The (${}^6\mathrm{Li},{}^6\mathrm{Li}^{*}\left[3.56\mathrm{MeV}\right]$) reaction at 100 MeV/u as a probe of Gamow-Teller transition strengths in the inelastic scattering channel

Background: Inelastic neutrino-nucleus scattering is important for understanding core-collapse supernovae and the detection of emitted neutrinos from such events in earth-based detectors. Direct measurement of the cross sections is difficult and has only been performed on a few nuclei. It is, therefore, important to develop indirect techniques from which the inelastic neutrino-nucleus scattering cross sections can be determined.

Purpose: This paper presents a development of the $({}^6\mathrm{Li},{}^6\mathrm{Li}^{*}[T=1,T_z=0,0^{+},3.56\mathrm{MeV}])$ reaction at 100 MeV/u as a probe for isolating the isovector spin-transfer response in the inelastic channel $(\mathrm{\Delta }S=1,\mathrm{\Delta }T=1,\mathrm{\Delta }{T}_z=0)$ from which the Gamow-Teller transition strengths from nuclei of relevance for inelastic neutrino-nucleus scattering cross sections can be extracted.

Method: By measuring the ${}^6\mathrm{Li}$ ejectile in a magnetic spectrometer and selecting events in which the 3.56 MeV $\gamma$ ray from the decay of the ${}^6\mathrm{Li}^{*}\left[3.56\mathrm{MeV}\right]$ state is detected, the isovector spin-transfer selectivity is obtained. High-purity germanium clover detectors served to detect the $\gamma$ rays. Doppler reconstruction was used to determine the $\gamma$ energy in the rest frame of ${}^6\mathrm{Li}$. From the ${}^6\mathrm{Li}$ and 3.56 MeV $\gamma$-momentum vectors the excitation energy of the residual nucleus was determined.

Results: In the study of the ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^6\mathrm{Li}^{*}[3.56\mathrm{MeV}\left]\right)$ reaction, the isovector spin-transfer excitation-energy spectrum in the inelastic channel was successfully measured. The strong Gamow-Teller state in ${}^{12}\mathrm{C}$ at 15.1 MeV was observed. Comparisons with the analog ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^6\mathrm{He})$ reaction validate the method of extracting the Gamow-Teller strength. In measurements of the ${}^{24}\mathrm{Mg},{}^{93}\mathrm{Nb}({}^6\mathrm{Li},{}^6\mathrm{Li}^{*}[3.56\mathrm{MeV}\left]\right)$ reactions, the 3.56 MeV $\gamma$ peak could not be isolated from the strong background in the $\gamma$ spectrum from the decay of the isoscalar excitations. It is argued that by using a $\gamma$-ray tracking array instead of a clover array, it is feasible to extend the mass range over which the $({}^6\mathrm{Li},{}^6\mathrm{Li}^{*})$ reaction can be used for extracting the isovector spin-transfer response up to mass numbers of $\sim 25$ and perhaps higher.

Conclusions: It is demonstrated that the $({}^6\mathrm{Li},{}^6\mathrm{Li}^{*}[3.56\mathrm{MeV}\left]\right)$ reaction probe can be used to isolate the inelastic isovector spin-transfer response in nuclei. Application to nuclei with mass numbers of about 25 or more, however, will require a more efficient $\gamma$-ray array with a better tracking capability.

Figure 1

A simplified level diagram of ${}^6\mathrm{Li}$ based on Ref. [35]. The $\alpha$ decay of the $J^{\pi }=0^{+},T=1$ state at $E_{\mathrm{x}}=3.56\mathrm{MeV}$ is isospin and parity forbidden, and this state decays to the ground state via $\gamma$ emission [36, 37].

Figure 2

The Doppler-reconstructed $\gamma$-ray energy spectrum gated on the ${}^{12}\mathrm{C}[15.1\mathrm{MeV};T=1]$ excitation. The 3.56 MeV $\gamma$ line from the decay of the ${}^6\mathrm{Li}^{*}\left[3.56\mathrm{MeV}\right]$ excited state is observed and the signal gate (red hatched) and sideband gate for background subtraction (blue hatched) are indicated. The solid yellow line is a fit to the spectrum with a simulated detector response and a double-exponential background (blue dashed line).

Figure 3

Comparison of the ${}^{12}\mathrm{C}$ inelastic-scattering singles and coincidence double-differential cross-sectional spectra at $0.{25}^{\circ }$ for the ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^6\mathrm{Li}^{\prime })$ and the ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^6\mathrm{Li}^{*}[3.56\mathrm{MeV}\left]\right)$ reactions, respectively. Note that the latter data have been multiplied by a factor of 2. See the text for details.

Figure 4

Double-differential cross sections for the ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^6\mathrm{Li}^{*}[3.56\mathrm{MeV}\left]\right)$ reaction for $0.5^{\circ }$-wide bins at (a) $0.5^{\circ }$, (b) $1.{75}^{\circ }$, and (c) $2.{75}^{\circ }$. Differential cross sections for excitation-energy ranges of (d) 13.1–17.1 MeV and (e) 17.1–22.1 MeV. The results from the multipole-decomposition analysis (MDA) are superimposed (for details see the text).

Figure 5

GT unit cross section for the $({}^6\mathrm{Li},{}^6\mathrm{Li}^{*}[3.56\mathrm{MeV}\left]\right)$ reaction at 100 MeV/u as a function of target mass number. The red marker is the extracted unit cross section for the ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^6\mathrm{Li}^{*}[3.56\mathrm{MeV}\left]\right){}^{12}\mathrm{C}\left(15.1\mathrm{MeV}\right)$ reaction from the present paper. The blue marker refers to the unit cross section from Ref. [50] for the analog transition measured in a ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^6\mathrm{He})$ experiment at 100 MeV/u. The black markers refer to calculated unit cross sections in DWBA, and the blue dashed line is a fit to these unit cross sections. For details, see the text.

Figure 6

Doppler-reconstructed $\gamma$-ray spectra for the $({}^6\mathrm{Li},{}^6\mathrm{Li}^{\prime }+\gamma )$ reaction on (a) ${}^{12}\mathrm{C}$, (b) ${}^{24}\mathrm{Mg}$, and (c) ${}^{93}\mathrm{Nb}$ for the excitation-energy ranges indicated at the bottom of each panel. In (a), the dashed purple line indicates the fitted 3.56 MeV photopeak, and the solid blue line indicates the fitted exponential background. The dot-dashed red line indicates the simulated response if the $\gamma$-ray position could be measured with a precision of 2 mm. In (b) and (c), the dashed purple lines indicate the simulated 3.56 MeV photopeak assuming one unit of GT strength. The dot-dashed red line indicates the simulated response assuming a position resolution for the $\gamma$-ray detection of 2 mm, assuming one unit of GT strength.