The intraband electromagnetic transitions in the framework of collective Hamiltonian for chiral and wobbling modes are calculated. By going beyond the mean field approximation on the orientations of rotational axis, the collective Hamiltonian provides the descriptions on both yrast band and collective excitation bands. For a system with one $h_{11/2}$ proton particle and one $h_{11/2}$ neutron hole coupled to a triaxial rotor ($γ=-30^\circ$), the intraband electromagnetic transitions given by the one-dimensional and two-dimensional collective Hamiltonian are compared to the results by the tilted axis cranking approach and particle rotor model. Compared with the tilted axis cranking approach, the electromagnetic transitions given by the collective Hamiltonian have a better agreement with those by the particle rotor model, due to the consideration of the quantum fluctuations.
The recently reported wobbling bands in $^{135}$Pr are investigated by the collective Hamiltonian, in which the collective parameters, including the collective potential and the mass parameter, are respectively determined from the tilted axis cranking (TAC) model and the harmonic frozen alignment (HFA) formula. It is shown that the experimental energy spectra of both yrast and wobbling bands are well reproduced by the collective Hamiltonian. It is confirmed that the wobbling mode in $^{135}$Pr changes from transverse to longitudinal with the rotational frequency. The mechanism of this transiti…
The behavior of the collective rotor in wobbling motion is investigated within the particle-rotor model for the nucleus $^{135}$Pr by transforming the wave functions from the $K$-representation to the $R$-representation. After reproducing the experimental energy spectra and wobbling frequencies, the evolution of the wobbling mode in $^{135}$Pr, from transverse at low spins to longitudinal at high spins, is illustrated by the distributions of the total angular momentum in the intrinsic reference frame (azimuthal plot). Finally, the coupling schemes of the angular momenta of the rotor and the hi…
The simple, longitudinal, and transverse wobblers are systematically studied within the framework of collective Hamiltonian, where the collective potential and mass parameter included are obtained based on the tilted axis cranking approach. Solving the collective Hamiltonian by diagonalization, the energies and the wave functions of the wobbling states are obtained. The obtained results are compared with those by harmonic approximation formula and particle rotor model. The wobbling energies calculated by the collective Hamiltonian are closer to the exact solutions by particle rotor model than …
The wobbling motion of a triaxial rotor coupled to a high-j quasiparticle is treated semiclassi- cally. Longitudinal and transverse coupling regimes can be distinguished depending on, respectively, whether the quasiparticle angular momentum is oriented parallel or perpendicular to the rotor axis with the largest moment of inertia. Simple analytical expressions for the wobbling frequency and the electromagnetic E2 and M1 transition probabilities are derived assuming rigid alignment of the quasiparticle with one of the rotor axes and harmonic oscillations (HFA). Transverse wobbling is characteri…
The existence of one-phonon and possible two-phonon transverse wobbling bands is proposed for the first time in two even-even nuclei, $^{134}$Ce and $^{136}$Nd. The predominant $E2$ character of the $ΔI = 1$ transitions connecting the one-phonon wobbling band in $^{134}$Ce to the two-quasiparticle yrast band supports the wobbling interpretation. The extracted wobbling frequencies decrease with increasing spin, indicating the transverse character of the wobbling motion, with the angular momenta of the two quasiparticles aligned perpendicular to the axis of collective rotation. A candidate for t…
We have studied the precession mode, the rotational excitation built on the high-$K$ isomeric state, in comparison with the recently identified wobbling mode. The random-phase-approximation (RPA) formalism, which has been developed for the nuclear wobbling motion, is invoked and the precession phonon is obtained by the non-collective axially-symmetric limit of the formalism. The excitation energies and the electromagnetic properties of the precession bands in $^{178}$W are calculated, and it is found that the results of RPA calculations well correspond to those of the rotor model; the correspo…
The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with wobbling motion in rotating nuclei lead to the appearance of two- or three-dimensional rotation.
A two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar motions in triaxial nuclei is proposed to investigate the chiral and wobbling modes. In the 2DCH, the collective potential and the mass parameters are determined from three-dimensional tilted axis cranking (TAC) calculations. The broken chiral and signature symmetries in the TAC solutions are restored by the 2DCH. The validity of the 2DCH is illustrated with a triaxial rotor ($γ=-30^\circ$) coupling to one $h_{11/2}$ proton particle and one $h_{11/2}$ neutron hole. By diagonalizing the 2DCH, the angular momenta and energ…
Two new bands built on the two-quasiparticle $π(h_{11/2})^2$ configuration of the even-even nucleus $^{130}$Ba are investigated using constrained triaxial covariant density functional theory combined with quantum particle rotor model calculations. The energy difference between the two bands, as well as the available electromagnetic transition probabilities $B(M1)_{\textrm{out}}/B(E2)_{\textrm{in}}$ and $B(E2)_{\textrm{out}}/B(E2)_{\rm{in}}$, are well reproduced. The analysis of the angular momentum geometry reveals that the higher band represents transverse wobbling motion of a two-quasipartic…
The $g$-factor and static quadrupole moment for the wobbling mode in the nuclide $^{133}$La are investigated as functions of the spin $I$by employing the particle rotor model. The model can reproduce the available experimental data of $g$-factor and static quadrupole moment. The properties of the $g$-factor and static quadrupole moment as functions of $I$ are interpreted by analyzing the angular momentum geometry of the collective rotor, proton-particle, and total nuclear system. It is demonstrated that the experimental value of the $g$-factor at the bandhead of the yrast band leads to the con…
Two newly observed bands built on a two-quasiparticle configuration in 130Ba have been investigated for the first time with the microscopic projected shell model. The experimental energy spectra and the available electromagnetic transition probabilities are well reproduced. The wobbling character of the higher band is revealed by the angular momentum projected wavefunctions via the K plot and the azimuthal plot. This provides the first strong microscopic evidence for wobbling motion based on a two-quasiparticle configuration in even-even nuclei.
We study in the cranked Nilsson plus random phase approximation low-lying quadrupole excitations of positive parity and negative signature in 156Dy and 162Yb at high spins. Special attention is paid to a consistent description of wobbling excitations and their identification among excited states. A good agreement between available experimental data and the results of calculations is obtained. We found that in 156Dy the lowest odd spin gamma-vibrational states transform to the wobbling excitations after the backbending, associated with the transition from axially-symmetric to nonaxial shapes. S…
The three moments of inertia associated with the wobbling mode built on the superdeformed states in 163Lu are investigated by means of the cranked shell model plus random phase approximation to the configuration with an aligned quasiparticle. The result indicates that it is crucial to take into account the direct contribution to the moments of inertia from the aligned quasiparticle so as to realize J_x > J_y in positive-gamma shapes. Quenching of the pairing gap cooperates with the alignment effect. The peculiarity of the recently observed 163Lu data is discussed by calculating not only the el…
Some developments of nuclear-structure physics uniquely related to Copenhagen School are sketched based on theoretical considerations versus experimental findings and one-particle versus collective aspects. Based on my personal overview I pick up the following topics; (1) Study of vibration in terms of particle-vibration coupling; (2) One-particle motion in deformed and rotating potentials, and yrast spectroscopy in high-spin physics; (3) Triaxial shape in nuclei: wobbling motion and chiral bands; (4) Nuclear structure of drip line nuclei: in particular, shell-structure (or magic numbers) chan…
Using a schematic solvable many-body Hamiltonian, one studies a new type of proton-neutron excitations within a time dependent variational approach. Classical equations of motion are linearized and subsequently solved analytically. The harmonic state energy is compared with the energy of the first excited state provided by diagonalization as well as with the energies obtained by a renormalized RPA and a boson expansion procedure. The new collective mode describes a wobbling motion, in the space of isospin, and collapses for a particle-particle interaction strength which is much larger than the…
We present an analysis of electromagnetic elastic form factors, helicity amplitudes and strong decay widths of non-strange baryon resonances, within a collective model of the nucleon. Flavor-breaking and stretching effects are considered. Deviations from the naive three-constituents description are pointed out.
By using the general triaxial rotor model (TRM) and the phonon-configuration mixing scheme within an anharmonic-vibrator(AHV) framework, a series of global correlations between electromagnetic properties of nuclear $2^+_1$ and $2^+_2$ states are analytically established. The correlations from both models can roughly describe the experimental data involving quadrupole collectivity with few exceptions. Furthermore, there seems to be a robust orthogonal transformation between the AHV and TRM bases for realistic nuclear systems, suggesting that the two models may in fact be describing the collecti…
We study the electromagnetic form factors of the nucleon in a collective model of baryons. Using the algebraic approach to hadron structure, we derive closed expressions for both elastic and transition form factors, and consequently for the helicity amplitudes that can be measured in electro- and photoproduction. Effects of spin-flavor symmetry breaking and of swelling of hadrons with increasing excitation energy are considered.
The collective structure of atomic nuclei intermediate between spherical and quadrupole deformed structure presents challenges to theoretical understanding. However, models have recently been proposed in terms of potentials which are soft with respect to the quadrupole deformation variable beta. To test these models, information is needed on low-spin states of transitional nuclei. The present work involves measurement of electromagnetic decay properties of low-spin states for nuclei in the A=100 (gamma-soft) and N=90 (axially symmetric) transition regions. Population in beta-decay and thermal …
In the present paper, we carry out a detailed analysis of the presence and mixing of various families of collective bands in $^{188}$Pb. Making use of the interacting boson model, we construct a particular intermediate basis that can be associated with the unperturbed bands used in more phenomenological studies. We use the E2 decay to construct a set of collective bands and discuss in detail the B(E2)-values. We also perform an analysis of these theoretical results (Q, B(E2)) to deduce an intrinsic quadrupole moment and the associated quadrupole deformation parameter, using an axially deformed…
Symmetry breaking is an importance concept in nuclear physics and other fields of physics. Self-consistent coupling between the mean-field potential and the single-particle motion is a key ingredient in the unified model of Bohr and Mottelson, which could lead to a deformed nucleus as a consequence of spontaneous breaking of the rotational symmetry. Some remarks on the finite-size quantum effects are given. In finite nuclei, the deformation inevitably introduces the rotation as a symmetry-restoring collective motion (Anderson-Nambu-Goldstone mode), and the rotation affects the intrinsic motion…
Collective P- and T- odd moments produced by parity and time invariance violating forces in reflection asymmetric nuclei are considered. The enhanced collective Schiff, electric dipole and octupole moments appear due to the mixing of rotational levels of opposite parity. These moments can exceed single-particle moments by more than two orders of magnitude. The enhancement is due to the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. In turn these nuclear moments induce enhanced T- and P- odd effects in atoms and molecules. First a …
Nucleon elastic and transition form factors are analyzed in the framework of a collective model of baryons. Effects of meson cloud couplings and relativistic corrections are considered.
We review the theory of nuclear collective vibrations evolved over decades from phenomenological quasiclassical picture to sophisticated microscopic approaches. The major focus is put on the underlying microscopic mechanisms of emergent effects, which define the properties of giant resonances and soft modes. The response of atomic nuclei to electromagnetic and weak fields is discussed in detail. Astrophysical implications of the giant resonances and soft modes are outlined.
In this work, we explore the ground state of QCD system and the relevant collective modes in a parallel electromagnetic (EM) field within the effective three-flavor Nambu--Jona-Lasinio model. From the features of neutral chiral condensates, three critical EM fields are identified in our study: $e\bar{I}_2^{c_i}~(i=1,2,3)$. Moreover, competition between QCD and QED anomalies is found: the negativeness of $π_{\rm d}^*$ and $π_{\rm s}^*$ is a signal of QCD anomaly dominance for all the flavors, and the positiveness of $π_{\rm s}^*$ beyond $e\bar{I}_2^{c_1}$ indicates QED anomaly dominance for str…
A strength function method is adopted to describe a coupling between electric and magnetic modes of different multipolarity. The collective vibrations are analysed for a separable residual interaction in the framework of the random-phase approximation. The coupling between $M2$ and $E1$ giant resonances is considered as an illustrative example.
Mixing of the shell model (SM) eigenstates due to the coupling via the common decay channel leads in many cases to the formation of a collective eigenstate which carries many features of the nearby decay channel. This generic mechanism in open quantum systems explains the phenomenological Ikeda diagram and generalizes it for various clusters/correlations in the vicinity of the respective cluster decay thresholds. The near-threshold collectivization of the SM states may also influence their electromagnetic decays. We discuss this phenomenon on the example of B(EL) decays of near-threshold 2+ st…
In this paper, we present new analytical solutions of the Bohr Hamiltonian problem that we derived with the Tietz-Hua potential, here used for describing the β-part of the nuclear collective potential plus harmonic oscillator one for the γ-part. Also, we proceed to a systematic comparison of the numerical results obtained with this kind of β-potential with others which are widely used in such a framework as well as with the experiment. The calculations are carried out for energy spectra and electromagnetic transition probabilities for γ-unstable and axially symmetric deformed nuclei. In the sa…
Collective excitations of N = 1 supersymmetric electromagnetic plasma are studied. Since the Keldysh-Schwinger approach is used, not only equilibrium but also non-equilibrium plasma, which is assumed to be ultrarelativistic, is under consideration. The dispersion equations of photon, photino, electron and selectron modes are written down and the self-energies, which enter the equations, are computed in the Hard Loop Approximation. The self-energies are discussed in the context of effective action which is also given. The photon modes and electron ones appear to be the same as in the usual ultr…
We investigate the electromagnetic mass differences of SU(3) baryons, using an "model-independent approach" within a chiral soliton model. The electromagnetic self-energy corrections to the masses of the baryon are expressed as the baryonic two-point correlation function of the electromagnetic currents. Using the fact that the electromagnetic current can be treated as an octet operator, and considering possible irreducible representations of the correlation function, we are able to construct a general collective operator for the electromagnetic self-energies, which consists of three unknown pa…
