Excitation of the Isovector Spin Monopole Resonance via the Exothermic ${}^{90}\mathrm{Zr}({}^{12}\mathrm{N},{}^{12}\mathrm{C})$ Reaction at $175\mathrm{MeV}/u$

The (${}^{12}\mathrm{N}$, ${}^{12}\mathrm{C}$) charge-exchange reaction at $175\mathrm{MeV}/u$ was developed as a novel probe for studying the isovector spin giant monopole resonance (IVSMR), whose properties are important for better understanding the bulk properties of nuclei and asymmetric nuclear matter. This probe, now available through the production of ${}^{12}\mathrm{N}$ as a secondary rare-isotope beam, is exothermic, is strongly absorbed at the surface of the target nucleus, and provides selectivity for spin-transfer excitations. All three properties enhance the excitation of the IVSMR compared to other, primarily light-ion, probes, which have been used to study the IVSMR thus far. The ${}^{90}\mathrm{Zr}({}^{12}\mathrm{N},{}^{12}\mathrm{C})$ reaction was measured and the excitation energy spectra up to about 70 MeV for both the spin-transfer and non-spin-transfer channels were deduced separately by tagging the decay by $\gamma$ emission from the ${}^{12}\mathrm{C}$ ejectile. Besides the well-known Gamow-Teller and isobaric analog transitions, a clear signature of the IVSMR was identified. By comparing with the results from light-ion reactions on the same target nucleus and theoretical predictions, the suitability of this new probe for studying the IVSMR was confirmed.

Figure 1

Two-body reaction kinematics on the $q\text{−}\omega$ plane, showing the exothermic nature of the (${}^{12}\mathrm{N}$, ${}^{12}\mathrm{C}$) reaction and the low linear momentum transfer in comparison with other probes. The excitation energy ($E_x$) in ${}^{90}\mathrm{Nb}$ is shown on the right, with $E_x=\omega +\mathrm{\Delta }m$, where $\mathrm{\Delta }m=5.60\mathrm{MeV}$ is the ground-state mass difference between ${}^{90}\mathrm{Nb}$ and ${}^{90}\mathrm{Zr}$.

Figure 2

(a) Double-differential cross sections for the GT channel. The error bars denote only statistical uncertainties. The inset shows the angular distribution of the cross sections for the peak in the energy range $A$ and is compared with a DWBA calculation for the GTGR. (b) Idem, but for the Fermi channel. The inset shows the angular distribution for the peak in the energy range $B$ and is compared with DWBA for the IAS.

Figure 3

(a) Comparison of the double-differential cross-section spectra of the present Letter with past experiments [13, 14, 43]. (b) Differences of the spectra with respect to that of the 200-MeV ($p$, $n$) spectrum [43]. (c) The isovector spin monopole strength distribution in ${}^{90}\mathrm{Zr}$ from the experimental data compared with theoretical predictions [6].

Figure 4

Ratios of the unit cross sections ${\widehat{\sigma }}_{\mathrm{GT}}/{\widehat{\sigma }}_F$ as a function of incident beam energy. The dashed curve shows ${\widehat{\sigma }}_{\mathrm{GT}}/{\widehat{\sigma }}_F=[(E/A)/(55\mathrm{MeV}){]}^2$. See text and Ref. [49] for details.