High-energy Octupole Resonance Research Articles

Вихрова октупольна мода у кінетичній моделі колективних збуджень в ядрах

The nature of a new isoscalar octupole resonance found within a kinetic model based on the Vlasov equation for finite Fermi systems with moving surfaces is studied. It is shown that this octupole resonance is due to dynamic effects of the nuclear surface, like the low-energy isoscalar dipole resonance (vortex dipole mode) observed in heavy nuclei. It is found that the velocity field associated with the new octupole resonance has a vortex character in the surface region of the nuclear liquid and, moreover, the vortex motion of nucleons is fragmented into three areas near the nuclear surface. At the same time, the velocity field associated with the high-energy octupole resonance found within our kinetic model displays an octupole deformation form and includes a compression within the nuclear fluid, which is consistent with the corresponding quantum calculations in the random phase approximation.

Shape evolution of giant resonances in Nd and Sm isotopes

Giant multipole resonances in Nd and Sm isotopes are studied by employing the quasiparticle-random-phase approximation on the basis of the Skyrme energy-density-functional method. Deformation effects on giant resonances are investigated in these isotopes which manifest a typical nuclear shape change from spherical to prolate shapes. The peak energy, the broadening, and the deformation splitting of the isoscalar giant monopole (ISGMR) and quadrupole (ISGQR) resonances agree well with measurements. The magnitude of the peak splitting and the fraction of the energy-weighted strength in the lower peak of the ISGMR reflect the nuclear deformation. The experimental data on ISGMR, ISGDR, and ISGQR are consistent with the nuclear-matter incompressibility $K \simeq 210-230$ MeV and the effective mass $m^*_0/m \simeq 0.8-0.9$. However, the high-energy octupole resonance (HEOR) in $^{144}$Sm seems to indicates a smaller effective mass, $m^*_0/m \simeq 0.7-0.8$. A further precise measurement of HEOR is desired to determine the effective mass.

Recoil-corrected continuum shell model calculations for11B(p,n)11C,11B(p,p′)11B*,12C(e,e′x)

Background: The recoil-corrected continuum shell model provides coupled-channels solutions for bound and unbound wave functions from realistic effective interactions. The wave functions are antisymmetric and contain no spurious components because the calculations are performed in the center-of-mass system.Purpose: This model has now been extended to include 1$\ensuremath{\hbar}\ensuremath{\omega}$ excitations in the structure of $p$-shell target (residual) nuclei, hence allowing 0$s$-shell knockout processes. Several reactions involving the ${}^{12}$C compound system are investigated to demonstrate the utility of the model.Methods: The states of ${}^{11}$B and ${}^{11}$C are constructed in the nonspurious 0$\ensuremath{\hbar}\ensuremath{\omega}$ plus 1$\ensuremath{\hbar}\ensuremath{\omega}$ model space. An interaction, fitted to Cohen and Kurath (8-16) plus Reid soft core $g$-matrix elements, is employed. One nucleon is coupled to these states to create a basis for the bound and scattering states for ${}^{12}$C.Results: Calculated elastic and inelastic cross sections agree well with available data. The calculated transverse response at high momentum transfer is lower than that extracted from data. Although significant, meson exchange currents are not sufficient to give agreement with data. Likewise inclusion of 0$s$-shell knockout is not sufficient to provide agreement. The high-energy octupole resonance appears at low momentum transfer and an energy of 106/${A}^{1/3}$.Conclusions: The model should provide meaningful predictions for states near the proton drip line via the ($p$,$n$) reaction. Coupled-channels solutions are necessary for describing ${}^{12}$C($e$,${e}^{\ensuremath{'}}x$) at low momentum transfer. Lack of strength at low energy and momentum transfer in optical model calculations of ${}^{12}$C($e$,${e}^{\ensuremath{'}}x$) is at least partly attributable to the omission of giant resonances. Data for (${\ensuremath{\pi}}^{+}$,${\ensuremath{\pi}}^{+\ensuremath{'}}p$)/(${\ensuremath{\pi}}^{\ensuremath{-}}$,${\ensuremath{\pi}}^{\ensuremath{-}\ensuremath{'}}p$) could verify this conclusion. Lack of strength in the transverse response may be attributable to recoil terms which are omitted in most calculations.

Self-consistency and search for collective effects in semiclassical pairing theory

A simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter, is used to study the effects of a self-consistent pairing interaction on the nuclear response. Effects due to the finite size of nuclei are suitably taken into account. The semiclassical equations of motion derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov problem are solved in an improved (linear) approximation in which the pairing field is allowed to oscillate and to become complex. The new solutions are in good agreement with the old ones and also with the result of well-known quantum approaches. The role of the Pauli principle in eliminating one possible set of solutions is also discussed. The pairing-field fluctuations have two main effects: they restore the particle-number symmetry which is broken in the constant-$\Delta$ approximation and introduce the possibility of collective eigenfrequencies of the system due to the pairing interaction. A numerical study with values of parameters appropriate for nuclei, shows an enhancement of the density-density strength function in the region of the low-energy giant octupole resonance, while no similar effect is present in the region of the high-energy octupole resonance and for the giant monopole and quadrupole resonances.

The effect of deformation in the isoscalar giant dipole resonance

Background-free inelastic scattering spectra have been obtained for144,148,150,152,154Sm with 386 MeV α particles at forward angles (including 0°) to investigate the effect of deformation on the isoscalar giant dipole resonance. The strength distributions for isoscalar giant resonances have been extracted via a multipole decomposition analysis using angular distributions calculated in the framework of the density-dependent single-folding model. The effects of deformation are found to be different for the low- and high-excitation energy components of the isoscalar giant dipole resonance. Evidence has been obtained for the theoretically-predicted mixing between the isoscalar giant dipole resonance and the high energy octupole resonance.

The effect of deformation in the isoscalar giant dipole resonance

Background-free inelastic scattering spectra have been obtained for 144,148,150,152,154 Sm with 386 MeV α particles at forward angles (including 0°) to investigate the effect of deformation on the isoscalar giant dipole resonance. The strength distributions for isoscalar giant resonances have been extracted via a multipole decomposition analysis using angular distributions calculated in the framework of the density-dependent single-folding model. The effects of deformation are found to be different for the low- and high-excitation energy components of the isoscalar giant dipole resonance. Evidence has been obtained for the theoretically-predicted mixing between the isoscalar giant dipole resonance and the high energy octupole resonance.

The effect of deformation in the isoscalar giant dipole resonance

Background-free inelastic scattering spectra have been obtained for 144,148,150,152,154Sm with 386 MeV α particles at forward angles (including 0°) to investigate the effect of deformation on the isoscalar giant dipole resonance. The strength distributions for isoscalar giant resonances have been extracted via a multipole decomposition analysis using angular distributions calculated in the framework of the density-dependent single-folding model. The effects of deformation are found to be different for the low- and high-excitation energy components of the isoscalar giant dipole resonance. Evidence has been obtained for the theoretically-predicted mixing between the isoscalar giant dipole resonance and the high energy octupole resonance.

Systematic study ofL⩽3giant resonances in Sm isotopes via multipole decomposition analysis

Background-free inelastic scattering spectra have been obtained for five Sm isotopes with $386\text{\ensuremath{-}}\text{MeV}$ $\ensuremath{\alpha}$ particles at forward angles (including $0\ifmmode^\circ\else\textdegree\fi{}$) to investigate the effect of deformation on the compressional-mode giant resonances. The strength distributions for the $L\ensuremath{\leqslant}3$ isoscalar giant resonances have been extracted via a multipole decomposition analysis using angular distributions calculated in the framework of the density-dependent single-folding model. We observed a splitting of the giant monopole resonance because of its mixing with the giant quadrupole resonance. For the isoscalar giant dipole resonance, the observed effects of deformation are different for the low- and high-excitation-energy components. Evidence has been obtained for the theoretically predicted mixing between the isoscalar giant dipole resonance and the high energy octupole resonance.

Compressional-mode giant resonances in deformed nuclei

Background-free inelastic scattering spectra have been obtained for the Sm isotopes with 400 MeV α particles at forward angles (including 0°) to investigate the effect of deformation on the compressional-mode giant resonances. The strength distributions for the isoscalar giant resonances (L⩽3) have been extracted for the spherical nucleus 144Sm and the deformed nucleus 154Sm. We have observed that the effects of deformation are different for the low- and high-excitation-energy components of the isoscalar giant dipole resonance in 154Sm. Evidence for the theoretically predicted coupling between the isoscalar dipole resonance and the high-energy octupole resonance is reported.

Isoscalar giant dipole resonance in 90Zr, 116Sn, 144Sm and 208Pb excited by 240 MeV α particle scattering

The giant resonance regions of 90Zr, 116Sn, 144Sm and 208Pb were investigated using 240 MeV α particle scattering at small angles including 0°. E1 strengths corresponding to 91±11%, 89±10%, 105±12% and 95±13% of the isoscalar E1 energy-weighted sum rule were identified beteen 18≤E x≤31 MeV, 16≤E x≤30 MeV, 15≤E x≤27 MeV and 15≤E x≤25 MeV with centroid energies of 24.8±0.4 MeV, 22.5±0.3 MeV, 21.6±0.3 MeV and 19.3±0.3 MeV and rms widths of 3.2±0.2 MeV, 3.5±0.2 MeV, 3.2±0.2 MeV and 2.5±0.2 MeV for 90Zr, 116Sn, 144Sm and 208Pb, respectively. Parameters obtained for the isoscalar giant monopole resonance, isoscalar giant quadrupole resonance and high energy octupole resonance are in agreement with accepted values.

Folding model analysis of the excitation of low-lying states and the high energy octupole resonance in116Snby 240 MeV α scattering

The sum rule strength of the high energy octupole resonance (HEOR) and the transition rates of low-lying ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states of ${}^{116}\mathrm{Sn},$ excited by 240 MeV \ensuremath{\alpha} scattering, have been determined from deformed potential and folding model analyses. Deformed potential cross sections for both the low-lying ${3}^{\ensuremath{-}}$ state and the HEOR are greater than folding cross sections by a factor of 1.18. The high energy octupole resonance was found to exhaust $(70\ifmmode\pm\else\textpm\fi{}15)%$ and $(83\ifmmode\pm\else\textpm\fi{}15)%$ of the $E3$ energy-weighted sum rule from the two analyses, respectively. The data for the low-lying states are fit well by the calculations made with both models using electromagnetic values for the transition rates. Optical-model parameters were obtained from fits to elastic scattering data. The differential cross sections for the elastic scattering and inelastic scattering exciting the low-lying ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states in ${}^{116}\mathrm{Sn}$ were measured over the angle range from ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=1.6\ifmmode^\circ\else\textdegree\fi{}$ to 35.2\ifmmode^\circ\else\textdegree\fi{}.

Evidence for the Isoscalar Giant Dipole Resonance in208PbUsing InelasticαScattering at and near 0°

The isoscalar giant dipole resonance (ISGDR) in ${}^{208}\mathrm{Pb}$ has been investigated using inelastic scattering of 200 MeV $\ensuremath{\alpha}$ particles at and near 0\ifmmode^\circ\else\textdegree\fi{} where the angular distribution of the ISGDR can be clearly differentiated from those of other modes. The ``difference of spectra'' technique was employed to separate the ISGDR from the high-energy octupole resonance (HEOR). These data provide the clearest evidence yet for the ISGDR adjacent to the HEOR. With these results, all expected isoscalar $\ensuremath{\lambda}\ensuremath{\le}3$ resonances in ${}^{208}\mathrm{Pb}$ have been identified.

High energy octupole resonance in 116Sn.

The region of excitation energy from 7\ensuremath{\le}${\mathit{E}}_{\mathit{x}}$\ensuremath{\le}38 MeV in $^{116}\mathrm{Sn}$ was studied with inelastic scattering of 240 MeV \ensuremath{\alpha} particles. Parameters obtained for the isoscalar giant monopole resonance and the isoscalar giant quadrupole resonance are in agreement with accepted values. A peak exhausting (67\ifmmode\pm\else\textpm\fi{}10)% of the E3 energy-weighted sum rule at ${\mathit{E}}_{\mathit{x}}$=21.8\ifmmode\pm\else\textpm\fi{}0.5 MeV with width \ensuremath{\Gamma}=7.1\ifmmode\pm\else\textpm\fi{}0.5 MeV was identified as the isoscalar high energy octupole resonance (HEOR). The energy and width are consistent with previous measurements made with proton, $^{3}\mathrm{He}$, and \ensuremath{\alpha} particle projectiles. The observed strength of the HEOR is in agreement with measurements made with $^{3}\mathrm{He}$ inelastic scattering, but is roughly three to four times larger than measurements made with \ensuremath{\alpha} particle and proton inelastic scattering. \textcopyright{} 1996 The American Physical Society.

The “other” giant dipole resonance: Evidence for the isoscalar giant dipole resonance in 208Pb from inelastic α scattering at 0°

The isoscalar giant dipole resonance (ISGDR) in 208Pb has been investigated using inelastic scattering of 200 MeV α particles at and near 0° where the angular distribution of the ISGDR can be clearly differentiated from other modes. The “difference of spectra” technique was employed to separate the contribution from the high-energy octupole resonance (HEOR). Preliminary angular distribution data provide clear evidence for the ISGDR adjacent to the HEOR.

Looking for the isoscalar giant dipole resonance in 208Pd using inelastic a scattering at and near O°

The isoscalar giant dipole resonance (ISGDR) in 208Pb has been investigated using inelastic scattering of 200 MeV α particles at and near 0° where the angular distribution of the ISGDR can be clearly differentiated from other modes. The “difference of spectra” technique was employed to separate the contribution from the high-energy octupole resonance (HEOR). Results from a preliminary analysis of the data are consistent with the expected positions of the ISGOR and HEOR, as well as their expected angular distributions near 0°.

Isoscalar high-energy octupole resonance inZr92in inelastic electron scattering

The giant-resonance region in $^{92}\mathrm{Zr}$ has been studied by inelastic electron scattering of the effective momentum transfer range $0.65\ensuremath{\le}{q}_{\mathrm{eff}}\ensuremath{\le}1.18$ ${\mathrm{fm}}^{\ensuremath{-}1}$. The high-energy octupole resonance was identified at ${E}_{x}=25\ifmmode\pm\else\textpm\fi{}0.3$ MeV with a width of 6.3\ifmmode\pm\else\textpm\fi{}0.3 MeV exhausting 39\ifmmode\pm\else\textpm\fi{}4% of the $T=0$ $E3$ energy weighted sum rule. This result is in good agreement with a recent ($^{3}\mathrm{He}$, $^{3}\mathrm{He}$') result and the recent random-phase approximation calculations, and its strength is inconsistent with the trend of low strength of the high-energy octupole resonances observed by inelastic proton scattering.NUCLEAR REACTIONS $^{92}\mathrm{Zr}$(e,e'), enriched target, ${E}_{0}=220$ MeV, $\ensuremath{\theta}=32\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}61\ifmmode^\circ\else\textdegree\fi{}$, $q=0.65\ensuremath{-}1.18$ ${\mathrm{fm}}^{\ensuremath{-}1}$. Measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}d{E}_{x}}$ up to 33 MeV in excitation energy; deduced excitation energy, width, sum rule exhaustion of isoscalar high-energy octupole resonance.