The electric dipole moments (EDMs) of neutron-odd nuclei with even protons are systematically evaluated. We first derive the relation between the EDM and the magnetic moment operators by making use of the core polarization scheme. This relation enables us to calculate the EDM of neutron-odd nuclei without any free parameters. From this calculation, one may find the best atomic system suitable for future EDM experiments.
We consider T=0 states in even-even and odd-odd N=Z nuclei. The g factors that emerge are isoscalar. We find that the single j shell model gives simple expressions for these g factors which for even-even nuclei are suprisingly close to the collective values for K=0 bands. The g factors of many 2+ in even-even nuclei and 1+ and 3+ states in odd-odd nuclei have g factors close to 0.5.
Conflicting coupling of unpaired nucleons in the odd-odd nuclei is discussed. A very simple explanation is suggested for the damping of the energy spacing of the lowest levels in the rotational bands in the odd-odd nuclei in the case of a "conflicting" coupling of the odd proton and neutron comparative to those of the bands based on the state of the strongly-coupled particle in the neighbouring odd nuclei entering the "conflicting" configuration.
Some binding-energy-related quantities serving as effective order parameters have been used to analyze the shape phase transition in the odd Sm nuclei. It is found that the signals of phase transition in the odd Sm nuclei are greatly enhanced in contrast to the even Sm nuclei. A further analysis shows that the transitional behaviors related to pairing in the Sm nuclei can be well described by the mean field plus pairing interaction model, with a monotonic decrease in the pairing strength $G$.
After identifying the nuclei in the regions near A =80 and A = 160 for which beta-decay rates have the greatest effect on weak and main r-process abundance patterns, we apply the finite-amplitude method (FAM) with Skyrme energy-density functionals (EDFs) to calculate beta-decay half-lives of those nuclei in the quasiparticle random-phase approximation (QRPA). We use the equal filling approximation to extend our implementation of the charge-changing FAM, which incorporates pairing correlations and allows axially symmetric deformation, to odd-A and odd-odd nuclei. Within this framework we find d…
We present a systematic analysis of the description of odd nuclei by the Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and blocking of the odd nucleon. Current and spin densities in the Skyrme functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on basic properties (binding energies, odd-even staggering, separation energies and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6, and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z < 92 are considered. The calculations demonstrate that the TOMF eff…
Simple methods in the frame work of the broken pair model have been worked out for odd-odd nuclei. The reliability of the model has been tested by reproducing the shell model results of limiting cases in which the broken pair model exactly coincides with the shell model. The model is then applied to calculate the energy levels of some nuclei in the Zirconium region. The model results compare reasonably well with the shell model as well as with the experimental data.
A fully consistent relativistic random phase approximation is applied to study the systematic behavior of the isovector giant dipole resonance of nuclei along the $β$-stability line in order to test the effective Lagrangians recently developed. The centroid energies of response functions of the isovector giant dipole resonance for stable nuclei are compared with the corresponding experimental data and the good agreement is obtained. It is found that the effective Lagrangian with an appropriate nuclear symmetry energy, which can well describe the ground state properties of nuclei, could also re…
The effect of deformation on the excitation of multiple giant dipole resonances is studied. Analytical expressions are derived in the framework of the interacting boson model for the energies and E1 properties of giant dipole resonances in spherical and deformed nuclei, and a numerical treatment of transitional nuclei is proposed. Coulomb-excitation cross sections are calculated in $^{238}$U and in the samarium isotopes.
We use the finite amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute beta-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.
The nuclear shell model assumes an effective mean-field plus interaction Hamiltonian in a specific configuration space. We want to understand how various interaction matrix elements affect the observables, the collectivity in nuclei and the nuclear level density for odd-A and odd-odd nuclei. Using the sd and pf shells, we vary specific groups of matrix elements and study the evolution of energy levels, transition rates and the level density. In all cases studied, a transition between a "normal" and a collective phase is induced, accompanied by an enhancement of the level density in the collect…
In order to extract informations on pairing correlations in nuclei from experimental mass differences, the different contributions to odd-even mass differences are investigated within the Skyrme HFB method. In this first paper, the description of odd nuclei within HFB is discussed since it is the key point for the understanding of the above mentioned contributions. To go from an even nucleus to an odd one, the advantage of a two steps process is demonstrated and its physical content is discussed. New results concerning time-reversal symmetry breaking in odd-nuclei are also reported. PACS: 21.1…
Two types of average neutron-proton interaction formulas are compared: In the first type, neutron-proton interactions for even-even and odd-$A$ nuclei extracted from experimental binding energies show a smooth behavior as a function of mass number $A$ and are dominated by the contribution from the symmetry energy. Whereas in the second type large systematic staggering is seen between even-$A$ and odd-$A$ nuclei. This deviation is understood in term of the additional neutron-proton interaction in odd-odd nuclei relative to the neighboring even-even and odd-$A$ systems. We explore three possible…
We perform shell model calculations in odd-odd nuclei using a quadrupole-quadrupole interaction and single-particle splittings chosen so as to obtain the SU(3) results. Elliott had shown that such an interaction gives rotational bands for which the energies go as I(I+1). This is certainly true for eve-even and for odd-even or even-odd nuclei with $K\neq 1/2$. We have looked at odd-odd nuclei e.g $^{22}Na$ and found somewhat different behaviour. In $^{22}Na$ the $I=1^+_1 T=0$ and $I=0^+_1 T=1$ states are degenerate, and a rotational band built on the $I=0^+_1 T=1$ state behaves in a normal fash…
The iterative quasi-particle-random-phase approximation (QRPA) method we previously developed to accurately calculate properties of individual nuclear states is extended so that it can be applied for nuclei with odd numbers of neutrons and protons. The approach is based on the proton-neutron-QRPA (pnQRPA) and uses an iterative non-hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method is used to calculate excitation energies of proton-neutron multiplets for several nuclei. The influence of a pairing interaction in the $T=…
We study the interplay between the isoscalar (T=0) and isovector (T=1) pairing correlations in N=Z odd-odd nuclei from 14N to 58Cu by using three-body model calculations. The strong spin-triplet T=0 pairing correlation dominates in the ground state of 14N, 18F, 30P, and 58Cu with the spin-parity J^π=1+, which can be well reproduced by the present calculations. The magnetic dipole and Gamow-Teller transitions are found to be strong in 18F and 42Sc as a manifestation of SU(4) symmetry in the spin-isospin space. We also discuss the spin-quadrupole transitions in these nuclei.
The low-energy isoscalar dipole response of heavy spherical nuclei is studied by using a semiclassical model, based on the solution of the linearized Vlasov kinetic equation for finite Fermi systems. In this translation-invariant model the excitations of the center of mass motion are exactly separated from the internal ones. The low-energy dipole strength function displays three resonance structures in the energy region up to 15 MeV. Calculations of the velocity fields associated with the resonance structures at the centroid energies show a vortex (toroidal) character of two overlying resonanc…
Electromagnetic dipole absorption cross-sections of transitional nuclei with large-amplitude shape fluctuations are calculated in a microscopic way by introducing the concept of Instantaneous Shape Sampling. The concept bases on the slow shape dynamics as compared to the fast dipole vibrations. The elctromagnetic dipole strength is calculated by means of RPA for the instantaneous shapes, the probability of which is obtained by means of IBA. Very good agreement with the experimental absorption cross sections near the nucleon emission threshold is obtained.
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are derived within the single-j interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to ^{167}Er and ^{161}Dy. We find consistency with the former measurements but not with the latter.
We study the isoscalar (T=0) and isovector (T=1) pairing correlations in N=Z nuclei. They are estimated from the double difference of binding energies for odd-odd N=Z nuclei and the odd-even mass difference for the neighboring odd-mass nuclei, respectively. The empirical and BCS calculations based on a T=0 and T=1 pairing model reproduce well the almost degeneracy of the lowest T=0 and T=1 states over a wide range of even-even and odd-odd N=Z nuclei. It is shown that this degeneracy is attributed to competition between the isoscalar and isovector pairing correlations in N=Z nuclei. The calcula…
Quantum shape-phase transitions in odd-even nuclei are investigated in the framework of the interacting boson-fermion model. Classical and quantum analysis show that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially near the critical point. Experimental evidence for the occurrence of spherical to axially-deformed transitions in odd-proton nuclei Pm, Eu and Tb (Z=61, 63, 65) is presented.
Chiral rotation observed in $^{128}$Cs is studied using the newly developed microscopic triaxial projected shell model (TPSM) approach. The observed energy levels and the electromagnetic transition probabilities of the nearly degenerate chiral dipole bands in this isotope are well reproduced by the present model. This demonstrates the broad applicability of the TPSM approach, based on a schematic interaction and angular-momentum projection technique, to explain a variety of low- and high-spin phenomena in triaxial rotating nuclei.
The Kerman-Klein-Donau-Frauendorf (KKDF) model is a linearized version of the Kerman-Klein (equations of motion) formulation of the nuclear many-body problem. In practice, it is a generalization of the standard core-particle coupling model that, like the latter, provides a description of the spectroscopy of odd nuclei in terms of the properties of neighboring even nuclei and of single-particle properties, that are the input parameters of the model. A divers sample of recent applications attest to the usefulness of the model. In this paper, we first present a concise general review of the funda…
An article by Covello, Gargano and Itaco [Phys.Rev. C 56, 3092 (1997)] tries to find evidence for the important role of the residual tensor force between the valence proton and neutron in doubly odd deformed nuclei. It is shown that observable effects discussed by these authors do not fully justify their rather strong conclusions.
It is shown that a consistent description of magnetic dipole properties in transitional nuclei can be obtained in the interacting boson model-2 by F-spin breaking mechanism, which is associated with differences between the proton and neutron deformations. In particular, the long standing anomalies observed in the $g$-factors of the Os-Pt isotopes are resolved by a proper inclusion of F-spin breaking.
We present a formalism to describe proton emission from odd-odd nuclei based on a scattering like approach. Special emphasis is given to the case of transitions between states with different deformations. As an example we estimate the proton half-life of the odd-odd nucleus $^{58}$Cu. Our calculations show that the change of deformation in the decay process has a significant influence on the half-life. In addition, the angular momentum coupling of proton and neutron orbitals can result in an important $K$-hindrance of the decay. To fully account for the observed half-life in $^{58}$Cu, one has…
The electric dipole excitation of various nuclei is calculated with a Random Phase Approximation phenomenological approach. The evolution of the strength distribution in various groups of isotopes, oxygen, calcium, zirconium and tin, is studied. The neutron excess produces $E1$ strength in the low energy region. Indexes to measure the collectivity of the excitation are defined. We studied the behavior of proton and neutron transition densities to determine the isoscalar or isovector nature of the excitation. We observed that in medium-heavy nuclei the low-energy $E1$ excitation has characteris…
The effects of ground-state correlations on the damping of isovector giant dipole resonances in $LS$ closed shell nuclei $^{16}$O and $^{40}$Ca are studied using extended random-phase-approximation (RPA) approaches derived from the time-dependent density-matrix theory. It is pointed out that unconventional two-body amplitudes of one particle--three hole and three particle--one hole types which are neglected in most extended RPA theories play an important role in the fragmentation of isovector dipole strength.
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.
While bulk properties of stable nuclei are successfully reproduced by mean-field theories employing effective interactions, the dependence of the centroid energy of the electric giant dipole resonance on the nucleon number A is not. This problem is cured by considering many-particle correlations beyond mean-field theory, which we do within the "Quasiparticle Time Blocking Approximation". The electric giant dipole resonances in $^{16}$O, $^{40}$Ca, and $^{208}$Pb are calculated using two new Skyrme interactions.
The giant dipole resonance (GDR) in deformed nuclei is analyzed using the self-consistent separable random-phase-approximation (SRPA) with Skyrme forces SkT6, SkM$^*$, SLy6 and SkI3. The deformed nuclei $^{150}$Nd and $^{238}$U are used as representative rare-earth and actinide samples. Dependencies of the dipole strength distributions on some basic characteristics of the Skyrme functional and nuclear matter properties (isoscalar and isovector effective masses, time-odd contributions) are discussed. Particular attention is paid to the fragmentation structure of the GDR strength which are shown…
We study the systematics of the giant dipole resonance width $Γ$ in hot rotating nuclei as a function of temperature $T$, spin $J$ and mass $A$. We compare available experimental results with theoretical calculations that include thermal shape fluctuations in nuclei ranging from A=45 to A=208. Using the appropriate scaled variables, we find a simple phenomenological function $Γ(A,T,J)$ which approximates the global behavior of the giant dipole resonance width in the liquid drop model. We reanalyze recent experimental and theoretical results for the resonance width in Sn isotopes and $^{208}$Pb…
The quartet condensation model (QCM) is extended for the treatment of isovector and isoscalar pairing in odd-odd N=Z nuclei. In the extended QCM approach the lowest states of isospin T=1 and T=0 in odd-odd nuclei are described variationally by trial functions composed by a proton-neutron pair appended to a condensate of 4-body operators. The latter are taken as a linear superposition of an isovector quartet, built by two isovector pairs coupled to the total isospin T=0, and two collective isoscalar pairs. In all pairs the nucleons are distributed in time-reversed single-particle states of axia…
Isoscalar dipole strength distributions in spherical medium- and heavy-mass nuclei are calculated within random phase approximation (RPA) or quasiparticle RPA. Different Skyrme-type interactions corresponding to incompressibilities in the range 200 - 250 MeV are used. The results are discussed in comparison with existing data on isoscalar giant dipole resonances. Two main issues are raised, firstly the calculated giant resonance energies are somewhat higher than the observed ones, and secondly a sizable fraction of strength is predicted below 20 MeV which needs to be experimentally confirmed.
We study the nature of the low-lying dipole strength in neutron-rich nuclei, often associated to the Pygmy Dipole Resonance. The states are described within the Hartree-Fock plus RPA formalism, using different parametrizations of the Skyrme interaction. We show how the information from combined reactions processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states.
The isovector M1 transitions between low-lying T=1 and T=0 states in odd-odd N=Z nuclei are analyzed. Simple analytical expressions for M1 transition strengths are derived within a single-j-shell approximation for both j=l+1/2 and j=l-1/2 cases. The large B(M1) values for the j=l+1/2 case are attributed to quasi-deuteron configurations. The B(M1) values for the j=l-1/2 case are found to be small due to partly cancellation of spin and orbital parts of the M1 matrix element.
Masses of superheavy (SH) nuclei with $Z=98-128$, including odd and odd-odd nuclei, are systematically calculated within the microscopic-macroscopic model based on the deformed Woods-Saxon potential. Ground states are found by minimizing energy over deformations and configurations. Pairing in odd particle-number systems is treated either by blocking or by adding the BCS energy of the odd quasiparticle. Three new parameters are introduced which may be interpreted as the constant mean pairing energies for even-odd, odd-even and odd-odd nuclei. They are adjusted by a fit to masses of heavy nuclei…
We extend the algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei by combining the eikonal approximation for the scattering with a description of odd-mass nuclei in terms of the interacting boson-fermion model. We derive closed expressions for the transition matrix elements for one of the dynamical symmetries and discuss the interplay between collective and single-particle degrees of freedom in an application to elastic and inelastic proton scattering from $^{195}$Pt.
We provide a description of odd-odd self-conjugate nuclei in the sd shell in a formalism of collective quartets and pairs. Quartets are four-body structures carrying isospin T=0 while pairs can have either T=0 or T=1. Both quartets and pairs are labeled by the angular momentum J and they are chosen so as to describe the lowest states of 20Ne (quartets) and the lowest T=0 and T=1 states of 18F (pairs). We carry out configuration interaction calculations in spaces built by one quartet and one pair for 22Na and by two quartets and one pair for 26Al. The spectra that are generated are in good agre…
The experimentally observed $ΔI = 1$ doublet bands in some odd-odd nuclei are analyzed within the orthosymplectic extension of the Interacting Vector Boson Model (IVBM). A new, purely collective interpretation of these bands is given on the basis of the obtained boson-fermion dynamical symmetry of the model. It is illustrated by its application to three odd-odd nuclei from the $A\sim 130$ region, namely $^{126}Pr$, $^{134}Pr$ and $^{132}La$. The theoretical predictions for the energy levels of the doublet bands as well as $E2$ and $M1$ transition probabilities between the states of the yrast b…
We introduce a new Bose-Fermi framework for studying spectral properties and quantum phase transitions (QPTs) in odd-mass nuclei, in the presence of configuration mixing. A detailed analysis of odd-mass Nb isotopes discloses the effects of an abrupt crossing of states in normal and intruder configurations (Type II QPT), accompanied by a gradual evolution from spherical- to deformed-core shapes within the intruder configuration (Type I QPT). The pronounced presence of both types of QPTs demonstrates, for the first time, the occurrence of intertwined QPTs in odd-mass nuclei.
A simple model based on the group SO(5) suggests that both the like-particle and neutron-proton components of isovector pairing correlations in odd-A nuclei are Pauli blocked. The same effect emerges from Monte Carlo Shell-model calculations of proton-rich nuclei in the full fp shell. There are small differences between the two models in their representation of the effects of an odd nucleon on the competition between like-particle and neutron-proton pairing, but they can be understood and reduced by using a two-level version of the SO(5) model. On the other hand, in odd-odd nuclei with N not e…
Isoscalar dipole nuclear response reveals the low- and high-energy resonances. The nature of isoscalar dipole resonances in heavy spherical nuclei is studied by using the translation-invariant kinetic model of small oscillations of finite Fermi systems. Calculations of the velocity field at the centroid energy show a pure vortex character of the low-energy isoscalar dipole resonance in spherical nuclei and confirm the anisotropic compression character of the high-energy one. The evolution of the velocity field in dependence on the excitation energy of the nucleus within the resonance width is …
A fully symmetry unrestricted Time-Dependent Density Functional Theory extended to include pairing correlations is used to calculate properties of the isovector giant dipole resonances of the deformed open-shell nuclei 172Yb (axially deformed), 188Os (triaxially deformed), and 238U (axially deformed), and to demonstrate good agreement with experimental data on nuclear photo-absorption cross-sections for two different Skyrme force parametrizations of the energy density functional: SkP and SLy4.
Using an alpha decay level scheme, an explanation for the fine structure in odd nuclei is evidenced by taking into account the radial and rotational couplings between the unpaired nucleon and the core of the decaying system. It is stated that the experimental behavior of the alpha decay fine structure phenomenon is directed by the dynamical characteristics of the system.
Recent results of the description of quadrupole moments of odd semi-magic nuclei are briefly reviewed. They are based on the self-consistent theory of finite Fermi systems with account for the phonon-particle coupling (PC) effects. The self-consistent model for describing the PC effects was developed previously for magnetic moments. Account for the non-pole diagrams is an important ingredient of this model. In addition to previously reported results for the odd In and Sb isotopes, which are the proton-odd neighbors of even tin nuclei, we present new results for odd Bi isotopes, the odd neighbo…
The effective surface approximation is extended accounting for derivatives of the symmetry energy density per particle. Using the analytical isovector surface energy constants within the Fermi-liquid droplet model, one obtains energies and sum rules of the isovector dipole resonance structure in a reasonable agreement with the experimental data and other theoretical approaches.
The E1 strength is systematically analyzed in very neutron-rich Sn nuclei, beyond $^{132}$Sn until $^{166}$Sn, within the Relativistic Quasiparticle Random Phase Approximation. The great neutron excess favors the appearance of a deformed ground state for $^{142-162}$Sn. The evolution of the low-lying strength in deformed nuclei is determined by the interplay of two factors, isospin asymmetry and deformation: while greater neutron excess increases the total low-lying strength, deformation hinders and spreads it. Very neutron rich deformed nuclei may not be as good candidates as stable spherical…
Theoretical studies of low-lying dipole strength in even-even spherical nuclei within the relativistic quasiparticle time blocking approximation (RQTBA) are presented. The RQTBA developed recently as an extension of the self-consistent relativistic quasiparticle random phase approximation (RQRPA) enables one to investigate effects of coupling of two-quasiparticle excitations to collective vibrations within a fully consistent calculation scheme based on covariant energy density functional theory. Dipole spectra of even-even $^{130}$Sn -- $^{140}$Sn and $^{68}$Ni -- $^{78}$Ni isotopes calculated…
Binding energies, quadrupole deformation parameters, spins and parities of the neutron-deficient odd $Z=N+1$ nuclei in the $A\sim 80$ region are calculated in the relativistic mean field approximation. The ground-state and low-lying configurations of the recently observed $^{77}$Y, $^{79}$Zr and $^{83}$Mo nuclei are analyzed. The calculated results are compared with other theoretical predictions.
Low-energy dipole excitations have been investigated theoretically in N=50, several N=82 isotones and the Z=50 Sn isotopes. For this purpose a method incorporating both HFB and multi-phonon QPM theory is applied. A concentration of one-phonon dipole strength located below the neutron emission threshold has been calculated in these nuclei. The analysis of the corresponding neutron and proton dipole transition densities allows to assign a genuine pattern to the low-energy excitations and making them distinct from the conventional GDR modes. Analyzing also the QRPA wave functions of the states we…
Accurate estimates of the binding energy of nuclei far from stability that cannot be produced in the laboratory are crucial to our understanding of nuclear processes in astrophysical scenarios. Models based on energy density functionals have shown that they are capable of reproducing all known masses with root-mean-square error better than 800 keV, while retaining a firm microscopic foundation. However, it was recently pointed out in [M. Hukkanen et al., arXiv:2210.10674] that the recent BSkG1 model fails to account for a contribution to the binding energy that is specific to odd-odd nuclei, a…
The interplay of pairing is explored for the spectral statistics of nuclear systems with emphasis on the nearest neighbor spacing distributions by employing the kernel density and maximum likelihood estimation techniques. Different sequences prepared by all the available empirical data for low-lying energy levels of even and odd-mass nuclei in the 34 < A < 206 mass region. A deviation to more regular dynamics is apparent for even-mass nuclei in compare to odd-mass ones, and there are suggestions of effects due to unclosed proton shells on more chaotic dynamics.
After shortly analyzing data relevant to fission hindrance of odd-A nuclei and high-$K$ isomers in superheavy (SH) region we point out the inconsistency of current fission theory and propose an approach based on the instanton formalism. A few results of this method, simplified by replacing selfconsistency by elements of the macro-micro model, are given to illustrate its features.
