Extended Theory of Finite Fermi Systems for magic and nonmagic nuclei

Consideration is given to a short review of the main features, recent results, and prospects of the Extended Theory of Finite Fermi Systems (ETFFS), which has been applied in the past 15 years to collective excitations in the neutral channel for nuclei with and without pairing. The theory is an extension of the Migdal standard TFFS to include in a consistent way the single-particle continuum and more complex 1p1h ⊗ phonon or 2qp ⊗ phonon configurations beyond the RPA or QRPA ones; i.e., the theory takes into account all three known mechanisms of giant-resonance width. To the most extent, the theory was developed and applied to nuclei without pairing. A quantitative explanation of the giant-resonance widths was obtained, with the complex configurations contributing about half of the width. In addition, a large part of the observed giant-resonance gross and fine structures can be directly traced back to the specific complex configurations, and the recent results of the (α, α′) experiments in ⁴⁰Ca and ⁵⁸Ni could be explained. Consistent use of the Green’s function method makes it possible to include and calculate some effects which were practically unstudied earlier. These are ground-state correlations induced by complex configurations and “refined” basis effects, in particular, the second (or quasiparticle-phonon) mechanism of pairing. Both of them can be studied in current experiments. In the past five years, the ETFFS has been developed and applied actively to even—even and odd-mass nuclei with pairing. Calculations of the E1 pygmy resonance in Ca and Sn isotopes have shown that this phenomenon, which is important for (n, γ) and (γ, n) reactions, cannot be explained without allowing for complex configurations. Consideration of the single-particle continuum and the practical universality of the interaction parameters allow the ETFFS to be used for calculations of unstable nuclei. The prospects and status of the necessary development of a self-consistent ETFFS for nuclei with pairing are discussed. The text was submitted by the author in English.     

Anharmonic Effects in the Theory of Finite Fermi Systems

Physics of Atomic Nuclei - Some results obtained by E.E. Saperstein and his coauthors in the theory of the ground state and low-lying excited states of magic and semimagic nuclei are...     

Inelastic Neutrino Scattering on Hot Nuclei of Supernova Matter within the Theory of Finite Fermi Systems

The Nozières–Pines method for describing neutron scattering on a heated Fermi liquid (liquid ³He) is used to calculate cross sections for inelastic neutrino scattering on the isotope ⁵⁴Fe, which is an element that plays a key role in the cooling of supernovae. The calculation in question is performed on the basis of the the theory of finite Fermi systems with the aid of the DF3-a Fayans energy density functional.     

Magnetic moments of odd-odd spherical nuclei

We analyze the time-like processes $ \gamma\gamma\rightarrow B\overline{B}$ and $ p\bar{p}\rightarrow\gamma M$ at large Mandelstam variables within the handbag approach, for which the process amplitudes factorize in hard partonic subprocesses and annihilation form factors. The latter represent moments of baryon-antibaryon generalized parton distributions (GPDs). Symmetry relations restrict the number of independent annihilation form factors for the ground state baryons drastically. We determine these form factors from the present BELLE data on $ \gamma\gamma\rightarrow B\overline{B}$ with the help of simplifying assumptions. The knowledge of these form factors allow for predictions of $ p\bar{p}\rightarrow\gamma M$ for various mesons which may be probed at FAIR.     

Quadrupole moments and the structure of the even titanium and chromium nuclei

The energies of the six circular transitions (n = 13 → n = 12 through n = 8 → n = 7) of the K^?Pb exotic atom have been measured to high precision (typically ～ 50 ppm) using Ge (Li) spectrometers. The data acquisition system was computer controlled and stabilized, the energy calibration spectrum was taken simultaneously with the data spectrum. The experimental energies of the six transitions were corrected for ADC nonlinearities and data-calibration spectrum shifts, as well as the presence of unresolved noncircular transition contaminants. The energies of five of the transitions (13 → 12 through 9 → 8) were computed from quantum electrodynamics, including all significant orders of vacuum polarization, electron screening and nuclear polarization. The mass of the K^? was adjusted to achieve a best fit with the experimental energies: the result was m_K^? = 493.657 ± 0.020 MeV.     

Quadrupole moments of hadrons

We study an Abelian Higgs model in three, four and five dimensions using the mean field perturbation expansion with covariant gauge fixing. In four and five dimensions the mean field analysis shows three phases; a confined phase, a Coulomb phase with massless spin waves, and a Higgs phase in which the spin waves aquire a mass. The Higgs and confined phases are shown to be connected. In three dimensions we find a single phase.     

Pair fluctuations in ultra-small Fermi systems within self-consistent RPA at finite temperature

A self-consistent version of the thermal random phase approximation (TSCRPA) is developed within the Matsubara Green’s function (GF) formalism. The TSCRPA is applied to the many level pairing model. The normal phase of the system is considered. The TSCRPA results are compared with the exact ones calculated for the Grand Canonical Ensemble. Advantages of the TSCRPA over the thermal mean field approximation (TMFA) and the standard thermal random phase approximation (TRPA) are demonstrated. Results for correlation functions, excitation energies, single particle level densities, etc., as a function of temperature are presented.     

Quadrupole moments in the cadmium isotopes

Contrary to theoretical predictions and previous experimental results, a new systematic study of the static quadrupole moments Q₂₊ in the even-mass cadmium isotopes using the re-orientation effect shows no evidence of significant variation in Q₂₊ with mass number. For ¹¹⁶Cd, B(E2: 0⁺ → 2⁺) is found to be 20% lower than the previously adopted value.     

Magnetic moments of spherical nuclei: Status of the problem and unsolved issues

Dipole magnetic moments of more than 100 odd spherical nuclei are calculated within the theory of finite Fermi systems. For the effective interaction of nucleons within the theory of finite Fermi systems, use is made of a version that takes into account nuclear-medium-modified amplitudes for the exchange of one pion and one rho meson. A new tensor local charge ζ _t is incorporated in the theory of finite Fermi systems in addition to the known orbital (ζ _l ) and spin (ζ _s ) local charges. Good agreement with experimental data, at a level of 0.1 to 0.2μ _N , is obtained for the overwhelming majority of the nuclei considered here. Several cases of a significant discrepancy with experimental data, at a level of 0.3 to 0.5μ _N , are revealed. Possibilities for removing these discrepancies are discussed. A detailed comparison with known results obtained within the multiparticle shell model is performed for 2p-to 1f-shell nuclei. Cases where the standard theory of finite Fermi systems must be extended by taking into account multiparticle configurations are found. Magnetic moments are analyzed for a number of long isotopic chains. Several new experimental values of magnetic moments for copper isotopes far from the beta-stability valleys are known. For the example of the copper-isotope chain, it is shown how the emergence of a deformation in the ground state of a nucleus can be revealed on the basis of a systematic analysis of magnetic moments.     

Collective excitations in neutron-rich nuclei within the model of a Fermi liquid drop

We discuss a new mechanism of splitting of giant multipole resonances (GMR) in spherical neutron-rich nuclei. This mechanism is associated with the basic properties of an asymmetric drop of nuclear Fermi liquid. In addition to well-known isospin shell-model predictions, our approach can be used to describe the GMR splitting phenomenon in the wide nuclear-mass region A ～ 40–240. For the dipole isovector modes, the splitting energy, the relative strength of resonance peaks, and the contribution to the energy-weighted sum rules are in agreement with experimental data for the integrated cross sections for photonuclear (γ, n) and (γ, p) reactions.     

Effect of time-odd fields on odd-even mass differences of semi-magic nuclei

The effect of time-odd fields of Skyrme interaction on neutron odd-even mass differences is studied in the framework of axially deformed Skyrme Hartree-Fock(DSHF)+BCS model. To this end, we take into account both the time-even and time-odd fields to calculate the one-neutron and two-neutron separation energies and pairing gaps of semi-magic Ca, Ni, and Sn isotopic chains. In the calculations, a surface-type pairing interaction(IS pairing) and an isospin dependent contact pairing interaction(IS+IV pairing)are adopted on top of Skyrme interactions SLy4, SLy6 and Sk M*, respectively. We find that the time-odd fields have in general small effects on pairing gaps, but achieve better agreement with experimental data using SLy4 and Sly6 interactions, respectively.It is also shown that the calculations with IS+IV pairing reproduce the one-neutron separation energies of Sn isotopes better than those with the IS pairing interaction when the contributions of the time-odd fields are included.     

Exchange symmetry of the effective interaction in the Landau-Migdal theory of Finite Fermi Systems

We investigate the particle exchange symmetry of the phenomenological effective particle-hole interaction used in the theory of Finite Fermi Systems. We find that experimental data and consistency relations support an interaction which is antisymmetric at the surface and in the exterior region of the nucleus and nonsymmetric in the interior. Besides, we show that the number of adjustable parameters of the effective interaction can be reduced substantially by the use of generalized Ward identities without any loss of agreement with experimental data.     

Finite temperature calculation of angular velocities and moments of inertia in rotating nuclei

The rotational properties of nuclei in the statistical region are predicted on the basis of a simple BCS model. A back-bending, which disappears as the temperature increases, is observed in the plot of the moment of inertia versus the square of the angular velocity.     

Quadrupole moments of neutron isomers in Sm isotopes

The quadrupole moments of the neutron isomers in^140,142Sm were determined by measuring the quadrupole interaction of Sm in Gd using single crystals. The moment for the 10⁺ isomer in¹⁴⁰Sm was determined to be ¦Q¦=167(48) fm² and for the 7^? isomer in¹⁴²Sm ¦Q¦=112(27) fm². The quadrupole moments are a measure for a deformation which turned out to be very similar to the deformation found for corresponding proton isomers in Gd isotones.     

Quadrupole moments of superdeformed bands in 193Tl

Lifetimes of states in the two strongest superdeformed (SD) bands in ¹⁹³Tl were measured using the Doppler-shift attenuation method. The reaction ¹⁷⁶Yb(²³Na,6n)¹⁹³Tl at a beam energy of 129 MeV was used and γ-rays were detected by the Gammasphere array. Quadrupole moments of 18.3(10) eb and 17.4(10) eb were extracted for SD bands 1 and 2, respectively, using the fractional Doppler-shifts of the SD transitions. The previously reported linking transitions of these SD bands to normal deformed near yrast levels could not be confirmed. No other candidates for linking transitions could be established. Received: 27 April 1999     

Finite size α-particle calculations of absolute α-decay for spherical nuclei

Recently some important results have been obtained in calculating absolute α-decay widths, the calculations having been performed in the zero range α-particle approximation. In this paper the effects of the finite size of the α-particle are considered. Two important effects have been found: (i) for the finite size calculation, the absolute α-decay widths decrease by 2–3 orders of magnitude, and (ii) the finite size effects are strongly dependent on the shell model configuration of the initial nucleus. In the framework of the superfluid model the absolute probabilities of finite size α-particle emission have been calculated for the favored α-transitions of more than 200 spherical nuclei. The theoretical α-widths turn out to be smaller than the experimental ones by a factor of 10, which is approximately constant for all the nuclei studied.