The isovector monopole state and the escape width of double analog resonances

An irreducible vector operator is used to generate isovector monopole states with welldefined values of T and T_z in N > Z nuclei. Reduced transition strengths are calculated in two different ways and the results seem compatible. The Wigner-Eckart theorem is used to derive expressions for the mixing of the monopole states with the ground state and its analog states. Expressions for the escape widths of the monopole states are also derived. An application is made to double analog resonances, and it is found, contrary to expectations, that the mixing with the T?1 monopole state is unable to account for the observed elastic partial width of these resonances in medium and heavy nuclei. The reason for this is the small escape width of the monopole state.     

The width of the single and double analogs; A simple relation

The total width of the double isobaric analog resonance is related to the width of the single analog resonance. An estimate of both width is given, using the isovector monopole state as the main doorway in Coulomb mixing.     

E0 andM1 excitations in56Ni

The centroid energy and the decay width of the giant monopole resonance in the unstable nucleus⁵⁶Ni are predicted. The resulting 0⁺, ΔT=0 strength distribution, including the escape and the spreading width, displays a structure centered at around 18 MeV with the total width of about 5 MeV. We also study theM1 response in this nucleus which shows a strong isovector transition at 9.6 MeV and a weak isoscalar one at 7.5 MeV.     

Monopole breathing modes in208Pb

We give a detailed account of investigations on the structure of giant monopole resonances in²⁰⁸Pb. A part of the results of this paper has already been published in “Short Notes” in this journal. The calculations are based on a renormalized correlation function technique which turned out to be very suitable for our purposes. The calculations predict an isoscalar resonance atE≈13 MeV and an isovector resonance atE≈20.5 MeV. The width of both states is mainly due to the spreading.     

A sum rule description of giant resonances at finite temperature

A generalization of the sum rule approach to collective motion at finite temperature is presented. The m₁ and m_?1 sum rules for the isovector dipole and the isoscalar monopole electric modes have been evaluated with the modified SkM force for the ²⁰⁸Pb nucleus. The variation of the resulting giant resonance energies with temperature is discussed.     

Analog spin wave functions and spreading widths of isobaric analog resonances

The coupling of the isobaric analog state (IAS) to the giant isovector monopole state has been shown by Mekjian and Auerbach to dramatically affect the calculation of the spreading width. We show that the inclusion of this coupling is equivalent to a new definition of the IAS as an eigenstate of analog spin in which each proton radial wave function is distorted relative to the corresponding neutron radial wave functions by the central Coulomb field.     

An investigation of the influence of the pairing correlations on the properties of the isobar analog resonances inA = 208 nuclei

Within the quasi-particle random phase approximation (QRPA), the method of the self-consistent determination of the isovector effective interaction which restores a broken isotopic symmetry for the nuclear part of the Hamiltonian is given. The effect of the pairing correlations between nucleons on the following quantities were investigated for theA = 208 nuclei: energies of the isobar analog 0⁺ states, the isospin admixtures in the ground state of the even-even nuclei, and the differential cross-section for the²⁰⁸Pb(³He,t)²⁰⁸Bi reaction atE(³He)=450 MeV. Both couplings of the excitation branches withT ^z = T⁰ ± 1, and the analog state with isovector monopole resonance (IVMR) in the quasi-particle representation were taken into account in our calculations. As a result of these calculations, it was seen that the pairing correlations between nucleons have no considerable effect on theT = 23 isospin admixture in the ground state of the²⁰⁸Pb nucleus, and they cause partially an increase in the isospin impurity of the isobar analog resonance (IAR). It was also established that these correlations have changed the isospin structure of the IAR states, and shifted the energies of the IVMR states to the higher values.     

Excitation of isovector giant resonances by inelastic scattering of positive pions on90Zr at 226 MeV

We studied the region of giant resonances with positive pions of 226 MeV scattered inelastically on⁹⁰Zr. Two groups of resonances were seen: the first structure between 12 and 19 MeV excitation energy is explained as a sum of the isoscalar quadrupole resonance at 14 MeV, the isovector dipole resonance at 16.5 MeV and possibly some E₀ strength. The second group between 24 and 34 MeV excitation energy also corresponds to more than a simple multipolarity and may be described as a sum of a monopole and a quadrupole isovector resonance.     

Pygmy dipole resonance in nuclei

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.     

201 MeV proton excitation of giant resonances in 208Pb: Macroscopic and microscopic analysis

The region of the giant resonances in ²⁰⁸Pb has been investigated by inelastic scattering of 201 MeV protons. To test the analysis, angular distributions were measured for the low-lying 3^?, 5^?, 2⁺ and 4⁺ collective states. The giant isoscalar quadrupole resonance (ISGQR) is split into two structures, one at 9.0 MeV with a full width at half-maximum Γ = 1.0 MeV, the other one at 10.6 MeV (Γ = 2.0 MeV), with fine structures at 8.9, 9.3, 10.1, 10.6 and 11 MeV. A macroscopic analysis using the distorted-wave Born approximation (DWBA) leads for the low-lying collective levels, as well as for the ISGQR, to transition probabilities too small by a factor of two, compared with those obtained in other reactions. Microscopic analysis using the distorted-wave impulse approximation (DWIA), with three different sets of random phase approximation (RPA) transition densities, is in very good agreement with the data. At forward angles, in the 12 to 16 MeV excitation energy region, a strong resonance at 13.5 MeV (Γ = 3.6 MeV) is accounted for by the Coulomb excitation of the isovector giant dipole resonance (IVGDR); at larger angles the results are compatible with the excitation of the isoscalar monopole resonance (ISGMR) located at 13.9 MeV (Γ = 2.6 MeV).A resonance located at 21.5 MeV (Γ = 5.7 MeV) appears as the superposition of an isovector quadrupole resonance (IVGQR) excited by Coulomb interaction and a resonance of multipolarity L = 1 ΔT = 0 (ISGDR “squeezing mode”).     

Quadrupole excitations in the two-center shell model (II)

The distribution of the isoscalar, T = 0, and isovector T = 1, strength of quadrupole modes in the deformed nucleus ²⁴Mg is investigated. A finite-range residual interaction is used in the particle-hole basis of a rotating two-center shell-model potential of two ¹²C nuclei. The model calculation describes semi-quantitatively the main features of the available experimental data for the T = 0, E2 excitations and predicts the location and structure of the isovector, T = 1, E2 strength for which no data has been published to date.     

Position and width of the monopole giant resonance in208Pb

The positions and widths of the monopole giant resonances in²⁰⁸Pb are calculated. The calculated widths include the effects of the single particle decay width and of the spreading width. We find the isoscalar resonance at E_res?13.0 MeV, while the isovector resonance is found at E_res?20.5 MeV. Due to the asymmetry of the resonance curves an unambiguous value for the widths can not be defined. Instead we present the form of the resonance curve in numerical form in table 1.     

Excitation of giant resonances in the Ca isotopes in (π±, π0) reactions

The excitation of the giant isovector dipole and monopole resonances in the even-A Ca isotopes in pion single-charge-exchange reactions is studied theoretically. Transition densities obtained from a sum-rule approach and from a microscopic charge-exchange RPA are employed in DWIA calculations. The relation of the (π^±, π⁰) cross sections to proton and neutron densities is discussed.     

Scaling- and antiscaling-type oscillations in isoscalar and isovector nuclear monopole vibrations

Isoscalar (T = 0) and isovector (T = 1) giant monopole resonances are studied using a localscale version of the ATDHF theory developed on the basis of a rigorous energy-density functional approach. Due to the strong coupling between the bulk and surface density vibrations, the monopole collective motion is split into four normal modes. Two of them, lower in energy, correspond to scaling-type density vibrations. The other two are of antiscaling-type in which the nuclear surface oscillates opposite in phase to the scaling-type vibrations. Excitation energies, transition densities, T = 0 and T = 1 energy weighted sum rules and other properties of breathing even-even nuclei are calculated using different Skyrme-type effective forces. The strong sensitivity of the antiscaling-type vibrations to the particular form of the approximate energy-density functionals is demonstrated.