Dipole Resonance States Research Articles

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.

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 $^{17}\mathrm{O}$.

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.

Isospin and spin-isospin dipole oscillations in12C

Recent measurements of the cross-sections for excitation of 12C by electron scattering provide us with values of the longitudinal form factor tZZ(q, Ex) and transverse form factor i~r(q, Ex) for values of the excitation energy Ex in the giant resonance region and large values of momentum transfer q(> 0.5 fm-1). The longitudinal form factor F z is due to the isospin dipole oscillation (T-mode oscillation), while the transverse form factor F r is due to the spin-isospin dipole oscillation (aT-mode oscillation) as well as the v-mode oscillation. Since the q dependence of the oscillator strength for the ~v-modc differs from that for the T-mode, _F~(q, Ex) for large q (> 0.5 fln -1) is mainly due to the ~v-mode oscillation and F for small q to the T-mode oscillation--_~(q, Ex) is related to Fz(q, Ex) through the Siegert theorem in the limit of q-* 0. Figure 1-1 and Fig. 1-2 show the experimental values (1) of F~(q, Ex) ~nd F~(q, Ex) as a function of Ex for a fixed value of q(~ 0.75 fm-1). Since q is large, i~(q, Ex) (Fig. 1-2) gives us information on the strength of the ~v-mode oscillations, while Fz (q, Ex) is related to the strength of the v-mode oscillation. In Fig. 1-1 there are three peaks of i~Z(q, Ex) at Ex : 22.0, 23.8 and 25.5 MeV, which are experimentally identified as the dipole resonance states (1-). If we compare these with the doubly-split giant resonance observed in the photo-excitation of ~2C, the two lower peaks (22.0 and 23.8 MeV) together should correspond to the lower peak (~-~ 23 MeV) and the 25.5 ~ e V peak to the higher peak of the photo-excitation. In Fig. 1-2 we also find the two small corresponding peaks of F~(q, Ex) at Ex ~ 23 MeV and 25.5 MeV. These two peaks are also seen more clearly in the Stanford data for q ~ 0.54 fm -1 (2). Therefore, some dipole states with large oscillator strength of the ~v-mode must exist in the region of the lower peak (~-~ 23 MeV) as well as the higher peak (~ 25.5 MeV) of the giant resonance. Likewise, there should be some dipole states with large oscillator strength of the v-mode in the both regions. Previous calculations of the form factors for photo-excitation of ~2C based on the conventional j-j coupling shell model (~) could not obtain the large second peak at

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.

16O dipole resonance states

A one-step calculation for 16O(γ,n) 15O is attempted considering a coupling between different channels in final states. Our calculation method allows a unified description of both discrete and continuous levels.