Isoscalar giant monopole, dipole, and quadrupole resonances in ${}^{90,92}\mathbf{Zr}$ and ${}^{92}\mathbf{Mo}$

The isoscalar giant monopole, dipole, and quadrupole strength distributions have been deduced in ${}^{90,92}\mathrm{Zr}$ and ${}^{92}\mathrm{Mo}$ from “background-free” spectra of inelastic $\alpha$-particle scattering at a beam energy of 385 MeV at extremely forward angles, including $0^{\circ }$. These strength distributions were extracted by a multipole-decomposition analysis based on the expected angular distributions of the respective multipoles. All these strength distributions for the three nuclei practically coincide with each other, affirming that giant resonances, being collective phenomena, are not influenced by nuclear shell structure near $A\sim 90$, contrary to the claim in a recent measurement.

Figure 1

A vertical position spectrum measured at the spectrometer angle of $\theta =0^{\circ }$ (average angle $0.7^{\circ }$ in the laboratory frame). The central region represents true+instrumental background events. The off-center regions represent only instrumental background events. The true events were obtained by subtracting instrumental background events from the true+instrumental background events.

Figure 2

Excitation-energy spectra for the ($\alpha ,{\alpha }^{\prime }$) reaction at $E_{\alpha }=385$ MeV at the spectrometer angle of $\theta =0^{\circ }$ (average angle $0.7^{\circ }$ in the laboratory frame) for ${}^{90}\mathrm{Zr}$, ${}^{92}\mathrm{Zr}$, and ${}^{92}\mathrm{Mo}$ in (a), (b), and (c), respectively. In each panel, the blue hatched region represents the instrumental background. The solid red and green histograms show the energy spectra before and after the instrumental-background subtraction, respectively.

Figure 3

(a) Excitation-energy spectra measured at the spectrometer angle of $\theta =0^{\circ }$ (average angle $0.7^{\circ }$ in the laboratory frame) for the three nuclei, ${}^{90}\mathrm{Zr}$ (solid blue), ${}^{92}\mathrm{Zr}$ (red dashed), and ${}^{92}\mathrm{Mo}$ (green dash-dotted). (b) Difference spectra of average angles $0.7^{\circ }$ and $2.0^{\circ }$ for the three nuclei, ${}^{90}\mathrm{Zr}$ (solid blue), ${}^{92}\mathrm{Zr}$ (red dashed), and ${}^{92}\mathrm{Mo}$ (green dash-dotted). The difference spectra comprise essentially the monopole strength (see text).

Figure 4

Typical angular distributions for inelastic $\alpha$ scattering from ${}^{90}\mathrm{Zr}$. The solid line (black) through the data shows the sum of various multipole components obtained from MDA. The dash-dotted (red), dashed (blue), dash-double-dotted (green), and dotted (magenta) curves indicate contributions from $L=0$, 1, 2, and 3, respectively, with the transferred angular momentum $L$ indicated for each of the curves. The solid gray line shows the IVGDR contribution.

Figure 5

Typical angular distributions for inelastic $\alpha$ scattering from ${}^{92}\mathrm{Mo}$. The solid line (black) through the data shows the sum of various multipole components obtained from MDA. The dash-dotted (red), dashed (blue), dash-double-dotted (green), and dotted (magenta) curves indicate contributions from $L=0$, 1, 2, and 3, respectively, with the transferred angular momentum $L$ indicated for each of the curves. The solid gray line shows the IVGDR contribution.

Figure 6

(a) Angular distribution of the ratio of the differential cross sections for elastic scattering to Rutherford scattering for 385 MeV $\alpha$ particles from ${}^{90}\mathrm{Zr}$ (solid black circles). Solid gray squares are from earlier work [10] and the solid red line is the optical-model fit to the data. In (b) and (c), angular distribution of differential cross sections for the $2^{+}$ state and $3^{-}$ states are shown, where the solid red lines show the corresponding results of the DWBA calculations (see text). The rectangular box in (b) represents the ${}^{16}\mathrm{O}$ contamination region in the ${}^{90}\mathrm{Zr}$ target.

Figure 7

(a) Angular distribution of the ratio of the differential cross sections for elastic scattering to Rutherford scattering for 385 MeV $\alpha$ particles from ${}^{92}\mathrm{Zr}$ (solid black circles). The solid red line is the optical-model fit to the data. In (b) and (c), angular distribution of differential cross sections for the $2^{+}$ state and $3^{-}$ states are shown, where the solid red lines show the corresponding results of the DWBA calculations (see text).

Figure 8

Same as Fig. 7, but for ${}^{92}\mathrm{Mo}$.

Figure 9

ISGMR strength distributions for ${}^{90}\mathrm{Zr}$, ${}^{92}\mathrm{Zr}$, and ${}^{92}\mathrm{Mo}$ [(a), (b), (c), respectively]. The solid line in each panel is the Lorentzian fit to the data.

Figure 10

ISGDR strength distributions for ${}^{90}\mathrm{Zr}$, ${}^{92}\mathrm{Zr}$, and ${}^{92}\mathrm{Mo}$ [(a), (b), (c), respectively]. The solid line in each panel is the two-peak fit to the data. The dashed and dash-dotted lines in each panel, respectively, represent the “low-energy” and “high-energy” components of the “bimodal” ISGDR strength distribution.

Figure 11

ISGMR (a) and ISGDR (b) strength distributions for ${}^{90}\mathrm{Zr}$ (blue circles), ${}^{92}\mathrm{Zr}$ (red squares), and ${}^{92}\mathrm{Mo}$ (green triangles). The solid line in (a) represents the Lorentzian fit to the data for ${}^{90}\mathrm{Zr}$. In (b), the solid line is the two-peak Lorentzian fit to the data, the dashed and dash-double-dotted lines, respectively, represent the “low-energy” and “high-energy” components of the “bimodal” ISGDR strength distribution for ${}^{90}\mathrm{Zr}$ (see text).

Figure 12

ISGQR strength distributions for ${}^{90}\mathrm{Zr}$, ${}^{92}\mathrm{Zr}$, and ${}^{92}\mathrm{Mo}$ [(a), (b), (c), respectively]. The solid line in each panel is the Lorentzian fit to the data.