Isovector Vibrations Research Articles

Isovector vibrations in nuclear matter at finite temperature

We consider the propagation and damping of isovector excitations in heated nuclear matter within the Landau Fermi-liquid theory. Results obtained for nuclear matter are applied to calculate the Giant Dipole Resonance (GDR) at finite temperature in heavy spherical nuclei within Steinwedel and Jensen model. The centroid energy of the GDR slightly decreases with increasing temperature and the width increases as $T^2$ for temperatures $T < 5$ MeV in agreement with recent experimental data for GDR in $^{208}$Pb and $^{120}$Sn. The validity of the method for other Fermi fluids is finally suggested.

The enhancement of giant-dipole strength and its consequences for the effective mass of the nucleon and the electromagnetic polarizabilities and quadrupole sum-rule of the nucleus

Using recent experimental results on Compton scattering by 208Pb at energies below pion threshold we explore the effects of enhancement due to mesonic currents and isovector vibrations on the giant resonances of nuclei. Quantitative information is given for the enhancements of the electric polarizability, the diamagnetic susceptibility and the energy-weighted quadrupole sum rule. It is shown that the average of results available from different laboratories on the “nonretarded” enhancement constant K GDR in the A = 197–209 mass range favours an effective nucleon mass of m ∗ m = 3 4 . Some new results for the amplitude of Compton scattering by the giant resonances of nuclei are presented which allow a treatment of the retardation problem in a zero-order approximation.

Magnetic dipole electroexcitations in rare-earth nuclei

The M1 excitation of K π = 1 + states through inelastic electron scattering is studied in rare-earth nuclei within a quasiparticle RPA approach with quadrupole-quadrupole, spin-spin and spin-quadrupole residual interactions. The spurious state is removed exactly by a procedure which restores the rotational invariance of the RPA hamiltonian and leads to almost purely isovector vibrations. The DWBA (e, e') form factors and the strongly orbital low-energy M1 spectrum are in a good agreement with the rich experimental data. The purely collective scissor state has largest overlaps with the orbital low-energy RPA excitations but a single overlap does not exceed 15%. Nevertheless, a number of low-lying 1 + states, including the strongest experimentally observed M1 state, can be interpreted as isovector rotational vibrations due to their large overlaps with proposed phonon rotational states, in which only several quasiparticle pairs perform a scissor-type vibrational motion.

Rotational isovector vibrations in titanium nuclei

The strong M1 states with K π = 1 + in 44,46,48,50 Ti are described microscopically with a deformed Woods-Saxon potential plus QRPA using a parameter-free self-consistent quadrupole force and an interaction, which restores the rotational symmetry. The available experimental data (energies, B(M1) values and (e, e') form factors in 46,48Ti) are well described in terms of isovector quadrupole rotational vibrations. These RPA states correspond to the scissor-type of isovector motion described by the two-rotor model, but they overlap only 20–30% with the collective isovector rotational state of this model since only few quasiparticle configurations take part in the RPA rotational vibration.

Boson quasispin in the generalised Bohr-Mottelson model

It is shown that the GBMM (an outgrowth of the Bohr-Mottelson model to encompass isovector vibrations) is endowed with an Sp(20, R) algebraic structure. This is connected with the fact that independent proton and neutron harmonic oscillations, which are described by U(10), are the main part of this model. The interaction between the different vibrations are described by the non-compact generators of Sp(20, R). A mathematically rigorous statement (complementary to the geometrical formulation) of this new symplectic model is presented. The algebraic setting of GBMM enabled us to introduce in a natural way a discrete boson variable, B-spin, which classifies the states according to their d- z (isoscalar-isovector) symmetry character. By using group-theoretic and recursive techniques we have explicitly constructed a basis associated with the group chain U(10) ⊃ N SU d+z (5)⊗ (B, B 0 SU B(2)⊃ SO d+z L ⊃ SO d+z L 0 (2) This basis is indispensable for future applications of GBMM. Finally, we compare the F-spin (IBM-2) and B-spin (GBMM) concepts.

Symmetry-restoring interactions for Kπ = 1 + isovector vibrations

The low-lying isovector 1 + states are studied by a symmetry-restoring RPA approach in some rare-earth nuclei. A new velocity-dependent residual interaction is proposed in order to restore the rotational invariance of the hamiltonian in the quasiparticle random-phase approximation with an axially-symmetric Woods-Saxon potential. A new quadrupole interaction is introduced with a self-consistently determined coupling strength. Calculations for six rare-earth nuclei ( 154Sm, 156,158Gd, 164Dy, 168Er, 174Yb) show a good agreement with the experimental energies and B(M1) values. The M1 transitions, corresponding to the experimental strong magnetic dipole states, have in all apart from one case a predominant orbital contribution. The largest orbital contribution (90%) is found in 154Sm. About half of the low-energy ( E < 5MeV, B(M1)↑>0.1 μ N 2) states in each nucleus have an orbital character with a (10–40)% spin admixture. The M1 strength is concentrated in the region 2–9 MeV with a maximum around 5 MeV and corresponds to ΔN osc = 0 transitions.

Microscopic calculation of the restoring force for scissor isovector vibrations

The restoring force for scissor isovector vibrations is calculated microscopically with the wave functions of an axially symmetric Woods-Saxon potential from a density-dependent symmetry energy. The experimental energies of the low-lying magnetic dipole states in rare-earth nuclei are well reproduced. It is found that only outer particles, which contribute to the nuclear moment of inertia, take part in this collective vibration. They are about half of the total number of nucleons.

Monopole and Quadrupole Giant Resonances in Rotating Triaxially Deformed Nuclei. II: A Microscopic Description of the Isoscalar and Isovector Modes

Microscopic calculations are performed for the isoscalar and isovector monopole and quadrupole giant resonances built on high-spin yrast states. The results of the calculation show that the shapes of the strength functions for both the isoscalar and isovector vibrations are determined mainly by the deformation parameters of the mean field. The effects of rotation on the isoscalar and isovector quadrupole modes are found to be quite different: The rotation-splittings of the former become significant at very high-spins, while those of the latter remain small. It is also demonstrated that the. transformation of the strength functions from the rotating frame into the laboratory frame is crucial to accurately evaluate the rotation­ splittings of the quadrupole modes.

Elastic isovector vibrations and the boundary conditions

The elastic model, which successfully explains the isoscalar giant resonances, is now applied to study the isovector giant resonances. In solving the Lam\'e equation, we employ the boundary condition that the displacement shall vanish at the surface. The results are compared with those obtained under the contrasting boundary condition that the stresses shall be absent at the surface. It was found that the results are dependent on the type of boundary conditions. Future experimental data will allow the assessment of the correct choice of boundary conditions.NUCLEAR STRUCTURE Nuclear giant resonances, isovector vibrational nodes. Electric and magnetic multipoles.

Velocity dependence of the nucleon-nucleon interaction, exchange currents and enhancement of the dipole sum rule in nuclei

A model is employed to describe the velocity dependence of the effective nucleon-nucleon interaction in nuclear matter. The interactions in this model consist of π − and ρ-meson exchange, together with short-range correlations induced by the strongly repulsive potential resulting from ω-meson exchange. With known coupling strengths, these interactions produce an effective mass m ∗/m = 0.75 in nuclear matter. Through the formalism of Fermi liquid theory, the exchange-current correction to the orbital g-factor, δg l , can be described in terms of the velocity dependence in the neutron-proton interaction, and, within the model, this can be related to the effective mass m ∗ . With m ∗/m = 0.75 , the δg l for the proton turns out to be 0.22, 45% of it coming from π-meson exchange. Additional contributions to m ∗/m in nuclei come from the coupling of vibrations to quasiparticles; these are especially important in the nuclear surface, and tend to increase the effective mass, when averaged over both nuclear volume and surface, so that 〈m ∗/m〉 av. ≳ 1 . In so far as these contributions arise from isovector vibrations, we can use the same model as for π- and ρ-meson exchange, and show that the same relation between m ∗/m and δg l holds, so that for 〈m ∗/m〉 av. = 1 , δg l = 0. The contributions from coupling to vibrations will depend upon the single-particle state, however; states of high-angular momentum will tend to have 〈m ∗/m〉 av. < 1 and δg l > 0. Finally, the enchancement δg l in gl can be connected with the enhancement k in the dipole sum rule originating from the giant-resonance region. This connection is not very precise, but gives a small positive κ ∼ 0.2.