Differences in the structure of isoscalar and isovector “stretched” excitations in 24Mg and 28Si

A comparison of theoretical distorted wave impulse approximation results with the experimental data for the excitation of “stretched” 6^?T = 0 and 6^?T = 1 levels in ²⁴Mg and ²⁸Si by 135 MeV protons suggests significant differences in the structure of the isoscalar and isovector levels. This is consistent with the results of a recent study of the (π, π′) reaction on ²⁸Si.     

Microscopic description of the E0, E2 and E1 giant resonances in 40Ca, 48Ca and 56Ni

The isovector E1 as well as the isoscalar, isovector and full electromagnetic E2 and E0 strength distributions for ⁴⁰Ca, ⁴⁸Ca and ⁵⁶Ni have been calculated in a large energy range up to 50 MeV of excitation. The microscopic model used includes the continuum RPA, 1p1h⊗phonon configurations and ground state correlations induced by these configurations. It is shown that the latter effect gives an increase of the energy weighted sum rules of 4–7%. In all these nuclei the isoscalar E0 and E2 resonances are spread out over the broad energy region. We obtained a reasonable good agreement with the available experimental data including the recent ones for the isoscalar E0 resonance in ⁴⁰Ca. The theoretical transition densities show a rather strong dependence on the excitation energy.     

The width of the 5.11 MeV state in 10B and isovector parity mixing

We review estimates for effects of parity mixing on the α-capture of vector polarized ⁶Li to the 5.16 MeV, 2⁺, T = 1 state in ¹⁰B. The cross section depends on the ⁶Li polarization direction because of isovector parity mixing with the 5.11 MeV, 2^?, T = 0 state. The effect is enhanced due to isospin conservation. The α-width of the 5.11 MeV state, an important parameter for calculating the enhancement, has been measured to be 0.98 ± 0.07 keV. The consequences of parity mixing are reevaluated using best available values for the relevant parameters.     

On the excitation of isovector dipole strength by inelastic proton scattering in the giant resonance region in light nuclei

A detailed comparison between inelastic α and p scattering in the giant resonance region of ^{24, 26}Mg, ²⁸Si and ⁴⁰Ca shows that there is no evidence for ΔT = 1, E1 excitation in the (p, p′) spectra. This is consistent with DWBA calculations using a recently obtained isovector interaction potential.     

Shell-model study on magnetic dipole excitation of N = 28 isotones

Magnetic dipole excitation of N = 28 isotones — ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr, ⁵⁴Fe and ⁵¹V — is studied in terms of the shell model by assuming $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{n?m}}\text{(}\text{p}\text{3}\text{2}\text{p}\text{1}\text{2}\text{f}\text{5}\text{2}\text{)}{}^{\mathrm{m}}$ configurations with m = 0, 1 and 2 on an inert ⁴⁰Ca core. Strength distributions observed in (e,e′) and (p,p′) experiments are fairly well reproduced. Interference of proton and neutron excitations enhances B(M1) values around E_x = 10 MeV and reduces those of low-lying states. The strength for T = T₀ + 1 states substantially increases when orbital magnetization is not taken into account, whereas no appreciable consequences can be seen for T = T₀ states. In comparison with single-particle model predictions with m = 0, about 20–30% reduction of the total strength is obtained due to ground-state configuration mixing. It is shown that the isoscalar spin component is reduced as well as the isovector one. However, the theoretical total strength is still much larger than experimental values, and coupling with high-lying configurations and possible delta-hole excitation might be required in order to account for the discrepancy. In an odd-mass nucleus ⁵¹V, the ground-state transition strength is distributed continuously over a wide energy range, being very strongly fragmented.     

A comment on the isovector dipole and Gamow-Teller transitions in 90Zr

It is suggested on the basis of transition strength and excitation energy arguments, that the resonance at 18.5 MeV observed in the ⁹⁰Zr(³He, t)⁹⁰Nb-experiment corresponds to a T=4 isovector dipole state.     

A microscopic theory of giant electric isovector resonances

The electric multipole isovector (τ = 1) giant resonances for Δτ_z = 0, ± 1 are studied using the self-consistent HF-RPA theory.The distributions of strength, energies, the isospin compositions and other properties of the J = 0⁺, 1^?, 2⁺ resonances in the ⁴⁸Ca, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb regions are calculated. Sum rules for the charge-exchange Δτ_z = ±1 excitations are derived.     

High-resolution (e,e') study of isovector M1 and M2 transitions in the oxygen isotopes: (III). 18O

The excitation energy region in ¹⁸O from about E_x = 11–27 MeV has been studied with low-momentum transfer, but high-resolution inelastic electron scattering. Two sharp lines are prominent in the spectra, corresponding to the excitation of T = 2 levels at 16.399 ± 0.005 MeV and 18.871 ± 0.005 MeV of J^π = 2^? and 1⁺, respectively. In contradiction to theoretical predictions no more strong M2 transitions could be found. Broad peaks were observed at 18.5, 19.7, 20.2, 22.5 and 23.8 MeV, the latter two are due to the giant dipole resonance as known from photonuclear reactions. The spectra show in addition considerable fine structure and the application of a cross correlation function technique for its analysis resulted in the location of twelve more low multipolarity weak transitions in the excitation energy range between 16 and 19 MeV. Tentative J^π assignments are given for these levels. The spectra of isospin T = 2 states of A = 18 nuclei are discussed in view of the existing experimental and theoretical work. Finally, the pattern of the isovector M1 and M2 strength distributions of all the three oxygen isotopes ^16,17,18O is discussed.     

Semimicroscopic description of giant octupole resonances in deformed nuclei

The strength functions b(E3, ω) are calculated, and the positions and widths of giant octupole resonances in deformed nuclei are found. It is shown that the giant octupole isoscalar resonances have energies (19–20) MeV for the rare-earth nuclei and (17–18) MeV for the actinides and the widths (5–7) MeV. The energies of the giant octupole isovector resonances are defined by the value of the isovector constant κ⁽³⁾₁.     

Collective magnetic dipole transitions: Dependence of the energies and rates on the nuclear effective interaction

The dependence on the properties of the effective interaction of the energies of and excitation strengths to magnetic dipole states in open shell nuclei is studied. In particular the single j-shell for ⁴⁸Ti is used as an example. In this case there are two 1⁺ states with isospin T = 2 and one with isospin T = 3. The conditions for having a strong low-lying collective 1⁺ state are examined. Focus is also given on the excitation strength to the analog T = 3 state since this is of relevance also to β⁺ Gamow-Teller reactions and to double beta decay. It is found that in the rotational limit there is no strength to the T = 3 state and there is an overly strong low-lying 1⁺T = 2 state. This is almost also true for a quadrupole-quadrupole interaction. At the other extreme, as shown by Halse, with a pairing interaction all the strength goes to the T = 3 state. Other interactions considered are pairing plus quadrupole, spin-dependent delta and Kuo-Brown bare and renormalized, and matrix elements taken from the spectrum of ⁴²Sc. It is found that the β⁺ strength can be reduced either by making the two-body J = 2 T = 1 matrix element or J = 1 T = 0 matrix element more attractive, just as was shown by others in heavier nuclei. However such parameter changes have effects on other properties of the 1⁺ spectrum, which can serve as indicators as to whether or not these changes are justified.     

Properties of isovector 1+ states in A=28 nuclei and nuclear muon capture

A method is proposed for taking into account, in a calculation of partial rates of muon capture by nuclei, experimental information about strength functions for Gamow-Teller and isovector M1 transitions. The method, which amounts to choosing an orthogonal transformation that acts in the subspace of wave functions for excited states, requires neither modifying transition operators nor introducing effective charges. The matrix of the above transformation is constructed as a product of the matrices of reflection in a plane. All calculations are performed on the basis of the multiparticle shell model. Numerical results are obtained for isovector states in A=28 nuclei. Strength functions for Gamow-Teller and isovector M1 transitions in ²⁸Si are considered, and the lifetimes of 1⁺ states in ²⁸Al and the branching fractions for gamma decays of this state are calculated. Owing to taking into account experimental information about the properties of isovector states, the branching fractions for the γ decays of the 1⁺ state at 2.201 MeV in ²⁸Al are successfully described for the first time. The above transformation of the wave functions changes substantially the distribution of partial rates of allowed muon capture by a ²⁸Si nucleus among the 1⁺ states of the final nucleus ²⁸Al in relation to the results of the calculations with the eigenfunctions of the Hamiltonian of the multiparticle shell model. The muon-capture rates calculated with the transformed functions agree well with experimental data.     

Lifetime measurements of levels in 34Ar: Isoscalar and isovector matrix elements for E2 analogue transitions

Mean lifetimes have been measured for the low-lying levels in ³⁴Ar(T_z = ? 1) excited by the bombardment of ³He-implanted Au targets with a beam of 80 MeV ³²S. The lifetimes determined by fitting Doppler-broadened γ-ray lineshapes are as follows (E_x in keV, τ in fs): 2091, 460 ± 60; 3288, 280 ± 50; 3871, > 270 and 4128, 1301⁺¹⁷⁰_?130. The resulting transition matrix elements for the 2⁺₁ → 0⁺₁ and 2⁺₂ → 0⁺₁ transitions are compared with those for the analogue transitions in ³⁴S (T_z = + 1) and ³⁴Cl(T_z = 0) to determine the isoscalar and isovector components. The component values are compared with theoretical calculations and with values of the ratio of neutron to proton matrix elements determined by inelastic scattering with strongly interacting probes.     

Competition of isoscalar and isovector proton-neutron pairing in nuclei

We use shell model techniques in the complete pf shell to study pair correlations in nuclei. Particular attention is paid to the competition of isoscalar and isovector proton-neutron pairing modes which is investigated in the odd-odd N = Z nucleus ⁴⁶V and in the chain of even Fe-isotopes. We confirm the dominance of isovector pairing in the ground states. An inspection of the level density and pair correlation strength in ⁴⁶V, however, shows the increasing relative importance of isoscalar correlations with increasing excitation energy. In the Fe-isotopes we find the expected strong dependence of the proton-neutron isovector pairing strength on the neutron excess, while the dominant J = 1 isoscalar pair correlations scale much more gently with neutron number. We demonstrate that the isoscalar pair correlations depend strongly on the spin-orbit splitting.     

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”).     

Nuclear viscosity and widths of giant resonances

We write down a set of coupled hydrodynamic equations of the Navier-Stokes type which describe the motion of two compressible, viscous nuclear fluids. The solutions of these equations give rise to giant resonances of both isoscalar and isovector type. The viscosity terms in the equations are responsible for the damping of these resonances. Within this framework we obtain expressions for the width of the resonances as a function of the mass number A, and relations between the widths and the excitation energies for various multipolarities (J = 0⁺, 1^?, 2⁺, 3^?, 4⁺), and isospins (T = 0,1). The A dependence of the calculated widths exhibit the experimental trends of the giant dipole and isoscalar quadrupole widths. Also, as a result of the calculation we obtain estimates of the values of viscosity coefficients in nuclei.     

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.     

Investigation of giant E3 resonances by (N, γ) reactions

Effects related to the presence of giant E3 resonances are investigated by nucleon radiative capture according to the direct-semidirect model. The γ-ray angular distributions from the ²⁰⁸Pb(N, γ₀) reactions are calculated in the energy region above the giant dipole resonance and the influence of the E1–E3 and E2–E3 interferences is discussed. The results provide indications of an appreciable effect on the 90° photon emission when a collective isovector E3 excitation is present.     

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.     

Relativistic mean-field description of collective motion in nuclei: the pion field

The influence of the pion field on isovector dipole and spin-dipole collective oscillations is investigated in a time-dependent model based on relativistic mean field theory. We find that the inclusion of the long range pion-nucleon interaction provides an additional strong damping mechanism for the isovector dipole vibrations. The inclusion of the pion field has also a strong effect on the dynamics of spin-dipole vibrations, and in particular on the splitting of excitation energies of theJ ^π (0^?,1^?,2^?) components of the isovector spin-dipole resonance.