Constraining the solar neutrino survival probability curve by using ${}^6\mathrm{Li}$, ${}^7\mathrm{Li}$, ${}^{12}\mathrm{C}$, ${}^{18}\mathrm{O}$, ${}^{19}\mathrm{F}$, and ${}^{42}\mathrm{Ca}$ nuclear targets

Precise measurement of the survival probability $P_{ee}$ of solar electron neutrino (${\nu }_e$) as a function of its energy [$P_{ee}(E_{\nu e})$] is one of the key issues in neutrino physics. Current $P_{ee}$ data, due to their limited accuracy, still allow for nonstandard interactions (NSIs) to be alternatives to the standard one, which is based on the MSW-LMA prediction. In order to determine $P_{ee}$ values at several values of $E_{\nu e}$ with higher accuracy, we propose to use several target nuclei with different threshold energies for ${\nu }_e$ detection. We examined charged-current (CC) responses of various nuclei seeking the ones: (a) having large and concentrated Gamow-Teller (GT) transition strength in the low excitation-energy region, and (b) having appropriate and a variety of reaction $Q$ values, i.e., $\approx 1$ to 17 MeV, in the (${\nu }_e,e^{-}$) reaction. As a result, we found that systematic solar ${\nu }_e$ measurements with target nuclei ${}^6\mathrm{Li}$, ${}^7\mathrm{Li}$, ${}^{12}\mathrm{C}$, ${}^{18}\mathrm{O}$, ${}^{19}\mathrm{F}$, and ${}^{42}\mathrm{Ca}$ can put strong constraints on the $P_{ee}(E_{\nu e})$ curve and thus on these NSI models. In addition, we notice that three of these nuclei, ${}^6\mathrm{Li}$, ${}^7\mathrm{Li}$, and ${}^{12}\mathrm{C}$, have large and concentrated neutral-current (NC) responses with detection threshold-energies of 3.56, 0.48, and 15.11 MeV, respectively. Note that the NC measurement is flavor independent. Thus, the measured results should represent the original strength of ${\nu }_e$ from the Sun.

Figure 1

Theoretical predictions and experimental data for the ${\nu }_e$ survival probability $P_{ee}$ as a function of its energy $E_{\nu e}$ (original figure: from [20]). Theoretical prediction from the MSW-LMA solution is shown by the pink band, where uncertainties of oscillation parameters are included. Also shown are the MSW-LMA + nonstandard interaction (NSI) solutions for ${\epsilon }^{\prime }=-0.5,+0.5$, and $+1.0$. Four experimental $P_{ee}$ values from the latest Borexino analysis under the HZ-SSM assumption are plotted for $pp\text{−}{\nu }_e$, ${}^7\mathrm{Be}\text{−}{\nu }_e$, $pep\text{−}{\nu }_e$, and also ${}^8\mathrm{B}\text{−}{\nu }_e$ [15]. In addition to these, a $P_{ee}$ value for ${}^7\mathrm{Be}\text{−}{\nu }_e$ is available from KamLAND-Zen measurement [21], and values for ${}^8\mathrm{B}\text{−}{\nu }_e$ are available from Super-Kamiokande [13] and SNO [22]. For the six candidates of target nuclei to be discussed in this paper, the threshold energies for ${\nu }_e$ detection, i.e., the $Q_{\mathrm{EC}}$ values, are indicated.

Figure 2

Spectra of (a) ${}^{37}\mathrm{Cl}({}^3\mathrm{He},t){}^{37}\mathrm{Ar}$ [35] and (b) ${}^{18}\mathrm{O}({}^3\mathrm{He},t){}^{18}\mathrm{F}$ [36] CE reactions measured at $\mathrm{\Theta }=0°$ with an energy resolution of $\approx 30\mathrm{keV}$. The origins of the $E_x$ axes are shifted by the amount of g.s.–g.s. $Q_{\mathrm{EC}}$ values, i.e., 0.81 and 1.66 MeV for the ${}^{37}\mathrm{Ar}$ and ${}^{18}\mathrm{F}$ nuclei, respectively. As a result, the minimum energy of ${\nu }_e$ needed to excite each state, i.e., the $Q_{\mathrm{EC}}$ value, can be seen directly. The $B(\mathrm{GT})$ value derived by using Eq. (3) is given for each GT state. In the ${}^{37}\mathrm{Ar}$ spectrum [(a)], the vertical scale is expanded [in terms of $B(\mathrm{GT})$] by a factor of 2.5 compared to that of (b). In the ${}^{18}\mathrm{O}\to {}^{18}\mathrm{F}$ transition [(b)], the GT strength is much concentrated in the $J^{\pi }=1_1^{+}$ g.s., i.e., the LeSGT state [36]. The IAS at 1.04 MeV is excited with $B(\mathrm{F})=N-Z=2$.

Figure 3

The flux of solar ${\nu }_e\mathrm{s}$ from various fusion processes as a function of $E_{\nu e}$. The $Q_{\mathrm{EC}}$ values of candidates for target nuclei are indicated.

Figure 4

Energy-level diagram and GT and Fermi transitions in $A=7$ nuclei. Properties of excitations caused by the ${}^7\mathrm{Li}({\nu }_e,e^{-}){}^7\mathrm{Be}$ CE reaction are indicated in red. Decay properties of the states in ${}^7\mathrm{Be}$ are shown in blue. The strength [$B(\mathrm{GT})=1.06$] in the square brackets given for the GT transition from the ${}^7\mathrm{Li}$ g.s. to the ${}^7\mathrm{Be}$ 0.43 MeV state is borrowed from that of the mirror (isospin analogous) GT transition studied in the ${\beta }^{+}$ decay of the ${}^7\mathrm{Be}$ g.s. to the ${}^7\mathrm{Li}$ 0.48 MeV state.

Figure 5

Energy-level diagram and the prominent GT and Fermi transitions in $A=18$ nuclei. Properties of $T_z=+1\to 0$ transitions caused by the ${}^{18}\mathrm{O}({\nu }_e,e^{-}){}^{18}\mathrm{F}$ CE reaction are indicated in red. Decay properties of ${}^{18}\mathrm{F}$ are shown in blue. Properties of $T_z=-1\to 0$ transitions from ${}^{18}\mathrm{Ne}$ to ${}^{18}\mathrm{F}$ are shown in black. We see that the $T_z=\pm 1\to 0$ mirror g.s.–g.s. GT transitions have $B(\mathrm{GT})$ values of 3.08(2) and 3.09(3), respectively; they are consistent within uncertainties.

Figure 6

Energy-level diagram and the prominent $\mathrm{GT}+\text{Fermi}$ g.s.–g.s. transitions in $A=19$ nuclei. Properties of the transition caused by the ${}^{19}\mathrm{F}({\nu }_e,e^{-}){}^{19}\mathrm{Ne}$ CE reaction are indicated in red. Decay properties of the g.s. of ${}^{19}\mathrm{Ne}$ are shown in blue.

Figure 7

Energy-level diagram and GT transitions in $A=6$ nuclei, where ${}_2{}^6{\mathrm{He}}_4$ and ${}_4{}^6{\mathrm{Be}}_2$ are mirror nuclei. Properties of the excitation caused by the ${}^6\mathrm{Li}({\nu }_e,e^{-}){}^6\mathrm{Be}$ CE reaction are indicated in red. The strength [$B(\mathrm{GT})=1.58$] in the square brackets, given for the GT transition from the ${}^6\mathrm{Li}$ g.s. to the ${}^6\mathrm{Be}$ g.s., is borrowed from that of the mirror (isospin analogous) GT transition studied in the ${\beta }^{-}$ decay of the ${}^6\mathrm{He}$ g.s. to the ${}^6\mathrm{Li}$ g.s., where the factor of three, i.e., the difference of the relevant spin CG coefficients, is corrected.

Figure 8

Energy-level diagram and the prominent GT and Fermi transitions in $A=42$ nuclei. Properties of excitations caused by the ${}^{42}\mathrm{Ca}({\nu }_e,e^{-}){}^{42}\mathrm{Sc}$ CE reaction are indicated in red, while the decay properties of isospin analogous GT transitions from ${}^{42}\mathrm{Ti}$ are shown in black. The strength [$B(\mathrm{GT})=2.17$] in the square brackets for the GT transition from the ${}^{42}\mathrm{Ca}$ g.s. to the 0.61 MeV state in ${}^{42}\mathrm{Sc}$ is borrowed from that of the mirror (isospin analogous) GT transition studied in the ${\beta }^{+}$ decay of the ${}^{42}\mathrm{Ti}$ g.s. to the 0.61 MeV state in ${}^{42}\mathrm{Sc}$. Decay properties of the states in ${}^{42}\mathrm{Sc}$ are shown in blue.

Figure 9

Energy-level diagram and the important transitions in $A=12$ nuclei. Properties of the GT transition caused by the ${}^{12}\mathrm{C}({\nu }_e,e^{-}){}^{12}\mathrm{N}$ CE reaction are indicated in red. The decay properties of the $1^{+}$ g.s. of ${}^{12}\mathrm{N}$ and its IAS at 15.11 MeV in ${}^{12}\mathrm{C}$ are shown in blue. Note that the vertical energy scale of this diagram is reduced by a factor of two compared to those for other target nuclei.