Ground-state Shell Corrections Research Articles

Role of spin-orbit strength in the prediction of closed shells in superheavy nuclei

Using the microscopic-macroscopic approach based on the modified two-center shell model, the ground-state shell corrections are analyzed as a function of spin-orbit strength for even-$Z$ superheavy nuclei in the $\ensuremath{\alpha}$-decay chains containing $^{295--300,302,304}120$ nuclei. The influence of the spin-orbit strength on the positions of shell closures and the description of the low-lying one-quasiparticle spectra for $^{251}\mathrm{Cf}, ^{243}\mathrm{Cm}, ^{243}\mathrm{Bk}$, and $^{251}\mathrm{Es}$ nuclei are studied in detail. The importance of studying the nuclear structure of actinides for predicting the next double magic nucleus beyond $^{208}\mathrm{Pb}$ is demonstrated.

Landscape of the island of stability with self-consistent mean-field potentials

Incorporating effective nucleon mass from the noncovariant energy-density functional, the Schr\"odinger-equivalent central and spin-orbit mean-field potentials are determined and used in the microscopic-macroscopic method to calculate the ground-state shell corrections in superheavy nuclei with the charge numbers $Z=112--126$. The island of stability of superheavy nuclei is found to be rather flat and looks like one of coral reef origin due to the interplay between the proton shells at $Z=114$ and 120, and neutron shells at $N=174$ and 184, respectively. The shape coexistence in superheavy nuclei depends on spin-orbit potentials and can affect the spectrum of $\ensuremath{\alpha}$ decay. The one-quasiparticle spectra, isomeric states, and possible $\ensuremath{\alpha}$-decay energies are predicted in the nuclei of $\ensuremath{\alpha}$-decay chains of $^{295}119$ and $^{295--297,299}120$.

Shaping the archipelago of stability by the competition of proton and neutron shell closures

The evolution of superheavy nuclei in proton and neutron number is explored by investigating the ground-state shell correction energy in the $Z=112\text{--}126$ and $N=170\text{--}190$ region of the $(Z,N)$ plane. Cuts through the $(Z,N)$-dependent distribution of shell corrections are chosen for constant neutron-proton differences as accessible in $\ensuremath{\alpha}$-decay chains and varying the neutron number at fixed charge number. A new approach is used, integrating elements of energy-density functional theory into the microscopic-macroscopic method. The topology of the shell correction implies for binding energies a distribution resembling in shape a ridge on a coral reef, formed by the competition of proton and neutron shell closures at $Z=114$ and $Z=120$, and $N=174$ and $N=184$, respectively. $^{288}\mathrm{Fl}$ is predicted as the next double magic nucleus after $^{208}\mathrm{Pb}$, and $^{304}120$ is identified as the most likely candidate for next-to-next double magic nucleus.

Predictions of identification and production of new superheavy nuclei with Z=119 and 120

Effective single-particle potentials obtained from the established nonrelativistic nuclear energy density functional approach are incorporated into the microscopic-macroscopic method to calculate the ground-state shell corrections, mass excesses, and ${Q}_{\ensuremath{\alpha}}$ values for heaviest nuclei. The low-lying one-quasiparticle states are studied in the isotonic chains with neutron numbers $N=175$, 176, and 177. The isomeric states are discussed in the odd isotopes. The possible $\ensuremath{\alpha}$-decay chains of nuclei $^{295}119$ and $^{295,297}120$ are analyzed and compared with the available experimental data. The termination of the $\ensuremath{\alpha}$-decay chains by spontaneous fission is analyzed. The production cross sections are calculated for superheavy nuclei with $112\ensuremath{\le}Z\ensuremath{\le}120$ in the actinide-based complete fusion reactions with projectiles $^{48}\mathrm{Ca}, ^{48,50}\mathrm{Ti}, ^{54}\mathrm{Cr}, ^{58}\mathrm{Fe}$, and $^{64}\mathrm{Ni}$.

Level densities and shell corrections of superheavy nuclei

The intrinsic level densities of superheavy nuclei in the α-decay chains of 296;298;300120 nuclei are calculated using the single-particle spectra obtained with the modifed two-center shell model. The level density parameters are extracted and compared with their phenomenological values used in the calculations of the survival of excited heavy nuclei. The dependences of the level density parameters on the mass and charge numbers as well as on the ground-state shell corrections are studied.

Level densities of heaviest nuclei

The intrinsic level densities of superheavy nuclei in the α-decay chains of 296,298,300120 are calculated using the single-particle spectra obtained with the modified two-center shell model. The role of the shell and pairing effects on the level density as well as their quenching with excitation energy are studied. The extracted level density parameter is expressed as a function of mass number, ground-state shell correction, and excitation energy. The results are compared with the phenomenological values of level density parameters used to calculate the survival of excited heavy nuclei.

Microscopic-macroscopic method for studying single-particle level density of superheavy nuclei

The intrinsic level densities of superheavy nuclei in the a-decay chains of 296,298,300120 nuclei are calculated using the single-particle spectra obtained with the modified two-center shell model. The level density parameters are extracted and compared with their phenomenological values used in the calculations of the survival of excited heavy nuclei. The dependences of the level density parameters on the mass and charge numbers as well as on the ground-state shell corrections are studied.

Impact of nuclear structure on production and identification of new superheavy nuclei

Using the microscopic-macroscopic approach based on the modified two-center shell model, the low-lying quasiparticle spectra, ground-state shell corrections, mass excesses and Qα-values for even Z superheavy nuclei with 108 ≤ Z ≤ 126 are calculated and compared with available experimental data. The predicted properties of superheavy nuclei show that the next doubly magic nucleus beyond 208Pb is at Z ≥ 120. The perspective of using the actinide-based complete fusion reactions for production of nuclei with Z = 120 is studied for supporting future experiments.

Ground-state energy of finite Fermi systems

We study the ground-state shell correction energy of a fermionic gas in a mean-field approximation. Considering the particular case of three-dimensional harmonic trapping potentials, we show the rich variety of different behaviors (erratic, regular, supershells) that appear when the number-theoretic properties of the frequency ratios are varied. For self-bound systems, where the shape of the trapping potential is determined by energy minimization, we obtain accurate analytic formulas for the deformation and the shell correction energy as a function of the particle number $N$. Special attention is devoted to the average of the shell correction energy. We explain why in self-bound systems it is a decreasing (and negative) function of $N$.

Nuclear structure and dynamics from heavy - ion induced fission reactions

The study of heavy - ion fusion and fission reactions at near - barrier energies continues to be a rich source of information as regards nuclear structure and dynamics. From a comprehensive statistical model analysis of the fusion and the fission data including information on the pre - scission neutrons, for a large number of compound nuclei with masses around 200, it has been possible to determine reliably the fission barrier, the nuclear moment of inertia and the shell correction at the saddle point. Interestingly, it is found that for the nuclei in the mass region around 200, a significantly large fraction of the ground state shell correction persists at the deformed saddle - point. Systematic measurements of the fission fragment angular distributions spanning a range of projectiles with A = 9 to 19, bombarding the Th,U and Np targets have clearly brought out role of the entrance channel dynamics involving a new type of non - equilibrium fission, which we call pre - equilibrium fission comempeting with the equilibrium compound nucleus fission. A new model which takes into account the deformation and the spin values of the target and the projectile, the orientation and the entrance channel mass asymmetry dependence of the interacting nuclei has been developed which provides a good description of the fission fragment angular distribution data both at above and below barrier energies.

Tests of the fission-evaporation competition in the deexcitation of heavy nuclei

In order to verify methods of calculating the fission-evaporation competition in reactions used to synthesize new super-heavy nuclei in ``cold'' $(1n)$ and ``hot'' $(3n,4n)$ fusion reactions, we present an analysis of existing experimental data on the evaporation-residue cross sections in two selected reactions, $^{208}\mathrm{Pb}$($^{16}\mathrm{O}$, xn) and $^{236}\mathrm{U}$($^{12}\mathrm{C}$, xn), for which complementary experimental information necessary to unambiguously calculate the survival probabilities is available: precisely measured fusion excitation functions and saddle-point energies of the fissioning nuclei, deduced from experiments. Standard statistical model calculations, with shell effects accounted for by the Ignatyuk formula, were carried out assuming the ground state shell corrections of M\"oller et al., and zero shell correction at the saddle configuration (resulting from the presented systematics). Good agreement of the calculated evaporation-residue cross sections with experimental data for different xn reaction channels at low excitation energies leaves no room for modifications of the conventional way of calculating the ${\ensuremath{\Gamma}}_{n}/{\ensuremath{\Gamma}}_{f}$ ratio, particularly for including into this ratio an additional preexponential factor (such as the Kramers fission hindrance factor or an effective collective factor) significantly different from 1.

SHELL CORRECTION ENERGIES IN CALCULATIONS OF THE SURVIVAL PROBABILITY

Analysis of existing data on experimental fission barriers for about 90 nuclei shows that the shell correction energy practically vanishes at the barrier configuration. Statistical model calculations, with shell effects accounted for by the Ignatyuk formula, were carried out for the decay of the 248 Cf compound nucleus assuming the ground state shell corrections of Möller et al., and the vanishing shell correction energy at the barrier. The results are consistent with existing experimental data on fusion- and xn evaporation-residue cross sections in the 12 C +236 U reaction.

Shell corrections for finite depth potentials with bound states only

A new method of calculating unique values of ground-state shell corrections for finite depth potentials is shown, which makes use of bound states only. It is based on (i) a general formulation of extracting the smooth part from any fluctuating quantity proposed by Strutinsky and Ivanjuk, (ii) a generalized Strutinsky smoothing condition suggested recently by Vertse et al., and (iii) the technique of the Lanczos σ factors. Numerical results for some spherical heavy nuclei (132,154Sn, 180,208Pb and 298114) are presented and compared to those obtained with the Green's function oscillator expansion method.

On the stability of the transeinsteinium elements

We calculate ground-state properties of nuclei in the Z≧100 region. The most stable superheavy elements are predicted for lower neutron number than in previous investigations, namely110288X and110290X, both with a calculated half-life of around 200 days. A new feature is a local minimum in the ground-state shell correction at Z=110 andN=162. Elements in this region are therefore expected to show increased stability relative to some earlier expectations.

Statistical properties of excited fissioning nuclei

The phenomenon of the disappearance of the shell effects on the thermodynamic properties of nuclei with increasing excitation energy has been examined quantitatively on the basis of numerical calculations based on realistic shell model single particle level schemes. It is shown that shell effects disappear at moderate excitation energies and above these excitation energies, the thermodynamic behaviour of the nucleus is identical to that of the equivalent liquid drop model nucleus. Implications of the above feature in the interpretation of some aspects of fission of excited nuclei such as mass-asymmetry and angular anisotropy are examined. The relationship of the phenomenon of washing out of shell effects at high excitation energies with the temperature smearing method of determining ground state shell correction energies is also outlined.

The equivalence of the Strutinsky type smoothing and the temperature averaging method

The Fermi gas model of the nucleus at high temperatures can be used to define a ground state shell correction. We demonstrate analytically that the shell correction so obtained is the same as that obtained from the Strutinsky type method.

Statistical properties of excited nuclei and the determination of the ground-state shell correction energies

It is shown that the ground-state shell correction energies of nuclei can be obtained from a study of the high temperature behaviour of their thermodynamic properties without recourse to Strutinsky's smearing procedure.

Fragment-Shell Influences in Nuclear Fission

Potential-energy surfaces and shell-correction-energy surfaces for nuclei in the $A\ensuremath{\simeq}200$ region and for actinide ($A\ensuremath{\gtrsim}230$) have been calculated in the improved two-center model. These surfaces are shown in a two-dimensional representation as a function of the elongation and the constriction of the nuclear shape. Both the ground-state shell corrections and the fission barriers in the $A\ensuremath{\cong}200$ region agree well with experiment. It is found that the saddlepoint position in this region is shifted significantly towards smaller deformations compared with the liquid-drop-model prediction, this shift arising from a very pronounced valley in the shell-correction surface at the position of the liquid-drop-model saddle point. The implications of this finding for a nuclear mass formula and for the application of the liquid-drop model to fission of these nuclei are discussed. In both mass regions ($A\ensuremath{\cong}200 \mathrm{and} A\ensuremath{\gtrsim}230$) the shell corrections alone show pronounced structure which changes slowly with mass number. At small deformations, up to the region of the second maximum in the potential, this structure is determined by the compound-nucleus shell structure. At larger deformations this structure is shown to arise from the shell structure of the nascent fragments, thus establishing the importance of fragment shells early in the fission process for the entire mass range $A\ensuremath{\gtrsim}200$. As a consequence of these studies the regions of validity for the liquid-drop model in describing nuclear fission are explained. Finally, it is shown that the recently observed symmetry in the mass distribution of $^{257}\mathrm{Fm}$ is due to the approach to the nucleus $^{264}\mathrm{Fm}$, which can split symmetrically into the two energetically strongly favored $^{132}\mathrm{Sn}$ nuclei.