Reexamination of isoscalar giant resonances in ${}^{12}\mathrm{C}$ and ${}^{93}\mathrm{Nb}$ through ${}^6\mathrm{Li}$ scattering

Inelastic ${}^6\mathrm{Li}$ scattering at 100 MeV/u on ${}^{12}\mathrm{C}$ and ${}^{93}\mathrm{Nb}$ has been measured with the high-resolution magnetic spectrometer Grand Raiden. The magnetic-rigidity settings of the spectrometer covered excitation energies from 10 to 40 MeV and scattering angles in the range $0^{\circ }<{\theta }_{\text{lab.}}<2^{\circ }$. The isoscalar giant monopole resonance was selectively excited in the present data. Measurements free of instrumental background and the very favorable resonance-to-continuum ratio of ${}^6\mathrm{Li}$ scattering allowed for precise determination of the $E0$ strengths in ${}^{12}\mathrm{C}$ and ${}^{93}\mathrm{Nb}$. It was found that the monopole strength in ${}^{12}\mathrm{C}$ exhausts $52\pm 3^{\text{(stat.)}}\pm 8^{\text{(sys.)}}\%$ of the energy-weighted sum rule (EWSR), which is considerably higher than results from previous $\alpha$-scattering experiments. The monopole strength in ${}^{93}\mathrm{Nb}$ exhausts $92\pm 4^{\text{(stat.)}}\pm {10}^{\text{(sys.)}}\%$ of the EWSR, and it is consistent with measurements of nuclei with mass number of $A\approx 90$. Such comparison indicates that the isoscalar giant monopole resonance distributions in these nuclei are very similar, and no influence due to nuclear structure was observed.

Figure 1

Double-differential cross section for the $({}^6\mathrm{Li},{}^6\mathrm{Li}\prime )$ reaction on ${}^{12}\mathrm{C}$. (a) Spectra for scattering angles at $0.{33}^{\circ }$ (close to the ISGMR maximum) and $2.{76}^{\circ }$ (near the first minimum of the ISGMR angular distribution). (b) The difference between the above two spectra, which represents the ISGMR cross section in ${}^{12}\mathrm{C}$.

Figure 2

Double-differential cross section for the $({}^6\mathrm{Li},{}^6\mathrm{Li}\prime )$ reaction on ${}^{93}\mathrm{Nb}$. (a) Spectra for scattering angles at $0.{23}^{\circ }$ (close to the ISGMR maximum) and $1.{92}^{\circ }$ (near the first minimum of the ISGMR angular distribution). (b) The difference between the above two spectra, which represents the ISGMR cross section in ${}^{93}\mathrm{Nb}$.

Figure 3

Angular distributions for the $({}^6\mathrm{Li},{}^6\mathrm{Li}\prime )$ reaction on ${}^{12}\mathrm{C}$ (top) and ${}^{93}\mathrm{Nb}$ (bottom) at different excitation energies. The experimental data were fitted with MDA using DWBA calculations for angular-momentum transfers of $\mathrm{\Delta }L=0-3$. The contribution of the IVGDR in ${}^{93}\mathrm{Nb}$ was subtracted from the data before applying the MDA (see the text for details).

Figure 4

Double-differential cross sections for ${}^6\mathrm{Li}$ scattering on ${}^{12}\mathrm{C}$ (top) and ${}^{93}\mathrm{Nb}$ (bottom) at different angles. The colors of the stacked histograms represent the contributions from excitations with different angular-momentum transfers.

Figure 5

ISGMR strength of ${}^{12}\mathrm{C}$. The data are compared with results from a ${}^{12}\mathrm{C}(\alpha ,{\alpha }^{\prime })$ experiment reported in Ref. [25]. The dashed line is a sum of multiple Lorentzian functions fitted to the data (see Table 2). The dash-dotted line corresponds to a theoretical calculation based on antisymmetrized molecular dynamics extracted from Ref. [45]. The solid red line is a QRPA calculation (shifted by a constant factor $\mathrm{\Delta }=1\mathrm{MeV}$) as described in the text.

Figure 6

ISGMR strength of ${}^{93}\mathrm{Nb}$. The data are compared with results from a ${}^{92}\mathrm{Mo}(\alpha ,{\alpha }^{\prime })$ experiment reported in Ref. [21]. The dashed line is a sum of multiple Lorentzian functions fitted to the data (see Table 2). The solid red line corresponds to a QRPA calculation (shifted by a constant factor $\mathrm{\Delta }=1\mathrm{MeV}$) as described in the text.