Nuclear physics is a very abstract field with little accessibility for wider audiences, and yet it is a field of physics with far reaching implications for everyday life. The Nuclear Beavers demonstration is a hands-on experience that offers an intuitive lens into nuclear structure and decay. We aim to provide a more accessible entry point for students and educators by substituting complex nuclear structures and interactions with tactile building blocks following well-defined rules, thereby opening nuclear physics concepts to the general public.

When multiple fission modes coexist in a given nucleus, distinct fragment yield distributions appear. Multimodal fission has been observed in a number of fissioning nuclei spanning the nuclear chart, and this phenomenon is expected to affect the nuclear abundances synthesized during the rapid neutron-capture process (r-process). In this study, we generalize the previously proposed hybrid model for fission-fragment yield distributions to predict competing fission modes and estimate the resulting yield distributions. Our framework allows for a comprehensive large-scale calculation of fission fragment yields suited for r-process nuclear network studies. Nuclear density functional theory is employed to obtain the potential energy and collective inertia tensor on a multidimensional collective space defined by mass multipole moments. Fission pathways and their relative probabilities are determined using the nudged elastic band method. Based on this information, mass and charge fission yields are predicted using the recently developed hybrid model. Fission properties of fermium isotopes are calculated in the axial quadrupole-octupole collective space for three energy density functionals (EDFs). Disagreement between the EDFs appears when multiple fission modes are present. Within our framework, the UNEDF1$_{\textrm{HFB}}$ EDF agrees best with experimental data. Calculations in the axial quadrupole-octupole-hexadecapole collective space improve the agreement with the experiment for SkM$^{*}$. We also discuss the sensitivity of fission predictions on the choice of EDF for several superheavy nuclei. Fission fragment yield predictions for nuclei with multiple fission modes are sensitive to the underlying EDF. For large-scale calculations in which a minimal number of collective coordinates is considered, UNEDF1$_{\textrm{HFB}}$ provides the best description of experimental data.

In the Ge-Sr mass region, isotopes with neutron number N <= 40 are known to feature rapid shape changes with both nucleon number and angular momentum. To gain new insights into their structure, inelastic proton scattering experiments in inverse kinematics were performed on the rare isotopes 74,76Kr. This work focuses on observables related to the J pi = 4+1 states of the Kr isotopes and, in particular, on the hexadecapole degree of freedom. By performing coupled-channels calculations, hexadecapole deformation parameters /34 were determined for the J pi = 4+1 states of 74,76Kr from inelastic proton scattering cross sections. Two possible coupled-channels solutions were found. A comparison to predictions from nuclear energy density functional theory, employing both non-relativistic and relativistic functionals, clearly favors the large, positive /34 solutions. These /34 values are unambiguously linked to the well deformed prolate configuration. Given the /32 - /34 trend, established in this work, it appears that /34 values could provide a sensitive measure of the nuclear shell structure.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

The nuclear fission process is a dramatic example of the large-amplitude collective motion in which the nucleus undergoes a series of shape changes before splitting into distinct fragments. This motion can be represented by a pathway in the many-dimensional space of collective coordinates. The collective action along the fission pathway determines the spontaneous fission half-lives as well as mass and charge distributions of fission fragments. We study the performance and precision of various methods to determine the minimum action and minimum-energy fission trajectories in the collective space. We apply the nudged elastic band method (NEB), grid-based methods, and Euler Lagrange approach to the collective action minimization in two and three dimensional collective spaces. The performance of various approaches to the fission pathway problem is assessed by studying the collective motion along both analytic energy surfaces and realistic potential energy surfaces obtained with the Hartree-Fock-Bogoliubov theory. The uniqueness and stability of the solutions is studied. The NEB method is capable of efficient determination of the exit points on the outer turning surface that characterize the most probable fission pathway and constitute the key input for fission studies. This method can also be used to accurately compute the critical points (i.e., local minima and saddle points) on the potential energy surface of the fissioning nucleus that determine the static fission path. The NEB method is the tool of choice for finding the least-action and minimum energy fission trajectories. It will be particularly useful in large-scale fission calculation of superheavy nuclei and neutron-rich fissioning nuclei contributing to the astrophysical r-process recycling.

The properties of toroidal hyperheavy even-even nuclei and the role of toroidal shell structure are extensively studied within covariant density functional theory. The general trends in the evolution of toroidal shapes in the $Z\approx 130-180$ region of nuclear chart are established for the first time. These nuclei are stable with respect of breathing deformations. The most compact fat toroidal nuclei are located in the $Z\approx 136, N\approx 206$ region of nuclear chart, but thin toroidal nuclei become dominant with increasing proton number and on moving towards proton and neutron drip lines. The role of toroidal shell structure, its regularity, supershell structure, shell gaps as well as the role of different groups of the pairs of the orbitals in its formation are investigated in detail. The lowest in energy solutions at axial symmetry are characterized either by large shell gaps or low density of the single-particle states in the vicinity of the Fermi level in at least one of the subsystems (proton or neutron). Related quantum shell effects are expected to act against the instabilities in breathing and sausage deformations for these subsystems. The investigation with large set of covariant energy density functionals reveals that substantial proton $Z=154$ and 186 and neutron $N=228$, 308 and 406 spherical shell gaps exist in all functionals. The nuclei in the vicinity of the combination of these particle numbers form the islands of stability of spherical hyperheavy nuclei. The study suggests that the $N=210$ toroidal shell gap plays a substantial role in the stabilization of fat toroidal nuclei.

The systematic investigation of the ground state and fission properties of even-even actinides and superheavy nuclei with $Z=90-120$ from the two-proton up to two-neutron drip lines with proper assessment of systematic theoretical uncertainties has been performed for the first time in the framework of covariant density functional theory (CDFT). These results provide a necessary theoretical input for the r-process modeling in heavy nuclei and, in particular, for the study of fission recycling. Four state-of-the-art globally tested covariant energy density functionals (CEDFs), namely, DD-PC1, DD-ME2, NL3* and PC-PK1, representing the major classes of the CDFT models are employed in the present study. Ground state deformations, binding energies, two neutron separation energies, $\alpha$-decay $Q_{\alpha}$ values and half-lives and the heights of fission barriers have been calculated for all these nuclei. Theoretical uncertainties in these physical observables and their evolution as a function of proton and neutron numbers have been quantified and their major sources have been identified. Spherical shell closures at $Z=120$, $N=184$ and $N=258$ and the structure of the single-particle (especially, high-$j$) states in their vicinities as well as nuclear matter properties of employed CEDFs are two major factors contributing into theoretical uncertainties. However, different physical observables are affected in a different way by these two factors. For example, theoretical uncertainties in calculated ground state deformations are affected mostly by former factor, while theoretical uncertainties in fission barriers depend on both of these factors.

Parametric correlations are studied in several classes of covariant density functional theories (CDFTs) using a statistical analysis in a large parameter hyperspace. In the present manuscript, we investigate such correlations for two specific types of models, namely, for models with density dependent meson exchange and for point coupling models. Combined with the results obtained previously in Ref. [1] for a non-linear meson exchange model, these results indicate that parametric correlations exist in all major classes of CDFTs when the functionals are fitted to the ground state properties of finite nuclei and to nuclear matter properties. In particular, for the density dependence in the isoscalar channel only one parameter is really independent. Accounting for these facts potentially allows one to reduce the number of free parameters considerably.

The study of nuclear limits has been performed and new physical mechanisms and exotic shapes allowing the extension of nuclear landscape beyond the commonly accepted boundaries have been established. The transition from ellipsoidal to toroidal shapes plays a critical role in potential extension of nuclear landscape to hyperheavy nuclei. Rotational excitations leading to the birth of particle (proton or neutron) bound rotational bands provide a mechanism for an extension of nuclear landscape beyond spin zero proton and neutron drip lines.

We calculate field isotope shifts for nobelium atoms using nuclear charge distributions which come from different nuclear models. We demonstrate that comparing calculated isotope shifts with experiment can serve as a testing ground for nuclear theories. It also provides a way of extracting parameters of nuclear charge distribution beyond nuclear root mean square (rms) radius, e.g., parameter of quadrupole deformation beta. The measurements of at least two atomic transitions is needed to disentangle the contributions of the changes in deformation and nuclear rms radius into field isotopic shift. We argue that a previous interpretation of the isotope measurements in terms of delta(r(2)) between No-252,No-254 isotopes should be amended when nuclear deformation is taken into account. We calculate isotope shifts for other known isotopes and for hypothetically metastable isotope No-286 for which the predictions of nuclear models differ substantially.

Background: The phenomenon of reflection-asymmetric nuclear shapes is relevant to nuclear stability, nuclear spectroscopy, nuclear decays and fission, and the search for new physics beyond the standard model. Global surveys of ground-state octupole deformation, performed with a limited number of models, suggest that the number of pear-shaped isotopes is fairly limited across the nuclear landscape.Purpose: We carry out a global analysis of ground-state octupole deformations for particle-bound even-even nuclei with $Z\ensuremath{\le}110$ and $N\ensuremath{\le}210$ using nuclear density functional theory (DFT) with several nonrelativistic and covariant energy density functionals. In this way, we can identify the best candidates for reflection-asymmetric shapes.Methods: The calculations are performed in the frameworks of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory and relativistic Hartree-Bogoliubov theory using DFT solvers employing harmonic oscillator basis expansion. We consider five Skyrme and four covariant energy density functionals.Results: We predict several regions of ground-state octupole deformation. In addition to the ``traditional'' regions of neutron-deficient actinide nuclei around $^{224}\mathrm{Ra}$ and neutron-rich lanthanides around $^{146}\mathrm{Ba}$, we identified vast regions of reflection-asymmetric shapes in very neutron-rich nuclei around $^{200}\mathrm{Gd}$ and $^{288}\mathrm{Pu}$, as well as in several nuclei around $^{112}\mathrm{Ba}$. Our analysis suggests several promising candidates with stable ground-state octupole deformation, primarily in the neutron-deficient actinide region, that can be reached experimentally. Detailed comparison between Skyrme and covariant models is performed.Conclusions: Octupole shapes predicted in this study are consistent with the current experimental information. This work can serve as the starting point of a systematic search for parity doublets in odd-mass and odd-odd nuclei, which will be of interest in the context of new physics searches.

The properties of hyperheavy nuclei and the extension of nuclear landscape to hyperheavy nuclei are extensively studied within covariant density functional theory. Axial reflection symmetric and reflection asymmetric relativistic Hartree-Bogoliubov (RHB) calculations are carried out. The role of triaxiality is studied within triaxial RHB and triaxial relativistic mean field + BCS frameworks. With increasing proton number beyond Z~130 the transition from ellipsoidal-like nuclear shapes to toroidal ones takes place. The description of latter shapes requires the basis which is typically significantly larger than the one employed for the description of ellipsoidal-like shapes. Many hyperheavy nuclei with toroidal shapes are expected to be unstable towards multifragmentation. However, three islands of stability of spherical hyperheavy nuclei have been predicted for the first time in Ref. [1]. Proton and neutron densities, charge radii, neutron skins and underlying shell structure of the nuclei located in the centers of these islands have been investigated in detail. Large neutron shell gaps at N=228, 308 and 406 define approximate centers of these islands in neutron number. On the contrary, large proton gap appear only at Z=154 in the (Z~156, N~310) island. As a result, this is the largest island of stability of spherical hyperheavy nuclei found in the calculations. The calculations indicate the stability of the nuclei in these islands with respect of octupole and triaxial distortions. Fission barriers in neutron-rich superheavy nuclei are studied in triaxial RHB framework; the impact of triaxiality on the heights of fission barriers is substantial in some parts of this region. Based on the results obtained in the present work, the extension of nuclear landscape to hyperheavy nuclei is provided.

Octupole deformed shapes in neutron-rich actinides and superheavy nuclei as well as extremely deformed shapes of the N similar to Z light nuclei have been investigated within the framework of covariant density functional theory. We confirmed the presence of new region of octupole deformation in neutron-rich actinides with the center around Z similar to 96, N similar to 196 but our calculations do not predict octupole deformation in the ground states of superheavy Z >= 108 nuclei. As exemplified by the study of Ar-36, the nodal structure of the wavefunction of occupied single-particle orbitals in extremely deformed structures allows to understand the formation of the alpha-clusters in very light nuclei, the suppression of the alpha-clusterization with the increase of mass number, the formation of ellipsoidal mean-field type structures and nuclear molecules.

What are the limits of the existence of nuclei? What are the highest proton numbers Z at which the nuclear landscape and periodic table of chemical elements cease to exist? These deceivably simple questions are difficult to answer especially in the region of hyperheavy (Z≥126) nuclei. We present the covariant density functional study of different aspects of the existence and stability of hyperheavy nuclei. For the first time, we demonstrate the existence of three regions of spherical hyperheavy nuclei centered around (Z∼138, N∼230), (Z∼156, N∼310) and (Z∼174, N∼410) which are expected to be reasonably stable against spontaneous fission. The triaxiality of the nuclei plays an extremely important role in the reduction of the stability of hyperheavy nuclei against fission. As a result, the boundaries of nuclear landscape in hyperheavy nuclei are defined by spontaneous fission and not by the particle emission as in lower Z nuclei. Moreover, the current study suggests that only localized islands of stability can exist in hyperheavy nuclei.

A systematic search for axial octupole deformation in the actinides and superheavy nuclei with proton numbers Z = 88-126 and neutron numbers from the two-proton drip line up to N = 210 was performed in covariant density functional theory (DFT) using four state-of-the-art covariant energy density functionals representing different model classes. The nuclei in the Z similar to 96, N similar to 196 region of octupole deformation were investigated in detail and the systematic uncertainties in the description of their observables were quantified. A similar region of octupole deformation exists also in Skyrme DFT and microscopic+macroscopic approaches but it is centered at somewhat different particle numbers. Theoretical uncertainties in the predictions of the regions of octupole deformation increase on going to superheavy nuclei with Z similar to 120, N similar to 190. There are no octupole deformed nuclei for Z = 112-126 in covariant DFT calculations. This agrees with Skyrme DFT calculations, but disagrees with Gogny DFT and microscopic+ macroscopic calculations which predict an extended Z similar to 120, N similar to 190 region of octupole deformation.

Theoretical uncertainties in the predictions of inner fission barrier heights in superheavy elements have been investigated in a systematic way for a set of state-of-the-art covariant energy density functionals which represent major classes of the functionals used in covariant density functional theory. They differ in basic model assumptions and fitting protocols. Both systematic and statistical uncertainties have been quantified where the former turn out to be larger. Systematic uncertainties are substantial in superheavy elements and their behavior as a function of proton and neutron numbers contains a large random component. The benchmarking of the functionals to the experimental data on fission barriers in the actinides allows to reduce the systematic theoretical uncertainties for the inner fission barriers of unknown superheavy elements. However, even then they on average increase on moving away from the region where benchmarking has been performed. In addition, a comparison with the results of non-relativistic approaches is performed in order to define full systematic theoretical uncertainties over the state-of-the-art models. Even for the models benchmarked in the actinides, the difference in the inner fission barrier height of some superheavy elements reaches $5-6$ MeV. This uncertainty in the fission barrier heights will translate into huge (many tens of the orders of magnitude) uncertainties in the spontaneous fission half-lives.

Submitted for the DNP17 Meeting of The American Physical Society Hyperheavy nuclei in covariant density functional theory: the existence and stability1 ABHINAYA GYAWALI, SYLVESTER AGBEMAVA, ANATOLI AFANASJEV, Mississippi State University — The limits of existence of finite nuclei is one of interesting questions of modern low-energy nuclear physics. A lot of theoretical efforts have been dedicated to the study of superheavy nuclei with Z < 126 [1,2]. However, very little is known about existence and stability of hyperheavy nuclei with proton numbers Z > 126. Almost all investigations of such nuclei consider only spherical shapes for the ground states [2]. However, the study of superheavy nuclei [2] indicates that such assumption leads in many cases to misinterpretation of the situation. Thus, we performed a systematic investigation of such nuclei for proton numbers from 122 up to 184 and from two-proton drip line up to two-neutron one within the axial relativistic Hartree-Bogoliubov theory [3]. The calculations are carried out in large deformation space extending from megadeformed oblate shapes via spherical ones up to scission configuration. The stability of such nuclei against fission (including triaxial and octupole shapes) and beta-decays have been investigated and the islands of their stability have been defined. [1] S.E. Agbemava et al, Phys. Rev. C 92, 054310 (2015). [2] M. Bender et al, Phys. Lett. B 515, 42 (2001). [3] A. Gyawali et al, in preparation. 1This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award No. DE-SC0013037 and by Department of Energy, National Nuclear Security Administration under Award Number DE-NA0002925. Abhinaya Gyawali Mississippi State University Date submitted: 29 Jun 2017 Electronic form version 1.4

The analysis of statistical and systematic uncertainties and their propogation to nuclear extremes has been performed. Two extremes of nuclear landscape (neutron-rich nuclei and superheavy nuclei) have been investigated. For the first extreme, we focus on the ground state properties. For the second extreme, we pay a particular attention to theoretical uncertainties in the description of fission barriers of superheavy nuclei and their evolution on going to neutron-rich nuclei.