Giant Dipole Resonance States Research Articles

The pygmy dipole resonance in neutron-rich nuclei

The pygmy dipole resonance (PDR), which has been observed via the enhancement of the electric dipole strength E1 of atomic nuclei, is studied within a microscopic collective model. The latter employs the Hartree-Fock (HF) method with effective nucleon-nucleon interactions of the Skyrme types plus the random-phase approximation (RPA). The results of the calculations obtained for various even-even nuclei such as 16-28O, 40-58Ca, 100-120Sn, and 182-218Pb show that the PDR is significantly enhanced when the number of neutrons outside the stable core of the nucleus is increased, that is, in the neutron-rich nuclei. As the result, the relative ratio between the energy weighted sum of the strength of the PDR and that of the GDR (giant dipole resonance) does not exceed 4%. The collectivity of the PDR and GDR states will be also discussed.

Sum Rules of the Multiple Giant Resonance States

Various sum rules for multiple giant dipole resonance states are derived. For the triple giant dipole resonance states, the energy-weighted sum of the transition strengths requires a model to be related to those of the single and double giant dipole resonance states. It is also shown that the non-diagonal matrix elements of the double commutator between the dipole operator and the nuclear Hamiltonian give useful identities for the excitation energy and transition strength of each excited state. Using those identities, the relationship between width of the single dipole state and those of the multiple ones is qualitatively discussed.

Transitions between complex configurations in the excitation of the double giant resonance

The transitions between complex configurations, to which the giant dipole resonance (GDR) and the double giant dipole resonance (DGDR) doorway states are coupled, are taken into account in second order perturbation theory for the reaction amplitude. It is proved that only transitions between GDR and DGDR doorway states play an essential role in the Coulomb excitation of the DGDR.

E1 transitions in rare earth nuclei and the SPDF boson model

Electric-dipole (E1) transitions between low-lying states of well deformed rare-earth nuclei are investigated using an SPDF boson model. The model can treat both the high-lying Giant Dipole Resonance (GDR) and the low-lying octupole vibrational bands. The p- boson is related to the GDR state while the f- boson is to the octupole vibration. The E1 operator T( E1) consists of p and f boson terms; the two p boson terms are determined by the experimental data on the GDR states. The remaining ƒ → d E1 transition charge is determined by fitting experimental B( E1) values between low-lying collective states. The present method has been applied to 156Gd, whose low-energy positive parity bands are well described by the SU(3) limit of IBM. It has been found that the E1 operator determined in this way gives the spin dependence of the B( E1) branching ratios close to the experimental results.

Microscopic origin of the giant resonance structure

Microscopic calculations of the fine structure of giant resonances for spherical nuclei are presented. Excited states are described by wave functions which take into account the coupling of simple one-phonon configurations with two-phonon states. Few examples are presented: the γ-decay of resonances to the ground and low-lying excited states and the relativistic Coulomb excitation of the double giant dipole resonance states.

The potential energy surfaces and the giant dipole resonances of46,48,50Ti

The low energy and giant dipole resonance properties of46,48,50Ti have been investigated within the framework of the collective model of Gneuss and Greiner. The starting potential energy surfaces were taken from Rebel and Habs from which the low energy properties were compared with both an asymmetric rotator model and a shell model calculation. The giant dipole absorption cross sections compared favourably with the experimental data. However, the scarcity of data relating to theγ-scattering from the giant dipole resonance states to the low lying levels made any detailed comparison incomplete.

Photoneutron cross sections forO17

Photoneutron cross sections involving the emission of one and two neutrons from $^{17}\mathrm{O}$ have been measured over the energy interval 8.5 to 39.7 MeV using monoenergetic photons from positron in-flight annihilation. The 6-MeV wide giant dipole resonance is observed to be centered at 23 MeV and a pygmy resonance is seen at about 13 MeV. Such structure as is apparent in the cross sections is not as pronounced as for the cases of $^{16}\mathrm{O}$ and $^{18}\mathrm{O}$. Comparison of the total photoneutron cross section with recent ground-state data indicates that much of the pygmy resonance decays to the ground or first excited state of $^{16}\mathrm{O}$, but that the giant dipole resonance decays mainly to highly excited states in the daughter. Excellent agreement is observed between the present results and a recent two-particle, one-hole shell-model calculation of the isospin-split giant dipole resonance states for this nucleus. New photoneutron cross-section results for $^{16}\mathrm{O}$ up to 39.7 MeV are reported as well.NUCLEAR REACTIONS $^{17}\mathrm{O}(\ensuremath{\gamma},n)$, ${E}_{\ensuremath{\gamma}}=8.5\ensuremath{-}39.7$ MeV and $^{16}\mathrm{O}(\ensuremath{\gamma},n)$, ${E}_{\ensuremath{\gamma}}=15.9\ensuremath{-}39.7$ MeV; measured $4\ensuremath{\pi}$ neutron yield for monenergetic photons; $\ensuremath{\sigma}({E}_{\ensuremath{\gamma}},1n)$, $\ensuremath{\sigma}({E}_{\ensuremath{\gamma}},2n)$, integrated cross sections, isospin splitting of the giant resonance for $^{17}\mathrm{O}$.

A measurement of the 50Ti(γ, n) and 50Ti(γ, n 0) cross sections

Measurements of the 50Ti(γ, n) and 50Ti(γ, n 0) cross sections have been made in the energy range of the giant dipole resonance (GDR). Assuming the GDR is split into two isospin components, approximated as Lorentzians, a calculation based on statistical decay of the GDR states is consistent with the experimental results.

The radiative capture reactions 40Ca(α, γ)44Ti and 48Ca(α, γ)52Ti in the region of the giant dipole resonance

Abstract An investigation of the reactions 40Ca(α,γ)44Ti and 48Ca(α,γ)52Ti in the region of the giant dipole resonance (GDR) has been completed. For the 40Ca(α,γ) reaction, 90° excitation functions over the bombarding energy range 6.5–17.5 MeV were obtained for γ- transitions to the ground state and first excited state in 44Ti and for a sum of the unresolved transitions to the third and fourth excited states in 44Ti. Angular distributions were measured at the extrema of the excitation functions. These data suggest that the 40Ca(α,γ) reaction proceeds predominantly via an isospin forbidden El transition and populates the T = 1, GDR states of 44Ti via T = 0 isospin impurities. The results provide an estimate of the isospin mixing in the GDR as well as support for a possible giant quadrupole resonance somewhat lower in excitation energy in 44Ti. The excitation functions exhibit a gross structure which reflects the isospin mixing in the GDR of 44Ti, and a structure of intermediate width which may reflect T = 0 α- cluster states in 44Ti. The 48 Ca (α,γ o ) differential cross section was investigated at 90° over the bombarding energy range 6.0–14.0 MeV. The cross section for the isospin allowed 48 Ca (α γ 0 ) reaction was found to be a factor of 20 smaller than that for the isospin forbidden 40 Ca (α,γ 0 ) reaction.

The 36Ar(α, γ 0) 40Ca reaction at excitation energies in the region of the giant dipole resonance

The differential cross section for the 36Ar(α, γ 0) 40Ca reaction was measured at 90° to the beam direction in 125 keV, 50 keV and 50 keV intervals over the bombarding energy ranges 6–17 MeV, 6.54–8.81 MeV and 11.67–13.65 MeV, respectively. Gamma-ray angular distributions were measured at eighteen bombarding energies. The results indicate that the reaction proceeds through isolated 1 − levels and to a lesser extent 2 + levels. Excitation energies and partial decay widths for the 1 − levels are presented. From a comparison of the 36Ar(α, γ o0 40Ca, 39K(p,γ 0) 40Ca and 40Ca(γ, n 0) 39Ca excitation functions, it is shown that the α-capture reaction most probably leads to exciting the predominantly T = 1 giant dipole resonance states through a T = 0 isospin impurity. The result presented here, that the α-reduced widths decrease by a factor of 40 over the excitation energy region considered, is discussed with regard to variations in the degree of isospin mixing with energy and a shell-model calculation.

Calculation of photonuclear resonance cross sections by coupled channel reaction theory

The methods of nuclear reaction theory are applied to calculate the properties of giant dipole resonance states in 16O. The resonances are treated as scattering states in which a nucleon interacts with the corresponding mass-15 system and induces various nuclear reactions in the channels with total quantum numbers J π = 1 −. The wave functions produced by this model are used to compute several photonuclear cross sections for a range of energies.