Precise determination of electron-capture $Q$ value of $^{113}$Sn decay related to electron neutrino mass measurements

This study utilizes the JYFLTRAP double Penning trap to precisely measure the electron-capture $Q$ value of $^{113}$Sn, identifying a favorable allowed transition to a low-lying excited state in $^{113}$In that, when combined with advanced atomic corrections, significantly enhances sensitivity for future electron neutrino mass measurements.

The Gist

The Big Picture: Weighing the Invisible Ghost

Imagine you are trying to weigh a ghost. You can't put it on a scale, but you know that when the ghost interacts with the world, it leaves behind a tiny, specific amount of energy. If you can measure that energy with extreme precision, you can figure out how heavy the ghost is.

In the world of physics, that "ghost" is the neutrino. It is a tiny, nearly massless particle that zips through everything without stopping. For decades, scientists have known neutrinos exist and that they have some mass, but they don't know exactly how much. Knowing this mass is crucial because it helps us understand how the universe began, why there is more matter than antimatter, and what dark matter might be.

This paper is about a team of scientists who built a super-precise "scale" to weigh a specific type of atomic decay, hoping to find a better way to catch that neutrino ghost.

The Experiment: The Atomic Balance Scale

The scientists used a machine called JYFLTRAP, which is essentially a high-tech, magnetic balance scale located in Finland.

1. The Setup: They created a specific type of atom called Tin-113 ($^{113}\text{Sn}$). This atom is unstable; it wants to change into a different element, Indium-113 ($^{113}\text{In}$).
2. The Process (Electron Capture): Instead of shooting out a particle like a cannonball (which is how most radioactive decay works), this atom "swallows" one of its own electrons. It's like a hungry atom eating its own lunch.
3. The Measurement: When the atom eats the electron, it releases a tiny bit of energy. The scientists used the JYFLTRAP machine to measure the mass of the "before" atom (Tin) and the "after" atom (Indium) with incredible accuracy. By comparing the two, they calculated exactly how much energy was released. This is called the Q-value.

The Analogy: Imagine you have a heavy backpack (the Tin atom). You take a small rock out of it (the electron) and the backpack suddenly becomes lighter (the Indium atom). By weighing the backpack before and after with a scale so precise it can detect the weight of a single grain of sand, you can calculate exactly how much energy was released when the rock was removed.

The Discovery: Finding the "Sweet Spot"

The team didn't just measure the main energy release; they looked for a very specific, rare scenario.

• The Problem: Usually, when an atom decays, the energy is spread out over a wide range, like a rainbow. To find the neutrino's mass, you need to look at the very edge of that rainbow (the "endpoint"). But the edge is often blurry and hard to see.
• The Solution: The scientists found that Tin-113 has a special "shortcut." It can decay into a specific excited state of Indium where the energy released is extremely close to the energy required to hold an electron in place.

The Analogy: Think of a golfer trying to sink a ball into a cup.

• Most decays are like hitting the ball from far away; it might roll near the cup, but it's hard to tell exactly how hard you hit it.
• This specific decay of Tin-113 is like the golfer standing right on the edge of the cup. The ball is so close to falling in that even the tiniest nudge (the mass of the neutrino) will determine if it goes in or not.

They found two such "sweet spots" (transitions):

1. One where the energy difference is about 15 keV.
2. One where the energy difference is about 9.6 keV.

The 9.6 keV transition is the star of the show. It is an "allowed" transition (meaning it happens relatively easily) and the energy is so close to the electron's binding energy that it creates a resonance.

The Resonance Effect: Imagine pushing a child on a swing. If you push at just the right moment (resonance), the swing goes huge. In this atom, because the energy levels are so perfectly matched, the "swing" of the decay rate gets amplified. This makes the "endpoint" events (the ones sensitive to neutrino mass) happen five times more often than expected. This is a massive boost for detection.

The Results: A New Precision Record

The team achieved two major milestones:

1. Super-Precise Weighing: They measured the mass difference between Tin and Indium with six times more precision than the previous best records. It's like upgrading from a bathroom scale to a scale that can weigh a single bacterium.
2. Validating the Candidate: They confirmed that Tin-113 is a viable candidate for future neutrino experiments. While it isn't as "loud" (has a lower decay rate) as the current favorite, Holmium-163, it has unique advantages:
   • It has a manageable half-life (about 115 days), making it easier to produce and handle in a lab.
   • It emits a clear "signature" (a gamma ray) that acts like a barcode, allowing scientists to filter out background noise easily.

Why This Matters

Currently, the best experiments to measure neutrino mass use Tritium (a heavy hydrogen) or Holmium. This paper suggests that Tin-113 could be a powerful new player in the game.

Because of the "resonance" effect they discovered, Tin-113 could allow scientists to see the neutrino's mass more clearly than ever before. If future experiments can harness this, we might finally crack the code on the absolute mass of the neutrino, solving one of the biggest mysteries in modern physics.

Summary in One Sentence

Scientists used a magnetic super-scale to weigh atoms with record-breaking precision, discovering that a specific type of Tin atom acts like a perfectly tuned musical instrument that amplifies the tiny signal of the neutrino's mass, offering a promising new path to weigh the universe's most elusive ghost.

Technical Summary

1. Problem Statement

Determining the absolute mass scale of neutrinos remains one of the most critical open questions in particle physics and cosmology. While neutrino oscillation experiments have confirmed that neutrinos have mass, they only provide mass-squared differences, leaving the absolute mass scale and hierarchy undetermined.

Direct kinematic measurements of weak nuclear decays offer a model-independent method to probe the absolute neutrino mass by analyzing the energy-momentum conservation at the spectral endpoint. Currently, the most sensitive experiments utilize low Q-value transitions in Tritium ($^3$H) $\beta$-decay (e.g., KATRIN) and Holmium-163 ($^{163}$Ho) electron capture (EC) (e.g., ECHo, HOLMES).

However, there is a need to identify new isotopes with ultra-low Q-value transitions (specifically ground-state-to-excited-state, or gs-to-es) to enhance sensitivity. Transitions where the Q-value is close to atomic shell binding energies can exhibit resonant enhancements near the spectral endpoint, significantly increasing the fraction of decays sensitive to neutrino mass. The paper addresses the need for high-precision Q-value measurements for Tin-113 ($^{113}$Sn) to evaluate its potential as a candidate for future neutrino mass experiments.

2. Methodology

The study employed high-precision mass spectrometry and advanced theoretical modeling:

Experimental Approach:

• Facility: The experiment was conducted at the JYFLTRAP double Penning trap mass spectrometer at the University of Jyväskylä, Finland.
• Ion Production: Radioactive $^{113}$Sn ions were produced via fusion-evaporation reactions using a 50 MeV $\alpha$-beam on a natural Cadmium target at the IGISOL facility.
• Separation & Purification: Ions were mass-separated using a dipole magnet and purified in a radiofrequency-quadrupole cooler-buncher (RFQ-CB) and a purification Penning trap using sideband buffer gas cooling to remove isobaric contaminants (specifically $^{113}$In).
• Measurement Technique: The Phase-Imaging Ion-Cyclotron-Resonance (PI-ICR) technique was used to measure the cyclotron frequency ratio ($R = \nu_{c,d}/\nu_{c,p}$) between the parent isomer ($^{113m}$Sn) and the daughter nucleus ($^{113}$In).
  • Two accumulation times (244 ms and 738 ms) were used to ensure unambiguous integer revolution assignment.
  • The method achieves a systematic uncertainty in the frequency ratio below $10^{-10}$.
• Q-Value Calculation: The isomeric Q-value ($Q^m_{EC}$) was derived from the mass difference. The ground-state-to-ground-state Q-value ($Q_{EC}$) was then calculated by subtracting the known isomeric excitation energy ($E^*_m = 77.389(19)$ keV).

Theoretical Approach:

• Atomic Physics: The self-consistent many-electron Dirac–Hartree–Fock–Slater (DHFS) method was used to calculate electron wave functions, binding energies, and corrections (exchange, overlap, shake-up, and shake-off).
• Nuclear Physics: The Nuclear Shell Model (using the NuShellX code with the $jj45pnb$ interaction) was employed to calculate nuclear matrix elements and partial half-lives.
• Spectral Analysis: Theoretical energy-release spectra were generated, explicitly including contributions from subthreshold atomic states (states where the Q-value is slightly below the binding energy but the resonance width extends into the observable region).

3. Key Contributions

• High-Precision Q-Value Determination: The study provides the most precise measurement of the $^{113}$Sn EC Q-value to date, improving the precision of the ground-state-to-ground-state transition by a factor of eight compared to the Atomic Mass Evaluation 2020 (AME2020).
• Identification of Candidate Transitions: By combining the new precise Q-value with nuclear level data, the authors identified two specific gs-to-es transitions in $^{113}$Sn that are energetically allowed and possess low Q-values suitable for neutrino mass studies.
• Theoretical Validation of Resonance Enhancement: The paper demonstrates that including subthreshold atomic states in the spectral function enhances the EC rate near the zero-neutrino-momentum region by a factor of five, a critical factor for experimental sensitivity.
• Comprehensive Decay Modeling: The authors calculated partial half-lives and energy-release spectra for the identified transitions, accounting for complex atomic and nuclear corrections.

4. Results

Experimental Results:

• Isomeric Q-value ($Q^m_{EC}$): $1116.64(19)$ keV.
• Ground-State-to-Ground-State Q-value ($Q_{EC}$): $1039.25(19)$ keV.
• Atomic Mass Excess of $^{113}$Sn: Determined as $-88327.87(27)$ keV/$c^2$. This value is in excellent agreement with AME2020 but offers a sixfold improvement in precision.
• Isomeric Mass Excess: $-88250.48(27)$ keV/$c^2$.

Candidate Transitions for Neutrino Mass:
Two transitions from the $^{113}$Sn ground state ($1/2^+$) to excited states in $^{113}$In were identified:

1. To $1024.280$ keV state ($5/2^+$):
   • Decay Type: Second-forbidden non-unique.
   • $Q^*_{EC} = 14.97(20)$ keV.
   • Distance to L1 shell ($\Delta L_1$): $10.95(20)$ keV.
2. To $1029.650$ keV state ($1/2^+$ or $3/2^+$):
   • Decay Type: Allowed (Gamow-Teller).
   • $Q^*_{EC} = 9.60(20)$ keV.
   • Distance to L1 shell ($\Delta L_1$): $5.58(20)$ keV.
   • Distance to L2 shell ($\Delta L_2$): $5.87(20)$ keV.

Theoretical Predictions:

• The allowed transition to the 1029.650 keV state is identified as the most promising candidate. Its small energy difference ($\Delta L \approx 5.6$ keV) from the L-shell binding energies leads to a strong resonant enhancement of endpoint events.
• Calculated partial half-lives for this transition are on the order of $10^9$–$10^5$ years (depending on the specific spin assignment and shell), though experimental values suggest a longer half-life ($\sim 30,000$ years), indicating potential discrepancies in the nuclear matrix element calculations for weak transitions.
• The inclusion of subthreshold states significantly boosts the spectral density near the endpoint.

5. Significance

• New Candidate for Neutrino Mass: $^{113}$Sn is established as a viable complementary candidate to $^{163}$Ho and $^{159}$Dy for future neutrino mass experiments. While its overall EC rate is lower than $^{163}$Ho, its allowed transition nature and proximity to L-shell binding energies offer unique advantages.
• Experimental Feasibility: The moderate half-life of $^{113}$Sn ($115.09$ days) and the availability of a clean $\gamma$-tagging cascade (via the 1029.650 keV transition) facilitate scalable source production and effective background rejection in cryogenic microcalorimeters.
• Methodological Advancement: The work highlights the critical importance of high-precision Penning trap mass spectrometry in identifying ultra-low Q-value transitions and demonstrates the necessity of including subthreshold atomic effects in theoretical spectral models to accurately predict experimental sensitivities.
• Future Outlook: The paper concludes that while $^{113}$Sn shows great promise, further precise measurements of the branching ratio for the 1029.650 keV transition are required to fully assess its potential for achieving sub-eV neutrino mass sensitivity.