Medium-heavy Nuclei Research Articles

Collective model description of parity-doublet bands in odd mass nuclei

The yrast parity doublet rotational bands in odd medium mass and heavy nuclei are described by a quadrupole–octupole axially symmetric collective model within the strong coupling assumption regarding the odd nucleon. Energy levels of the same spin and opposite parity are interpreted as symmetric and antisymmetric quantum states of the quadrupole–octupole shape fluctuation. The energy spectrum and the associated electromagnetic transitions of the parity doublet bands observed in 21 selected nuclei, are reproduced with a very good accuracy. Predictions are performed for energies of unobserved states and electromagnetic properties. The model parameters are used to establish the static or dynamic nature of the octupole correlations in the ground state and their evolution with spin. A general systematization of the octupole effects as a function of nucleon numbers is realized in conjunction with results on even–even nuclei.

Microscopic derivation of the octupole magic numbers from symmetry considerations

The valence shells of medium mass and heavy nuclei consist of the normal and the intruder parity orbitals; therefore the Shell Model SU(3) symmetry of Elliott cannot have a straightforward application on them. The proxy-SU(3) can be applied instead, since it uses a unitary transformation, meant to act on the intruder orbitals to alter their parity and transform them to their proxy orbitals. The inverse unitary operator transforms the proxy orbitals back to the intruder ones. The highest weight proxy-SU(3) irreducible representations (irreps) allows one to determine the corresponding number of occupied intruder orbitals. In this way we obtain the so-called ‘octupole magic numbers’ 32, 56, 90, 134 and 194 without any parameter. Moreover, the proxy (unitary) mapping and its inverse transformation make the proxy space eligible for the calculation of observables associated with octupole deformation and the relevant treatment of mixed parity states. The implemented study validates the proxy-SU(3) approach with respect to the octupole deformation and suggests its full applicability in the corresponding mass regions.

Properties of charge-exchange giant spin-dipole resonances in medium-heavy closed-shell parent nuclei: A semimicroscopic description

Properties of charge-exchange giant spin-dipole resonances in medium-heavy closed-shell parent nuclei: A semimicroscopic description

Shape Coexistence in Even–Even Nuclei: A Theoretical Overview

The last decade has seen a rapid growth in our understanding of the microscopic origins of shape coexistence, assisted by the new data provided by the modern radioactive ion beam facilities built worldwide. Islands of the nuclear chart in which shape coexistence can occur have been identified, and the different microscopic particle–hole excitation mechanisms leading to neutron-induced or proton-induced shape coexistence have been clarified. The relation of shape coexistence to the islands of inversion, appearing in light nuclei, to the new spin-aligned phase appearing in N=Z nuclei, as well as to shape/phase transitions occurring in medium mass and heavy nuclei, has been understood. In the present review, these developments are considered within the shell-model and mean-field approaches, as well as by symmetry methods. In addition, based on systematics of data, as well as on symmetry considerations, quantitative rules are developed, predicting regions in which shape coexistence can appear, as a possible guide for further experimental efforts that can help in improving our understanding of the details of the nucleon–nucleon interaction, as well as of its modifications occurring far from stability.

A U(6) Boson Model for Deformed Nuclei

The Interacting Boson Model is one of the most famous group-theoretical nuclear models, which established the use of the U(6) symmetry in nuclei, built upon the s,d bosons, which derive by nucleon pairs. In this article, it is suggested that the symmetric pairs of the valence harmonic oscillator quanta can be used approximately as the s and d bosons of a new U(6) Boson Model, applicable in medium mass and heavy nuclei. The main consequence of this interpretation is that the number of bosons is the number of the pairs of the valence harmonic oscillator quanta, which occur from the occupation of the Shell Model orbitals by nucleons.

Nuclear data activities for medium mass and heavy nuclei at Los Alamos

Nuclear data is critical for many modern applications from stockpile stewardship to cutting edge scientific research. Central to these pursuits is a robust pipeline for nuclear modeling as well as data assimilation and dissemination. We summarize a small portion of the ongoing nuclear data efforts at Los Alamos for medium mass to heavy nuclei. We begin with an overview of the NEXUS framework and show how one of its modules can be used for model parameter optimization using Bayesian techniques. The mathematical framework affords the combination of different measured data in determining model parameters and their associated correlations. It also has the advantage of being able to quantify outliers in data. We exemplify the power of this procedure by highlighting the recently evaluated 239Pu cross section. We further showcase the success of our tools and pipeline by covering the insight gained from incorporating the latest nuclear modeling and data in astrophysical simulations as part of the Fission In R-process Elements (FIRE) collaboration. We advocate for the adoption of tranmission protocols such as the Unified Reaction Structures for Astrophysics (URSA) for the rapid inclusion of nuclear data into astrophysical simulations.

STUDY OF THE EXCITATION OF THE ISOMERIC STATE 7/2+ 81Sе NUCLEAR IN THE REACTION (γ,n) BY THE METHOD OF ISOMERIC RELATIONSHIPS

Selenium is known for the transitional nature of the region from light to medium-heavy nuclei and their insufficient study. The 82Se(γ, n)81mSe reaction yield was measured, and its cross-section in the range of gamma-ray energies 9…19 MeV was calculated. A comparison of the experimental results with theoretical calculations performed using the TALYS-1.9 software complex. The dominance of the statistical mechanism for this (γ, n) reaction was found.

Nucleon-pair truncation of the shell model for medium-heavy nuclei

Background: Establishing computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations.Purpose: We propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum.Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast.Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: $^{44,46,48}\mathrm{Ti}$, $^{48,50}\mathrm{Cr}$, $^{52}\mathrm{Fe}$, $^{60,62,64}\mathrm{Zn}$, $^{66,68}\mathrm{Ge}$, $^{68}\mathrm{Se}$, and $^{108,110}\mathrm{Xe}$. We predict low-lying states of $^{112--114}\mathrm{Ba}$ and $^{116--120}\mathrm{Ce}$, nuclei difficult to reach by large-scale SM calculations.Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.

Recent Progress of Shell-Model Calculations, Monte Carlo Shell Model, and Quasi-Particle Vacua Shell Model

Nuclear shell model is a powerful approach to investigate nuclear structure microscopically. However, the computational cost of shell-model calculations becomes huge in medium-heavy nuclei. I briefly review the theoretical framework and the code developments of the conventional Lanczos diagonalization method for shell-model calculations. In order to go beyond the conventional diagonalization method, the Monte Carlo shell model and the quasiparticle-vacua shell model were introduced. I present some benchmark examples of these models.

Properties of Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei: A semimicroscopic description

The basic version of the semimicroscopic particle-hole dispersive optical model is adopted and implemented to describe main properties of the Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei. Calculation results obtained for $^{48}\mathrm{Ca}, ^{90}\mathrm{Zr}, ^{132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ are compared with available experimental data.

Role of tensor interaction as salvation of cluster structure in Ti44

Background: The $^{44}$Ti nucleus has been known to have a $^{40}$Ca+$\alpha$ cluster structure, and inversion doublet structure has been observed; however, $\alpha$ cluster structure tends to be washed out when the breaking of the $\alpha$ cluster is allowed due to the spin-orbit interaction. Nevertheless, $\alpha$ clustering in medium-heavy nuclei is quite a hot subject recently. Purpose: The tensor interaction has been known to play an essential role in the strong binding of the $^4$He nucleus, which induces the two-particle-two-hole (2p2h) excitation. Since this excitation is blocked when another nucleus approaches, it is worthwhile to show whether the tensor effect works to keep the distance between $^4$He and $^{40}$Ca and becomes the salvation of the clustering in $^{44}$Ti. Methods: The spin-orbit effect is included in the cluster model by using the antisymmetrized quasi cluster model (AQCM) developed by the authors. We have also developed an improved version of the simplified method to include the tensor contribution ($i$SMT), which allows us to estimate the tensor effect within the cluster model. The competition of these two is investigated in the medium-heavy mass region for the first time. Results: According to AQCM, the spin-orbit interaction completely breaks the $\alpha$ cluster and restores the symmetry of $jj$-coupling shell model when the $\alpha$ cluster approaches the $^{40}$Ca core. On the other hand, $i$SMT gives a large distance between $\alpha$ and $^{40}$Ca due to the tensor effect. Conclusions: In $^{44}$Ti, because of the strong spin-orbit and tensor contributions, two completely different configurations ($jj$-coupling shell model and cluster states) almost degenerate, and their mixing becomes important.

On Tensor Correlations in the Formation of Charge-Exchange Giant Spin-Multipole Resonances in Medium-Heavy Magic Parent Nuclei

On Tensor Correlations in the Formation of Charge-Exchange Giant Spin-Multipole Resonances in Medium-Heavy Magic Parent Nuclei

Description of Nb93 stellar electron-capture rates by the projected shell model

Capture of electrons by nuclei is an important process in stellar environments where excited nuclear states are thermally populated. However, accurate treatment for excited configurations in electron capture (EC) rates has been an unsolved problem for medium-heavy and heavy nuclei. In this work, we take the $^{93}$Nb $\rightarrow$ $^{93}$Zr EC rates as the example to introduce the Projected-Shell-Model (PSM) in which excited configurations are explicitly included as multi-quasiparticle states. Applying the prevalent assumption that the parent nucleus always stays in its ground state in stellar conditions, we critically compare the obtained PSM results with the recently-measured Gamow-Teller transition data, and with the previous calculations by the conventional shell model and the quasiparticle random-phase approximation. We discuss important ingredients that are required in theoretical models used for stellar EC calculations, and demonstrate effects of the explicit inclusion of excited nuclear states in EC rate calculations, especially when both electron density and environment temperature are high.

Significantly improved estimates of neutron capture cross sections relevant to the r process

Background: The $r$ process is thought to be a dominant mechanism for the production of medium mass and heavy nuclei. Despite extensive study, neither the process nor its site, and, consequently, the origin of these elements, is well understood. One of the principal reasons is the lack of adequate knowledge of neutron capture cross sections in neutron-rich nuclei, especially up to a few hundred keV. Existing statistical model calculations differ widely and are unreliable more than a few nucleons beyond stability.Purpose: To provide a new, more reliable empirical method to estimate neutron capture cross sections.Method: To use an entirely empirical approach by exploiting a newly discovered correlation between two-neutron separation energies and neutron capture cross sections.Results: It is shown that there is a compact correlation between neutron capture cross sections and ${S}_{2n}$ for ${S}_{2n}$ values from 10 to 16 MeV, encompassing nuclei in five mass regions comprising seven classes of nuclei from $A\ensuremath{\approx}110$ through the actinides over Maxwellian energy distributions from $kT=5$ to 100 keV. As a consequence, many unknown cross sections can be predicted by interpolation, with accuracies on the order of $\ifmmode\pm\else\textpm\fi{}25%$. In other cases, the cross sections can still be predicted with greatly improved accuracy compared to current models. Finally, it is shown that, in very neutron-rich nuclei, measurements of ${S}_{2n}$ can replace more difficult or impossible neutron capture measurements to estimate $r$-process abundances.Conclusions: A new approach to estimate neutron capture cross section allows much improved predictions of these key ingredients into $r$-process calculations, perhaps providing an enhanced ability to model this process and to better define its site(s).

Properties of isoscalar giant multipole resonances in medium-heavy closed-shell nuclei: A semimicroscopic description

The semimicroscopic particle-hole dispersive optical model (PHDOM) is implemented to describe main properties of Isoscalar Giant Multipole Resonances (up to L=3) in medium-heavy closed-shell nuclei. The main properties are characterized by the strength distribution, transition density, partial and total probabilities of direct one-nucleon decay. Calculation results obtained for the 208Pb nucleus are compared with available experimental data.

The islands of shape coexistence within the Elliott and the proxy-SU(3) Models

A novel dual-shell mechanism for the phenomenon of shape coexistence in nuclei within the Elliott SU(3) and the proxy-SU(3) symmetry is proposed for all mass regions. It is supposed, that shape coexistence is activated by large quadrupole-quadrupole interaction and involves the interchange among the spin-orbit (SO) like shells within nucleon numbers 6-14, 14-28, 28-50, 50-82, 82-126, 126-184, which are being described by the proxy-SU(3) symmetry, and the harmonic oscillator (HO) shells within nucleon numbers 2-8, 8-20, 20-40, 40-70, 70-112, 112-168 of the Elliott SU(3) symmetry. The outcome is, that shape coexistence may occur in certain islands on the nuclear map. The dual-shell mechanism predicts without any free parameters, that nuclei with proton number (Z) or neutron number (N) between 7-8, 17-20, 34-40, 59-70, 96-112, 146-168 are possible candidates for shape coexistence. In the light nuclei the nucleons flip from the HO shell to the neighboring SO-like shell, which means, that particle excitations occur. For this mass region, the predicted islands of shape coexistence, coincide with the islands of inversion. But in medium mass and heavy nuclei, in which the nucleons inhabit the SO-like shells, shape coexistence is accompanied by a merging of the SO-like shell with the open HO shell. The shell merging can be accomplished by the outer product of the SU(3) irreps of the two shells and represents the unification of the HO shell with the SO-like shell.

Variational approach with the superposition of the symmetry-restored quasiparticle vacua for nuclear shell-model calculations

We propose a variational calculation scheme utilizing the superposition of the angular-momentum, parity, number projected quasiparticle vacua, that is especially suitable for applying to medium-heavy nuclei in shell-model calculations. We derive a formula for the energy variance with quasi-particle vacua and apply the energy-variance extrapolation to the present scheme for further precise estimation of the exact shell-model energy. The validity of the method is presented for the shell-model calculation of $^{132}$Ba in the $50 \leq Z,N \leq 82$ model space. We also discuss the feasibility of this scheme in the case of the $^{150}$Nd in the $50 \leq Z \leq 82$ and $82 \leq Z \leq 126$ model space and demonstrate that its neutrinoless-double-beta-decay matrix element is obtained showing good convergence.

Development of an accurate DWIA model of coherent π0 —photoproduction to study neutron skins in medium heavy nuclei

Despite decades of studies which have seen the nuclear charge distribution being measured with increasing precision, the neutron distribution remains elusive. The difference between the neutron and proton distributions is often expressed as the difference of their root mean square radii: the neutron skin thickness. Recently, the A2 collaboration at MaMi has measured the skin thickness in lead through coherent pion photoproduction [1] with a very high precision. However, they do not include theoretical uncertainties, which can be significant for this process.A new reaction code in the distorted wave impulse approximation (DWIA) is developed to help the (ongoing) analysis of the recent measurement by the A2 collaboration at MaMi of the coherent pion photoproduction cross section on 116,120,124Sn isotopes [2] and to properly quantify the theoretical uncertainties.

Realistic shell-model calculations for astrophysically relevant Gamow-Teller distributions

Electron-capture reaction rates on medium-heavy nuclei are a key ingredient to describe the evolution of core-collapse and thermonuclear supernovae. To estimate these rates it is necessary to know the Gamow-Teller strength distributions involved. In this paper we report some preliminary results of the calculations of Gamow-Teller strength distributions for pf-shell nuclei performed in the framework of the realistic shell model.

Signatures of octupole shape phase transitions in radioactive nuclei

We analyze the octupole deformations and the related collective excitations in medium-heavy and heavy nuclei based on the microscopic framework of the nuclear energy density functional theory. Constrained self-consistent mean-field calculation with a given energy density functional is performed to provide for each nucleus a potential energy surface with axial quadrupole and octupole shape degrees of freedom. Spectroscopic properties are computed by means of the interacting-boson Hamiltonian, which is determined by mapping the fermionic potential energy surface onto the bosonic counterpart. The overall systematics of the calculated spectroscopic observables exhibit phase transitional behaviors between stable octupole deformation and octupole vibration characteristic of the octupole-soft potential within the set of nuclei in light actinide and rare-earth regions, Th, Ra, Sm, Gd, and Ba isotopes, where octupole shapes are most likely to occur.