Realistic Nuclei Research Articles

Pseudo-Spin Symmetry and the Hints for Unstable and Superheavy Nuclei

The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree–Fock (RHF) theory, that takes the important degrees of freedom associated with the π-meson and ρ-tensor (ρ-T) couplings into account, provides an appropriate description of the PSS restoration in realistic nuclei, particularly for the pseudo-spin (PS) doublets with high angular momenta (l˜). The investigations of the PSS within the RHF theory are recalled in this paper by focusing on the effects of the Fock terms. Aiming at common artificial shell closures appearing in previous relativistic mean-field calculations, the mechanism responsible for the PSS restoration of high-l˜ orbits is stressed, revealing the manifestation of nuclear in-medium effects on the PSS, and thus, providing qualitative guidance on modeling the in-medium balance between nuclear attractions and repulsions. Moreover, the essential role played by the ρ-T coupling, that contributes mainly via the Fock terms, is introduced as combined with the relations between the PSS and various nuclear phenomena, including the shell structure and the evolution, novel halo and bubble-like phenomena, and the superheavy magicity. As the consequences of the nuclear force in complicated nuclear many-body systems, the PSS itself and the mechanism therein can not only deepen our understanding of nuclear microscopic structure and relevant phenomena, but also provide special insight into the nature of the nuclear force, which can further enrich our knowledge of nuclear physics.

Emerging γ-soft-like spectrum in 196Pt in the SU3-IBM (I)* *This research is supported by the Educational Department of Jilin Province, China (JJKH20210526KJ), C.-X. Z. gratefully acknowledges support from the Project Supported by Scientific Research Fund of Hunan University of Art and Science (23ZZ04)

Recently, studies have argued that a spherical-like spectrum emerges in the SU3-IBM, thus creating new approaches to understanding γ-softness in realistic nuclei. In a previous study, γ-softness with degeneracy of the ground and quasi-γ bands was observed. In this paper, another special point connected to the middle degenerate point is discussed. It is found to be related to the properties of 196Pt. This emergent γ-softness is also shown to be important for understanding the prolate-oblate asymmetric shape phase transition. The low-lying spectra, values, and quadrupole moments in 196Pt are discussed, and we show that the new model can account for several observed features. This is the first part of the discussion on the γ-soft-like spectrum of 196Pt.

Small-scale dosimetry for alpha particle 241Am source cell irradiation and estimation of γ-H2AX foci distribution in prostate cancer cell line PC3

BackgroundThe development of new targeted alpha therapies motivates improving alpha particle dosimetry. For alpha particles, microscopic targets must be considered to estimate dosimetric quantities that can predict the biological response. As double-strand breaks (DSB) on DNA are the main cause of cell death by ionizing radiation, cell nuclei are relevant volumes necessary to consider as targets. Since a large variance is expected of alpha particle hits in individual cell nuclei irradiated by an uncollimated alpha-emitting source, the damage induced should have a similar distribution. The induction of DSB can be measured by immunofluorescent γ-H2AX staining. The cell γ-H2AX foci distribution and alpha particle hits distribution should be comparable and thereby verify the necessity to consider the relevant dosimetric volumes.MethodsA Monte Carlo simulation model of an 241Am source alpha particle irradiation setup was combined with two versions of realistic cell nuclei phantoms. These were generated from DAPI-stained PC3 cells imaged with fluorescent microscopy, one consisting of elliptical cylinders and the other of segmented mesh volumes. PC3 cells were irradiated with the 241Am source for 4, 8 and 12 min, and after 30 min fixated and stained with immunofluorescent γ-H2AX marker. The detected radiation-induced foci (RIF) were compared to simulated RIF.ResultsThe mesh volume phantom detected a higher mean of alpha particle hits and energy imparted (MeV) per cell nuclei than the elliptical cylinder phantom, but the mean specific energy (Gy) was very similar. The mesh volume phantom detected a slightly larger variance between individual cells, stemming from the more extreme and less continuous distribution of cell nuclei sizes represented in this phantom. The simulated RIF distribution from both phantoms was in good agreement with the detected RIF, although the detected distribution had a zero-inflated shape not seen in the simulated distributions. An estimate of undetected foci was used to correct the detected RIF distribution and improved the agreement with the simulations.ConclusionTwo methods to generate cell nuclei phantoms for Monte Carlo dosimetry simulations were tested and generated similar results. The simulated and detected RIF distributions from alpha particle-irradiated PC3 cells were in good agreement, proposing the necessity to consider microscopic targets in alpha particle dosimetry.

Rates of Stellar Tidal Disruption

Tidal disruption events occur rarely in any individual galaxy. Over the last decade, however, time-domain surveys have begun to accumulate statistical samples of these flares. What dynamical processes are responsible for feeding stars to supermassive black holes? At what rate are stars tidally disrupted in realistic galactic nuclei? What may we learn about supermassive black holes and broader astrophysical questions by estimating tidal disruption event rates from observational samples of flares? These are the questions we aim to address in this Chapter, which summarizes current theoretical knowledge about rates of stellar tidal disruption, and compares theoretical predictions to the current state of observations.

Realistic shell model and nuclei around 132Sn

This contribution reports on a shell-model study of nuclei in the 132Sn region employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential renormalized through the use of the Vlow−k approach. We shall focus on some selected results for nuclei with a few valence particles and/or holes with respect to 132Sn, namely Sn isotopes with N > 82 and 130Te, which have, in part, been discussed in previous papers. Results are compared with experiments, and predictions that may provide guidance to future experiments are also discussed. It is the aim of this contribution to underline the importance of studying 132Sn neighbours to acquire a deep understanding of nuclear structure, that may be very useful also in other physics fields, and to show that the realistic shell model is a very effective tool to conduct these studies.

Relativistic interpretation of the nature of the nuclear tensor force**Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force.

Nucleon-pair approximation of low-lying states forN=Znuclei

In this paper the nucleon-pair approximation is studied for two typical cases of $N=Z$ nuclei, by using both schematic and effective interactions. The first case is given by four nucleons in a single-$j$ shell, for which we study the relevance of the seniority scheme, the spin-aligned isoscalar pair approximation, and the pair approximation of isoscalar pairs with spin 1, under different interactions. The nonorthogonality between wave functions with the lowest seniority quantum number and those of the spin-aligned pair approximation are studied with examples. In the second case we study low-lying states of two realistic nuclei, $^{20}\mathrm{Ne}$ and $^{24}\mathrm{Mg}$. In this case we find that, interestingly, the ground band states of these two nuclei are well described by both isovector and isoscalar pair approximations.

New perturbation method of diagonalizing the nuclear shell model Hamiltonian

We suggest a perturbation method for obtaining the lowest eigenvalues of the nuclear-shell -model Hamiltonian. We introduce a ``cutoff'' based on the features of the nuclear-shell-model Hamiltonian matrices. Our new method is exemplified by a few realistic nuclei. Overlaps between the wave functions of our approach and those of the exact shell model are presented. Some of electromagnetic quantities are also discussed.

Monte-Carlo dosimetry on a realistic cell monolayer geometry exposed to alpha particles

The energy and specific energy absorbed in the main cell compartments (nucleus and cytoplasm) in typical radiobiology experiments are usually estimated by calculations as they are not accessible for a direct measurement. In most of the work, the cell geometry is modelled using the combination of simple mathematical volumes. We propose a method based on high resolution confocal imaging and ion beam analysis (IBA) in order to import realistic cell nuclei geometries in Monte-Carlo simulations and thus take into account the variety of different geometries encountered in a typical cell population. Seventy-six cell nuclei have been imaged using confocal microscopy and their chemical composition has been measured using IBA. A cellular phantom was created from these data using the ImageJ image analysis software and imported in the Geant4 Monte-Carlo simulation toolkit. Total energy and specific energy distributions in the 76 cell nuclei have been calculated for two types of irradiation protocols: a 3 MeV alpha particle microbeam used for targeted irradiation and a 239Pu alpha source used for large angle random irradiation. Qualitative images of the energy deposited along the particle tracks have been produced and show good agreement with images of DNA double strand break signalling proteins obtained experimentally. The methodology presented in this paper provides microdosimetric quantities calculated from realistic cellular volumes. It is based on open-source oriented software that is publicly available.

Validity of pair approximations for nuclei in open shells

We study the validity of pair approximations of the nuclear shell model (SM) for a few realistic nuclei (${}^{130\ensuremath{-}131}$Te and ${}^{132}$I here) in open shells (i.e., nuclei with both valence protons and valence neutrons). We take a phenomenological shell model Hamiltonian, which includes the single-particle energy term, monopole and quadrupole pairing interactions for like particles, and quadrupole-quadrupole interactions between all valence nucleons. We make comparisons of energy levels and $B(E2)$ values calculated by pair approximations with those in the SM calculations. The overlaps between wave functions of the nucleon pair approximation (NPA) and those of the SM are presented explicitly for the low-lying states. Our calculated results demonstrate that the NPA is a remarkable approximation of the SM for these nuclei. The important role played by pairs with negative parity in some low-lying states is discussed.

Perturbative interpretation of relativistic symmetries in nuclei

Perturbation theory is used systematically to investigate the symmetries of the Dirac Hamiltonian and their breaking in atomic nuclei. Using the perturbation corrections to the single-particle energies and wave functions, the link between the single-particle states in realistic nuclei and their counterparts in the symmetry limits is discussed. It is shown that the limit of S-V=const and relativistic harmonic oscillator (RHO) potentials can be connected to the actual Dirac Hamiltonian by the perturbation method, while the limit of S+V=const cannot, where S and V are the scalar and vector potentials, respectively. This indicates that the realistic system can be treated as a perturbation of spin-symmetric Hamiltonians, and the energy splitting of the pseudospin doublets can be regarded as a result of small perturbation around the Hamiltonian with RHO potentials, where the pseudospin doublets are quasidegenerate.

SD-pair structure in the pair approximation of the nuclear shell model

In this paper we study the structure coefficients of collective pairs with spin zero and spin two (SD) in a number of configurations by a few realistic nuclei. We investigate the robustness of these structure coefficients with respect to different configurations and the evolution of SD-pair structure coefficients with valence nucleon number.

Pairing in hot rotating nuclei

Nuclear pairing properties are studied within an approach that includes the quasiparticle-number fluctuation (QNF) and coupling to the quasiparticle-pair vibrations at finite temperature and angular momentum. The formalism is developed to describe noncollective rotations about the symmetry axis. The numerical calculations are performed within a doubly folded equidistant multilevel model as well as several realistic nuclei. The results obtained for the pairing gap, total energy, and heat capacity show that the QNF smoothes out the sharp SN phase transition and leads to the appearance of a thermally assisted pairing gap in rotating nuclei at finite temperature. The corrections due to the dynamic coupling to SCQRPA vibrations and particle-number projection are analyzed. The effect of backbending of the momentum of inertia as a function of squared angular velocity is also discussed.

NUCLEAR PAIRING AT FINITE TEMPERATURE AND ANGULAR MOMENTUM

An approach is proposed to nuclear pairing at finite temperature and angular momentum, which includes the effects of the quasiparticle-number fluctuation and dynamic coupling to pair vibrations within the self-consistent quasiparticle random-phase approximation. The numerical calculations of pairing gaps, total energies, and heat capacities are carried out within a doubly folded multilevel model as well as several realistic nuclei. The results obtained show that, in the region of moderate and strong couplings, the sharp transition between the superconducting and normal phases is smoothed out, causing a thermal pairing gap, which does not collapse at a critical temperature predicted by the conventional Bardeen-Cooper-Schrieffer's (BCS) theory, but has a tail extended to high temperatures. The theory also predicts the appearance of a thermally assisted pairing in hot rotating nuclei.

Modeling the influence of aerosols on cloud microphysical properties in the east Asia region using a mesoscale model coupled with a bin‐based cloud microphysics scheme

A bin‐based microphysics scheme for cloud is implemented into a three‐dimensional nonhydrostatic model and off‐line coupled with a global aerosol transport model to reproduce realistic and inhomogeneous condensation nuclei (CN) fields. This coupling makes it possible to calculate cloud microphysical properties over a larger area under more realistic environmental conditions. Using the model, nested grid simulations are performed for two precipitation events associated with transitional synoptic‐scale forcing during the spring over an area of the East China Sea. The nested grid simulations reproduce the general features of the horizontal distributions of variables such as effective droplet radius derived from satellite data retrieval. Comparison of the relationships among simulated cloud variables with those among satellite‐derived variables reveals that the implementation of an inhomogeneous CN field results in a more accurate simulation of the distribution of cloud microphysical properties. Sensitivity tests with respect to CN concentration show that the simulated area and amount of precipitation are slightly affected by the CN concentration. Comparative simulations using bin‐based and bulk microphysical schemes indicate that the difference in cloud microphysics has little effect on precipitation except over the areas of elevated pollution (i.e., elevated CN). Comparison with previous reports indicates that the precipitation response to aerosols is dependent on the environmental conditions and the type of the cloud system.

Pairing within the self-consistent quasiparticle random-phase approximation at finite temperature

An approach to pairing in finite nuclei at nonzero temperature is proposed, which incorporates the effects due to the quasiparticle-number fluctuation (QNF) around Bardeen-Cooper-Schrieffer (BCS) mean field and dynamic coupling to quasiparticle-pair vibrations within the self-consistent quasiparticle random-phase approximation (SCQRPA). The numerical calculations of pairing gap, total energy, and heat capacity were carried out within a doubly folded multilevel model as well as realistic nuclei $^{56}\mathrm{Fe}$ and $^{120}\mathrm{Sn}$. The results obtained show that, under the effect of QNF, in the region of moderate and strong couplings, the sharp transition between the superconducting and normal phases is smoothed out, resulting in a thermal pairing gap, which does not collapse at the BCS critical temperature, but has a tail, which extends to high temperature. The dynamic coupling of quasiparticles to SCQRPA vibrations significantly improves the agreement with the results of exact calculations and those obtained within the finite-temperature quantal Monte Carlo method for the total energy and heat capacity. It also causes a deviation of the quasiparticle occupation numbers from the Fermi-Dirac distributions for free fermions.

Exploration of Pseudospin Symmetry in the Resonant States

Taking 120Sn as an example, we discuss the pseudospin symmetryin the single proton resonant states by examining the energies,widths and the wavefunctions. The information of the single protonresonant states in spherical nuclei are extracted from an analyticcontinuation in the coupling constant method within the framework ofthe self-consistent relativistic mean field theory under therelativistic boundary condition. We find small energy splitting ina pair of pseudospin partners in the resonant states. The lowercomponents of the Dirac wavefunctions of a pseudospin doublet agreewell in the region where nuclear potential dominates. It is concludedthat the pseudospin symmetry is also well conserved for the resonantstates in realistic nuclei.

Test of spin symmetry in anti-nucleon spectra

The spin symmetry in antinucleon spectra of a nucleus is tested by investigating the relations between the Dirac wave functions of the spin doublets and examining these relations in realistic nuclei within the relativistic mean-field model. In addition to the fact that the dominant components of the Dirac spinors of the spin doublet are nearly identical to each other, there is a differential relation between the smaller components which is found to be almost exactly fulfilled.

Pseudospin symmetry and spin symmetry in the relativistic Woods–Saxon

The pseudospin symmetry and spin symmetry in the relativistic Woods–Saxon are investigated systematically by solving the Dirac equation with scalar and vector potentials and found to be a good approximation in realistic nuclei such as 208Pb. The pseudospin breaking and spin breaking is shown in correlation with nuclear mean field. The surface diffusivity and the radius of the potential play a important role in the splittings of energy and wavefunction. The dependence of splittings with quantum numbers is also analyzed.

Pseudospin symmetry in the relativistic harmonic oscillator

Pseudospin symmetry in the relativistic harmonic oscillator is investigated systemically by solving the Dirac equation with vector and scalar potentials quadratic, and found to be a good approximation in realistic nuclei such as Pb 208 . The pseudospin breaking is shown in correlation with nuclear mean-field shaped by the harmonic oscillator frequency and the distance of well-bottom deviation from the center, which play a important role in the splittings of energy and wavefunction, especially for the doublets with fewer nodes and lower angular momentum. The energy-level crossings are found for all the pseudospin partners.