Transition probabilities and static moments of excited states in even-even nuclei

A new approach is made to calculate the generalized single-particle density matrixp ^μv in even-even nuclei. It is shown that this quantity is included in the three particle response function, for which we derived a renormalized equation. Taking into account in a consequent way the effective particle-hole interaction we received a formula for the static moment of excited states and the transition probability between such states which is essentially different from the usual RPA theory.     

Study of the Gamow-Teller resonance in 90Nb and 208Bi

An approach is proposed for studying the spreading properties of the Gamow-Teller resonance (GTR) in heavy nuclei including the coupling to 2p2h configurations and the ground-state correlations beyond RPA. The GTR is generated by a proton p-neutron h (πp-νh) phonon within the renormalized RPA. The second-order configuration mixing beyond RPA is realized by constructing two-phonon configurations, in which one of two intermediate phonon states is a πp-νh phonon. The numerical calculations are performed in the parent nuclei ⁹⁰Zr and ²⁰⁸Pb making use of M3Y nucleon-nucleon interaction and the single-particle wave functions obtained in the standard harmonic oscillator potential. The single-particle energies around the Fermi surface are substituted with the empirical values or those given by a Woods-Saxon potential. The results obtained provide a reasonable account for recent experimental findings on the GTR in these nuclei. The extension of the present approach to highly excited (hot) nuclei is also provided. The GTR is found to be stable against temperatures up to T = 6 MeV.     

Ground state correlation effects on the Gamow-Teller strength distribution in 48Ca

We calculate the Gamow-Teller strength distribution in ⁴⁸Ca using an extended second RPA which explicitly includes ground state correlations. The following effects are taken into account: (i) the reduction of the 1p1h matrix elements due to the partial occupation of single-particle orbitals, (ii) the modification of the 1p1h Green function in the presence of ground state correlations and 2p2h correlations in the excited states, (iii) renormalization of the external field and (iv) the pure 2p2h response due to unblocking of the ground state. The first three effects largely cancel in the region of the Gamow-Teller resonance while the last two cancel at higher energies. The resulting strength distribution is therefore quite similar to the one obtained previously in second RPA.     

The phonon-coupling model for Skyrme forces

A short review on the self-consistent RPA based on the energy-density functional of the Skyrme type is given. We also present an extension of the RPA where the coupling of phonons to the single-particle states is considered. Within this approach we present numerical results which are compared with data. The self-consistent approach is compared with the Landau–Migdal theory. Here we derive from the self-consistent ph interaction, the Landau–Migdal parameters as well as their density dependence. In the Appendix a new derivation of the reduced matrix elements of the ph interaction is presented.     

Thermo field dynamics in the treatment of the nuclear pairing problem at finite temperature

The use of the thermo field dynamics, in dealing with the study of nuclear properties at finite temperature, is discussed for the case of a nuclear Hamiltonian which includes a single-particle term and a monopole pairing residual two-body interaction. The rules of the thermo field dynamics are applied to double the Hilbert space, thus accounting for the thermal occupation of single-particle states, and to construct dual spaces, both for single-particle (BCS) and collective (RPA) degrees of freedom. It is shown that the rules of the thermo field dynamics yield to a temperature dependence of the equations describing quasiparticle and phonon excitations which is similar to the one found in the more conventional finite temperature Wick's theorem approach, namely: by dealing with thermal averages.     

Particle–particle Tamm–Dancoff approximation and particle–particle random phase approximation calculations for 18O and 18F nuclei

The nuclear structures of ¹⁸O and ¹⁸F nuclei are studied using particle–particle Tamm–Dancoff approximation (pp TDA) and particle–particle random phase approximation (pp RPA). All possible single-particle states of the allowed angular momenta are considered in the 0p and 1s–0d shells. The Hamiltonian is diagonalized in the presence of Warburton and Brown interactions. The results containing energy-level schemes and transition strength B(E2) are compared with the available experimental data.     

Single-particle Green function in the Calogero-Sutherland model for rational couplings β = p/q

We derive an exact expression for the single-particle Green function in the Calogero-Sutherland model for all the rational values of the coupling β. The calculation is based on Jack polynomial techniques and the results are given in the thermodynamical limit. Two types of intermediate states contribute. The first one consists of a particle propagating out of the Fermi sea and the second one consists of a particle propagating in one direction, q particles in the opposite direction and p holes.     

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1⁻, 2⁺ and 3⁻ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in ⁶⁰Ca are investigated in some detail.     

Generators of collective vibrations in heavy nuclei

Solving harmonic equations of motion for a realistic single-particle potential, the generators of various isoscalar collective vibrations up to a multipolarity of 4 are extracted. Transition strengths, transition currents, and energy systematics are studied in comparison with full RPA calculations, fluid dynamical calculations, and experimental data. It is shown that all these states can be well described by simple generators and that the influence of the detailed structure of the residual two-body force is small compared with that of the single-particle level scheme and of geometric constraints.     

Two-body propagators with dynamic effective interactions in a many-fermion medium: II. s-Channel

In open-shell nuclear structure calculations collective excitations of the closed-shell core play an important role. When the energies of these excitations are comparable to the spread of energies in the model space a dynamic treatment of the core states is essential. In a Green function formulation dynamic core states, represented by particle-hole phonons, are included in the effective interaction of the s-channel integral equation for the fourfermion vertex function Γ. The solution of the equation is obtained analytically and from it the s-channel two-body propagator K is calculated. The structure of the propagator K reveals that, in addition to poles corresponding to the normal shell model states, many new poles of K are obtained. These correspond to two-particle-n-phonon configurations. Furthermore, it is shown that, due to the phonons, correlations of the ground state are induced in the calculation of the propagator K. The difference between these correlations and the well-known particle-particle-RPA correlations also included in the formalism is pointed out. The expressions derived can easily be handled numerically. In the calculations the physical states of single-particle and single-hole nuclei can be incorporated by an appropriate dressing of the single-fermion Green function.     

Quenching of the mass operator associated with collective states in many-body systems

Giant resonances are understood as superposition of particle-hole excitations. The empirical systematics indicates that the associated spreading widths are considerably smaller than the sum of typical widths of single-particle and single-hole states, and that the centroid energy is in good agreement with the RPA predictions. These results imply a destructive interference between the different contributions to the mass operator associated with collective vibrations. We study the properties of the mechanism responsible for this quenching by inspecting contributions to the mass operator in the semiclassical limit of large single-particle angular momenta.     

Rotational bands on few-particle excitations of very high spin

An RPA formalism is developed to investigate the existence and properties of slow collective rotation around a non-symmetric axis, when there already exists a large angular momentum K along the symmetry axis built up by aligned single-particle spins. Both repeatability and E2 collectivity are required to distinguish the collective rotational-like solutions from the others, which may come lower in energy. First the formalism is applied to bands on high-K isomers in the well-deformed nucleus ¹⁷⁹Hf, where the rotational-model picture is reproduced for intermediate K-values in agreement with experiment. At high K the collectivity is suppressed even more than the diminishing vector-coupling coefficient of the rotational model would suggest, but the repeatability actually improves. The moment of inertia is predicted to remain substantially smaller than the rigid-body value, so the bands slope up steeply from the yrast line at spins where pairing effects are gone. A second application is to the initially spherical nucleus ²¹²Rn, which is believed to acquire an oblate deformation that increases steadily with K due to the oblate shape of the aligned orbitals. In this case the rotational-like excitations also exist but are still less favoured than in ¹⁷⁶Hf, even at comparable deformations. Some collective states may come closer to the average yrast trend, but they have lower repeatability because they are more like dressed single-particle excitations. The main differences between the two nuclei studied is interpreted as a general consequence of their different shell structure.     

Theory of magnetic excitations in KCoF3 at finite temperatures

Magnetic excitations in KCoF₃ at finite temperatures are studied by taking into account the residual orbital moment of the Co²⁺ ions. Equations of motion of Green functions related to all excitation operators between the molecular field states of the ⁴T₁ symmetry of the Co²⁺ ions are solved using the RPA approximation, and temperature-dependent dispersion curves are calculated.     

Self-consistent calculations within the Green’s function method including particle-phonon coupling and the single-particle continuum

The Green’s function method in the Quasiparticle Time Blocking Approximation is applied to nuclear excitations in ¹³²Sn and ²⁰⁸Pb. The calculations are performed self-consistently using a Skyrme interaction. The method combines the conventional RPA with an exact single-particle continuum treatment and considers in a consistent way the particle-phonon coupling. We reproduce not only the experimental values of low-and high-lying collective states but we also obtain fair agreement with the data of non-collective low-lying states that are strongly influenced by the particle-phonon coupling.     

Excited states of deformable nonaxial odd nuclei

Rotationally single-particle and vibrational excitations of deformable nonaxial odd nuclei are investigated with allowance for the interaction of collective and single-particle states. The ratios of excitation energies, of reduced probabilities of E2 transitions, and of quadrupole moments for deformed nonaxial odd nuclei are calculated up to high-spin states.     

Influence of isolated para-hydrogen molecules in solid ortho-hydrogen on the libron density of states

A Green function theory is used to calculate the influence of isolated para-hydrogen defects in solid hydrogen on the libron density of states. Librons are treated within the harmonic approximation (RPA).Extract from D 26     

A self-consistent microscopic description of the giant resonances including the particle continuum

The distribution of strength for the isovector dipole and isoscalar quadrupole modes in ¹⁶O and ²⁰⁸Pb is calculated in the framework of the RPA. Effects due to the self-consistency as well as the single-particle continuum are included. The various collective models and the coupled-channel reaction theory are related through the RPA sum rules.     

A general green function method for calculating electronic structure and vibrational modes at surfaces

We extend the (single-particle) Green function method for treating surface problems by (1) giving a simple analytical expression for the bulk Green function G₀⁺(ω) which is completely general, and (2) giving a new procedure for achieving self-consistency in electronic problems.     

Conserving RPA and the response of 48Ca

The connection between the single-particle self-energy and the corresponding conserving particle-hole (ph) interaction, discussed long ago by Kadanoff and Baym, is employed to study the response of ⁴⁸Ca. Second order self-energy contributions are taken into account in the construction of the energy dependent ph interaction. From this perspective it is possible to make contact with other approaches which also aim to incorporate the coupling to 2p2h excitations within the RPA framework. The method is used to study both the discrete low-energy states as well as the giant resonances in both ⁴⁸Ca and ⁴⁸Sc using a realistic G matrix interaction based on meson exchange. The calculated strength distribution compares favorably with experiment but the strength below 15 MeV is still somewhat too large as compared to experiment for all types of excitations. The quenching of magnetic and Gamow-Teller strength due to 2p2h admixture amounts to about 30%.