Alexander V. Avdeenkov

Quantum Bose liquids with logarithmic nonlinearity: self-sustainability and emergence of spatial extent

The Gross–Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose–Einstein condensates (BEC). However, in many physical situations, such as higher densities, it is unlikely that this approximation suffices; hence, one might need models which would account for long-range correlations and multi-body interactions. We show that the Bose liquid described by the logarithmic wave equation has a number of drastic differences from the GP one. It possesses the self-sustainability property: while the free GP condensate tends to spill all over the available volume, the logarithmic one tends to form a Gaussian-type droplet—even in the absence of an external trapping potential. The quasi-particle modes of the logarithmic BEC are shown to acquire a finite size despite the bare particles being assumed to be point-like, i.e. the spatial extent emerges here as a result of quantum many-body correlations. Finally, we study the elementary excitations and demonstrate that the background density changes the topological structure of their momentum space which, in turn, affects their dispersion relations. Depending on the density, the latter can be of the massive relativistic, massless relativistic, tachyonic and quaternionic type.

Impact of phonon coupling on the photon strength function

The pygmy dipole resonance and photon strength function in stable and unstable Ni and Sn isotopes are calculated within the microscopic self-consistent version of the extended theory of finite Fermi systems, which, in addition to the standard quasiparticle random-phase approximation approach, includes phonon coupling effects. The Skyrme force SLy4 is used. A pygmy dipole resonance in Ni72 is predicted at the mean energy of 12.4 MeV exhausting 25.7% of the total energy-weighted sum rule. The microscopically obtained photon E1 strength functions are compared with available experimental data and used to calculate nuclear reaction properties. Average radiative widths and radiative neutron capture cross sections have been calculated taking phonon coupling into account as well as uncertainties caused by various microscopic level density models. In all three quantities considered, the contribution of phonon coupling turned out to be significant and is found necessary to explain available experimental data.

Description of the giant monopole resonance in the even-A {sup 112-124}Sn isotopes within a microscopic model including quasiparticle-phonon coupling

We have calculated the strength distributions of the isoscalar giant monopole resonance (ISGMR) in the even-A tin isotopes (A=112-124) that were recently measured in inelastic {alpha} scattering. The calculations were performed within two microscopic models: the quasiparticle random phase approximation (QRPA) and the quasiparticle time blocking approximation (QTBA), which is an extension of the QRPA including quasiparticle-phonon coupling. We used a self-consistent calculational scheme based on the Hartree-Fock+Bardeen-Cooper-Schrieffer approximation. Within the RPA the self-consistency is full. The single-particle continuum is also exactly included at the RPA level. The self-consistent mean field and the effective interaction are derived from the Skyrme energy functional. In the calculations, two Skyrme force parametrizations were used: T5 with a comparatively low value of the incompressibility modulus of infinite nuclear matter (K{sub {infinity}}=202 MeV) and T6 with K{sub {infinity}}=236 MeV. The T5 parametrization gives theoretical results for tin isotopes in good agreement with the experimental data including the resonance widths. The results of the ISGMR calculations in {sup 90}Zr, {sup 144}Sm, and {sup 208}Pb performed with these Skyrme forces are discussed and compared with the experiment.

Extended theory of finite Fermi systems: Application to the collective and noncollective E1 strength in {sup 208}Pb

The Extended Theory of Finite Fermi Systems is based on the conventional Landau-Migdal theory and includes the coupling to the low-lying phonons in a consistent way. The phonons give rise to a fragmentation of the single-particle strength and to a compression of the single-particle spectrum. Both effects are crucial for a quantitative understanding of nuclear structure properties. We demonstrate the effects on the electric dipole states in

Pygmy dipole resonance in nuclei

^{208}

Quasiparticle-phonon interaction in the theory of finite Fermi systems

Pb (which possesses 50% more neutrons then protons) where we calculated the low-lying non-collective spectrum as well as the high-lying collective resonances. Below 8 MeV, where one expects the so called isovector pygmy resonances, we also find a strong admixture of isoscalar strength that comes from the coupling to the high-lying isoscalar electric dipole resonance, which we obtain at about 22 MeV. The transition density of this resonance is very similar to the breathing mode, which we also calculated. We shall show that the extended theory is the correct approach for self-consistent calculations, where one starts with effective Lagrangians and effective Hamiltonians, respectively, if one wishes to describe simultaneously collective and non-collective properties of the nuclear spectrum. In all cases for which experimental data exist the agreement with the present theory results is good.

Collisions of bosonic ultracold polar molecules in microwave traps

A brief survey of the state of the modern microscopic theory of the so-called pygmy dipole resonance in nuclei is given—in particular, some unresolved problems are listed. It is emphasized that, in order to explain the pygmy dipole resonance, it is necessary but not sufficient to take into account the coupling of single-particle degrees of freedom to photon degrees of freedom. The results of the calculations performed for the first time for the isovector pygmy dipole resonance and the isovector electric giant dipole resonance in 124Sn within a self-consistent approach involving, in addition to the standard quasiparticle random-phase approximation, a single-particle continuum and quasiparticle-phonon coupling of single-particle degrees of freedom to phonon degrees of freedom are presented. The results are found to be in satisfactory agreement with experimental data. The calculation of the isoscalar strength function in the energy region of the pygmy dipole resonance revealed that the nuclear-structure mechanism does not provide the isoscalar-strength suppression observed at energies in excess of 7 MeV in (α, α′γ) reactions; therefore, this suppression may stem from the reaction mechanism.

Stability of fermionic Feshbach molecules in a Bose-Fermi mixture

Within the Green’s function method and on the basis of the method developed by V.A. Khodel for analyzing anharmonic effects, effects of quasiparticle-phonon interaction in the second order in the amplitude of phonon production are studied in two problems as a natural development of A.B. Migdal’s theory of finite Fermi systems. Transitions between excited states and static moments of magic and nonmagic nuclei in excited states, each of which is described in the random-phase approximation, are considered. The results for this problem are found to differ considerably from those in the quasiparticle random-phase approximation. The inclusion of all second-order anharmonic effects in the extended theory of finite Fermi systems that extends the standard theory of finite Fermi systems to the case of taking into account quasiparticle-phonon interaction in order to describe excited states, but which does not take into account all such effects, is also considered. They are taken into account at a level that makes it possible to calculate static moments of odd nuclei—more precisely, the respective equation for the vertex function, which, in the theory of finite Fermi systems, is a basic ingredient that describes the interaction of a nucleus with an external field, is derived. Some numerical results obtained within the recently implemented self-consistent version of the extended theory of finite Fermi systems are also presented for 15 stable and unstable tin isotopes. These results give sufficient grounds to conclude that phenomenological systematics are inapplicable to giant dipole resonances in neutron-rich isotopes. The cross sections for radiative neutron capture that are calculated by usingmicroscopic strength functions for the neutron-rich isotopes 132Sn and 150Sn differ strongly from the cross sections calculated on the basis of a phenomenological description of giant dipole resonances. These results are of paramount importance for astrophysics and for the theory of nuclear data for reactors since they highlight the inapplicability of phenomenological systematics to giant dipole resonances and the need for self-consistent calculations for neutron-rich nuclei.

On Microscopic Theory of Radiative Nuclear Reaction Characteristics

The collisions between linear polar molecules, trapped in a microwave field with circular polarization, are theoretically analyzed. The microwave trap suggested by DeMille et al (2004 Eur. Phys. J. D 31 375) seems to be rather advantageous in comparison with other traps. Here we have demonstrated that the microwave trap can provide successful evaporative cooling for polar molecules in a rather broad range of frequencies of the ac field. We suggest that not only ground-state polar molecules but also molecules in some other states can be safely trapped. But the state in which molecules can be safely loaded and trapped depends on the frequency of the ac field.

Dynamics of ultracold polar molecules in a microwave field

In the wake of successful experiments in Fermi condensates, experimental attention is broadening to study resonant interactions in degenerate Bose-Fermi mixtures. Here, we consider the properties and stability of the fermionic molecules that can be created in such a mixture near a Feshbach resonance. To do this, we consider the two-body scattering matrix in the many-body environment, and assess its complex poles. The stability properties of these molecules strongly depend on their center-of-mass motion, because they must satisfy Fermi statistics. At low center-of-mass momenta the molecules are more stable than in the absence of the environment due to Pauli-blocking effects , while at high center-of-mass momenta nontrivial many-body effects render them somewhat less stable.