Measurement of $\gamma$ rays from giant resonances excited by the ${}^{12}\mathrm{C}(p,p^{\prime }$) reaction at 392 MeV and $0^{\circ }$

We measured both the differential cross section (${\sigma }_{p,p^{\prime }}=d^2\sigma /d\mathrm{\Omega }d{E}_x$) and the $\gamma$-ray emission probability [$R_{\gamma }\left(E_x\right)={\sigma }_{p,p^{\prime }\gamma }/{\sigma }_{p,p^{\prime }}$] from the giant resonances excited by ${}^{12}\mathrm{C}(p,p^{\prime })$ reaction at 392 MeV and $0^{\circ }$, using a magnetic spectrometer and an array of NaI(Tl) counters. The absolute value of $R_{\gamma }\left(E_x\right)$ was calibrated by using the well-known $\gamma$-ray emission probability from ${}^{12}\mathrm{C}^{*}(15.11$ MeV, $1^{+},T=1$) and ${}^{16}\mathrm{O}^{*}(6.9$ MeV, $2^{+},T=0$) states within 5% uncertainty. We found that $R_{\gamma }\left(E_x\right)$ starts from zero at $E_x=16$ MeV, increases to a maximum of $53.3\pm 0.4\pm 3.9$% at $E_x=27$ MeV, and then decreases. We also compared the measured values of $R_{\gamma }\left(E_x\right)$ with statistical model calculation based on the Hauser-Feshbach formalism in the energy region $E_x=16–32$ MeV and discussed the features of $\gamma$-ray emission probability quantitatively.

Figure 1

(a) Grand Raiden spectrometer in the experimental setup at $0^{\circ }$, (b) focal plane detectors, and (c) $\gamma$-ray detector.

Figure 2

Two-dimensional histogram with $E$ ($\gamma$-ray energy measured by the detector) at $y$ axis and $E_x$ at $x$ axis with each point showing a coincidence event. Accidental background has not been subtracted.

Figure 3

(a) Time difference between GAM trigger and PS trigger. (b) $\gamma$-ray energy spectrum (red solid line) and background spectrum (blue dotted line) for the 15.11-MeV state ($1^{+},T=1$) of ${}^{12}\mathrm{C}$.

Figure 4

Double differential cross section of the ${}^{12}\mathrm{C}(p,p^{\prime }$) reaction at $E_p=392$ MeV and $\theta =0^{\circ }$. The bin width is 0.02 MeV.

Figure 5

(a) Differential cross section of the ${}^{12}\mathrm{C}(p,p^{\prime })$ reaction as a function of scattering angle (black circles) and comparison with previous experiment [21] (red open circles). Solid (SFO) and dashed (Cohen-Kurath) lines are the DWBA calculation results for the transitions to 15.1-MeV state (see text for details). (b) Differential cross section for ${}^{16}\mathrm{O}(p,p^{\prime })$ reaction as a function of scattering angle and comparison with previous experiment [22].

Figure 6

(a) Spin-flip component $\mathrm{\Sigma }{d}^2\sigma /d\mathrm{\Omega }d{E}_x$ (shaded region) is compared with $d^2\sigma /d\mathrm{\Omega }d{E}_x$ (solid line). The spin-flip cross section for ${}^{12}\mathrm{C}\left(\mathit{p},\mathit{n}\right){}^{12}\mathrm{N}$ reaction (blue open squares), the contribution of quasifree process (dotted line), and their sum (red circles) are obtained from Ref. [23]. (b) Non-spin-flip component $(1-\mathrm{\Sigma })d^2\sigma /d\mathrm{\Omega }d{E}_x$ (shaded region) is compared with $d^2\sigma /d\mathrm{\Omega }d{E}_x$ (solid line). The calculation of Coulomb excitation (red circles) is also shown. The bin width is 0.2 MeV.

Figure 7

Double differential cross section for the giant resonance region in ${}^{12}\mathrm{C}$ fitted with various resonances (dotted lines) [33] and a quasifree continuum (dash-dotted line). The red dashed curve shows the overall fit obtained from the sum of all contributions.

Figure 8

Differential cross section as a function of scattering angle at various excitation energies in the giant resonance region of ${}^{12}\mathrm{C}$. Dotted and solid black lines show the result of DWBA calculations (see text). (a) A data point (red open circle) from another experiment [38] is also shown.

Figure 9

Measured $\gamma$-ray spectrum (black data points) after background subtraction and response function (red line) for the (a) 15.11-MeV state ($J^{\pi }=1^{+}$) of ${}^{12}\mathrm{C}$ and (b) 6.9-MeV state ($J^{\pi }=2^{+}$) of ${}^{16}\mathrm{O}$ (see text for details).

Figure 10

(a)–(f) $\gamma$-ray energy spectrum (black solid line) and background energy spectrum (red dashed line) at various excitation energies in the giant resonance region of ${}^{12}\mathrm{C}$. (g) The decay scheme of ${}^{12}\mathrm{C}^{*}$.

Figure 11

The $\gamma$-ray spectrum (black data points), background spectrum (blue dash-dotted line), total fit (red solid line), and $\gamma$ rays from the excited states of the daughter nuclei (grey dotted lines) are shown for various $E_x$ regions.

Figure 12

Total $\gamma$-ray emission probability $R_{\gamma }\left(E_x\right)$ as a function of $E_x$. The error bars include both statistical and systematic uncertainties.

Figure 13

The $\gamma$-ray emission probability as a function of scattering angle at various excitation energies in the giant resonance region of ${}^{12}\mathrm{C}$.

Figure 14

Comparison between the measured $\gamma$-ray emission probability (data points) and the statistical model prediction (red solid line). The black dashed line shows the $\gamma$-ray emission probability obtained from the fit [Eq. (12)]. The red band shows the uncertainty in calculation due to the error in $C_{\text{QF}}$. The $\gamma$-ray emission probability from quasifree process (blue dash-dotted line) is also shown. The quantity $S_{pp}$ represents the two proton emission threshold (27.2 MeV) for ${}^{12}\mathrm{C}$.