J. Speth

Nuclear structure calculations with a density-dependent force in 208Pb

Abstract Excitation energies and excitation probabilities in 208 Pb of the low lying states as well as of strongly collective high lying states (generalized multipole resonances) are calculated, using a large configuration space and a density dependent interaction. Within the extended theory of finite Fermi systems moments of excited states and transition probabilities between excited states are calculated. The theoretical results are in fair agreement with the experimental values.

On the use of Skyrme forces in self-consistent RPA calculations

Abstract Self-consistent random-phase (RPA) calculations including the continuum are presented using Skyrme forces. The density-dependent interpretation of the interaction is favoured as it does not violate the spin stability. A possible density dependence of the momentum-dependent S- and P-interaction is taken into account, which allows one to vary the incompressibility K and the effective mass m ∗ /m independently. It is shown by analytic relations that these two quantities are the only degrees of freedom left in the parameterization of this Skyrme force, if the ground-state properties shall be reproduced , except for a still open degree of freedom in the spin exchange parameterization. The Landau parameters are discussed as a function of these degrees of freedom in order to find the best possible particle-hole interaction. Continuum calculations of the 1 − , 2 + and 3 − states in 16 O are presented and compared with-discretized continuum calculations. It is found that the existing Skyrme forces do not show enough attraction and in addition cause relatively large isospin impurities, in 16 O as well as in 208 Pb. The influence of large configuration spaces is discussed. A systematic search for an interaction with a stronger particle-hole interaction is presented which seems to favour interactions with a high effective mass, but a low compression modulus.

A dynamical theory of the giant dipole resonance in nuclei

Abstract Calculations of the giant dipole resonance in the particle-hole model, employing empirical values for the unperturbed particle and hole energies have been unsuccessful in pushing the dipole state to a sufficiently high energy. It is argued that unperturbed levels, corresponding to an effective mass of m ∗ /m ∼ 0.60–0.64 , should be employed. The couplings of particles and holes to vibrations are the crucial ingredients in these considerations. This also has the consequence of spreading out the M1 strength. A new interpretation of experimental strengths is proposed.

Nuclear polarization in muonic 204, 206, 207, 208Pb in the random-phase approximation

Abstract We have calculated muonic-atom nuclear polarization (NP) energy shifts for 208 Pb using the renormalized random-phase approximation (RPA) to describe the nuclear excitations. Our RPA spectra are in good agreement with a number of direct experimental measurements, giving us confidence that the present NP results are more reliable than those of previous calculations by other authors. We find generally smaller energy shifts than in earlier work, in disagreement with several empirical determinations of these effects. Through a more critical examination of the data, we argue that those empirical determinations may be incorrect, and we suggest that the difficulties in fitting the data may lie in the splittings rather than in the absolute values of the transition energies, as has been assumed previously. Using empirical properties of some low-lying states in the isotopes 204, 206, 207, 208 Pb, we adjust and extend our results to provide a nearly complete and successful description of all such effects in these isotopes.

Low- and high-energy collective states of deformed nuclei

Abstract The low-lying and high-lying Kπ = 0+, 1+ and 2+ states, as well as the Kπ = 0− and 1− resonances for nuclei in the deformed rare earth region are studied in the framework of the quasi-particle random phase approximation. A large configuration space and a density-dependent zero range force has been used. Fair agreement with the data is found for the properties of the low-lying collective states. In the giant resonance region we have calculated the centroid energies, B(Eλ) distributions and the splitting of the giant dipole and giant quadrupole resonances. Interestingly the isoscalar monopole resonances are also found to split into two pieces with a centroid energy around 15 MeV. In addition, the transition densities of the most collective states are calculated and compared with the phenomenological β- and γ-vibrations. The results of the present calculation suggest a reinterpretation of this phenomenological picture.

Electric multipole moments and transition probabilities of single-particle states in the lead region

Abstract Within the theory of finite Fermi systems we have calculated electric quadrupole moments as well as E2 and E3 transition probabilities for single-particle states in the lead region. We studied their dependence on the force parameters of the residual interaction and give a set of parameters which yields good agreement with a large group of experimental data in this region.

The influence of the π- and ρ-exchange potential on magnetic properties of nuclei

Abstract A generalized particle-hole interaction is suggested which includes in addition to the zero-range terms of the Landau-Migdal theory also explicitly the contributions of the one-pion- and one-rho-exchange potential. Using this force, magnetic resonances in 208 Pb and magnetic moments and transition probabilities in the neighbouring odd-mass nuclei are calculated. We include in the analysis also excitation energies and transition probabilities of unnatural parity states in 16 O and 12 C. From the comparison of the theoretical values with the experimental data, the Migdal parameters g 0 and g ′ 0 are deduced. The large value of g′ 0 = 0.76 (m∗/m = 1) indicates that not only pion condensation but also “so-called” precritical phenomena do not exist in nuclei. Due to our (nevertheless) relatively weak spin-dependent force the theoretical interpretation of magnetic moments and transition probabilities has to be modified.

Effects of two-particle-two-hole correlations on the longitudinal quasielastic response in 12C☆

Abstract In an extended RPA theory which includes 1p1h as well as 2p2h excitations we have calculated the quasielastic charge response in 12C for momentum transfers of 200, 250 and 300 MeV c . Using a realistic G-matrix interaction in local density approximation we find reasonable agreement with the (e, e) data for 200 and 250 MeV c while at 300 MeV c , as a result of shell truncations, the agreement starts to degrade.

E0 properties in the lead region

Abstract The theory of finite Fermi systems is applied to monopole properties in the lead region-isotope shifts, isomer shifts, and E0 transition rates. A density-dependent delta interaction is used. It is noted that the L = 0 properties are much more sensitive to the density dependence than are the other properties such as M1 and E2 transitions.

Change of nuclear radii due to rotation: Calculation of Mössbauer and muonic isomer shifts

Abstract Mossbauer and muonic isomer shifts of 2 + rotational states are calculated for rare-earth nuclei in good agreement with experiment using Migdals effective p-h and p-p interactions. The second-order cranking equations are developed in the framework of the theory of finite Fermi systems. In contrast to the pairing-plus-quadrupole model, the results of this work show a small stretching contribution for most nuclei, but a dominating role for the Coriolis antipairing effect. Shrinking charge radii are found for Dy and Os isotopes and some other nuclei as a consequence of the CAP mechanism. Detailed information is given about the redistribution of protons and neutrons due to rotation. It is seen that only a few levels within the range of the diffuse Fermi edge take part in the redistribution and determine the isomer shifts. Shrinking m.s. proton radii and, at the same time, increasing m.s. neutron radii are obtained for the “back-bending” nuclei 158, 160, 162 Dy 160, 162 Er and 164, 166 Yb.