We present a calculation of the properties of vibrational states in deformed, axially--symmetric even--even nuclei, within the framework of a fully self--consistent Quasparticle Random Phase Approximation (QRPA). The same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels. We have tested our software in the case of spherical nuclei against fully self consistent calculations published in the literature, finding excellent agreement. We investigate the consequences of neglecting the spin-orbit and Coulomb residual interactions in QRPA. Furthermore we discuss the improvement obtained in the QRPA result associated with the removal of spurious modes. Isoscalar and isovector responses in the deformed ${}^{24-26}$Mg, $^{34}$Mg isotopes are presented and compared to experimental findings.
Systematic investigation of the accuracy of the description of the energies of deformed one-quasiparticle states has been performed in covariant density functional theory in actinide and rare-earth mass regions. The sources of the discrepancies between theory and experiment are analyzed. Although some improvements in the description of ground state configurations and one-quasiparticle spectra can be achieved by better parametrization of the relativistic mean field Lagrangian, the analysis suggests that spectroscopic quality of their description can be achieved only in theoretical framework whi…
We develop a new framework of the deformed quasiparticle-random-phase approximation (QRPA) where the Skyrme density functional and the density-dependent pairing functional are consistently treated. Numerical applications are carried out for the isovector dipole and the isoscalar quadrupole modes in the spherical $^{20}$O and in the deformed $^{26}$Ne nuclei, and the effect of the momentum dependent terms of the Skyrme effective interaction for the energy-weighted sum rule is discussed. As a further application, we present for the first time the moments of inertia of $^{34}$Mg and $^{36}$Mg usi…
The Heavy Shell Model (HSM) (Y. Sun and C.-L. Wu, Phys. Rev. C 68, 024315 (2003)) was proposed to take the advantages of two existing models, the projected shell model (PSM) and the Fermion Dynamical Symmetry Model (FDSM). To construct HSM, one extends the PSM by adding collective D-pairs into the intrinsic basis. The HSM is expected to describe simultaneously low-lying collective and quasi-particle excitations in deformed nuclei, and still keeps the model space tractable even for the heaviest systems. As the first numerical realization of the HSM, we study systematically the band structures f…
We use the axially-deformed Skyrme Quasiparticle Random-Phase Approximation (QRPA) together with the SkM* energy-density functional, both as originally presented and with the time-odd part adjusted to reproduce the Gamow-Teller resonance energy in 208Pb, to calculate the matrix elements governing the neutrinoless double-beta decay of 76Ge, 130Te, 136Xe, and 150Nd. Our matrix elements in 130Te and 136Xe are significantly smaller than those of previous QRPA calculations, primarily because of the difference in pairing or deformation between the initial and final nuclei. In 76Ge and 150Nd our resu…
We formulate a new scheme of the Hartree-Fock-Bogoliubov mean-field theory applicable to weakly bound and pair correlated deformed nuclei using the coordinate-space Green's function technique. On the basis of a coupled-channel representation of the quasiparticle wave function expanded in terms of the partial waves, we impose the correct boundary condition of the asymptotically out-going waves on the continuum quasiparticle states. We perform numerical analysis for $^{38}$Mg to illustrate properties of the continuum quasiparticle states and the pair correlation in deformed nuclei near the neutr…
The structure of Ne, Na, Mg, Al, Si and S nuclei near the neutron drip-line region is investigated in the frame-work of relativistic meannfield (RMF) and non-relativistic Skyrme Hartree-Fock formalisms. The drip-line of these nuclei are pointed out. We analysed the large deformation structures and many of these neutron rich nuclei are quite deformed. New magic number are seen for these deformed nuclei.
Beta-decay properties of even and odd-A neutron-rich Ge, Se, Kr, Sr, Ru, and Pd isotopes involved in the astrophysical rapid neutron capture process are studied within a deformed proton-neutron quasiparticle random-phase approximation. The underlying mean field is described self-consistently from deformed Skyrme Hartree-Fock calculations with pairing correlations. Residual interactions in the particle-hole and particle-particle channels are also included in the formalism. The isotopic evolution of the various nuclear equilibrium shapes and the corresponding charge radii are investigated in all…
Frontiers Science Center for Rare isotope, Lanzhou University（兰州大学稀有同位素前沿科学中心）；School of Nuclear Science and Technology, Lanzhou University（兰州大学核科学与技术学院）；State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与技术国家重点实验室）；Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University（中山大学中法核工程与技术学院）
Covariant density functional theory is used to analyze the evolution of low-lying M1 strength in superfluid deformed nuclei in the framework of the self-consistent Relativistic Quasiparticle Random Phase Approximation (RQRPA). In nuclei with a pronounced neutron excess two scissor modes are found. Besides the conventional scissor mode, where the deformed proton and neutron distributions oscillate against each other, a new soft M1 mode is found, where the deformed neutron skin oscillates in a scissor like motion against a deformed proton-neutron core.
An extension of the previously proposed Variable Moment of Inertia with Softness model VMIS has been applied to describe successfully the effect of backbending in some deformed e-e nuclei. The model shows good results in the rare earth and actinide regions.
The 62Sm, 64Gd, 64Dy, 70Y b, 72Hf and 74W nuclei are classified as deformed nuclei. Low-lying bands are one of the most fundamental excitation modes in the energy spectra of deformed nuclei. In this paper a theoretical analysis of the experimental data within the phenomenological model is presented. The energy spectra of ground states are calculated. It is found the low-lying spectra of ground band states are in good agreement with the experimental data.
We calculate the binding energy and deformation parameter for light nuclei with and without pairing using a deformed relativistic mean field model. The role of BCS-type pairing effect is analyzed for Ne and F isotopes. The calculated odd-even staggering and the deformation parameters argue strongly against the role of pairing in the light nuclei.
We discuss the notion of partial dynamical symmetry in relation to nuclear spectroscopy. Explicit forms of Hamiltonians with partial $SU(3)$ symmetry are presented in the framework of the interacting boson model of nuclei. An analysis of the resulting spectrum and electromagnetic transitions demonstrates the relevance of such partial symmetry to the spectroscopy of axially deformed nuclei.
We present analytic expressions of the Coulomb interaction between a spherical and a deformed nuclei which are valid for all separation distance. We demonstrate their significant deviations from commonly used formulae in the region inside the Coulomb radius, and show that they remove various shortcomings of the conventional formulae.
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.
Weakly-bound deformed nuclei have been studied by the Skyrme Hartree-Fock-Bogoliubov (HFB) approach in large coordinate-space boxes. In particular, the box-size dependence of the HFB calculations of weakly-bound deformed nuclei are investigated, including the particle density and pairing density distributions at nuclear surfaces, the near-threshold resonant and continuum quasiparticle spectra, and energetic properties. The box size may have larger influences in pairing properties than in other bulk properties. We demonstrate that large-box calculations of weakly-bound nuclei are important to p…
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…
Magnetic form factors corresponding to elastic electron scattering from odd-A nuclei are presented. The calculations are carried out in plane-wave Born approximation. The one-body properties are obtained in a deformed self-consistent mean-field calculation based on a Skyrme HF+BCS method. Collective effects are also included in the cranking approximation. Results on several stable nuclei are compared with the available experimental information. It is shown that a deformed formalism improves the agreement with experiment in deformed nuclei, while reproducing equally well spherical nuclei by tak…
The consequences of the spontaneous breaking of rotational symmetry are investigated in a field theory model for deformed nuclei, based on simple separable interactions. The crucial role of the Ward-Takahashi identities to describe the rotational states is emphasized. We show explicitly how the rotor picture emerges from the isoscalar Goldstone modes, and how the two-rotor model emerges from the isovector scissors modes. As an application of the formalism, we discuss the M1 sum rules in deformed nuclei, and make connection to empirical information.
Potential energies, moments of inertia, quadrupole and octupole moments of dinuclear systems are compared with the corresponding quantities of strongly deformed nuclei. As dinuclear system we denote two touching nuclei (clusters). It is found that the hyperdeformed states of nuclei are close to those of nearly symmetric dinuclear systems, whereas the superdeformed states are considered as states of asymmetric dinuclear systems. The superdeformed and hyperdeformed states constructed from two touching clusters have large octupole deformations. The experimental measurement of octupole deformation…
We present a study of deformed nuclei in the framework of the sdg interacting boson model utilizing both numerical diagonalization and analytical $1/N$ expansion techniques. The focus is on description of high-spin states which have recently become computationally accessible through the use of computer algebra in the $1/N$ expansion formalism. A systematic study is made of high-spin states in rare-earth and actinide nuclei.
The single-particle spectrum of deformed shell-model states in nuclei, is shown to exhibit a supersymmetric pattern. The latter involves deformed pseudospin doublets and intruder levels. The underlying supersymmetry is associated with the relativistic pseudospin symmetry of the nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.
The thermal evolution of the shell correction energy is investigated for deformed nuclei using Strutinsky prescription in a self-consistent relativistic mean-field framework. For temperature independent single-particle states corresponding to either spherical or deformed nuclear shapes, the shell correction energy $Δ_{sc}$ steadily washes out with temperature. However, for states pertaining to the self-consistent thermally evolving shapes of deformed nuclei, the dual role played by the single-particle occupancies in diluting the fluctuation effects from the single-particle spectra and in drivi…
Non-trivial geometrical effects in relativistic central collisions of deformed nuclei are studied using a simple version of optical Glauber model. For very small impact parameters large centrality and eccentricity fluctuations are observed. In very high multiplicity collisions of oblate nuclei (e.g. Au and Cu) significant fraction of events with elliptic flow strength v_2 dependent on oblateness beta_2 is predicted.
Background: Collective excitations of nuclei and their theoretical descriptions provide an insight into the structure of nuclei. Replacing traditional phenomenological interactions with unitarily transformed realistic nucleon-nucleon interactions increases the predictive power of the theoretical calculations for exotic or deformed nuclei. Purpose: Extend the application of realistic interactions to deformed nuclei and compare the performance of different interactions, including phenomenological interactions, for collective excitations in the sd-shell. Method: Ground-state energies and charge r…
From the semi-empirical formalisms of Bohr-Mottelson, a new model, based on the effect of beta- and gamma- head energies and the variable moment of inertia, was developed to calculate the ground state rotational band of almost all deformed e-e nuclei. The model can be tuned for nuclei with experimentally available beta- and gamma-vibrational energies as well as for those with unmeasured beta- and gamma-vibrations.
Reaction cross-sections are calculated using the Coulomb modified Glauber model for deformed target nuclei. The deformed nuclear matter density of the target is expanded into multipoles of order k = 0,2,4.The reaction cross-sections between some spherical and deformed nuclei are studied at energy range (10-1000 MeV/nucleon). The most significant effects in the intermediate energy range are the Coulomb field and in-medium effect that modified the trajectory of the incident beams. Introducing the deformation effect beside the Coulomb field and in-medium effect improves the agreement with the exp…
We present a detailed discussion of the solution of Nambu-Gor'kov equations in superfluid nuclei, which provide a consistent framework to deal with the interplay between particle-hole and particle- particle channel, including the effects of the fragmentation of the quasiparticle strength and of the pairing interaction induced by the exchange of collective vibrations. The coupling between quasiparticle and vibrations is determined from the experimental polarizability of the low-lying collective surface vibrations. This coupling is used to renormalize the properties of quasiparticles obtained fr…
Correlations and the formation of bound states (nuclei) are essential for the properties of nuclear matter in equilibrium as well as in nonequilibrium. In a quantum statistical approach, quasiparticle energies are obtained for the light elements that reflect the influence of the medium. We present analytical fits for the quasiparticle energy shifts of light nuclei that can be used in various applications. This is a prerequisite for the investigation of warm and dense matter that reproduces the nuclear statistical equilibrium and virial expansions in the low-density limit as well as relativisti…
We investigate the deformation properties of atomic nuclei in a hadronic chiral SU_f(3) model approach. The parameters are fitted to hadron mass properties and adjustments for spherical finite nuclei have been performed. Using these parameters the deformation of a series of light and heavy nuclei are obtained in a two-dimensional self-consistent calculation. In addition we discuss a case of superdeformation in a heavy nucleus.
This work presents an older, but still interesting description of a superfluid condensate with two components (protons and neutrons), confined by time-dependent deformed harmonic oscillator potentials either in collective uniform rotation, or opposite angular oscillation.
The thermodynamic properties of hot nuclei are described within the canonical and microcanonical ensemble approaches. These approaches are derived based on the solutions of the BCS and self-consistent quasiparticle random-phase approximation at zero temperature embedded into the canonical and microcanonical ensembles. The obtained results agree well with the recent data extracted from experimental level densities by Oslo group for $^{94}$Mo, $^{98}$Mo, $^{162}$Dy and $^{172}$Yb nuclei.
We consider deformed nuclei within an effective theory that exploits the small ratio between rotational and vibrational excitations. For even-even nuclei, the effective theory predicts small changes in the rotational constants of bands built on multi-phonon excitations that are linear in the number of excited phonons. In 166Er and 168Er, this explains the main variations of the rotational constants of the two-phonon gamma vibrational bands. In 232Th, the effective theory correctly explains the trend that the rotational constants decrease with increasing spin of the band head. We also study the…
We discuss characteristic features of SU(3) partial dynamical symmetry in relation to nuclear spectroscopy and compare with previous broken-SU(3) calculations for ^{168}Er.
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.
In the frame work of the hydrodynamical model, a new model of the ground state rotational bands of deformed e-e nuclei is developed by introducing the variable moment of inertia, and the effect of beta- and gamma- vibrational bands. The model is applied to calculate the energies of the ground state band of 158Dy. The results of our calculations are in close agreement with data compared with other existing models.
We have performed self-consistent Skyrme Hartree-Fock-Bogolyubov calculations for nuclei close to $^{254}$No. Self-consistent deformations, including $β_{2,4,6,8}$ as functions of the rotational frequency, were determined for even-even nuclei $^{246,248,250}$Fm, $^{252,254}$No, and $^{256}$Rf. The quasiparticle spectra for N=151 isotones and Z=99 isotopes were calculated and compared with experimental data and the results of Woods-Saxon calculations. We found that our calculations give high-order deformations similar to those obtained for the Woods-Saxon potential, and that the experimental qu…
The properties of kaonic nuclei are studied using a two-dimensional Skyrme-Hartree-Fock model with a $KN$ Skyrme force. We focus in particular on the instability of the solutions for a too strong $KN$ interaction, which determines a maximum value of the kaon binding in this approach. We then analyze the change of the deformation properties of several core-deformed nuclei caused by the added kaon, and find a shrinking of the core and in some cases a complete loss of deformation.
Low-frequency $K^π=0^{+}$ states in deformed neutron-rich nuclei are investigated by means of the quasiparticle-random-phase approximation based on the Hartree-Fock-Bogoliubov formalism in the coordinate space. We have obtained the very strongly collective $K^π=0^{+}$ modes not only in neutron-rich Mg isotope but also in Cr and Fe isotopes in N=40 region, where the onset of nuclear deformation has been discussed. It is found that the spatially extended structure of neutron quasiparticle wave functions around the Fermi level brings about a striking enhancement of the transition strengths. It is…
We explore the rotational feature of deformed halos by performing the angular momentum projection (AMP) on the ground state wave functions obtained from the deformed relativistic Hartree-Bogoliubov theory (DRHBc) in continuum. The DRHBc+AMP approach self-consistently describes the coupling between single particle bound states and the continuum not only in the ground state but also in rotational states. The rotational modes of deformed halos in $^{42}$Mg and $^{44}$Mg are investigated by studying properties of rotational states such as excitation energy, configuration, and density distribution.…
Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac eigenfunctions of realistic relativistic mean field calculations of deformed nuclei to determine if these eigenfunctions satisfy these pseudospin symmetry constraints.
Initial eccentricity of the interacting volume of QCD matter created in collisions of prolate and oblate nuclei is studied using optical Glauber simulation. Collisions of prolate 165-Ho + 165-Ho nuclei and Au+Au nuclei are investigated (assuming oblate ground-state deformation for 197-Au nucleus). Qualitative predictions are obtained for RHIC energies.
A formula to evaluate the effects of a general deformation on the Coulomb direct contribution to the energy of the Isobaric Analog State (IAS) is presented and studied via a simple yet physical model. The toy model gives a reasonable account of microscopic deformed Hartree-Fock-Bogolyubov (HFB) calculations in a test case, and provides a guidance when predicting unknown IAS energies. Thus, deformed HFB calculations, to predict the IAS energies, are performed for several neutron-deficient medium-mass and heavy nuclei which are now planned to be studied experimentally.
The relationship between the deformed harmonic oscillator and the formation of molecular cluster structures, whereby valence neutrons are exchanged between cluster cores, is examined. It is found that there is a strong connection between the properties of the valence orbitals associated with deformed structures in the deformed harmonic oscillator and the molecular orbitals created by linear combinations of single-centre orbitals around nuclear clusters. The conclusion is that in addition to the appearance of clustering in the deformed harmonic oscillator that \emph{every} prolate deformed clus…
The coordinate-space Hartree-Fock-Bogoliubov (HFB) approach with quasiparticle blocking has been applied to study the odd-A weakly bound nuclei $^{17,19}$B and $^{37}$Mg, in which halo structures have been reported in experiments. The Skyrme nuclear forces SLy4 and UNEDF1 have been adopted in our calculations. The results with and without blocking have been compared to demonstrate the emergence of deformed halo structures due to blocking effects. In our calculations, $^{19}$B and $^{37}$Mg have remarkable features of deformed halos.
Examples of the change of neutron shell-structure in both weakly-bound and resonant neutron one-particle levels in nuclei towards the neutron drip line are exhibited. It is shown that the shell-structure change due to the weak binding may lead to the deformation of those nuclei with the neutron numbers $N \approx$ 8, 20, 28 and 40, which are known to be magic numbers in stable nuclei. Nuclei in the "island of inversion" are most easily and in a simple manner understood in terms of deformation. As an example of spectroscopic properties other than single-particle energies, magnetic moments of so…
A collective vector-boson model with broken SU(3) symmetry is applied to several deformed even-even nuclei. The model description of ground and $γ$ bands together with the corresponding B(E2) transition probabilities is investigated within a broad range of SU(3) irreducible representations (irreps) $(λ,μ)$. The SU(3)-symmetry characteristics of rotational nuclei are analyzed in terms of the bandmixing 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…
Using an angular momentum projected single particle basis, a pnQRPA approach is used to study the $2νββ$ properties of ten isotopes, exhibiting various quadrupole deformations. The mother and daughter nuclei exhibit different quadrupole deformations. Since the projected basis enables a unified description of deformed and spherical nuclei, situations where the nuclei involved in the double beta decay process are both spherical, both deformed or one spherical and another deformed, can be treated through a sole formalism. Dependence of single $β^-$ and $β^+$ strength distribution on atomic mass n…
We have investigated the effects of the neutron-proton interaction in several doubly odd deformed nuclei within the framework of the particle-rotor model. In this paper, we show some selected results of our study which evidence the importance of the tensor-force effects.
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 …
Techniques from effective field theory are applied to nuclear rotation. This approach exploits the spontaneous breaking of rotational symmetry and the separation of scale between low-energy Nambu-Goldstone rotational modes and high-energy vibrational and nucleonic degrees of freedom. A power counting is established and the Hamiltonian is constructed at next-to-leading order.
We describe and apply a version of the finite amplitude method for obtaining the charge-changing nuclear response in the quasiparticle random phase approximation. The method is suitable for calculating strength functions and beta-decay rates, both allowed and forbidden, in axially-deformed open-shell nuclei. We demonstrate the speed and versatility of the code through a preliminary examination of the effects of tensor terms in Skyrme functionals on beta decay in a set of spherical and deformed open-shell nuclei. Like the isoscalar pairing interaction, the tensor terms systematically increase a…
The microscopic analysis of experimental data in $^{160,162}$Tm is presented within the two-quasiparticle-phonon model. The model includes the interaction between odd quasiparticles and their coupling with core vibrations. The coupling explains naturally the attenuation of the Coriolis interaction in rotating odd-odd nuclei. It is shown that the competition between the Coriolis and neutron-proton interactions is responsible for the signature inversion phenomenon.
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is introduced. The model is based on an effective Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel, and the pairing part of the Gogny force is used in the pairing channel. The RHFBz quasiparticle equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Carbon, Neon and Magnesium isotopes. The effect of the explicitly including the pion field is investigated for binding energies, deformation parameters…
Deformed Hartree-Fock-Bogoliubov calculations for finite nuclei are carried out. As residual interaction, a Brueckner G-matrix derived from a meson-exchange potential is taken. Phenomenological medium modifications of the meson masses are introduced. The binding energies, radii, and deformation parameters of the Carbon, Oxygen, Neon, and Magnesium isotope chains are found to be in good agreement with the experimental data.
A semi-microscopic model to study the neutron and proton induced backbending phenomena in some deformed even-even nuclei from the rare earth region, is proposed. The space of particle-core states is defined by the angular momentum projection of a quadrupole deformed product state. The backbending phenomena are described by mixing four rotational bands, defined by a set of angular momentum projected states, and a model Hamiltonian describing a set of paired particles moving in a deformed mean field and interacting with a phenomenological deformed core. The ground band corresponds to the configu…
