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Low-energy neutrino responses for 71Ga by electron capture rates, charge exchange reactions and shell model calculations

This study evaluates the weak Gamow-Teller responses for low-lying states in ${}^{71}\mathrm{Ga}$ by combining experimental electron capture rates, corrected charge exchange reaction data, and shell model calculations, finding that while excited states contribute approximately 4.2% to the total response, the Ga anomaly remains unexplained by these nuclear uncertainties.

Original authors: Yoritaka Iwata, Hiroyasu Ejiri, Shahariar Sarkar

Published 2026-08-18

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CC BY 4.0

Original authors: Yoritaka Iwata, Hiroyasu Ejiri, Shahariar Sarkar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep inside the sun, nuclear reactions constantly fuse atoms together, releasing a flood of tiny, ghostly particles called neutrinos. These particles zip through the universe almost entirely unimpeded, passing through planets and stars as if they were made of thin air. To catch them, scientists build massive detectors filled with special materials, such as liquid gallium, a soft metal that sits just below mercury on the periodic table. When a neutrino from the sun strikes a gallium atom, it can transform that atom into a different element, germanium, releasing a tiny signal that researchers can measure. For decades, these experiments have been our primary window into the sun's inner workings. However, a persistent mystery has clouded these observations: the detectors consistently find fewer neutrinos than the standard models of the sun predict. This discrepancy, known as the "gallium anomaly," has led some to wonder if the missing particles are not just hiding, but actually changing into a new, invisible type of particle that does not interact with normal matter at all.

To solve this puzzle, scientists must be absolutely certain about how the gallium atoms themselves behave when struck. The reaction depends on the internal structure of the atom, specifically how its protons and neutrons are arranged and how they respond to the incoming neutrino. The gallium atom has a ground state, its resting position, but it also has excited states, like rungs on a ladder, where it can jump to higher energy levels. If the atom jumps to these higher levels, it changes the total number of neutrinos the detector sees. For years, researchers assumed these jumps were rare or simple, but a new study suggests the reality is more complex. The team, led by physicists in Japan and India, set out to measure exactly how likely the gallium atom is to jump to these excited states when hit by a low-energy neutrino, a crucial piece of information that had been missing or uncertain.

The researchers approached this problem by combining three different ways of looking at the atom. First, they looked at data from electron capture, a natural process where a gallium atom absorbs an electron and turns into germanium, which acts like a mirror image of the neutrino reaction. Second, they used data from charge exchange reactions, a technique where scientists fire a beam of helium-3 nuclei at a gallium target to knock the atoms into excited states, mimicking the effect of a neutrino. Finally, they used powerful computer simulations based on the nuclear shell model, which treats the protons and neutrons inside the nucleus like electrons orbiting an atom, to predict how the atom should behave. The challenge was that the second method, the beam experiment, is influenced by a subtle force called the tensor interaction, a specific type of push and pull between the particles inside the nucleus that had been largely ignored in previous analyses.

In their analysis, the team realized that this tensor force was distorting the results of the beam experiments, making it look as though the atom was jumping to excited states more often than it actually was. By carefully correcting for this force using their computer models and the electron capture data, they were able to isolate the true signal. They found that the gallium atom does indeed jump to its first and second excited states, but the frequency of these jumps is much lower than some earlier estimates suggested. Specifically, the combined contribution of these two excited states to the total neutrino signal is about 4.2 percent, with an uncertainty of 1.2 percent. This value is slightly higher than what the computer simulations predicted on their own, but it is significantly lower than the uncorrected beam data.

The implications of this finding are direct and significant for the mystery of the gallium anomaly. The researchers calculated that even with these newly refined numbers, the total number of neutrinos the detector should see remains far higher than what the BEST experiment actually observed. The gap between the prediction and the observation is so large that the uncertainty in the nuclear physics cannot explain it. In other words, the missing neutrinos are not a result of the gallium atoms behaving in a strange or unexpected way. The study effectively rules out the idea that the anomaly is caused by a misunderstanding of how the detector works. Instead, the evidence points strongly toward the neutrinos themselves changing into a different, sterile state before they reach the detector. By clarifying the behavior of the gallium atom, this work has removed a major potential source of error, leaving the search for new physics as the only remaining explanation for the missing particles.

Technical Summary: Low-energy neutrino responses for 71Ga by electron capture rates, charge exchange reactions and shell model calculations

Problem Statement
The paper addresses the critical need for precise nuclear response data for the $^{71}\text{Ga}$ nucleus, specifically regarding low-lying states, to resolve the "Ga anomaly." This anomaly, recently highlighted by the BEST experiment, indicates a deficit of 17–18% in detected electron neutrinos compared to expectations, potentially suggesting a transition to a sterile neutrino state. A key uncertainty in interpreting these results lies in the accurate determination of the charged-current (CC) neutrino interaction rates for the ground state ( $1/2^-$ ), the first excited state ( $5/2^-$ at 175 keV), and the second excited state ( $3/2^-$ at 500 keV) of $^{71}\text{Ga}$ . While the ground state response is well-constrained by electron capture (EC) data, the responses for the excited states are complex, involving non-simple quasi-particle transitions, $l$ -forbidden transitions, and quadrupole-phonon components. Furthermore, previous determinations using Charge Exchange Reactions (CERs) often neglected the significant contribution of the tensor interaction operator, which is crucial for these specific excited states.

Methodology
The authors evaluate the Gamow-Teller (GT) nuclear matrix elements (NMEs), $B_i(\text{GT})$ , for the three low-lying states ( $i=0,1,2$ ) by integrating three distinct data sources:

Experimental Electron Capture (EC) Rates: Used primarily to establish the baseline NME for the ground state transition ( $^{71}\text{Ga} \to ^{71}\text{Ge}$ ).
High-Energy Resolution Charge Exchange Reactions (CERs): Utilizing $(^3\text{He}, t)$ reaction data on $^{71,69}\text{Ga}$ obtained at RCNP (Osaka University). The analysis focuses on the forward-angle $s$ -wave triton angular distributions corresponding to the $J_p=1, J_t=1, J_r=0$ ($110$) mode.
Interacting Shell Model (ISM) Calculations: Performed using the JUN45 effective interaction within the $fp$- $g_{9/2}$ model space. These calculations provide the theoretical NMEs for both the GT operator and the rank-1 tensor operator ( $T_1$ ).

A central methodological innovation is the explicit correction of CER data for the tensor interaction contribution. The authors recognize that the observed CER cross-section strength, $M_i(110)$ , is a mixture of the GT and tensor ( $T_1$ ) components: $M_i(110) = M_i(\text{GT}) + \epsilon M_i(T_1)$ . By calculating the tensor NMEs ( $M_i(\text{ISMT1})$ ) via the shell model and determining the mixing coefficient $\epsilon$ (found to be $0.26 \pm 0.06$ ) using data from the $l$ -forbidden transition in $^{69}\text{Ga}$ , the authors isolate the pure GT strength $M_i(\text{GT})$ for the excited states. A quenching coefficient of $k = 0.74$ is applied to the shell model NMEs to account for non-nucleonic correlations and medium effects.

Key Contributions and Results

First-Time Evaluation: This work presents the first evaluation of the neutrino responses for the first and second excited states of $^{71}\text{Ga}$ by combining experimental EC rates, tensor-corrected CER rates, and ISM calculations.
Tensor Correction: The study demonstrates that the tensor interaction significantly affects the CER cross-sections for the excited states, particularly the first excited state ( $5/2^-$ ), which is dominated by an $l$ -forbidden transition. Without correcting for the tensor contribution, the CER-derived GT strength is overestimated.
Quantitative Results:
- The ground state NME ( $M_0(\text{GT})$ ) is determined to be $0.603 \pm 0.02$ , consistent with the EC value of $0.585$.
- The first excited state ( $5/2^-$ ) exhibits a very small GT NME ( $0.01 \pm 0.05$ ), confirming its nature as a primarily $l$ -forbidden transition where the tensor component dominates the CER signal.
- The second excited state ( $3/2^-$ ) shows a GT NME of $0.255 \pm 0.03$ , attributed to quadrupole-phonon transitions.
Impact on Solar and $^{51}\text{Cr}$ Neutrino Rates: The combined contribution of the two excited states to the total neutrino interaction rate is found to be $4.2 \pm 1.2\%$ of the ground state rate. This value is slightly larger than the pure ISM prediction (where the total rate factor is $K=1.025$ ) but smaller than the uncorrected CER value (where the total rate factor is $K=1.073$ ). The resulting correction factor $K$ for the total rate in the tensor-corrected analysis is $1.042 \pm 0.012$ .

Significance and Claims
The authors claim that their re-analysis, which rigorously corrects for tensor interactions, provides a more realistic assessment of the nuclear responses for $^{71}\text{Ga}$ . The primary conclusion is that the observed "Ga anomaly" (the 17–18% deficit in neutrino detection) is far beyond the uncertainty range of these newly obtained nuclear responses. Consequently, the paper asserts that the anomaly cannot be attributed to uncertainties in the nuclear cross-sections or the contributions of excited states, thereby reinforcing the hypothesis that the deficit may indeed stem from new physics, such as electron-neutrino transitions to a sterile state. The work establishes a new methodology for extracting pure GT strengths from CER data in cases where tensor interactions are non-negligible.

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