Isovector Giant Resonance Research Articles

Macroscopic models for charge exchange reactions in N ≠ Z nuclei

Vlasov equations in the isospin channels are derived in the framework of the time dependent Hartree-Fock theory. The local equilibrium (hydrodynamic) approximation is then considered and applied to study isovector giant resonances excited in charge exchange reactions and μ − inclusive capture in N ≠ Z nuclei. The theoretical predictions well account for the observed energy splitting between different isospin fragments and for the quenching of the ΔT Z = + 1 strength.

Isovector giant resonances in light nuclei observed by ( 7Li, 7Be) reaction

Isovector giant resonances were studied with the ( 7Li, 7Be) reaction on 12C, 24Mg, 27Al, 28Si and 48Ti at an incident energy of 150 MeV. Differential cross sections were measured at forward scattering angles including 0°. We observed the octupole resonance at E x ∽ 16 MeV and the giant dipole resonance at E x ∽ 20 MeV in all residual nuclei.

(n, p) studies at the University of California at Davis

In recent years, we have been developing facilities for studying neutron-induced reactions at energies near 60 MeV. An important aspect of this program has been the development of capabilities for (n, p) reaction studies. Early data on a range of nuclei taken first with simple telescopes and later with large-area multiwire chamber telescopes are presented. Recently, a magnet and dual target system have been installed, which allow (n, p) measurements down to 0°. Spectra have been measured for 12C, 13C, 14C, and 90Zr(n,p) for 0°–40° at 65 MeV. The 90Zr data confirm the recently discovered isovector monopole resonance and provide evidence for two new isovector giant resonances: the spin monopole and the isospin T + 1 component of the quadrupole.

Spreading widths of isobaric analog states and the isovector giant monopole resonance

A global analysis of the experimental spreading widths Γ ↓ of 65 isobaric analog states (IAS) in the range A = 110 to 238 has been performed assuming isospin mixing via the Coulomb force with T < = T 0−1 doorway states mediated by coupling to the ( T 0−1)-component of the giant isovector monopole resonance (IVM). Excellent agreement has been achieved over the entire range, thus establishing general smooth trends for the parameters describing the resonance. The excitation energy of the resonance, E( IVM)≈V 0/A 1 3 −(T 0+1)V 1/A was found to reproduce the IAS data with V 0 in the range 155 to 170 MeV and V 1≈55 MeV. These values are taken from recent theoretical estimates of Auerbach and the extreme hydrodynamical estimate of Bohr, Damgaard and Mottelson. The charge-dependent matrix elements were found factors of two to three stronger than hydrodynamic or microscopic estimates, but in almost perfect agreement with an expression based on sum rules derived by Lane and Mekjian. A strength-function approach developed by MacDonald and Birse for the damping widths of isovector monopole resonances was successfully employed. However, it became necessary to introduce an explicit dependence on nuclear deformation to describe a splitting of the IVM strength due to coupling to the β-vibration component of the isovector quadrupole resonance (IVQ). The postulated β-dependence describes the strong increase with neutron excess of the spreading widths for several rare-earth nuclei, and an essentially one-parameter fit to all experimental spreading widths gives χ 2/⨍ ≈ 1.2 . It is further concluded that the density of doorway states which are responsible for the isospin mixing is much lower than the density of all underlying states of lower isospin with the same spin and parity as the IAS, and the ratio decreases exponentially with increasing excitation energy.

Excitation of isovector giant resonances in pion single-charge exchange at 120, 165, and 230 MeV.

We have measured doubly differential cross sections for the (${\ensuremath{\pi}}^{+}$,${\ensuremath{\pi}}^{0}$) and (${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$,${\ensuremath{\pi}}^{0}$) reactions at 120- and 230-MeV kinetic energies for $^{40}\mathrm{Ca}$, $^{60}\mathrm{Ni}$, and $^{120}\mathrm{Sn}$. Nuclear-excitation energies up to 60 MeV were observed. We have extracted excitation energies, widths, and maximum cross sections for the isospin components of the isovector monopole resonance and the isovector dipole resonance. The excitation energies and widths from the present data and from earlier measurements at 165 MeV are compared and found to be in agreement. The cross sections for the isovector monopole and isovector dipole resonances show the same increase with bombarding energy in all targets. No isovector quadrupole strength is required to fit the experimental data. We compare the energy dependences of the isovector-resonance cross sections with those of isobaric-analog states, and to distorted-wave impulse approximation calculations.

Measurements on isovector giant resonances in pion charge exchange.

We measured the energies, widths, and cross sections of the isovector monopole and dipole resonances in various nuclei between $^{40}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ with the reactions (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$,${\ensuremath{\pi}}^{0}$). Both resonances exhaust approximately the same substantial fraction of the cross section calculated in a random-phase-approximation--distorted-wave-impulse-approximation model. The excitation energies and widths of the monopole and dipole are in good agreement with random-phase-approximation calculations and for the dipole they are also in agreement with other data. No isovector quadrupole resonance was observed, and the upper limits for the cross sections for the light elements are well below the sum rule strength for the isovector monopole and giant dipole resonance.

Surface and elastic effects in isovector giant resonances.

The role of elastic and surface effects in the isovector collective excitations is investigated by using a sum rule approach. Simple and accurate relations among the frequencies of different giant resonances are derived. The recently observed M1 rotational state in deformed nuclei is also discussed.

Excitation of isovector giant resonances in 27Al by heavy ion charge exchange reaction.

Excitation of isovector giant resonances in $^{27}\mathrm{Al}$ was studied by using the $^{27}\mathrm{Al}$${(}^{7}$Li, $^{7}\mathrm{Be}$${)}^{27}$Mg reaction at incident energies of 100, 150, and 180 MeV. We observed the analog of the giant dipole resonance at ${E}_{x}$=14.3 MeV in $^{27}\mathrm{Mg}$. From the observed excitation function, we suggest that a peak at ${E}_{x}$=9.5 MeV is a resonance with a higher multipolarity than one. In the excitation energy region higher than the giant dipole resonance, no resonance was observed.

Two-fluid model description of isovector giant resonances in fast rotating nuclei

Isovector giant resonances of arbitrary multipolarity in fast rotating nuclei are studied by solving the inviscid two-fluid equation of relative motion in a rotating frame of reference. Both Coriolis and centrifugal forces are taken into account. The resulting expressions display in a quite simple way general features of giant multipole resonances of fast rotating nuclei, in addition to a good agreement with other calculations for the giant dipole resonance. Typical values for the resonance energies and their fragmentation due to nuclear deformation and rotation are given. In particular, enormously large resonance splitting should occur in the superdeformed states.

Comment on "(p,n) and (n,p) reactions as probes of isovector giant monopole resonances"

The importance of medium corrections in the excitation of the isovector giant monopole resonance by nucleons is investigated. A large reduction of the cross section, compared to calculations with free t matrices, is found at projectile energies around 100 MeV. This will make observation of the isovector monopole at these energies even more difficult than estimated by Auerbach et al. .AE

Reply to "Comment on `(p,n) and (n,p) reactions as probes of isovector giant monopole resonances' "

The role of medium corrections in isovector excitations induced by the (p,n) reaction near 120 MeV is examined in light of the preceding Comment by Bauhoff which addresses the issue of making reliable estimates of the sizes of (p,n) cross sections for exciting isovector monopole resonances. To establish confidence in such estimates it is important to examine in parallel the much better understood isobaric analog of the ground state and the relative importance of medium modifications on these monopole transitions. Our examination using both density-independent and density-dependent transition operators supports the assertion of Bauhoff.

ISOSPIN STRUCTURE OF GIANT RESONANCES

We analyze the isospin structure of isovector giant resonances. We set-up a theory, based on sum rules, to predict the centroid energies and the strengths of the various fragments, for a given Hamiltonian. Different operators are discussed and explicit examples are worked out.

(p,n) and (n,p) reactions as probes of isovector giant monopole resonances

Nucleon charge exchange reactions are explored as prospective probes of isovector giant monopole resonances. Using charge exchange transition densities based on random-phase approximation sum rules, distorted wave impulse approximation calculations are made for the (p,n) and (n,p) reactions exciting the isovector giant monopole resonances in several nuclei at bombarding energies of 120 and 800 MeV. Based on our calculations, the charge exchange reactions at 800 MeV appear more promising.

Coulomb displacement energies and decay widths of isobaric analog states from Sm( 3He, t) at θ = 0°

The 144,147,148,149,150,154Sm( 3He, t) 144,147,148,149,150,152,154Eu reactions leading to ground-state isobaric analog states (IAS) have been studied at θ = 0° and E(3He) = 45.9 MeV. The Coulomb displacement energies decrease more rapidly than A −1 3 . Approximately 110 keV of the total decrease of about 470 keV from A = 144 (spherical) to A = 154 (deformed) can be ascribed to deformation. No discontinuity is apparent at the transition from spherical to deformed shapes at N = 88–90. This is attributed to two effects: (i) rms radii increase with static deformations and with dynamical vibrations; (ii) Coulomb displacement energies depend on rms charge radii and on the rms radii of the neutron excess. The data suggest neutron deformations greater than proton deformations for A = 148 and 150 but smaller for A = 152 and 154. The IAS widths increase from ∼30 keV to ∼90 keV and can be attributed to mixing with the ( T 0−1) component of a proposed isovector giant monopole resonance.

Transition densities for charge-exchange components of giant isovector resonances and the proton-neutron density distributions in nuclei

Sum rules that hold in the case of a self-consistent charge-exchange random-phase approximation theory are used here to derive transition densities for the charge-exchange components of isovector giant resonances. The derived transition densities are then employed in a calculation of (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}, {\ensuremath{\pi}}^{0}$) cross sections.NUCLEAR STRUCTURE Transition densities to giant resonances are obtained from sum rules.

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.

Excitation of analog isovector giant resonances via the (n, p) reaction on 14N and 16O at 60MeV

Data were accumulated for the (n, p) reaction on 14N and 16O using 60MeV neutrons. Angular distributions of the cross sections for eight proton groups were extracted and compared to distorted-waves Born approximation (DWBA) calculations using a simple macroscopic model. Enhancements in the spectra were seen in each case in the region of excitation corresponding to the giant dipole resonance (GDR) of the target nucleus. DWBA calculations show that these excitations are primarily dipole and favor the use of the Goldhaber-Teller form factor. Comparison with photo-absorption measurements suggests that there may also be significant contributions to the (n, p) reaction from “spin-flip” dipole excitations. The other proton groups could be correlated with the results of other experiments and include excitations of analogs of the giant isovector “magnetic” dipole mode of 14N.

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.

Dynamics of nuclear fluid. VII. Isovector, spin-vector, and spin-isovector giant multipole resonances as elastic vibrations

Previously, we studied the isoscalar giant resonances as the elastic vibration of a nucleus, the peculiar properties of elasticity being a manifestation of the quantum stress tensor. We examine here the other types of collective vibrations involving elastic spin and isospin waves. Relevant electric and magnetic multipole states for the isovector, the spin vector, and the spin-isovector modes are determined. We find that for a given electric or magnetic state with multipolarity l different from zero, the lowest eigenenergies for the different modes of giant resonances (isoscalar, isovector, spin-vector, and spin-isovector) are approximately degenerate. On the other hand, the l/sup ..pi../ = 0/sup +/ states depend on the nuclear incompressibility and the symmetry energy coefficients. Their eigenenergies can be quite different. The theoretical eigenenergies for the giant isovector electric multipole states compare well with experimental data.

Strong-absorption signature of giant-resonance excitation in pion-nuclear reactions

Predictions of the eikonalized strong-absorption model for the small-angle excitation of isovector giant-resonance states, as well as for analog states, are given for pion-nuclear single-charge-exchange reactions. Spin-flip excitations are treated, particularly in connection with the recent observation of the giant dipole resonance in (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$,${\ensuremath{\pi}}^{0}$) on $^{40}\mathrm{Ca}$. The results trivially generalize to excitation of isoscalar resonances.NUCLEAR REACTIONS Pion single-charge-exchange; strong-absorption model. Excitation of giant-resonance states.