Low-lying Collective Excitations Research Articles

Microscopic shell-model description of irrotational-flow dynamics in 102Pd

The structure of the low-lying collective excitations in Pd is examined within the recently proposed microscopic shell-model version of the Bohr-Mottelson (BM) collective model. A good description of the excitation energies of the lowest ground, γ, and β bands, as well as the staggering function between the collective states of the γ band and some other energy-dependent quantities, is obtained. The low-energy intraband and interband quadrupole dynamics is reasonably well described within the present proton-neutron sympletic based shell-model approach without the use of an effective charge and compared with the predictions of nuclear structure models. The obtained results of the present study shed light on the question of the existence of irrotational-flow type quadrupole dynamics, which lies on the ground of the original BM model of quantized vibrations and surface-wave rotations in atomic nuclei.

Low-Lying Collective Excitations of Superconductors and Charged Superfluids

We investigate theoretically the momentum-dependent frequency and damping of low-lying collective excitations of superconductors and charged superfluids in the BCS–BEC crossover regime. The study is based on the Gaussian pair-and-density fluctuation method for the propagator of Gaussian fluctuations of the pair and density fields. Eigenfrequencies and damping rates are determined in a mutually consistent nonperturbative way as complex poles of the fluctuation propagator. Particular attention is paid to new features with respect to preceding theoretical studies, which were devoted to collective excitations of superconductors in the far BCS regime. We find that at a sufficiently strong coupling, new branches of collective excitations appear, which manifest different behavior as functions of the momentum and the temperature.

Microscopic shell-model description of strongly deformed nuclei: 158Gd

A recently proposed microscopic version of the Bohr–Mottelson collective model, defined by the following dynamical symmetry chain [Formula: see text] of the proton–neutron symplectic model (PNSM), is applied to the microscopic shell-model description of the low-lying collective excitations in a typical strongly deformed nucleus, namely, [Formula: see text]Gd. Detailed shell-model results are presented for the ground, [Formula: see text] and [Formula: see text] bands excitation levels, probability distributions and quadrupole collectivity. A good overall description is obtained for the excitation energies of the three bands under consideration in [Formula: see text]Gd without using an adjustable kinetic-energy term, as well as for the ground state intraband [Formula: see text] quadrupole collectivity and the known interband [Formula: see text] transition probabilities between the low-lying collective states without the use of an effective charge.

Angular stripe phase in spin-orbital-angular-momentum coupled Bose condensates

We propose that novel superfluid with supersolid-like properties - angular stripe phase - can be realized in a pancake-like spin-1/2 Bose gas with spin-orbital-angular-momentum coupling. We predict a rich ground-state phase diagram, including the vortex-antivortex pair phase, half-skyrmion phase, and two different angular stripe phases. The stripe phases feature modulated angular density-density correlation with sizable contrast and can occupy a relatively large parameter space. The low-lying collective excitations, such as the dipole and breathing modes, show distinct behaviors in different phases. The existence of the novel stripe phase is also clearly indicated in the energetic and dynamic instabilities of collective modes near phase transitions. Our predictions of the angular stripe phase could be readily examined in current cold-atom experiments with $^{87}$Rb and $^{41}$K.

Effect of correlation and disorder on the spin-wave spectra of Pd2MnSn, Ni2MnSn , and Cu2MnAl Heusler alloys: A first-principles study

Spin waves, also known as magnons, are low-lying collective excitations in magnetic materials, for which it is hard to achieve agreement between first-principles electronic structure calculations and experiments. It has been shown in literature [I. Galanakis and E. \ifmmode \mbox{\c{S}}\else \c{S}\fi{}a\ifmmode \mbox{\c{s}}\else \c{s}\fi{}\ifmmode \imath \else \i \fi{}o\ifmmode \breve{g}\else \u{g}\fi{}lu, J. Mater. Sci. 47, 7668 (2012)] using as a prototype three full Heusler alloys---${\mathrm{Pd}}_{2}\mathrm{MnSn}, {\mathrm{Ni}}_{2}\mathrm{MnSn}$, and ${\mathrm{Cu}}_{2}\mathrm{MnAl}$---that usual density-functional calculations for perfectly ordered compounds fail by a large margin to reproduce neutron scattering measurements of spin waves. We show for these three compounds that the inclusion of correlation effects in the form of the $\mathrm{GGA}+U$ approach and/or substitutional disorder accounted via the coherent potential approximation affects considerably the calculated magnetic properties and their agreement to the experimental data. We expect our results to pave the way for further studies on magnetic materials for which experimental magnonic data exist.

Bose–Einstein condensation on curved manifolds

Here we describe a weakly interacting Bose gas on a curved smooth manifold, which is embedded in the three-dimensional Euclidean space. To this end we start by considering a harmonic trap in the normal direction of the manifold, which confines the three-dimensional Bose gas in the vicinity of its surface. Following the notion of dimensional reduction as outlined in [L Salasnich et al, Phys. Rev. A 65, 043614 (2002)], we assume a large enough trap frequency so that the normal degree of freedom of the condensate wave function can be approximately integrated out. In this way we obtain an effective condensate wave function on the quasi-two-dimensional surface of the curved manifold, where the thickness of the cloud is determined self-consistently. For the particular case when the manifold is a sphere, our equilibrium results show how the chemical potential and the thickness of the cloud increase with the interaction strength. Furthermore, we determine within a linear stability analysis the low-lying collective excitations together with their eigenfrequencies, which turn out to reveal an instability for attractive interactions.

Исследование изменения формы ядер 96Zn и 96Mo с ростом энергии возбуждения

The observed properties of the low-lying collective excitations of 96Zr and 96Mo are investigated in the framework of the collective quadrupole nuclear model with the Bohr Hamiltonian, whose potential energy has two minima – spherical and deformed. Satisfactory description of the excitation energies and E2 transition probabilities is obtained. It is shown that in the case of 96Zr both minima are sufficiently deep. However, in the case of 96Mo a deformed minimum is only outlined.

Collective Reactions in the Continuum

We show that pre-equlibrium inelastic scattering reactions to the continuum contain substantial collective components in addition to the multistep direct and multistep compound reactions. These collective reactions are investigated for the vibrational nuclei 56Fe, 58Ni, 90Zr, 93Nb, 208Pb and 209Bi , and the strongly-deformed, rotational W nucleus. The collective cross-sections are calculated using the experimental data for low-lying collective excitations supplemented where necessary by the giant multipole resonances evaluated using the energy-weight ed sum rule. The MSC and MSD cross-sections are evaluated by the Feshbach-Kerman-Koonin theory using a consistent set of parameters determined by analyses of (p, xn) reactions, that have practically no collective components. The results are compared with high-resolution neutron inelastic scattering data and prove able to account for the absolute magnitude of the cross-sections and also their detailed structure.

Coexistence of Anderson-Bogoliubov phonon and quadrupole cluster vibration in the inner crust of neutron stars

Background: Low-lying collective excitations of inner crust matter in neutron stars are expected to have impact on observables such as the quasi-periodic oscillation in giant flares and the cooling of inner crust in transient phenomena. Coupling between Anderson-Bogoliubov superfluid phonon (AB phonon) in superfluid neutron gas and collective excitations of nuclear clusters is a key issue. Purpose: We intend to predict the nature of low-lying excitation modes of superfluid inner crust matter with focus on quadrupole excitations around a spherical nuclear cluster. We study how the AB phonon of neutron superfluid and possible quadrupole shape vibration of clusters are affected by the inhomogeneous structure of inner crust matter. Results: The calculated results indicate emergence of both AB phonon and quadrupole shape vibration of the cluster with small mixing between the two collective modes. The quadruple AB phonon is similar to that in uniform superfluid apart from small admixture of the shape vibration of cluster. The excitation energy and the collectivity of the cluster vibration mode shows strong and oscillatory dependence on the neutron chemical potential (the neutron gas density), leading to softening and instability in certain situations. This is caused by the resonance shell effect where unbound but resonant single-particle states of neutrons play a central role. Conclusions: The AB phonon of superfluid neutron gas and the quadrupole shape vibration of nuclear cluster coexist in inner crust. The coupling between the AB phonon and the quadrupole shape vibration is weak. The collectivity of the quadrupole shape vibration is governed by the resonance shell effect, and it suggests that emergence of deformed nuclear clusters is possible at any layer of inner crust.

Low-lying excitations of vortex lattices in condensates with anisotropic dipole-dipole interaction

We investigated the low-lying collective excitations of quasi-two-dimensional dipolar Bose-Einstein condensates confined in a rotating harmonic potential using the Bogoliubov--de Gennes equation. By varying the trap rotation frequency and dipolar interaction strength, we show how the anisotropic dipole-dipole interaction modifies the collective excitations of the condensates. In particular, under strong dipolar interaction, the vortex-displacement excitations differ significantly from the nondipolar case.

Collective electronic excitation in a trapped ensemble of photogenerated dipolar excitons and free holes revealed by inelastic light scattering

Photogenerated excitonic ensembles confined in coupled GaAs quantum wells are probed by a complementary approach of emission spectroscopy and resonant inelastic light scattering. Lateral electrostatic trap geometries are used to create dense systems of spatially indirect excitons and excess holes with similar densities in the order of 10$^{11}$ cm$^{-2}$. Inelastic light scattering spectra reveal a very sharp low-lying collective mode that is identified at an energy of 0.44 meV and a FWHM of only ~50 $\mu$eV. This mode is interpreted as a plasmon excitation of the excess hole system coupled to the photogenerated indirect excitons. The emission energy of the indirect excitons shifts under the application of a perpendicular applied electric field with the quantum-confined Stark effect unperturbed from the presence of free charge carriers. Our results illustrate the potential of studying low-lying collective excitations in photogenerated exciton systems to explore the many-body phase diagram, related phase transitions, and interaction physics.

Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons

We study the ground state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small ($\sim 3$) to very large ($\sim 10^7$) particle numbers. We use the correlated two-body basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground state energy and the one-body density for different values of the van der Waals parameter $C_{6}$. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the Diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

Self-consistent theory of finite Fermi systems and Skyrme–Hartree–Fock method

Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2+ excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surface excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.

Gapped excitations of unconventional fractional quantum Hall effect states in the second Landau level

We report the observation of low-lying collective charge and spin excitations in the second Landau level at $\ensuremath{\nu}=2+1/3$ and also for the very fragile states at $\ensuremath{\nu}=2+2/5$ and $2+3/8$ in inelastic light scattering experiments. These modes exhibit a clear dependence on filling factor and temperature substantiating the unique access to the characteristic neutral excitation spectra of the incompressible fractional quantum Hall effect (FQHE) states. A detailed mode analysis reveals low-energy modes at around 70 $\ensuremath{\mu}\mathrm{eV}$ and a sharp mode slightly below the Zeeman energy interpreted as gap and spin-wave excitation, respectively. The lowest-energy collective charge excitation spectrum at $\ensuremath{\nu}=2+1/3$ exhibits significant qualitative similarities with its cousin state in the lowest Landau level at $\ensuremath{\nu}=1/3$ suggesting similar magnetoroton minima in the neutral excitations. The mode energies differ by a scaling of 0.15 indicating different interaction physics in the $N=0$ and $N=1$ Landau levels. The striking polarization dependence in elastic and inelastic light scattering is discussed in the framework of anisotropic electron phases that allow for the stabilization of nematic FQHE states. The observed excitation spectra provide new insights by accessing quantum phases in the bulk of electron systems and facilitate comparison with different theoretical descriptions of those enigmatic FQHE states.

Stabilization of octupole deformation with angular-momentum increase in the alternating-parity bands

Background: Low-lying octupole collective excitations play an important role in describing the structure of nuclei in different regions of the nuclide chart. Ground state alternating-parity rotational bands combining both positive- and negative-parity states are known in several nuclei. The experimental data indicate that octupole deformation becomes stable with increase of the angular momentum.Purpose: We introduce a nondimensional characteristic of the spectra of the ground state alternating-parity bands and apply it to investigation of a stabilization of the octupole deformation with increase of the angular momentum.Method: We analyze the experimental data on the energies of the states belonging to the alternating-parity bands based on the ratio of the interpolated and the experimental energies of the negative-parity states. Interpolated energies are determined by the experimental energies of the neighboring positive-parity states assuming smooth dependence on the angular momentum.Results: The values of the ratio of the interpolated and the experimental energies of the negative-parity states belonging to the ground state alternating-parity bands of ${}^{144,146}\text{Ba}$ and some rare-earth and actinide nuclei are evaluated.Conclusion: It is shown that the angular-momentum dependence of the ratio of the interpolated and the experimental energies of the negative-parity states belonging to the ground state alternating-parity bands of ${}^{144,146}\text{Ba}$ and some rare-earth and actinide nuclei indicates stabilization of the octupole deformation with angular-momentum increase.

Microscopic nature of the radiative strength function: Structures, coupling with phonons

The microscopic nature of the radiative strength function, which is the most important characteristic necessary for the description of nuclear reactions involving gamma-ray photons both in astrophysics and in the theory of nuclear reactors, has been discussed. It has been shown that, in contrast to phenomenological approaches based on various modifications of the Lorentzian dependence for this function, the microscopic approach gives structures that are due to the effects both within the standard random phase approximation and of coupling with low-lying collective excitations (phonons), i.e., beyond the standard random phase approximation. Microscopic calculations of the strength function for several Sn and Ni isotopes have been performed within the self-consistent version of the extended theory of finite Fermi systems, where both of these effects are taken into account and the SLy4 Skyrme forces are used to calculate the mean field, effective interaction between nucleons, and characteristics of phonons. Microscopic radiative E1 strength functions have been used in the modern EMPIRE 3.1 code for the calculation of the cross sections for the radiative capture of neutrons and average radiative widths of neutron resonances. Reasonable agreement with the existing experimental data has been obtained with allowance for coupling with phonons. The integral characteristics of the pygmy dipole resonance in the unstable 68Ni nucleus have been explained. The existence of this resonance has been predicted in the unstable 72Ni nucleus.

Description of collective and quasiparticle excitations in deformed actinide nuclei: The first application of the multishell shell model for heavy nuclei

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 the 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 quasiparticle 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 for some deformed actinide nuclei, with a model space including up to 4-quasiparticle and 1-$D$-pair configurations. The calculated energy levels for the ground-state bands, the collective bands such as $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ bands, and some quasiparticle bands agree well with known experimental data. Some low-lying quasiparticle bands are predicted, awaiting experimental confirmation.

Fusion ofS32 + Zr94: Further exploration of the effect of the positiveQxnvalue neutron transfer channels

The effect of the positive $Q$-value neutron transfer (PQNT) channels on the subbarrier fusion process is still far from a clear understanding and hence is worth further investigation. To this end, we have measured the fusion excitation function for $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ at energies near and below the Coulomb barrier with rather good accuracy, and deduced the experimental fusion barrier distribution. The reaction system $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ is a good candidate for the evaluation of PQNT effect because it has multineutron transfer channels with positive ground-state ${Q}_{xn}$ values as well as the relatively weak low-lying ${3}^{\ensuremath{-}}$ vibrational state in $^{94}\mathrm{Zr}$. Our results show that the fusion cross sections of $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ are strongly enhanced at the lower-energy region. By means of a cross comparison of the $^{32}\mathrm{S}$,$^{40}\mathrm{Ca}+^{90,94,96}\mathrm{Zr}$ systems, further evidence is given that the positive ${Q}_{xn}$-value neutron transfer channels, rather than the strong low-lying ${3}^{\ensuremath{-}}$ vibrational state, bring about the additional subbarrier fusion enhancement. Relative to the coupled-channels results with couplings to the low-lying inelastic collective excitations, an unexpectedly large enhancement for the subbarrier fusion cross sections is observed in $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ compared to $^{32}\mathrm{S}+^{96}\mathrm{Zr}$. Some existing theoretical models have been discussed, but a good explanation cannot be achieved. Exact coupled-channels theory and more experiments on transfer reactions themselves are strongly desired to comprehensively understand the effect of transfer on fusion.

Anharmonicity of the excited octupole band in actinides using supersymmetric quantum mechanics

Background: Low-lying octupole collective excitations play an important role in the description of the structure of nuclei in the actinide region. Ground state alternating parity rotational bands combining both positive and negative parity states are known in several nuclei. However, only recently it has been discovered in ${}^{240}$Pu an excited positive parity rotational band having an octupole nature and demonstrating strong anharmonicity of the octupole motion in the band head energies.Purpose: To suggest a model describing both ground state and excited alternating parity bands, which includes a description of the anharmonic effects in the bandhead excitation energies and can be used to predict the energies of the excited rotational bands of octupole nature and the $E1$ transition probabilities.Methods: The mathematical technique of the supersymmetric quantum mechanics with a collective Hamiltonian depending only on the octupole collective variable which keeps axial symmetry is used to describe the ground state and excited alternating parity rotational bands.Results: The excitation energies of the states belonging to the lowest negative parity and the excited positive parity bands are calculated for ${}^{232}$Th, ${}^{238}$U, and ${}^{240}$Pu. The $E1$ transition matrix elements are also calculated for ${}^{240}$Pu.Conclusions: It is shown that the suggested model describes the excitation energies of the states of the lowest negative parity band with the accuracy around 10 keV. The anharmonicity in the bandhead energy of the excited positive parity band is described also. The bandhead energy of the excited positive parity band is described with the accuracy around 100 keV.

The stability condition and collective excitation of a trapped Bose–Einstein condensate with higher-order interactions

We take into account the higher-order corrections in two-body scattering interactions within a mean-field description, and investigate the stability conditions and collective excitations of a harmonically trapped Bose–Einstein condensate (BEC). Our results show that the presence of higher-order corrections causes drastic changes to the stability condition of a BEC. In particular, we predict that with the help of the higher-order interaction, a BEC can now collapse even for positive scattering lengths; whereas, a usually unstable BEC with a negative scattering length can be stabilized by positive higher-order effects. The low-lying collective excitations are significantly modified as well, compared to those without the higher-order corrections. The conditions for a possible experimental scenario are also proposed.