of these shapes with those at the ground state. The shapes are analyzed in a 10-dimensional deformation space. The analysis is performed within a macroscopic-microscopic approach. Even-even nuclei with proton number 98 ≤ Z ≤ 126 and neutron number 138 ≤ N ≤ 194 are considered.

DEFORMATIONS OF MULTIPOLARITY SIX AT THE SADDLE POINT OF HEAVIEST NUCLEI

Saddle-point configuration of heaviest nuclei is studied in a multidimensional deformation space. Main attention is given to the role of the deformation of multipolarity six of a general type, described by four independent parameters. The dependence of the potential energy of a superheavy nucleus on these parameters at the saddle-point configuration is illustrated. The analysis is performed within a macroscopic-microscopic approach.

Global microscopic calculations of ground-state spins and parities for odd-mass nuclei

Systematic calculations of ground-state spins and parities of odd-mass nuclei have been performed within the Hartree-Fock-BCS (HFBCS) approach and the finite-range droplet model for nuclei for which experimental data are available. The unpaired nucleon has been treated perturbatively, and axial and left-right reflection symmetries have been assumed. As for the HFBCS approach, three different Skyrme forces have been used in the particle-hole channel, whereas the particle-particle matrix elements have been approximated by a seniority force. The calculations have been done for the 621 nuclei for which the Nubase 2003 data set gives assignments of spins and parities with strong arguments. The agreement of both spin and parity in the self-consistent model reaches about 80% for spherical nuclei, and about 40% for well-deformed nuclei regardless of the Skyrme force used. As for the macroscopic-microscopic approach, the agreement for spherical nuclei is about 90% and about 40% for well-deformed nuclei, with different sets of spherical and deformed nuclei found in each model.

Optimal reactions for synthesis of nuclides of element 108

The cross sections for the production of nuclides of element 108 via hot fusion evaporation reactions are studied using a two-parameter Smoluchowski equation. The optimal reactions for the synthesis of new nuclides of element 108 with mass numbers from 266 to 271 are suggested. The macroscopic-microscopic approach predicts a strong deformed shell closure at Z � 108 and N = 162. The synthesis of more nuclides of element 108 is meaningful to the confirmation of the existence of this deformed shell closure.

ROLE OF HIGHER-MULTIPOLARITY DEFORMATIONS IN THE POTENTIAL ENERGY OF HEAVIEST NUCLEI

Potential energy of the superheavy nucleus 284114 is analyzed in a 6-dimensional deformation space. This space includes two quadrupole, three hexadecapole and one multipolarity-6 deformation parameter. The energy is minimized simultaneously in all 6 degrees of freedom. The analysis is done within a macroscopic-microscopic approach. As in the studies of other superheavy nuclei, the result is found to be very individual for a given nucleus. A more general feature is a small effect of one (γ4) of the hexadecapole deformation parameters on the energy of the nucleus.

SADDLE-POINT MASSES OF EVEN-EVEN ACTINIDE NUCLEI

In the framework of the macroscopic-microscopic approach the Yukawa folding procedure is used together with the Lublin-Strasbourg Drop liquid-drop type energy to describe atomic nuclei in the actinide region. The nuclear deformation is described by a 4-dimensional shape parametrisation similar to the well-known Funny-Hills expression. It is demonstrated that left-right asymmetry and non-axiality are present at the first and second saddle and should be included in the theoretical description. The importance of a different deformation of the proton and the neutron distribution also appears in the present analysis.

Particle number projection in the macroscopic–microscopic approach

We perform nuclear ground-state pairing calculations with the monopole pairing interaction. The particle number fluctuations are taken into account by the particle number projection method, with variation after projection. The pairing-correction energies obtained in this approach are compared to the BCS-model results. We discuss extensively how to properly incorporate different pairing models in global macroscopic–microscopic nuclear mass calculations. A method to calculate the smoothly changing part of the particle number projected energy is developed based on the Strutinsky procedure, making it possible to extract a pairing-shell energy. The behavior of the different pairing models is investigated in detail in the nuclei 164Er and 165Tm. Calculations are then performed along the β-stability line and for several isotope and isotone chains from the proton drip-line to the neutron drip-line. The single-particle energy levels used are obtained from two different single-particle potentials: the folded-Yukawa and the modified-harmonic oscillator potentials. The pairing calculations in the two potentials differ slightly in the fine-structure but the overall results are very similar. When comparing the particle number projected model and the BCS model it is found that the pairing-shell energy is quite insensitive to which microscopic pairing model is used.

Description of α-decay half-lives of heaviest nuclei

The accuracy in describing α-decay half-lives T α of heavy and superheavy nuclei is studied. A simple five-parameter phenomenological formula, expressing T α as a function of the α-decay energy Q α, is considered. It is found that such a formula can describe measured values of T α within a factor of 1.3 for even-even, 2.1 for odd-even, 3.2 for even-odd, and 4.0 for odd-odd nuclei when measured values of Q α are taken. This accuracy is decreased by a factor of about 4 when theoretical values of Q α are used. The latter are obtained within a macroscopic-microscopic approach and reproduce the experimental values of Q α of the same nuclei with an average accuracy of about 190 keV for even-even, 270 keV for odd-even, 260 keV for even-odd, and 330 keV for odd-odd nuclei. In the analysis, 201 nuclei with proton number Z = 84–111 and neutron number N = 128–161, with measured values of both Q α and T α, are taken.

Influence of different proton and neutron deformations on fission barriers

The response of the nuclear energy with respect to relative changes of proton versus neutron distributions is investigated. Contrary to most macroscopic–microscopic approaches, different multipole deformations of both distributions are admitted. The average part of the total energy is evaluated using the Yukawa-folded model, while microscopic energy corrections are obtained within the Strutinsky and BCS methods.

Nuclear Data Sheets for A = 251

Nuclear spectroscopic information for known nuclides of mass number 251 with Z = 96 to 102 (Cm,Bk,Cf,Es, Fm,Md,No) and N = 155 to 149 have been evaluated and presented together with adopted energies and Jπ of levels in these nuclei. No excited state data are yet available for 251Cm. This evaluation supersedes previous full evaluation of A = 251 by A. Artna-Cohen (1999Ar21) with literature cutoff date of Jul 1999. Inconsistencies and discrepancies are noted. The adopted values of level energies, level spins and parities are given, and γ-ray energies, γ-ray intensities, as well as other nuclear properties are presented. The references, Jπ arguments, and necessary comments are given. Theoretical studies are given as comments. New measurements have been reported in 251No, 251Md, 251Cf and 251Es. All adopted Q values are from 2003Au03. 2004Pa31 give calculated neutron separation energy by a macroscopic-microscopic approach.

SINGLE-PARTICLE EFFECTS IN DECAY CHAINS OF ODD-A SUPERHEAVY NUCLEI

Alpha-decay chain of 271 Ds (271110) is described theoretically. Transition energies [Formula: see text] and half-lives Tα are analyzed. The energies [Formula: see text] are described within a macroscopic-microscopic approach. Single-particle excitations of the nuclei are treated in the one-quasiparticle approximation. The half-lives Tα are described by a simple 3-parameter phenomenological formula expressing them as functions of [Formula: see text]. A good agreement with measured values is obtained. Average of the absolute values of the discrepancies for [Formula: see text] is 0.17 MeV. The half-lives Tα are reproduced within a factor of 3.8, on the average. No free parameters are used in the description.

α-decay properties of superheavy elementsZ=113−125in the relativistic mean-field theory with vector self-coupling of ω meson

We have investigated properties of $\alpha$-decay chains of recently produced superheavy elements Z=115 and Z=113 using the new Lagrangian model NL-SV1 with inclusion of the vector self-coupling of $\omega$ meson in the framework of the relativistic mean-field theory. It is shown that the experimentally observed alpha-decay energies and half-lives are reproduced well by this Lagrangian model. Further calculations for the heavier elements with Z=117-125 show that these nuclei are superdeformed with a prolate shape in the ground state. A superdeformed shell-closure at Z=118 lends an additional binding and an extra stability to nuclei in this region. Consequently, it is predicted that the corresponding $Q_\alpha$ values provide $\alpha$-decay half-lives for heavier superheavy nuclei within the experimentally feasible conditions. The results are compared with those of macroscopic-microscopic approaches. A perspective of the difference in shell effects amongst various approaches is presented and its consequences on superheavy nuclei are discussed.

Ground-state properties of superheavy elements in macroscopic-microscopic models

Masses, α-decay and spontaneous fission half-lives of superheavy elements are studied in macroscopic-microscopic approaches with two different macroscopic models and the delta-pairing interaction. Model mass deviations obtained with different formulae are 0.5-0.8MeV.

ROLE OF HIGHER MULTIPOLARITY DEFORMATIONS IN THE HEIGHT OF FISSION BARRIER OF A DEFORMED HEAVY NUCLEUS

Role of higher-multipolarity deformations of a nucleus in its (static) fission-barrier height [Formula: see text] is studied. The study is done within a macroscopic-microscopic approach. A heavy deformed nucleus 250 Cf is taken for the analysis. It is found that, in the case of axially symmetric shapes, the inclusion of higher-multipolarity deformations increases [Formula: see text].

ROLE OF HIGHER MULTIPOLARITY DEFORMATIONS IN THE FISSION-BARRIER HEIGHT OF A SPHERICAL SUPERHEAVY NUCLEUS

Role of the dimension of deformation space used in calculations of the (static) fission-barrier height [Formula: see text] is analyzed for a spherical nucleus. The superheavy nucleus 294116 is taken for the analysis. The study is done within a macroscopic-microscopic approach. It is found that the barrier height [Formula: see text] importantly decreases with increasing dimension of the space.

SENSITIVITY OF ONE-QUASIPARTICLE SPECTRA OF HEAVIEST NUCLEI TO VARIOUS FACTORS

Sensitivity of one-quasiparticle spectrum of a heavy nucleus to changes of such quantities as equilibrium deformation and pairing-interaction strength is studied. The study is done within a macroscopic-microscopic approach. The analysis is performed on the example of the nucleus 241 Am . Especially large sensitivity of the spectrum to changes of the quadrupole component of the equilibrium deformation is found.

INFLUENCE OF DIFFERENT PROTON AND NEUTRON DEFORMATIONS ON NUCLEAR ENERGIES

The response of nuclear energy with respect the change of proton and neutron distributions is investigated. Contrary to most macroscopic-microscopic approaches, different radii and multipole deformations of both distributions are admitted here. The average part of the total energy is evaluated using the Yukawa-folded model, while the microscopic energy corrections are obtained within the Strutinsky and BCS methods.

Superdeformed ground state of superheavy nuclei?

Problem of superdeformed ground state, predicted recently for superheavy nuclei, is considered within a macroscopic–microscopic approach. The results do not support this prediction.

Neutron Separation Energy for Heavy and Superheavy

The neutron separation energy is calculated within a macroscopic-microscopic approach for nuclei with proton and neutron numbers, Z=82−128 and N=126−190, respectively. The results are compared with existing experimental and other theoretical data.

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.