Identification of the ${\beta }^{+}$ Isovector Spin Monopole Resonance via the ${}^{208}\mathrm{Pb}$ and ${}^{90}\mathrm{Zr}(t,{}^3\mathrm{He})$ Reactions at $300\mathrm{MeV}/u$

The double-differential cross sections for the ${}^{208}\mathrm{Pb}$ and ${}^{90}\mathrm{Zr}(t,{}^3\mathrm{He})$ reactions at $300\mathrm{MeV}/u$ have been measured at the RI Beam Factory at RIKEN. This was the first physics experiment with the SHARAQ magnetic spectrometer. The combined analysis of the present $(t{,}^3\mathrm{He})$ data and previous ($n,p$) data provides the clearest identification for the ${\beta }^{+}$ isovector spin monopole resonance both in the ${}^{208}\mathrm{Tl}$ and ${}^{90}\mathrm{Y}$ nuclei, and puts the observations of this giant resonance on a firm foundation. The measured distributions of the ($t,{}^3\mathrm{He}$) monopole cross sections were well reproduced by the distorted-wave Born approximation calculation, where the target transition density was calculated with the self-consistent Hartree-Fock plus random-phase approximation using the T43 Skyrme interaction. A major part of the expected ${\beta }^{+}$ isovector spin monopole strength was found in the measured cross section spectra.

Figure 1

[Top] The cross section spectra at 0.27° in 1-MeV bins. The error bars include statistical errors only. The excitation energy is measured from the ground state of the daughter nuclei. [Others] The cross section spectra and the results of the MD analysis in 2-MeV bins. The monopole cross section spreads over a wide excitation energy region.

Figure 2

[Top] Comparison of the monopole cross section of the ($t,{}^3\mathrm{He}$) and ($n,p$) spectra at 0°. The ($n,p$) spectra were taken from Refs. 17, 18. [Bottom] Comparison of the ($t,{}^3\mathrm{He}$) monopole cross sections of the experimental data and the $\mathrm{DWBA}+\mathrm{HF}\mathrm{\text{−}}\mathrm{RPA}$ calculations. Only statistical errors are shown.

Figure 3

Systematics of the average energy of the monopole cross section distributions (see text). The excitation energy is measured from the ground state of the mother nuclei. The NSCL result [16] was obtained with an extrapolation to $q=0$.