The proper understanding of the equation of state (EoS) of highly asymmetric nuclear matter is essential when studying systems such as neutron stars (NSs). Using zero-range Skyrme interactions and finite-range interactions such as Gogny forces, momentum-dependent interactions (MDI) and simple effective interactions (SEI), we analyze the properties of the EoS and the influence they may have on the calculations for NSs.
We study the convergence properties of the Taylor series expansion of the EoS in powers of the isospin asymmetry and the accuracy of the results for $β$-stable nuclear matter when it is computed using the Taylor expansion of the EoS. The NS mass-radius relation for Skyrme and finite-range interactions is also analyzed. As none of the existing parametrizations of the standard Gogny D1 interaction are able to provide an NS inside the observational constraints, we propose a new parametrization, which we name D1M$^*$, that is able to provide NSs of $2 M_\odot$ while still providing the same good description of finite nuclei as D1M. A parametrization D1M$^{**}$ is also presented, which is fitted similarly as D1M$^*$ and provides NSs up to $1.91 M_\odot$.
An accurate determination of the core-crust transition point is necessary for the modeling of NSs for astrophysical purposes. We estimate the core-crust transition in NSs by finding where the nuclear matter in the core is unstable against fluctuations of the density. To do that, we employ two methods, the thermodynamical method and the dynamical method for zero-range and finite-range interactions. To apply the dynamical method to finite-range forces, we have explicitly derived the expression of the energy curvature matrix in momentum space.
Finally, the NS crustal properties, moment of inertia and tidal deformability are thoroughly analyzed using Skyrme and finite-range interactions.
The ground states of some nuclei are described by densities and mean fields that are spherical, while others are deformed. The existence of non-spherical shape in nuclei represents a spontaneous symmetry breaking.
Metz et al PRL (83), 1542 (1999) have presented evidence for supersymmetry in atomic nuclei but their model Hamiltonian fails to distinguish between irreducible representations that occur with multiplicities greater than one. This failure raises serious questions as to the validity of the evidence.
Shape/phase transitions in atomic nuclei have first been discovered in the framework of the Interacting Boson Approximation (IBA) model. Critical point symmetries appropriate for nuclei at the transition points have been introduced as special solutions of the Bohr Hamiltonian, stirring the introduction of additional new solutions describing wide ranges of nuclei. A short review of these recent developments will be attempted.
We present recent developments obtained in the so-called N2LO extension of the usual Skyrme pseudo-potential. In particular, we discuss the isovector splitting mass in infinite nuclear matter and the pairing gaps of selected semi-magic even-even nuclei.
This review presents some of the challenges in constructing models of atomic nuclei starting from theoretical descriptions of the strong interaction between nucleons. The focus is on statistical computing and methods for analyzing the link between bulk properties of atomic nuclei, such as radii and binding energies, and the underlying microscopic description of the nuclear interaction. The importance of careful model calibration and uncertainty quantification of theoretical predictions is highlighted.
The relation of the shell, collective and cluster models of the atomic nuclei is discussed from the viewpoint of symmetries. In the fifties the U(3) symmetry was found as their common part for a single shell problem. For multi major-shell excitations, considered here, the U(3)$\otimes$U(3) dynamical symmetry turns out to be their intersection.
This review consists of three parts: (a) what every atomic physicist needs to know about the physics of light nuclei; (b) what nuclear physicists can do for atomic physics; (c) what atomic physicists can do for nuclear physics. A brief qualitative overview of the nuclear force and calculational techniques for light nuclei will be presented, with an emphasis on debunking myths and on recent progress in the field. Nuclear quantities that affect precise atomic measurements will be discussed, together with their current theoretical and experimental status. The final topic will be a discussion of t…
Atomic experiments bring meaningful and valuable information on fundamental symmetries. The hypothesis of a large ($\sim 100$ eV) P-odd weak matrix element between single-particle states in heavy nuclei is inconsistent with the results of atomic PNC experiments. Upper limits on CP-violation obtained in atomic and molecular spectroscopy are as informative as those established in neutron physics. Very strict upper limits on T-odd, P-even interactions (nucleon-nucleon, electron-nucleon, electron-electron, and $β$-decay) are derived from the same atomic and neutron experiments.
The spectral statistics of low--lying states of several $fp$ shell nuclei are studied with realistic shell--model calculations. For Ca isotopes, we find significant deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.
The n,p-networks model is used to estimate binding energies and radii of proton-rich (N < Z) nuclei. These calculations have been made for some representative examples of even-Z and odd-Z nuclei with nucleon numbers lower than sixty. Good agreement is found in the comparison of these results with experimental data.
Origin of octupole deformation softness in atomic nuclei
Center for Exotic Nuclear Studies, Institute for Basic Science (IBS)（基础科学研究所）；Department of Physics, Ho Chi Minh City University of Education（胡志明市教育大学物理系）；Department of Theoretical Physics, Faculty of Physics and Engineering Physics, University of Science（理科大学物理与工程物理学院理论物理系）；Vietnam National University, Ho Chi Minh City（胡志明市越南国立大学）；Rare Isotope Science Project, Institute for Basic Science（基础科学研究所稀有同位素科学项目）；School of Physics and Astronomy, Tel Aviv University（特拉维夫大学物理与天文学学院）
Statistical spectroscopic results using the spectral distribution theory are obtained for the structure of neutron-rich light nuclei going towards the drip line and compared to experimental values available. These results will be useful for nuclear astrophysics problems where often averaged nuclear properties are adequate.
The incompressibility of finite fermionic systems is investigated using analytical approaches and microscopic models. The incompressibility of a system is directly linked to the zero-point kinetic energy of constituent fermions, and this is a universal feature of fermionic systems. In the case of atomic nuclei, this implies a constant value of the incompressibility in medium-heavy and heavy nuclei. The evolution of nuclear incompressibility along Sn and Pb isotopic chains is analyzed using global microscopic models, based on both non-relativistic and relativistic energy functionals. The result…
We present a new statistical tool based on random sampling to assess the confidence interval of Pearson's and Spearman's correlation coefficients. These estimators are then used to quantify the statistical correlations among the neutron skin thickness of atomic nuclei and the slope of the symmetry energy in the infinite nuclear medium.
Density dependent relativistic Hartree-Fock theory has been extended to describe properties of exotic nuclei. The effects of Fock exchange terms and of pi - and rho - meson contributions are discussed. These effects are found to be more important for neutron rich nuclei than for nuclei near the valley of stability.
The quantum phases of superconductivity and superfluidity are characterised mathematically by the Yang concept of Off-Diagonal Long Range Order (ODLRO), related to the existence of a large eigenvalue of the density matrix. We analyse how the Yang criterion applies for various Hamiltonians commonly employed to describe superfluid-type correlations in atomic nuclei. For like-particle pairing Hamiltonians the behaviour of the largest eigenvalue of two-body density matrix shows a clear evidence for a transition between a normal to a paired phase. However, this is not the case for the isoscalar pro…
We discuss the role of the broken symmetries in the connection of the shell, collective and cluster models. The cluster-shell competition is described in terms of cold quantum phases. Stable quasi-dynamical U(3) symmetry is found for specific large deformations for a Nilsson-type Hamiltonian.
The DIRHB package consists of three Fortran computer codes for the calculation of the ground-state properties of even-even atomic nuclei using the framework of relativistic self-consistent mean-field models. Each code corresponds to a particular choice of spatial symmetry: the DIRHBS, DIRHBZ and DIRHBT codes are used to calculate nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes, respectively. Reflection symmetry is assumed in all three cases. The latest relativistic nuclear energy density functionals are implemented in the codes, thus ena…
We report here an empirical formalism for predicting the cross-sections of neutron-rich nuclei produced in fragmentation of relativistic \b{eta}-unstable neutron-rich projectiles in the mid-mass region. The formalism is based on the abrasion-ablation picture of the projectile fragmentation reaction. It has been shown that the formalism can accurately reproduce the experimental cross-section data for nuclei produced in the fragmentation of 132Sn. The formalism, it is shown, can also reproduce the experimental cross-sections of neutron-rich nuclei produced in the fragmentation of 129Xe fairly ac…
To show the existence of precursor phenomena of the transition order$\ to$chaos in atomic nuclei a simple analysis has been made, based on a recent criterion proposed by Pavli\-chenkov. The basic idea is that nonlinear effects in rotational bands should lead to bifurcation, which qualitatively changes the spectrum for one of the nuclear excitation branches. Experimental data concerning the isotopes of Er, Hf, Yb, Os, Dy, W strongly support the above criterion.
Nuclear mean-field models are briefly reviewed to illustrate its foundation and necessity of state dependence in effective interactions. This state dependence is successfully taken into account by the density dependence, leading to the energy density functional. Recent results for photoabsorption cross sections in spherical and deformed Nd isotopes are shown.
The Pauli exclusion principle induces a repulsion between composite systems of identical fermions such as colliding atomic nuclei. Our goal is to study how heavy-ion fusion is impacted by this "Pauli repulsion". We propose a new microscopic approach, the density-constrained frozen Hartree-Fock method, to compute the bare potential including the Pauli exclusion principle exactly. Pauli repulsion is shown to be important inside the barrier radius and increases with the charge product of the nuclei. Its main effect is to reduce tunnelling probability. Pauli repulsion is part of the solution to th…
Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu-Goldstone modes using symmetry arguments only. We extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu-Goldstone modes. Symmetry arguments suffice to construct the low-lying …
Octupole deformed shapes in neutron-rich actinides and superheavy nuclei as well as extremely deformed shapes of the N~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~96, N~196 but our calculations do not predict octupole deformation in the ground states of superheavy Z~108 nuclei. As exemplified by the study of 36Ar, the nodal structure of the wavefunction of occupied single-particle orbitals in extremely deformed structures allo…
Description of a nuclear system in its ground state and at low excitations based on the equation of state (EoS) around normal density is presented. In the expansion of the EoS around the saturation point additional spin polarization terms are taken into account. These terms, together with the standard symmetry term, are responsible for appearance of the $α$-like clusters in the ground state configurations of the N=Z even-even nuclei. At the nuclear surface these clusters can be identified as alpha particles. A correction for the surface effects is introduced for atomic nuclei. Taking into acco…
Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schrödinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic interactions and currents. These ab-initio methods have been used to accurately compute properties of light nuclei -- including their spectra, moments, and transitions -- and the equation of state of neutron and nuclear matter. In this work we review selected results obtained by combining quantum Monte Carlo methods and recent Hamiltonians constructed within chir…
The properties of loosely bound proton-rich nuclei around A = 20 are investigated within the framework of nuclear shell model. In these nuclei, the strength of the effective interactions involving the loosely bound proton s1=2 orbit are significantly reduced in comparison with those in their mirror nuclei. We evaluate the reduction of the effective interaction by calculating the monopole-baseduniversal interaction (VMU) in the Woods-Saxon basis. The shell-model Hamiltonian in the sd shell, such as USD, can thus be modified to reproduce the binding energies and energy levels of the weakly bound…
It is shown, that the Gamow-like model with only one adjustable parameter - radius constant is able to reproduce well the alpha-decay half-lives for all even-even nuclei with the proton number larger than 50. The systematics for odd-A and odd-odd isotopes can be also well described when ones introduces an additional hindrance factor. Similar model based on the W. J. Swiatecki idea from 1955 is developed to reproduce the spontaneous fission half-lives of transactinide nuclei. The achieved accuracy of reproduction of the data is better than that obtained in more advanced theories.
Shell model studies have been done for very neutron - rich nuclei in the range Z=50-55 and N=82-87. Good agreement of the theoretical level spectra with the experimental one for N=82, 83 I and Te nuclei is shown. Then the results for three very neutron-rich nuclei 137Sn and 136-137Sb have been presented. The present calculation favour a 2- ground state for 136Sb instead of 1- identified through beta decay.Interesting observation about the E2 effective charges for this region has been discussed.
We study E1 resonances, breakup and fusion reactions for weakly bound Be nuclei. The absorbing-boundary condition (ABC) is used to describe both the outgoing and incoming boundary conditions. The neutron continuum plays important roles in response and reaction of neutron drip-line nuclei.
A systematics of the atomic nuclei in the frame of the nucleon number $A = Z + N$ and the proton-neutron difference $F = Z - N$ is considered. The classification scheme is provided by means of the non-compact algebra $sp(4,R)$. In this scheme the nuclei are ordered into isobaric multiplets, for which $A={fix}$, as well as in F-multiplets, for which $F={fix}$. The dependence of the mass excess $Δ$, the first exited states $E_{2^+}$ and the ratio $R_2=E_{4^+}/E_{2^+}$ on the nucleon number $A$ is empirically investigated within the $F$-multiplets. Appropriate filters are used to study the proper…
The spectroscopic strengths of two-nucleon transfer reactions constitute a stringent test for two-nucleon correlations in the nuclear wave functions. A comparison between the recently measured 198Hg(d,alpha)196Au reaction and the predictions from the nuclear quartet supersymmetry lends further support to the validity of supersymmetry in nuclear physics.
We perform Hartree-Fock+BCS calculations for even-even nuclei with 2 <= Z <= 82 and N ranging from outside the proton drip line to the experimental frontier on the neutron-rich side. The ground state solutions are obtained for 737 nuclei, together with shape-coexistence solutions for 480 nuclei. Our method features the Cartesian-mesh representation of single-particle wavefunctions, which is advantageous in treating nucleon skins and exotic shapes. The results are compared with those of the finite-range droplet model of Moller et al. as well as the experimental values.
An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to show how a very simple and schematic nucleon--nucleon interaction can produce an order$\to$chaos transition. The second part is devoted to a discussion of the wave function behaviour and decay of chaotic states using some simple models (to be published in Rivista Nuovo Cimento).
Neutron rich Zr nuclei with number of neutrons between $N$= 50 and 82 are investigated in the relativistic mean field approach in co-ordinate space. The resonant levels in the positive energy continuum have been explicitly included in the calculation. Odd nuclei have been treated in the blocking approximation. Our calculation indicates that the dripline for odd mass isotopes is far away from that for the even mass ones. Pairing interaction plays a significant role in stabilizing the even isotopes, thus extending the dripline for them.
The degrees of freedom associated with shape fluctuations and space orientation of atomic nuclei are analyzed with effective forces and large configuration spaces. A pedagogical theoretical introduction to the topic of symmetries restoration broken in the mean field approach as well as to the concept of generator coordinate is presented. We discuss global properties, like binding energies, two neutron separation energies and quadrupole moments, as well as spectroscopic ones like excitation energies or transition probabilities. The analysis covers selected examples of light and heavy nuclei, as…
A systematic analysis of the spherical-to-deformed shape phase transition in even-even rare-earth nuclei from $_{58}$Ce to $_{74}$W is carried out in the framework of the interacting boson model. These results are then used to calculate nuclear radii and electric monopole (E0) transitions with the same effective operator. The influence of the hexadecapole degree of freedom ($g$ boson) on the correlation between radii and E0 transitions thus established, is discussed.
The charge-dependent realistic nuclear Hamiltonian for a nucleus, composed of neutrons and protons, can be successfully approximated by a charge-independent one. The parameters of such a Hamiltonian, i.e., the nucleon mass and the NN potential, depend upon the mass number A, charge Z and isospin quantum number T of state of the studied nucleus.
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband $E2$ transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
The multinucleon transfer reactions in collisions of $^{136}$Xe+$^{198}$Pt at incident energies $E_{\textrm{lab}}=$5.25, 6.20, 7.98, 10.0, and 15.0 MeV/nucleon are investigated by using the improved quantum molecular dynamics model. It is found that 6.20 MeV/nucleon is the optimal incident energy for producing the neutron-rich heavy nuclei. About 80 unknown neutron-rich nuclei might be produced in this reaction with cross sections from 10$^{-6}$ to 10$^{-2}$ mb. The angular distributions of the neutron-rich isotopes are predicted.
Starting from a Skyrme interaction with tensor terms, the $β$-decay rates of $^{52}$Ca have been studied within a microscopic model including the $2p-2h$ configuration effects. We observe a redistribution of the strength of Gamow-Teller transitions due to the $2p-2h$ fragmentation. Taking into account this effect results in a satisfactory description of the neutron emission probability of the $β$-decay in $^{52}$Ca.
The influence of the diffuse surface layer of a finite nucleus on the mean square radii and their isotopic shift is investigated. We present the calculations within the Gibbs-Tolman approach using the experimental values of the nucleon separation energies. Results are compared with that obtained by means of direct variational method based on Fermi-like trial functions.
We discuss the sensitivity of fission barrier for heavy neutron-rich nuclei to fission paths in the two dimensional neutron-proton quadrupole plane. To this end, we use the constrained Skyrme-Hartree-Fock + BCS method, and examine the difference of fission barriers obtained with three constraining operators, that is, the neutron, proton, and mass quadrupole operators. We investigate $^{220}$U, $^{236}$U, and $^{266}$U, %from proton-rich to neutron-rich uranium isotopes, that is relevant to r-process nucleosynthesis. We find that the fission barrier heights are almost the same among the three c…
Recently, it has been reported that as one goes from oxygen to fluorine, just the addition of one more proton, provides extraordinary stability to fluorine which can bind six more neutrons beyond what oxygen can. It is shown here that this surprising stability can be understood if neutron rich nuclei, $^{24}O$ and $^{27}F$ are treated as bound states of eight and nine-tritons respectively. Also the recently discovered $^{42}Si$ is predicted to have a bound state structure of fourteen tritons.
Particle and pairing densities in spherical even-even neutron-rich nuclei are studied within the Skyrme-Hartree-Fock-Bogoliubov approach with the density-dependent pairing interaction. The influence of the density dependence of the pairing interaction on asymptotic properties of nucleonic distributions are analyzed. It is demonstrated that the size of the neutron halo dramatically depends on the behavior of the pairing interaction at low density.
The idea of treating the trinucleon systems as elementary entities in the elementary particle model (EPM) as an Effective Field Theory has been a success in explaining the weak charge-changing processes in nuclei. The EPM results are found to be as good as those obtained from nuclear microscopic models using two- and three-body forces. We extend this concept to investigate the validity of the elemental nature of $A=3$ nuclei through studies of nuclear structure of neutron-rich nuclei. By treating neutron-rich nuclei as primarily made up of tritons as its building blocks, we extract one- and tw…
We study the extremely neutron-rich nuclei for $Z = 17 - 23$, $37 - 40$ and $60 - 64$ regions of the periodic table by using axially deformed relativistic mean field formalism with NL3* parametrization. Based on the analysis of binding energy, two neutron separation energy, quadrupole deformation and root mean square radii, we emphasized the speciality of these considered regions which are recently predicted islands of inversion.
The nonlinear model of pionic condensate in nuclei by G. Preparata can be efficiently verified by investigation of the quasielastic knockout process of pions out of nuclei by high energy electrons. First, a momentum distribution (MD) of the collective pions has a bright maximum at q=0.3 Gev.Second the excitation spectrum of a recoil nucleus is concentrated at low energies E lesser than 1MeV. The results for the pion knockout from mesonic clouds of individual nucleons are absolutely different. The latter results are presented both for pion and rho-meson clouds localized on nucleons.
A comparative study of fission of actinides specially $^{238}$U, by proton and bremsstrahlung photon is performed. Relative mass distribution of $^{238}$U fission fragments have been explored theoretically for both proton and photon induced fission. The integrated yield along with charge distribution of the products are calculated to find out the neutron richness in comparison to the nuclei produced by r-process in nucleosynthesis. Some r-process nuclei in intermediate mass range for symmetric fission mode are found to be produced almost two order of magnitude more for proton induced fission t…
We discuss the present status of the description of the structure of the very neutron rich nuclei, in the framework of modern large scale shell model calculations. Particular attention is paid to the interaction related issues, as well as to the problems of the shell model approach at the neutron drip line. We present detailed results for nuclei around N=20 and, more briefly, we discuss some salient features of the regions close to N=8, 28 and 40. We show that most experimental features can be understood in a shell model context.
The moment of inertia of even-even deformed nuclei which are derived on the basis of hydrodynamical model yield values that are too small compared with the experimental [Davidson 1965] ones. We expect that these contradictions come from the consideration only the first term in $R$- expansion in spite of not containing parameters indicating deformity of the nucleus, and neglecting all other terms which include the deformation parameters $αλμ$. In this work, the first three terms in $R$- expansion are taken into account. The results are more realistic and too much better the previous ones.
We calculate the ground, first intrinsic excited states and density distribution for neutron-rich thorium and uranium isotopes, within the framework of relativistic mean field(RMF) approach using axially deformed basis. The total nucleon densities are calculated, from which the cluster-structures inside the parent nuclei are determined. The possible modes of decay, like α-decay and \b{eta} -decay are analyzed. We find the neutron-rich isotopes are stable against α-decay, however they are very much unstable against \b{eta} -decay. The life time of these nuclei predicted to be tens of second aga…
The N/Z ratio of free nucleons from collisions of neutron-rich nuclei as a function of their momentum is studied by means of Isospin dependent Quantum Molecular Dynamics. We find that this ratio is not only sensitive to the form of the density dependence of the symmetry potential energy but also its strength determined by the symmetry energy coefficient. The uncertainties about the symmetry energy coefficient influence the accuracy of probing the density dependence of the symmetry energy by means of the N/Z ratio of free nucleons of neutron-rich nuclei.
A detailed study fusion of neutron-rich colliding nuclei is performed using various isospin dependent potentials. For present study, Three different series namely, Ne-Ne, Ca-Ca, and Zr-Zr are taken into account and N/Z ratio.A monotonous increase (decrease) in the fusion barrier positions (heights) using a unified second order nonlinear parametrization in the normalized fusion barrier positions and heights with (N/Z-1) is presented. These predications are in good agreement with the available theoretical as well as experimental results.
A systematic study of the yrast-band structure for the proton-rich, even-even mass-80 nuclei is carried out using projected shell model approach. We describe the the energy spectra, transition quadrupole moments and gyromagnetic factors. The observed variations in energy spectra and transition quadrupole moments in this mass region are discussed in terms of the configuration mixing of the projected deformed Nilsson states as a function of shell filling.
