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 (cid:1) 3) have been extracted for the spherical nucleus 144 Sm and the deformed nucleus 154 Sm. 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 154 Sm. Evidence for the theoretically predicted coupling between the isoscalar dipole resonance and the high-energy octupole resonance is reported

coupling between the GMR and GQR by fitting the observed L = 0 and L = 2 strength distributions with the predicted number of Gaussian peaks from the adiabatic cranking model [4].Their results showed a fair agreement with the calculations of Abgrall et al. [4] but not with several other calculations [5][6][7][8].
Although the effects of coupling between the GMR and GQR in deformed nuclei, resulting in splitting of the GMR and broadening of the GQR, have been observed in previous measurements, there have been no published data so far on the ISGDR and the high energy octupole resonance (HEOR) in deformed nuclei.On the theoretical side, Nishizaki and Andō had predicted the K-splitting and the coupling between the ISGDR and HEOR some time ago [9].In this Letter, we report the results on both compressional-modes, the GMR and ISGDR, for the spherical nucleus 144 Sm and for the deformed nucleus 154 Sm.In particular, the effect of deformation on the ISGDR has been investigated for the first time and evidence has been obtained for the theoretically-predicted coupling between the ISGDR and HEOR.
The experiments were performed at the Research Center for Nuclear Physics (RCNP), Osaka University. 4 He ++ beams were accelerated by the AVF cyclotron and the ring cyclotron up to 400 MeV.The halofree beam bombarded thin (2-10 mg/cm 2 ), selfsupporting, metallic targets of 144 Sm, 148 Sm, 150 Sm, 152 Sm and 154 Sm.Here, results are presented only on the 144 Sm (spherical) and 154 Sm (deformed) nuclei in order to focus the discussion on the effects of deformation.
Inelastically-scattered particles were analyzed by a magnetic spectrometer, Grand Raiden [10].The vertical and horizontal positions in the focal plane were determined by a focal-plane detector system consisting of two multi-wire drift chambers (MWDCs) and two plastic scintillation counters.The angular distributions were measured with three different settings of the spectrometer system; details of the experimental settings are provided in Refs.[11,12].The typical energy resolution was ∼ 200 keV, sufficient to investigate the giant resonances of interest, with a width of ∼ 5 MeV.
In Grand Raiden, particles scattered from the target are focused vertically and horizontally at the focal plane.On the other hand, instrumental background events due to rescattering of α particles on the wall and pole surfaces of the spectrometer are not focused in the vertical direction.We obtained clean spectra by subtracting events at the off-median plane from those at the median plane [12].Energy spectra were obtained in the energy range of 8 < E x < 33 MeV over several angles between 0 • and 9 • (13.5 • for 144 Sm).The energy spectra at 0 • (average angle 0.7 • ) are shown in Fig. 1 for the Sm isotopes.
In order to identify strengths corresponding to different giant resonances, we have carried out a multipole-decomposition (MD) analysis [13] of the differential cross sections for each 1 MeV bin.In this method, the cross sections ( d 2 σ dΩ dE ) exp are expressed as the sum of the contributions from the various multipole components: where E x is the excitation energy and ( d 2 σ dΩ dE ) calc L are the distorted wave Born approximation (DWBA) cross sections exhausting the full energy-weighted sum rule (EWSR) for the transferred angular momentum L. The fractions of the EWSR, a L (E x ), for various multipole components were determined by minimizing χ 2 .The physical continuum is included in the MD analysis, since the (α, α ) spectra obtained in our measurements are free from any "non-physical" background.
In the DWBA calculations with the code ECIS95 [14], a folded-potential model was employed, with a nucleon-α interaction of the density-dependent Gaussian form, as described in Refs.[15,16].The nucleonα interaction is given by: where the ground-state density ρ 0 (r ) is unfolded by using the charge density distributions of the Fourier-Bessel expansion form taken from Ref. [17].To obtain the interaction parameters, we measured elastic scattering of α particles from 144 Sm at E α = 400 MeV and fitted the angular distributions with a single-folded potential; the interaction parameters were extracted to be V = 25.1 MeV, W = 14.2 MeV, α = 1.9 fm 2 and β = 4.5 fm 2 .
To simplify the calculations, macroscopic transition densities were used.These transition densities are described by Satchler [18] for the GMR (L = 0), the isovector giant dipole resonance (IVGDR) (L = 1, T = 1) and L 2 (BM transition density in Ref. [18]), and for the ISGDR by Harakeh and Dieperink [19].Multipole components up to L = 14 for 144 Sm, and L = 10 for 154 Sm were taken into account in the fit, because the first maximum of the angular distribution for the L = 14 transfer appears at 13 • and for the L = 10 • at 9 • .Use of L 14 multipoles in the fits resulted in negligible change in the extracted distributions for L = 0, 1, 2, 3.The strength distributions of the IVGDR were fixed by using those deduced from the photo-neutron cross sections [20].Since the experimental cross sections were obtained from the summation of the yield of the scattering particles within the acceptance of Grand Raiden, the calculated cross sections, ( dσ 2 dΩ dE ) calc L , were also folded over that angle.Fig. 2 shows the results of typical multipole fits to angular distributions for 144 Sm and 154 Sm.The strength distributions are expressed as: where m, A, r N , , and a L (E x ) are the nucleon mass, the mass number, the N th moment of the ground-state density, = (4/E 2 + 5/E 0 ) h2 /3mA (E 0 , E 2 are the centroid energies of the GMR and the GQR, respectively), and the respective EWSR fractions obtained by our MD analysis.
The results for the L = 0 and L = 2 strength distributions are shown in Fig. 3.Both the GMR and GQR strengths have a well-defined peak but extend to high excitation energies.The EWSR fractions integrated over measured excitation energies are about 200%.The cross section for each L component is well separated by a MD analysis.However, the strength distributions obtained from the comparison with the DWBA cross sections depend on the transition densities used in the analysis.Thus, a possible reason of these ex-cesses in the EWSR fractions is that the macroscopic transition densities of the GMR and the GQR used in this analysis are not valid in the high excitation energy region.Therefore, further analysis was carried out for the energy region, 8 to 19 MeV for the GMR and 9 to 15 MeV for the GQR.In 144 Sm, the GMR and the GQR were each fitted with a Breit-Wigner function.The fitting parameters are listed in Table 1, to-Fig.3. The L = 0 and L = 2 strength distributions for 144,154 Sm obtained from the multipole-decomposition analysis.The solid lines show the fits with two Breit-Wigner functions to the peak regions.The low-and high-excitation-energy components of the GMR and the GQR are indicated by hatched areas.In 154 Sm, the strength distribution obtained in the adiabatic cranking model (dashed lines) [4] and the fluid-dynamical model (dash-dotted lines) [9] are also drawn.Both the calculated strengths are assumed to exhaust the predicted EWSR fractions from 8 to 33 MeV.
gether with the EWSR fractions obtained by integrating E x S L (E x ) from 8 to 33 MeV.If the shape of the high excitation energy tail is assumed to be a polynomial function, the centroid energies are not affected, but the widths and the EWSR fractions are affected by 20-30%.
The GMR strength is expected to split into two components because of the coupling to the GQR.For comparison with the theoretical results, the "peak region" of the GMR in 154 Sm was fitted with two Breit-Wigner functions.The widths were fixed by using those of the GMR and GQR in 144 Sm.
The GQR strength, on the other hand, is predicted to split into three components by Abgrall et al. [4] and four components by Nishizaki and Andō [9].However, the strength distributions for the GQR were well fitted with only two Breit-Wigner functions in the excitation energy region from 9 to 15 MeV.This two-component fit is consistent with very small strengths associated with other components in the theoretical predictions.The results of the fits for 154 Sm are also presented in Table 1, previous results from Refs.[3,21] and [22] are also included for comparison.
Fig. 4 compares the centroid energies of each component with those from the two theoretical models viz. the adiabatic cranking model [4] and the fluiddynamical model [9].Both the models reproduce the peak energy of the high-excitation-energy (HE) component of the GMR.However, the low-excitationenergy (LE) component is higher in energy than the Table 1 The parameters for fits to the strength distributions of the GMR and GQR compared with the results in Refs.[3,21,22].The centroid energy E 0 , width Γ , the EWSR fractions obtained in the Breit-Wigner fits (F ) are listed theoretically predicted values.A similar behavior has been observed for 154 Sm by Youngblood et al. [3].Fig. 3 also shows a comparison between the fits with two Breit-Wigner functions to the GMR and GQR peaks in 154 Sm and the strength distributions obtained in the two theoretical models.The theoretical GMR strength was folded with two Breit-Wigner functions.The width of the LE component coupling to the K = 0 component of the GQR was taken to be equal to that of the GQR, and the width of the HE component as equal to that of the GMR in 144 Sm.For the GQR strength distributions, three or four Breit-Wigner functions were employed, each with a width equal to that of the GQR and the width of the coupling state to the GMR as equal to that of the GMR in 144 Sm.In addition, the strength distributions were shifted to a higher excitation energy by 0.6 MeV.As shown in Fig. 3, the experimental GMR and GQR strength distributions are in excellent agreement with both the theoretical models, except the slight shift in the GQR energy.
The isoscalar odd-parity giant resonances, ISGDR and HEOR, are also expected to couple, resulting in shifting of the strengths to lower excitation energies and broadening of the width of HEOR and ISGDR because of the K-splitting [9].The results of the MD analysis for the ISGDR and the HEOR are shown in Fig. 5.The EWSR fractions are 120-130% in the ISGDR, and 50-60% in the HEOR.In the spherical nucleus 144 Sm, the ISGDR strength has two distinct components as reported in Refs.[23,24], and the HEOR strength has a bump peaking at E x ∼ 22 MeV.In the deformed nucleus 154 Sm, on the other hand, the LE component of the ISGDR strength appears to split into two components (K = 0 and K = 1) and to be enhanced, whereas the HE component does not show any significant change.For the HEOR, the strength distribution is rather broad, without a discernible peak, and the strength is shifted toward low excitation energies.This broadening of the HEOR in deformed nuclei and the strength shift to lower excitation energies were reported also by Morsch et al. [25].
Although the ISGDR and HEOR strengths for 154 Sm would normally be expected to be ∼ 30% higher than those for 144 Sm due to the differences in the nuclear masses and radii.These would be further enhanced in 154 Sm because of the deformationinduced coupling between the ISGDR and HEOR  for the K = 0 and K = 1 components.In fact, the enhancement of both the ISGDR and HEOR strengths near E x ∼ 12.5 MeV in 154 Sm, in comparison with 144 Sm, is 50-100%, which is significantly larger than expected simply from mass and radius effects mentioned above.This is inferred to be evidence for a coupling between the two modes.A direct comparison of the observed ISGDR strength in 154 Sm with theoretical predictions is, however, complicated by the nature of the LE component of the ISGDR in spherical nuclei.According to recent theoretical work on the ISGDR [26][27][28][29][30], this LE component is of "non-bulk" origin-only the HE component of the ISGDR strength corresponds to a compressionalmode.On the other hand, considering the effects of deformation on the ISGDR and HEOR, Ref. [9] takes into account only the coupling between the HEOR and the compressional-mode ISGDR.Further theoretical work to investigate the effect of deformation on the "non-bulk" LE component of the ISGDR strength is clearly most urgently warranted.
In summary, clean inelastic scattering spectra, free from instrumental background, have been measured for the 144-154 Sm nuclei.The spectra have been decomposed into contributions of various multipoles by a multipole decomposition analysis using DWBA angular distributions obtained in the framework of the density-dependent single-folding model.The strength distributions for the GMR, ISGDR, GQR and HEOR have been determined for the spherical nucleus 144 Sm and the deformed nucleus 154 Sm.A coupling between the GMR and GQR, and the broadening of the GQR width have been confirmed in the deformed nucleus 154 Sm.The strength distributions of the GMR and GQR in 154 Sm are in good agreement with the calculations by Abgrall et al. [4] and by Nishizaki and Andō [9].For the ISGDR, the effects of deformation are different for the low-and high-excitation-energy components in 154 Sm.The coupling between the ISGDR and HEOR has been evidenced by enhancement and splitting of the low-excitation-energy component of the ISGDR, the broadening of the HEOR, and the shift of the HEOR strength towards lower excitation energies.

Fig. 4 .
Fig. 4. The peak energies for the HE (closed circles) and LE components (closed triangles) of the GMR are plotted as a function of the deformation parameter δ.The open squares are the peak energies for the GMR predicted the fluid-dynamical (FD) model [9], and the open triangles are those of the cranking model [4].The lines are drawn to guide the eye.

Fig. 5 .
Fig. 5. Comparison of the ISGDR and HEOR strength distributions in 144 Sm and 154 Sm.The solid lines are drawn to guide the eye.The HEOR strength in 154 Sm is enhanced at E x = 12.5 ∼ 17 MeV where the LE component of the ISGDR exists.