Decay Of Nuclei Research Articles

3D radiative transfer kilonova modelling for binary neutron star merger simulations

ABSTRACTThe detection of GW170817 and the accompanying electromagnetic counterpart, AT2017gfo, have provided an important set of observational constraints for theoretical models of neutron star mergers, nucleosynthesis, and radiative transfer for kilonovae. We apply the three-dimensional (3D) Monte Carlo radiative transfer code artis to produce synthetic light curves of the dynamical ejecta from a neutron star merger, which has been modelled with 3D smooth particle hydrodynamics and included neutrino interactions. Nucleosynthesis calculations provide the energy released from radioactive decays of r-process nuclei, and radiation transport is performed using grey opacities given as functions of the electron fraction. We present line-of-sight-dependent bolometric light curves, and find the emission along polar lines of sight to be up to a factor of ∼2 brighter than that along equatorial lines of sight. Instead of a distinct emission peak, our bolometric light curve exhibits a monotonic decline, characterized by a shoulder at the time when the bulk ejecta becomes optically thin. We show approximate band light curves based on radiation temperatures and compare these to the observations of AT2017gfo. We find that the rapidly declining temperatures lead to a blue to red colour evolution similar to that shown by AT2017gfo. We also investigate the impact of an additional, spherically symmetric secular ejecta component, and we find that the early light curve remains nearly unaffected, while after about $1\,$ d the emission is strongly enhanced and dominated by the secular ejecta, leading to the shift of the shoulder from ∼1–2 to 6–10 d.

Exchange correction for allowed β decay

We investigate the exchange effect between the final atom's bound electrons and those emitted in the allowed $\ensuremath{\beta}$ decay of the initial nucleus. The electron wave functions are obtained with the Dirac-Hartree-Fock-Slater self-consistent method, and we ensure the orthogonality between the continuum and bound electron states, in the potential of the final atom, by modifying the last iteration of the self-consistent method. We show that orthogonality plays an essential role in calculating the exchange correction. After imposing the orthogonality, we found considerable differences in magnitude and energy dependence compared to previous results. We argue that our findings can solve the mismatch between the previous predictions and experimental measurements in the low-energy region of the $\ensuremath{\beta}$ spectrum. First, we calculate the exchange effect for the low-energy $\ensuremath{\beta}$ transitions in $^{14}\mathrm{C}$, $^{45}\mathrm{Ca}$, $^{63}\mathrm{Ni}$, and $^{241}\mathrm{Pu}$, recently investigated in the literature. Next, we compute the total exchange correction for a large number of $\ensuremath{\beta}$ emitters with $Z$ from 1 to 102. From the systematic study, we found that for ultralow energy, i.e., 5 eV, the $Z$ dependence of the total exchange effect is affected by ${s}_{1/2}$ and ${p}_{1/2}$ orbitals closure. We also show that the contributions from orbitals higher than the $2{s}_{1/2}$ orbital are essential for correctly calculating the total effect, especially for low energies and heavy $\ensuremath{\beta}$ emitters. Finally, we provide an analytical expression of the total exchange correction for each atomic number for easy implementation in experimental investigations.

The decay Q value of neutrinoless double beta decay revisited

An earlier publication “The implication of the atomic effects in neutrinoless double beta (0νββ) decay” written by Mei and Wei has motivated us to compare the decay Q value (Qββ) derived from the decay of the parent nucleus to the daughter nucleus with the two ejected beta particles in the final state to the Qββ directly derived from the decay of the initial neutral atom to the final state of double-ionized daughter ion with the two ejected beta particles in the final state. We show that the results are the same, which is the mass-energy difference (ΔMc2) subtracted by the total difference of the atomic electron binding energy (ΔEb) between the ground states of initial and final neutral atoms. We demonstrate that ΔMc2 is the sum of Qββ and the atomic relaxation energy (ΔEb) of the atomic structure after the decay. Depending on the atomic relaxation time, the release of the atomic binding energy may not come together with the energy deposition of the two ejected beta particles.

A walk along the proton drip-line by β-decay spectroscopy

During the last decade we have carried out a systematic study of the β decay of neutron-deficient nuclei, providing rich spectroscopic information of importance for both nuclear structure and nuclear astrophysics. We present an overview of the most relevant achievements, including the discovery of a new exotic decay mode in the fp-shell, the β-delayed γ-proton decay in 56Zn, the first observation of the 2+ isomer in 52Co and the latest results on the heavier systems 60Ge and 62Ge. We also report on our deduced mass excesses in comparison with systematics and a recent measurement. Finally, we summarise our results on the half-lives of Tz = -1/2, -1 and -2 neutron-deficient nuclides, and analyse their trend.

Structure and α decay for the neutron-deficient nuclei with 89≤Z≤94 in the density-dependent cluster model combined with a relativistic mean-field approach

The density-dependent cluster model combined with relativistic mean-field theory is used to explore the structure and $\ensuremath{\alpha}$ decay for the neutron-deficient nuclei with $89\ensuremath{\le}Z\ensuremath{\le}94$, including two newly discovered nuclei $^{207}\mathrm{Th}$ [Phys. Rev. C 105, L051302 (2022)] and $^{214}\mathrm{U}$ [Phys. Rev. Lett. 126, 152502 (2021)]. The effective nucleon-nucleon interactions and matter density distributions from the relativistic mean field are employed to construct the $\ensuremath{\alpha}$-daughter potential with a double-folding model. The Pauli blocking effect is considered by normalizing the strength of the $\ensuremath{\alpha}$-daughter potential with the Bohr-Sommerfeld quantization condition. The $\ensuremath{\alpha}$-preformation factor is calculated with the cluster formation model. The calculated $\ensuremath{\alpha}$-decay half-lives for the 106 observed nuclei with $89\ensuremath{\le}Z\ensuremath{\le}94$ are in excellent agreement with experimental data. Extending this model to the unknown nuclei $^{201--204}\mathrm{Ac}$, $^{205--206}\mathrm{Th}$, $^{209--210}\mathrm{Pa}$, $^{212--213,220}\mathrm{U}$, $^{215--218,221}\mathrm{Np}$, and $^{220--227}\mathrm{Pu}$, the evolution of the $N=126$ shell closure with neutron number is explored for the high-$Z$ isotopes. The available $\ensuremath{\alpha}$-decay energies, preformation factors, and $\ensuremath{\alpha}$-decay half-lives show a regular change with increasing neutron number. Especially, the robustness of the $N=126$ shell closure is shown up to the Pu isotopes.

Observation of a Strongly Isospin-Mixed Doublet in ^{26}Si via β-Delayed Two-Proton Decay of ^{26}P.

β decay of proton-rich nuclei plays an important role in exploring isospin mixing. The β decay of ^{26}P at the proton drip line is studied using double-sided silicon strip detectors operating in conjunction with high-purity germanium detectors. The T=2 isobaric analog state (IAS) at 13 055keV and two new high-lying states at 13 380 and 11 912keV in ^{26}Si are unambiguously identified through β-delayed two-proton emission (β2p). Angular correlations of two protons emitted from ^{26}Si excited states populated by ^{26}P β decay are measured, which suggests that the two protons are emitted mainly sequentially. We report the first observation of a strongly isospin-mixed doublet that deexcites mainly via two-proton decay. The isospin mixing matrix element between the ^{26}Si IAS and the nearby 13 380-keV state is determined to be 130(21)keV, and this result represents the strongest mixing, highest excitation energy, and largest level spacing of a doublet ever observed in β-decay experiments.

Topical collection on light clusters in nuclei and nuclear matter: nuclear structure and decay, heavy-ion collisions, and astrophysics

Recent progress to treat clustering in nuclear systems has an impact to different branches of nuclear theory. Numerical methods as well as many-body theory (Green-function methods) have been worked out to describe few-body clusters in a nuclear environment where medium effects, in particular the antisymmetrization of the wave function (Pauli blocking) are of relevance. Nuclear structure (Hoyle – like states), nuclear reactions, and consequences for astrophysics (neutron stars, supernova explosions) are emerging applications. The main topics were (1) Cluster models, structure of light nuclei, cluster quantum phase transition; (2) Reaction theory, \(\alpha \)-decay of heavy and superheavy nuclei; (3) Clustering in nuclear matter and consequences for thermodynamic properties (4) Heavy-ion collisions and clustering in nonequilibrium systems, transport codes; (5) Astrophysical consequences of clustering.

An improved unified formula for alpha -decay and cluster radioactivity of heavy and superheavy nuclei

Improved NRDX empirical formula for alpha - and cluster decay half-lives is modified by adding the effects of angular momentum, isospin asymmetry and parity. The coefficients are determined using the latest experimental data for alpha -decay half-lives of 573 nuclei and the available 22 cluster decay half-lives. The modified formulas produced the alpha - and cluster decay half-lives and agree with calculations of other similar formulas. We used the new formulas to calculate the half-lives of cluster emissions of the SHN with Z=120, 122, 124, and 126, which have not yet been experimentally synthesized.

Building surrogate models of nuclear density functional theory with Gaussian processes and autoencoders

From the lightest Hydrogen isotopes up to the recently synthesized Oganesson (Z = 118), it is estimated that as many as about 8,000 atomic nuclei could exist in nature. Most of these nuclei are too short-lived to be occurring on Earth, but they play an essential role in astrophysical events such as supernova explosions or neutron star mergers that are presumed to be at the origin of most heavy elements in the Universe. Understanding the structure, reactions, and decays of nuclei across the entire chart of nuclides is an enormous challenge because of the experimental difficulties in measuring properties of interest in such fleeting objects and the theoretical and computational issues of simulating strongly-interacting quantum many-body systems. Nuclear density functional theory (DFT) is a fully microscopic theoretical framework which has the potential of providing such a quantitatively accurate description of nuclear properties for every nucleus in the chart of nuclides. Thanks to high-performance computing facilities, it has already been successfully applied to predict nuclear masses, global patterns of radioactive decay like β or γ decay, and several aspects of the nuclear fission process such as, e.g., spontaneous fission half-lives. Yet, predictive simulations of nuclear spectroscopy—the low-lying excited states and transitions between them—or of nuclear fission, or the quantification of theoretical uncertainties and their propagation to basic or applied nuclear science applications, would require several orders of magnitude more calculations than currently possible. However, most of this computational effort would be spent into generating a suitable basis of DFT wavefunctions. Such a task could potentially be considerably accelerated by borrowing tools from the field of machine learning and artificial intelligence. In this paper, we review different approaches to applying supervised and unsupervised learning techniques to nuclear DFT.

A theoretical study on the impact of centrifugal potential and fragment identification in the decay of compound nuclei (ACN = 60&100)

Decay analysis of compound nuclei such as [Formula: see text] and [Formula: see text] formed in [Formula: see text]Ca and [Formula: see text]Ni reactions, respectively, is studied using two theoretical frameworks, dynamical cluster-decay model (DCM) and PACE4. To explore the decay dynamics in a relatively lighter mass region [Formula: see text], two more reactions are picked (i) [Formula: see text]Mg forming the [Formula: see text] compound nucleus, (ii) another one involving the odd mass projectile, [Formula: see text]. In DCM, the fusion excitation functions are calculated using sticking [Formula: see text] and nonsticking [Formula: see text] limits of the moment of inertia. For the chosen reactions, fusion cross-sections are equivalent to evaporation residue (ER) cross-sections [Formula: see text] as fission cross-sections are negligible. A lower magnitude of maximum angular momentum [Formula: see text] is obtained via the [Formula: see text] approach in comparison to the [Formula: see text] approach and the angular momentum obtained via the [Formula: see text] approach is closer to the experimental observations. The structure and magnitude of fragmentation potential and preformation probability [Formula: see text] depend on the choice of moment of inertia and the magnitude of angular momentum involved. Besides this, PACE4 is employed to address the fusion cross-section of chosen reactions. The most probable decay channel is identified using both DCM and PACE4 approaches.

Fission channels for fragment isotopes from Fl298 with magic nucleon numbers

Short-lived systems such as superheavy nuclei decay mainly by $\ensuremath{\alpha}$ emission. However, fission fragment emission is also probable, as theoretical calculations prove it. $^{298}\mathrm{Fl}$ dynamics decay is studied with a specialized binary macroscopic-microscopic method combined with the mass inertia tensor. The multidimensional WKB tunneling method is used to obtain the penetrabilities and half-lives. The calculations are applied to fission channels around the isotopes of two presumably favored fragments, Pb and Sn. The choice is due to their proton magicity shell correction favorable fission valleys.

Unified description of α decay and cluster radioactivity using the neural network approach and universal decay law

The α decay and cluster radioactivity half-life of nuclei are calculated uniformly. The universal decay law (UDL) (Qi et al 2009 Phys. Rev. Lett. 103 072501) is refitted to include minimum angular momentum effect and unpaired nucleon effect. The UDL formula and neural network approach to describe α decay and cluster radioactivity half-life calculations were improved. We used the UDL formulas and neural network approach to predict the cluster radioactivity half-life of actinide nuclei and α decay half-life of superheavy nuclei Z = 117–120. We hope to contribute to the discovery of new atomic nucleus cluster radioactivity phenomena and theoretical studies of α decay of superheavy nuclei.

Temperature dependence of cluster decay

A universal decay law (UDL) for light cluster decay of excited nuclei is formulated by fitting the UDL half-lives to those evaluated within an excitation energy-dependent double folding model (DFM). The half-lives are evaluated within a preformed cluster model. The excitation energy dependence is introduced both in the energy of the emitted cluster and in the interaction potential through the density distributions of the interacting nuclei. The half-lives are found to decrease when the difference between the excitation energies of the parent and daughter nuclei, ΔE⁎> 0, increases, with the reduction being a few orders of magnitude for higher values of ΔE⁎. This can be of importance for nucleosynthesis calculations of heavy elements formed in extremely hot environments, as well as in highly energetic heavy-ion collisions. The UDL for excited nuclei is used to provide an estimate of the enhancement in the cluster decay rates of thermally excited nuclei such as those produced in r-process nucleosynthesis.

Coulomb corrections to Fermi beta decay in nuclei

We study the influence of the Coulomb force on the Fermi beta-decays in nuclei. This work is composed of two main parts. In the first part, we calculate the Coulomb corrections to super-allowed beta decay. We use the notion of the isovector monopole state and the self-consistent charge-exchange Random Phase Approximation to compute the correction. In the second part of this work, we examine the influence of the anti-analog state on isospin mixing in the isobaric analog state and the correction to the beta-decay Fermi transition.

Statistical model calculation of the compound nuclear fission timescale in fusion-fission reactions

In the decay of an excited heavy nucleus, both the fission or evaporation residue (ER) cross sections and the fission time are determined by the competition between the various evaporation channels and fission. Statistical model (SM) calculations for several heavy-ion-induced fusion-fission reactions are presented which reproduce the fission or ER excitation functions. The corresponding calculated fission times are found to depend upon the compound nuclei and their excitation energies. The multichance fission probabilities and the corresponding fission times are also obtained, and they are shown to depend sensitively on the shell correction energies and the neutron separation energies of the compound nuclei involved. The experimental neutron multiplicities are reproduced by adjusting the saddle-to-scission transition time interval. An additional delay time for compound nuclear formation is found necessary to fit the experimental neutron multiplicities for a system with higher entrance channel mass symmetry.

High-spin levels, β− decay and monopole effects in A = 128 hole nuclei near 132Sn

The high-spin levels and β− decay in neutron-rich hole nuclei of A=128 are studied by large-scale shell-model calculations with the extended pairing plus multipole-multipole force model. The excited energy and logft values of β− decay are predicted in the final states of 128Ag, 128Cd, and 128In by the cascaded decays calculated in A=128 hole nuclei. The 16+ level of 128Cd is predicted as a spin-trap isomer feeding the existing high-spin 16+ of 128In by β− decay. The monopole effects are investigated carefully in the β− decay process from the ground state 0+ of 128Cd to the 1+ levels of 128In, while the half-life is affected by monopole corrections acting on the configuration of final states.

Proliferation protection of uranium due to the presence of U-232 decay products as intense sources of hard gamma radiation

The objectives of the article are (1) to show the nuclear and physical causes of hard γ-quanta in the U-232 decay chain, (2) to propose tactics for handling uranium containing U-232, and (3) to assess the efficiency of its protective γ-barrier against uncontrolled proliferation. The authors show the general picture of the decay chains of U-232 nuclide transformations, on which the protection of uranium from its uncontrolled proliferation is based. During the decay of nuclei, their emission of α- or β-particles is only the first stage of the most complex process of rearrangement of both the internal structure of the nucleus itself, which consists in the rearrangement of the neutron and proton shells and the levels of its excitation, and in the rearrangement of the electron shells of the atom. As a rule, the daughter nucleus is in a highly excited state, which is removed by the emission of hard γ-quanta and internal conversion electrons. After the second case, the remaining excitation of the atom is removed by the emission of characteristic γ-quanta and Auger-electrons with characteristic γ-quanta. In addition, explanations are given for the quantum-mechanical reasons for the hard γ-radiation of Tl-208 and Bi-212, which complete the U-232 decay chain. The authors also proposed a tactic for handling uranium containing uranium-232. Since the hard γ-quanta of Tl-208 and Bi-212 appear only at the end of the U-232 decay chain, after its chemical purification from its decay products, U-232 itself does not pose a radiation hazard; therefore, at this time it is advisable to conduct all necessary operations for transporting the material to the plant, fabricating uranium-based fuel containing U-232, and transporting this fuel to the nuclear facility where it will be used.

Hyperfine interaction studies in the David Shirley group, 1960–1975. I. Low-temperature nuclear orientation

Under the leadership of David Shirley, the hyperfine interactions group at Berkeley became one of the world’s leading laboratories for its diversity of studies of the interaction between probe nuclei and their environment. One branch of those studies, low-temperature nuclear orientation, concerned the radioactive decays of nuclei whose spins were oriented in a variety of electromagnetic environments at temperatures in the mK range. In the years 1960–1975, this group did pioneering research that produced more than 50 papers in the field, and at least 16 graduate students completed their dissertation research. The present paper gives a brief introduction to the field of low-temperature nuclear orientation, summarizes the main accomplishments of the Shirley group, and discusses examples of the variety of results obtained in the group’s research. Paper II deals with other hyperfine interaction studies by the Shirley group.

Insights into the aftereffects phenomenon in solids based on DFT and time-differential perturbed γ−γ angular correlation studies in 111In (→ 111Cd) -doped tin oxides

Recently, a model based on a combined ab initio/time-differential perturbed $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ angular correlation (TDPAC) study in the $^{111}\mathrm{In}(\ensuremath{\rightarrow}^{111}\mathrm{Cd})$-doped ${\mathrm{SnO}}_{2}$ semiconductor was proposed to enlighten the origin of the dynamic hyperfine interactions (HFIs) observed in oxides after the electron-capture (EC) decay of the probe nucleus of the $^{111}\mathrm{In}$ parent. It was demonstrated that both the EC as well as the acceptor level introduced by the Cd impurity can contribute to the variation of the electric-field gradient (EFG) at the Cd site (responsible for this phenomenon) due to charge fluctuations of the electronic holes created [Darriba et al., J. Phys. Chem. C 122, 17423 (2018)]. To disentangle both effects, we performed here TDPAC reversible experiments in $^{111}\mathrm{In}(\ensuremath{\rightarrow}^{111}\mathrm{Cd})$-doped SnO in the temperature range 20--900 K and a complete electronic structure density functional theory study of the Cd-doped SnO system as a function of the charge state $(q)$ of the impurity. The isovalent $^{111}\mathrm{Cd}$ probe impurity in this isocationic oxide was selected to demonstrate that the acceptor character of the probe is not a necessary condition to observe this electronic phenomenon when the EC is already present. A majority fraction of probes sensed a time-dependent HFI (HFI1) for all temperatures, and the unexpected minority always sensed a static interaction (HFI2). Comparing results from these experiments, the ab initio calculations of the EFG tensor and defect formation energies, HFI1 and HFI2, were assigned to $^{111}\mathrm{Cd}$ probes localized at substitutional Sn sites free of defects [with the valence band (VB) completely filled, $q=0$] and with an electronic hole trapped $(q=1+)$, respectively. In addition, we show that the systems with charge state between these values have very similar formation energies at the top of the VB and different predicted EFGs, giving support from first principles to the existence of random fluctuations between different EFGs, necessary in the construction of the on-off perturbation factor used. We demonstrate that all the probes fill their electronic holes before the TDPAC time window except the outermost one, giving a quantification of the number of electronic holes involved in the production of the dynamic effect, only one in SnO. The probes related to HFI2 reach their stable electronic configuration $(q=1+)$ before the emission of the first \ensuremath{\gamma} ray $({\ensuremath{\gamma}}_{1})$ of the \ensuremath{\gamma}-\ensuremath{\gamma} cascade, while those related to HFI1 fill the last hole after the emission of ${\ensuremath{\gamma}}_{1}$, producing the dynamic interaction. Enlighted by these results and reviewing TDPAC experiments from the literature using probes with different nuclear decay characteristics, we concluded that, in the absence of EC decay of the probe nucleus of the parent, any probe impurity introducing acceptor or donor states (in semiconductors and insulators) whose ionization changes the EFG should observe a time-dependent HFI provided the lifetime of the nuclear levels that feed the ${\ensuremath{\gamma}}_{1}$ level and this level itself is shorter than the lifetime of the recovery process (i.e., the lifetime of the electronic holes or the ionized donor electrons).

Microscopic description of cluster decays based on the generator coordinate method

\noindent\textbf{Background:} While many phenomenological models for nuclear fission have been developed, a microscopic understanding of fission has remained one of the most challenging problems in nuclear physics. \noindent\textbf{Purpose:} We investigate an applicability of the generator coordinate method (GCM) as a microscopic theory for cluster radioactivities of heavy nuclei, which can be regarded as a fission with large mass asymmetry, that is, a phenomenon in between fission and $\alpha$-decays. \noindent\textbf{Methods:} Based on the Gamow theory, we evaluate the preformation probability of a cluster with GCM while the penetrability of the Coulomb barrier is estimated with a potential model. To this end, we employ Skyrme interactions and solve the one-dimensional Hill-Wheeler equation with the mass octupole field. We also take into account the dynamical effects of the pairing correlation using BCS wavefunctions constructed with an increased strength of the pairing interaction. \noindent\textbf{Results:} We apply this scheme to the cluster decay of $^{222}$Ra, i.e., $^{222}$Ra$\to^{14}$C+$^{208}$Pb, to show that the experimental decay rate can be reproduced within about two order of magnitude. We also briefly discuss the cluster radioactivities of the $^{228}$Th and $^{232}$U nuclei. For these actinide nuclei, we find that the present calculations reproduce the decay rates with the same order of magnitude and within two or three order of magnitude, respectively. \noindent\textbf{Conclusions:} The method presented in this paper provides a promising way to describe microscopically cluster decays of heavy nuclei.