Experimental data on $^{96}$Zr indicate coexisting spherical and deformed structures with small mixing amplitudes. Several collective low-lying states and E2 and M1 transitions are observed for this nucleus. The quadrupole-collective Bohr Hamiltonian depending on both $β$ and $γ$ shape variables with a potential having spherical and deformed minima, is applied consideration of these data. The relative depth of two minima, height and width of the barrier, rigidity of the potential near both minima are determined so as to achieve a satisfactory description of the observed properties of the low-lying collective quadrupole states of $^{96}$Zr. Good agreement with the experimental data on the excitation energies, $B(E2)$ and $B(M1; 2^+_2\rightarrow 2^+_1)$ reduced transition probabilities is obtained. It is shown that the low-energy structure of $^{96}$Zr can be described in a satisfactory way within the Geometrical Collective Model with a potential function supporting shape coexistence without other restrictions of its shape. However, the excitation energy of the $2^+_2$ state can be reproduced only if the rotation inertia coefficient is taken by four times smaller than the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of the $B(M1; 2^+_2 \rightarrow 2^+_1)$ and $B(M1; 3^+_1 \rightarrow 2^+_1)$ transition probabilities. An indication for the influence of the pairing vibrational mode on the $0^+_2 \rightarrow 0^+_1$ transition is confirmed in agreement with the previous result.
The article reviews the general version of the Bohr collective model for the description of quadrupole collective states, including a detailed study the model's kinematics. The general form of the classical and quantum Bohr Hamiltonian is presented together with a discussion of the tensor structure of the collective wave functions and with a short review of various methods of solving the Bohr Hamiltonian eigenvalue equation.The methods of derivation of the classical and quantum Bohr Hamiltonian from the microscopic many-body theory are recalled and the microscopic approach to the Bohr Hamilton…
We discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes. We consider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as well as axially symmetric and asymmetric shape fluctuations. Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinates and collective momenta, we microscopically derive the collective Hamiltonian of Bohr and Mottelson, which describes low-frequency quadrupole dynamics. We show that the five-dime…
The generalized Bohr Hamiltonian is applied to a description of low-lying collective excitations in even-even isotopes of Te, Xe, Ba, Ce, Nd and Sm. The collective potential and inertial functions are determined by means of the Strutinsky method and the cranking model, respectively. A shell-dependent parametrization of the Nilsson potential is used. An approximate particle-number projection is performed in treatment of pairing correlations. The effect of coupling with the pairing vibrations is taken into account approximately when determining the inertial functions. The calculation does not co…
Analytical expressions of the wave functions are derived for a Bohr Hamiltonian with the Manning{Rosen potential in the cases of γ-unstable nuclei and axially symmetric prolate deformed ones with γ=0. By exploiting the results we have obtained in a recent work on the same theme Ref. [1], we have calculated the B(E2) transition rates for 34 γ-unstable and 38 rotational nuclei and compared to experimental data, revealing a qualitative agreement with the experiment and phase transitions within the ground state band and showing also that the Manning-Rosen potential is more appropriate for such cal…
Experimental data on $^{96}$Zr indicate coexisting spherical and deformed structures with small mixing amplitudes. We investigate the properties of the low-lying collective states of $^{96}$Zr based on the collective quadrupole Bohr Hamiltonian. The $β$-dependent collective potential having two minima -- spherical and deformed, is fixed so to describe experimental data in the best way.Good agreement with the experimental data on the excitation energies, $B(E2)$ and $B(M1)$ reduced transition probabilities is obtained. It is shown that the low-energy structure of $^{96}$Zr can be reproduced in …
Eigenfunctions of the collective Bohr Hamiltonian with the Morse potential have been obtained by using the Asymptotic Iteration Method (AIM) for both gamma-unstable and rotational structures. B(E2) transition rates have been calculated and compared to experimental data. Overall good agreement is obtained for transitions within the ground state band, while some interband transitions appear to be systematically underpredicted in gamma-unstable nuclei and overpredicted in rotational nuclei.
The Generator Coordinate Method (GCM) in the Gaussian Overlap Approximation (GOA) is applied to a description of the nuclear quadrupole collective states. The full five-dimensional quadrupole tensor is used as a set of the generator coordinates.The integral Hill-Wheeler equation is reduced to a differential equation by using the Fourier transforms of the overlap and energy kernels. The differential Bohr Hamiltonian obtained this way is compared with that derived by the usual approach to the collective Hamiltonian in the GOA which does contain an additional approximation. The method of calculat…
Low-lying quadrupole shape dynamics is a typical manifestation of large amplitude collective motion in finite nuclei. To describe the dynamics on a microscopic foundation, we have formulated a consistent scheme in which the Bohr collective Hamiltonian for the five dimensional quadrupole shape variables is derived on the basis of the time-dependent Hartree-Fock-Bogoliubov theory. It enables us to incorporates the Thouless-Valatin effect on the shape inertial functions, which has been neglected in previous microscopic Bohr Hamiltonian approaches. Quantitative successes are illustrated for the lo…
The quadrupole vibrational modes of neutron-rich $N$=28 isotones ($^{48}$Ca, $^{46}$Ar, $^{44}$S and $^{42}$Si) are investigated using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory with several choice of energy density functionals, including nuclear pairing correlation. It is found that the quenching of $N$=28 shell gap and the proton holes in the $sd$-shell trigger quadrupole correlation and increase the collectivity of the low-lying 2$^+$ state in $^{46}$Ar. It is also found that the pairing correlation plays an important role to increase the collectivity. We also demonst…
Quadrupole excitations of even-even Ru and Pd isotopes are described within microscopic approach based on the general collective Bohr model which includes the effect of coupling with the pairing vibrations. The excitation energies and E2 transition probabilities observed in 104-114Ru and 106-110Pd are reproduced in the frame of the calculation containing no free parameters.
Collective low lying levels of light and medium Xenon isotopes are deduced from the Generalized Bohr Hamiltonian (GBH). The microscopic seven functions entering into the GBH are built from a deformed mean field of the Woods-Saxon type. Theoretical spectra are found to be close to the ones of the experimental data taking into account that the calculations are completely microscopic, that is to say, without any fitting of parameters.
We investigate the low-lying 2$^+$ states of $N=28$ isotones ($^{48}$Ca, $^{46}$Ar, $^{44}$S and $^{42}$Si) with using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory in which the pairing is taken into account self-consistently. The quadrupole mode with very small excitation energies emerges in $^{46}$Ar, $^{44}$S and $^{42}$Si due to the strong quadrupole correlations triggered by the quenching of the $N=28$ shell gap. The importance of the quadrupole correlations between the protons and neutrons, and the role of the pairing correlation to reinforce the lowest 2$^+$ mode are…
The phenomenological classification of collective quadrupole excitations by means of the Bohr Hamiltonian is reviewed with focus on signatures for triaxility. The variants of the microscopic Bohr Hamiltonian derived by means of the Adiabatic Time Dependent Mean Field theory from the Pairing plus Quadrupole-Quadrupole interaction, the Shell Correction Method, the Skyrme Energy Density Functional, the Relativistic Mean Field Theory, and the Gogny interaction are discussed and applications to concrete nuclides reviewed. The Generator Coordinate Method for the five dimensional quadrupole deformati…
Embedding of the 5-dimensional (5D) space of the Bohr Hamiltonian with a deformation-dependent mass (DDM) into a 6-dimensional (6D) space shows that the free parameter in the dependence of the mass on the deformation is connected to the curvature of the 5D space, with the special case of constant mass corresponding to a flat 5D space. Comparison of the DDM Bohr Hamiltonian to the 5D classical limit of Hamiltonians of the 6D interacting boson model (IBM), shows that the DDM parameter is proportional to the strength of the pairing interaction in the U(5) (vibrational) symmetry limit, while it is…
We calculate the eigenvalues and their corresponding eigenfunctions of the Bohrs collective Hamiltonian with the help of the modified Poschl-Teller potential model within -unstable structure. Our numerical results for the ground state beta and gamma band heads together with the electric quadrupole B(E2) transition rates are displayed and compared with those available experimental data.
The properties of the low-lying 2^+ states in the even-even nuclei around 132Sn are studied within the quasiparticle random phase approximation. Starting from a Skyrme interaction in the particle-hole channel and a density-dependent zero-range interaction in the particle-particle channel, we use the finite rank separable approach in our investigation. It is found that the fourth 2^+ state in 132Te could be a good candidate for a mixed-symmetry state.
An analytic, parameter-free (up to overall scale factors) solution of the Bohr Hamiltonian involving axially symmetric quadrupole and octupole deformations, as well as an infinite well potential, is obtained, after separating variables in a way reminiscent of the Variable Moment of Inertia (VMI) concept. Normalized spectra and B(EL) ratios are found to agree with experimental data for 226-Ra and 226-Th, the nuclei known to lie closest to the border between octupole deformation and octupole vibrations in the light actinide region.
Nuclei exhibit quantum phase transitions (earlier called ground state phase transitions) between different shapes as the number of nucleons is modified, resulting in changes in the ground and low lying nuclear states. Special solutions of the Bohr Hamiltonian appropriate for the critical point of such shape phase transitions, as well as other special solutions applicable to relevant nuclear regions are described.
The generalized Bohr Hamiltonian was used to describe the low-lying collective excitations in even-even isotopes of Ru, Pd, Te, Ba and Nd. The Strutinsky collective potential and cranking inertial functions were obtained using the Nilsson potential. The effect of coupling with the pairing vibrations is taken into account approximately when determining the inertial functions. The calculation does not contain any free parameter.
New analytic solutions of the quadrupole collective Bohr hamiltonian are proposed, exploiting an approximate separation of the beta and gamma variables to describe gamma-soft prolate axial rotors. The model potential is a sum of two terms: a beta-dependent term taken either with a Coulomb-like or a Kratzer-like form, and a gamma-dependent term taken as an harmonic oscillator. In particular it is possible to give a one parameter paradigm for a beta-soft, gamma-soft axial rotor that can be applied, with a considerable agreement, to the spectrum of 234U.
The coupling of the high-lying dipole mode to the low-lying quadrupole modes for the case of deformed gamma-unstable nuclei is studied. Results from the geometrical model are compared to those obtained within the dipole boson model. Consistent results are obtained in both models. The dipole boson model is treated within the intrinsic frame, with subsequent projection onto the laboratory frame. As an application, calculations of photonuclear cross-sections in gamma-unstable nuclei are presented.
The effect of quadrupole-type surface vibrations on the quadrupole response function of heavy nuclei is studied by using a model based on the solution of the linearized Vlasov equation with moving-surface boundary conditions. By using a separable approximation for the residual interaction, an analytical expression is obtained for the moving-surface response function. Comparison of the fixed- and moving-surface strength functions shows that surface vibrations are essential in order to achieve a unified description of the two characteristic features of the quadrupole response: the giant resonanc…
The low-lying level schemes and electromagnetic transitions of $^{109}$Te, $^{109}$I, and the neighboring even-even nucleus $^{108}$Te, are calculated within the framework of the $SD$-pair approximation of the nuclear shell model. Good agreement is obtained between the calculated results and experimental data. The favored components of low-lying bands are discussed in the collective nucleon-pair subspace. The weak-coupling picture shown in these nuclei and its relationship with residual quadrupole-quadrupole interaction between valence protons and neutrons are analyzed.
The chiral constituent quark model (\chiCQM) with general parameterization (GP) method has been formulated to calculate the quadrupole moments of the spin 3/2^+ decuplet baryons and spin 3/2^+ \to 1/2^+ transitions. The implications of such a model have been investigated in detail for the effects of symmetry breaking and GP parameters pertaining to the two- and three-quark contributions. It is found that the \chiCQM is successful in giving a quantitative and qualitative description of the quadrupole moments.
In the random-interaction ensembles, three proportional correlations between quadrupole moments of the first two $I^π=2^+$ states robustly emerge, including $Q(2^+_1)=\pm Q(2^+_2)$ correlations consistently with realistic nuclear survey, and the $Q(2^+_2)=-\frac{3}{7}Q(2^+_1)$ correlation, which is only observed in the $sd$-boson space. These correlations can be microscopically characterized by the rotational SU(3) symmetry and quadrupole vibrational U(5) limit, respectively, according to the Elliott model and the $sd$-boson mean-field theory. The anharmonic vibration may be another phenomenol…
We investigate the properties of the excited spectra of the even-even isotopes of krypton using a Generalised Bohr Hamiltonian with three different Skyrme functionals. In particular, we investigate the evolution of the low-lying $2^{+}_{1}$ and $4^{+}_{1}$ states and their associated electromagnetic transitions. The model reproduces quite nicely the energy trends apart from ${}^{88}$Kr, where none of the interactions used here are able to grasp a sudden change in the energy spectrum. Additionally, we explore the neutron deficient region ${}^{72-76}$Kr which is a proposed region for shape coexi…
The interrelation between the octupole phonon and the low-lying proton-neutron mixed-symmetry quadrupole phonon in near-spherical nuclei is investigated. The one-phonon states decay by collective E3 and E2 transitions to the ground state and by relatively strong E1 and M1 transitions to the isoscalar 2+ state. We apply the proton-neutron version of the Interacting Boson Model including quadrupole and octupole bosons (sdf-IBM-2). Two F-spin symmetric dynamical symmetry limits of the model, namely the vibrational and the γ-unstable ones, are considered. We derive analytical formulae for excitati…
The coupled dynamics of low lying modes and various giant resonances are studied with the help of the Wigner Function Moments method on the basis of Time Dependent Hartree-Fock equations in the harmonic oscillator model including spin-orbit potential plus quadrupole-quadrupole and spin-spin residual interactions. New low lying spin dependent modes are analyzed. Special attention is paid to the spin scissors mode.
We study the predictive power of Skyrme forces with respect to low lying quadrupole spectra along the chains of Sn, Cd, and Te isotopes. Excitation energies and B(E2) values for the lowest quadrupole states are computed from a collective Schroedinger equation which as deduced through collective path generated by constraint Skyrme-Hartree-Fock (SHF) plus self-consistent cranking for the dynamical response. We compare the results from four different Skyrme forces, all treated with two different pairing forces (volume versus density-dependent pairing). The region around the neutron shell closure …
The spherical-to-prolate shape transition in neutron-rich Cr isotopes from N = 34 to 42 is studied by solving the collective Schr\"odinger equation for the five-dimensional quadrupole collective Hamiltonian. The collective potential and inertial functions are microscopically derived with use of the constrained Hartree-Fock-Bogoliubov plus local quasiparticle random-phase approximation method. Nature of the quadrupole collectivity of low-lying states is discussed by evaluating excitation spectra and electric quadrupole moments and transition strengths. The result of calculation indicates that …
Basing on the Bohr collective quadrupole Hamiltonian the $A$-dependence of the Grodzins product is derived and the proportionality coefficient for the Grodzins relation is evaluated. The result obtained is in a correspondence with the experimental data.
We present a comprehensive study on the low-lying states of neutron-rich Er, Yb, Hf, and W isotopes across the $N=126$ shell with a multi-reference covariant density functional theory. Beyond mean-field effects from shape mixing and symmetry restoration on the observables that are relevant for understanding quadrupole collectivity and underlying shell structure are investigated. The general features of low-lying states in closed-shell nuclei are retained in these four isotopes around $N=126$, even though the shell gap is overall quenched by about 30\% with the beyond mean-field effects. These …
A fully quantal algebraic version of the Bohr-Mottelson unified model is presented with the important property that its quantisation is defined by its irreducible unitary representations which span the many-nucleon Hilbert space of every nucleus. The model is uniquely defined by the requirement that its Lie algebra of observables includes the nuclear quadrupole moments and kinetic energy. It then follows that there can be no non-zero isoscalar E2 transitions between any states belonging to its different irreducible representations and, as a result, the states of the model are uniquely defined …
Dependence of the kinetic energy term of the collective nuclear Hamiltonian on collective momentum is considered. It is shown that the fourth order in collective momentum term of the collective quadrupole Hamiltonian generates a sizable effect on the excitation energies and the matrix elements of the quadrupole moment operator. It is demonstrated that the results of calculation are sensitive to the values of some matrix elements of the quadrupole moment. It stresses the importance for a concrete nucleus to have the experimental data for the reduced matrix elements of the quadrupole moment oper…
The observed properties of the low-lying collective states of $^{96}$Zr are investigated within the geometrical collective model. The quadrupole-collective Bohr Hamiltonian with the potential having spherical and axially-symmetric deformed minima is applied. The role of triaxiality is investigated by rotating the potential in $γ$-degree of freedom so that the deformed minimum occurs at various axially asymmetric shapes. The change of excitation energies and reduced matrix elements of quadrupole transitions with increase of triaxiliaty is analyzed.
The isoscalar (IS) and isovector (IV) quadrupole responses of nuclei are systematically investigated using the time-dependent Skyrme Energy Density Functional including pairing in the BCS approximation. Using two different Skyrme functionals, Sly4 and SkM*, respectively 263 and 304 nuclei have been found to be spherical along the nuclear charts. The time-dependent evolution of these nuclei has been systematically performed giving access to their quadrupole responses. It is shown that the mean-energy of the collective high energy state globally reproduces the experimental IS and IV collective e…
A new scheme was recently proposed in which the usual SU(3) quadrupole-quadrupole interaction was replaced by an O(6) cubic interaction in the Interacting Boson Model, and also successfully applied to the description of $^{152}$Sm for the N = 90 rare earth isotones with X(5) symmetry. By using this new scheme, in the present work, we further explore the properties of another candidate of $^{150}$Nd for the N=90 with X(5) symmetry. The low-lying energy levels and E2 transition rates are calculated and compared with the experimental data. The results show that the new scheme can also reasonably …
The Bohr hamiltonian, also called collective hamiltonian, is one of the cornerstone of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the $V(β,γ)$ potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussi…
A sixth order quadrupole boson Hamiltonian is treated through a time dependent variational principle approach choosing as trial function a coherent state with respect to zeroth $b^{\dagger}_0$ and second $b^{\dagger}_2+b^{\dagger}_{-2}$ components of the quadrupole bosons. The coefficients involved in the model Hamiltonian are chosen so that the classical effective potential energy term has two distinct minima. The equation of motion for the radial coordinate is analytically solved and the resulting trajectories are extensively studied. One distinguishes three energy regions exhibiting differe…
Starting from an effective Skyrme interaction we present a method to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole and octupole states in the neutron-rich Sn isotopes is studied.
Shape and multiple shape coexistence of nuclei are investigated throughout the nuclear chart by calculating the low-lying spectra and the quadrupole shape invariants for even-even nuclei with $10\leq Z\leq 104$ from the proton drip line to the neutron one within a five-dimensional collective Hamiltonian based on the covariant density functional PC-PK1. The quadrupole shape invariants are implemented to characterize the quadrupole deformations of low-lying $0^+$ states and predict nuclear mass regions of shape and multiple shape coexistence. The predicted low-lying spectra and the shape or mult…
In the frame of the algebraic Riemann Rotational Model one computes the longitudinal, transverse and toroidal multipoles corresponding to the excitations of low-lying levels in the ground state band of several even-even nuclei by inelastic electron scattering (e,e'). Related to these transitions a new quantity, which accounts for the deviations from the Siegert theorem, is introduced. The intimate connection between the nuclear vorticity and the dynamic toroidal quadrupole moment is underlined. Inelastic differential cross-sections calculated at backscattering angles shows the dominancy of tor…
We study the oblate-prolate shape mixing in the low-lying states of proton-rich Kr isotopes using the five-dimensional quadrupole collective Hamiltonian. The collective Hamiltonian is derived microscopically by means of the CHFB (constrained Hartree-Fock-Bogoliubov) + Local QRPA (quasiparticle random phase approximation) method, which we have developed recently on the basis of the adiabatic self-consistent collective coordinate method. The results of the numerical calculation show the importance of large-amplitude collective vibrations in the triaxial shape degree of freedom and rotational eff…
The triaxial nature of low-lying rotational bands of $^{166}$Er is presented from the viewpoint of the Bohr Hamiltonian and from that of many-fermion calculations by the Monte Carlo shell model and the constrained Hartree-Fock method with projections. A recently proposed novel picture of those bands suggests definite triaxial shapes of those bands, in contrast to the traditional view with the prolate ground-state band and the $γ$-vibrational excited band. Excitation level energies and E2 transitions can be described well by the Bohr Hamiltonian and by the many-fermion approaches, where rather …
An analytical solution of the collective Bohr equation with a Coulomb-like and a Kratzer-like $γ-$unstable potential in quadrupole deformation space is presented. Eigenvalues and eigenfunctions are given in closed form and transition rates are calculated for the two cases. The corresponding SO(2,1)$\times$SO(5) algebraic structure is discussed.
We propose a collective model formalism which describes the strong parity shift observed in low-lying spectra of nuclei with octupole deformations together with the fine rotational band structure developed at higher angular momenta. The parity effect is obtained by the Schroedinger equation for oscillations of the reflection asymmetric (octupole) shape between two opposite orientations in an angular momentum dependent double-well potential. The rotational structure is obtained by a collective quadrupole-octupole rotation Hamiltonian. The model scheme reproduces the complicated beat staggering …
The properties of the collective low-lying states of Zr isotopes which include excitation energies and $E2$ reduced transition probabilities indicate that some of these states are mainly spherical and the other are mainly deformed ones. We investigate the properties of the low-lying collective states of $^{92-102}$Zr and their evolution with increase of the number of neutrons based on the five-dimensional Geometrical Quadrupole Collective Model. The quadrupole-collective Bohr Hamiltonian with a potential having spherical and deformed minima, is applied. The relative depth of two minima, height…
Experimental data indicate that the mass tensor of collective Bohr Hamiltonian cannot be considered as a constant but should be considered as a function of the collective coordinates. In this work our purpose is to investigate the properties of low-lying collective states of the odd nuclei $^{173}$Yb and $^{163}$Dy by using a new generalized version of the collective quadrupole Bohr Hamiltonian with deformation-dependent mass coefficients. The proposed new version of the Bohr Hamiltonian is solved for Davidson potential in $β$ shape variable, while the $γ$ potential is taken to be equal to the…
A model is presented that simultaneously describes shape coexistence and quadrupole and octupole collective excitations within a theoretical framework based on the nuclear density functional theory and the interacting boson model. An optimal interacting-boson Hamiltonian that incorporates the configuration mixing between normal and intruder states, as well as the octupole degrees of freedom, is identified by means of self-consistent mean-field calculations using a universal energy density functional and a pairing interaction, with constraints on the triaxial quadrupole and the axially-symmetri…
The coupled dynamics of low lying modes, including the scissors mode, and various giant quadrupole resonances are studied with the help of the Wigner Function Moments method generalized to take into account spin degrees of freedom. Equations of motion for collective variables are derived on the basis of Time Dependent Hartree-Fock equations in the model of harmonic oscillator with spin orbital mean field potential plus quadrupole-quadrupole residual interaction. Introducing spin allows one to consider new types of nuclear collective motion where the nucleons with spin 'up' oscillate against nu…
Low energy quadrupole excitations of the 84-110Mo nuclei are studied in the frame of the general Bohr collective model based on the ATDHFB method with the Skyrme effective interaction. Obtained energies of the 2_1, 4_1, 2_2 and 0_2 levels and B(E2) values for the 2_1 -> 0_g.s transitions are in good agreement with experimental data.
The global correlation in the observed variation with mass number of the $E2$ and summed $M1$ transition strengths is examined for rare earth nuclei. It is shown that a theory of correlated $S$ and $D$ fermion pairs with a simple pairing plus quadrupole interaction leads naturally to this universality. Thus a unified and quantitative description emerges for low-lying quadrupole and dipole strengths.
Making use of the finite rank separable approach for the quasiparticle random phase approximation enables one to perform nuclear structure calculations in very large two-quasiparticle spaces. The approach is extended to take into account the residual particle-particle interaction. The calculations are performed by using Skyrme interactions in the particle-hole channel and density-dependent zero-range interactions in the particle-particle channel. To illustrate our approach, we study the properties of the lowest quadrupole states in the even-even nuclei $^{128}$Pd, $^{130}$Cd, $^{124-134}$Sn, $…
The low-lying isovector dipole strengths in neutron rich nuclei $^{26}$Ne and $^{28}$Ne are investigated in the quasiparticle relativistic random phase approximation. Nuclear ground state properties are calculated in an extended relativistic mean-field theory plus BCS method where the contribution of the resonant continuum to pairing correlations is properly treated. Numerical calculations are tested in the case of isovector dipole and isoscalar quadrupole modes in the neutron rich nucleus $^{22}$O. It is found that in present calculation low-lying isovector dipole strengths at $E_x < 10$ MeV …
The possible existence of a "bubble" structure in the proton density of $^{34}$Si has recently attracted a lot of research interest. To examine the existence of the "bubble" structure in low-lying states, we establish a relativistic version of configuration mixing of both particle number and angular momentum projected quadrupole deformed mean-field states and apply this state-of-the-art beyond relativistic mean-field method to study the density distribution of the low-lying states in $^{34}$Si. An excellent agreement with the data of low-spin spectrum and electric multipole transition strength…
