Spontaneous Fission Lifetimes Research Articles

On the stability of superheavy nuclei

Potential energy surfaces of even–even superheavy nuclei are evaluated within the macroscopic-microscopic approximation. A very rapidly converging analytical Fourier-type shape parametrization is used to describe nuclear shapes throughout the periodic table, including those of fissioning nuclei. The Lublin Strasbourg Drop and another effective liquid-drop type mass formula are used to determine the macroscopic part of nuclear energy. The Yukawa-folded single-particle potential, the Strutinsky shell-correction method, and the BCS approximation for including pairing correlations are used to obtain microscopic energy corrections. The evaluated nuclear binding energies, fission-barrier heights, and \(Q_\alpha \) energies show a relatively good agreement with the experimental data. A simple one-dimensional WKB model à la Świa̧tecki is used to estimate spontaneous fission lifetimes, while \(\alpha \) decay probabilities are obtained within a Gamow-type model.

Cluster radioactivity of Og176118294

According to theory, cluster radioactivity becomes an important decay mode in superheavy nuclei. In this work, we predict that the strongly-asymmetric fission, or cluster emission, is in fact the dominant fission channel for $^{294}_{118}$Og$_{176}$, which is currently the heaviest synthetic isotope known. Our theoretical approach incorporates important features of fission dynamics, including quantum tunneling and stochastic dynamics up to scission. We show that, despite appreciable differences in static fission properties such as fission barriers and spontaneous fission lifetimes, the prediction of cluster radioactivity in $^{294}_{118}$Og$_{176}$ is robust with respect to the details of calculations, including the choice of energy density functional, collective inertia, and the strength of the dissipation term.

Fission properties of superheavy nuclei for r -process calculations

We computed a new set of static fission properties suited for r-process calculations. The potential energy surfaces and collective inertias of 3640 nuclei in the superheavy region are obtained from Self-Consistent Mean-Field calculations using the Barcelona-Catania-Paris-Madrid energy density functional. The fission path is computed as a function of the quadrupole moment by minimizing the potential energy and exploring octupole and hexadecapole deformations. The spontaneous fission lifetimes are evaluated employing different schemes for the collective inertias and vibrational energy corrections. This allows to explore the sensitivity of the lifetimes to those quantities together with the collective ground state energy along the superheavy landscape. We computed neutron induced stellar reaction rates relevant for r-process nucleosynthesis using the statistical approach and study the impact of collective inertias. The competition between different reaction channels including neutron induced rates, spontaneous fission and alpha decay is discussed for typical r-process conditions.

Benchmarking nuclear fission theory

We suggest a small set of fission observables to be used as test cases for validation of theoretical calculations. The purpose is to provide common data to facilitate the comparison of different fission theories and models. The proposed observables are chosen from fission barriers, spontaneous fission lifetimes, fission yield characteristics, and fission isomer excitation energies.

Spontaneous fission lifetimes from the minimization of self-consistent collective action

The spontaneous fission lifetime of ${}^{264}$Fm has been studied within nuclear density functional theory by minimizing the collective action integral for fission in a two-dimensional quadrupole collective space representing elongation and triaxiality. The collective potential and inertia tensor are obtained self-consistently using the Skyrme energy density functional and density-dependent pairing interaction. The resulting spontaneous fission lifetimes are compared with the static result obtained with the minimum-energy pathway. We show that fission pathways strongly depend on assumptions underlying collective inertia. With the nonperturbative mass parameters, the dynamic fission pathway becomes strongly triaxial and it approaches the static fission valley. On the other hand, when the standard perturbative cranking inertia tensor is used, axial symmetry is restored along the path to fission; an effect that is an artifact of the approximation used.

Spontaneous fission modes and lifetimes of superheavy elements in the nuclear density functional theory

Background: The reactions with the neutron-rich ${}^{48}\mathrm{Ca}$ beam and actinide targets resulted in the detection of new superheavy (SH) nuclides with $Z=104--118$. The unambiguous identification of the new isotopes, however, still poses a problem because their $\ensuremath{\alpha}$-decay chains terminate by spontaneous fission (SF) before reaching the known region of the nuclear chart. The understanding of the competition between $\ensuremath{\alpha}$-decay and SF channels in SH nuclei is, therefore, of crucial importance for our ability to map the SH region and to assess its extent.Purpose: We perform self-consistent calculations of the competing decay modes of even-even SH isotopes with $108\ensuremath{\le}Z\ensuremath{\le}126$ and $148\ensuremath{\le}N\ensuremath{\le}188$.Methods: We use the state-of-the-art computational framework based on self-consistent symmetry-unrestricted nuclear density functional theory capable of describing the competition between nuclear attraction and electrostatic repulsion. We apply the SkM* Skyrme energy density functional. The collective mass tensor of the fissioning superfluid nucleus is computed by means of the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (HFB) approach. This paper constitutes a systematic self-consistent study of spontaneous fission in the SH region, carried out at a full HFB level, that simultaneously takes into account both triaxiality and reflection asymmetry.Results: Breaking axial symmetry and parity turns out to be crucial for a realistic estimate of collective action; it results in lowering SF lifetimes by more than 7 orders of magnitude in some cases. We predict two competing SF modes: reflection symmetric modes and reflection asymmetric modes.Conclusions: The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow corridor formed by ${}^{280}\mathrm{Hs}$, ${}^{284}\mathrm{Fl}$, and ${}_{118}^{284}\mathrm{Uuo}$ that separates the regions of SH nuclei synthesized in ``cold-fusion'' and ``hot-fusion'' reactions. The region of long-lived SH nuclei is expected to be centered on ${}^{294}\mathrm{Ds}$ with a total half-life of $\ensuremath{\sim}1.5\phantom{\rule{0.28em}{0ex}}\mathrm{days}$. Our survey provides a solid benchmark for the future improvements of self-consistent SF calculations in the region of SH nuclei.

Study of spontaneous fission lifetimes using nuclear density functional theory

The spontaneous fission lifetimes have been studied microscopically by minimizing the collective action integral in a two-dimensional collective space of quadrupole moments (Q20 ,Q 22) representing elongation and triaxiality. The microscopic collective potential and inertia tensor are obtained by solving the self-consistent Hartree- Fock-Bogoliubov (HFB) equations with the Skyrme energy density functional and mixed pairing interaction. The mass tensor is computed within the perturbative Adiabatic Time- Dependent HFB (ATDHFB) approach in the cranking approximation. The dynamic fission trajectories have been obtained by minimizing the collective action using two different numerical techniques. The values of spontaneous fission lifetimes obtained in this way are compared with the static results.

Coupling of the pairing vibrations with the fission mode

The influence of collective pairing vibrations on the spontaneous fission lifetimes are studied. The Nilsson single-particle potential plus the monopole pairing residual interaction are used. The collective hamiltonian is obtained within the cranking model. The fission lifetimes are evaluated in the WKB approximation along the least-action trajectory in the three-dimensional space (ε 24, Δ p , Δ n ) . When taking into account the mean paring-field parameters (Δ p , Δ n ) as dynamical variables, the theoretical fission lifetimes decrease by a few orders of magnitude.

Influence of the quadrupole pairing interaction on the spontaneous fission lifetime of heavy nuclei

Abstract The influence of the quadrupole pairing interaction on the value of the collective potential and inertia of fissioning nuclei is presented. The calculation employed a Nilsson potential having quadrupole and hexadecapole deformations. The collective inertia and potential found were then used to estimate the spontaneous fission lifetimes of a number of Fm isotopes. It was found that the calculated lifetimes are very sensitive to the presence of the quadrupole pairing forces.

Lifetime predictions for super-heavy elements

Lifetime extrapolations are presented for elements of Z=104 to 115 based on the masses of Myers and Swiatecki. The letter mass values were calculated with the assumption of shell closures at Z=114, N=184. The extrapolation formulae of Viola and Seaborg were used for α and spontaneous fission lifetimes; the Moszkowski nomographs were used for EC and β lifetimes. Calculations were performed both with the shell stabilization predicted by the Myers-Swiatecki mass formula and with one half the predicted stabilization energy for each isotope. Since many isotopes of Z≦115 are predicted to have lifetimes of minutes or longer, it is concluded that proposed synthesis experiments stand a very good chance of success.

Fission and the Synthesis of Heavy Nuclei by Rapid Neutron Capture

The role of fission is examined in the synthesis of heavy nuclei by multiple capture of neutrons in thermo-nuclear explosions. We begin by reviewing evidence from the recent Tweed and Cyclamen experiments indicating that neutron-induced fission is a serious source of depletion in neutron capture chains which start from targets of $^{242}\mathrm{Pu}$ and $^{243}\mathrm{Am}$. An analysis of Tweed abundances (Sec. 2) is made to obtain capture-to-fission ratios for the odd-$A$ plutonium isotopes through $A=253$. We next use the liquid-drop model of Myers and Swiatecki plus empirical shell corrections and pairing energies, in order to correlate and predict spontaneous fission lifetimes (Sec. 3) and fission barriers (Sec. 4). For nuclei having $Z\ensuremath{\le}101$ and $N\ensuremath{\le}157$, we extrapolate the shell correction, assuming it to be a function of $N$ plus a function of $Z$, and thus obtain neutron binding energies, fission barriers, and spontaneous fission lifetimes for neutron-rich heavy nuclei (Sec. 6). Capture-to-fission ratios are estimated for many of these nuclei in Sec. 7, and qualitative agreement is found with laboratory and Tweed results. In Sec. 8, the Sec. 8, extrapolation is continued out to $N=159$ and $Z=104$. We conclude that by using the liquid-drop model plus semiempirical shell corrections, one can obtain capture-to-fission ratios and spontaneous fission half-lives which are usefully accurate. However, for predicting properties of nuclei having $Z>104$, $N\ensuremath{\gtrsim}159$, one needs, in this formalism, an accurate way of predicting shell corrections or nuclear masses.