Properties of states in \textsuperscript{19}Ne important for the \textsuperscript{18}F$(p,\alpha)$\textsuperscript{15}O reaction rate

This study determines the properties of key resonances in $^{19}$Ne using experimental angular distributions and theoretical modeling to refine the $^{18}$F($p,\alpha$)$^{15}$O reaction rate, revealing that previous estimates significantly underestimated the associated uncertainties for classical nova positron production.

The Gist

The Cosmic Mystery: Why Don't We See the "Nova Glow"?

Imagine a Classical Nova as a cosmic fireworks show. It happens when a small, dense star (a white dwarf) steals gas from a neighboring star. When enough gas piles up, it explodes in a thermonuclear blast.

Scientists have a big puzzle: They expect to see a very specific type of light coming from these explosions almost immediately after they happen. This light is a 511-keV gamma ray, which is essentially a "flash" created when a particle called a positron (the antimatter twin of an electron) crashes into an electron and annihilates.

The main culprit expected to create this flash is a radioactive isotope called Fluorine-18 ($^{18}\text{F}$). Think of $^{18}\text{F}$ as a glowing firework fuse. If it survives the explosion long enough, it decays and creates the flash we want to see.

The Problem: We haven't seen this flash yet. Why?
The answer lies in how fast the fuse burns out. In the hot, chaotic environment of a nova, the Fluorine-18 can be destroyed by colliding with a proton (a hydrogen nucleus) before it has a chance to decay. This reaction is written as $^{18}\text{F}(p, \alpha)^{15}\text{O}$.

If this reaction happens too fast, the Fluorine-18 is destroyed, the flash never happens, and our telescopes see nothing. If it happens slowly, the Fluorine-18 survives, and we should see the flash.

The Investigation: Mapping the "Traffic Jams"

To figure out how fast this destruction happens, the scientists in this paper studied the "traffic jams" inside a different atom called Neon-19 ($^{19}\text{Ne}$).

The Analogy:
Imagine the reaction between Fluorine-18 and a proton as a car trying to drive through a tunnel.

• The Tunnel: The tunnel is the energy landscape of Neon-19.
• The Bumps: Inside the tunnel, there are specific "bumps" or "speed bumps" (called resonances or energy states).
• The Traffic: If the car hits a bump at just the right speed, it gets stuck for a moment (a resonance), which makes it much more likely to crash into something else (the reaction happens).

For decades, scientists knew where some of these bumps were, but they weren't sure exactly how high they were, how wide they were, or how many of them existed. Some scientists thought there were only a few bumps; others suspected there were hidden ones.

What the Scientists Did

The team, led by researchers from Louisiana State University and Florida State University, built a "particle accelerator" (a giant machine that shoots particles at high speeds) to smash a beam of Helium-3 into a target of Calcium Fluoride.

The Experiment:

1. The Shot: They fired particles to create Neon-19 in an excited state (like hitting a bell to make it ring).
2. The Listen: They listened to how the Neon-19 "ringed" by detecting the particles it spit out (tritons, protons, and alpha particles).
3. The Map: By measuring the angles and energies of these spit-out particles, they could map out the exact location and shape of the "bumps" in the Neon-19 tunnel.

The Big Discovery: More Bumps Than We Thought

The team found six specific "bumps" (energy states) that are crucial for the reaction. Some of these were right at the edge of the tunnel entrance, and some were just below it.

The Twist:
Previous studies thought they had a pretty good handle on these bumps. They thought the uncertainty (the "fog" around the map) was small.
This paper says: "No, the fog is much thicker."

They found that:

1. There are more "bumps" than previously thought.
2. These bumps interact with each other in complex ways (like waves crashing into each other). Sometimes they cancel each other out; sometimes they amplify the reaction.
3. Because of this complex interaction, the speed at which Fluorine-18 gets destroyed is highly uncertain.

Why This Matters: The "What If" Scenario

Here is the most exciting part of the conclusion:

• Old View: We thought Fluorine-18 was destroyed very quickly. So, we didn't expect to see the 511-keV flash.
• New View: Because of the new data, it's possible that Fluorine-18 is destroyed much slower than we thought.

The Metaphor:
Imagine you are waiting for a bus.

• Old Theory: The bus leaves the station immediately. You miss it.
• New Theory: The bus might be stuck in traffic for a long time. If it stays, you might catch it.

If Fluorine-18 survives longer, the nova will produce more of the 511-keV gamma rays. This means:

1. We might finally see the flash! Future telescopes (like the COSI mission mentioned in the paper) might finally detect these explosions.
2. We can learn more about the universe. If we can see these flashes, we can measure how much new material (like Carbon, Nitrogen, and Oxygen) these explosions are creating and spreading across the galaxy.

Summary in One Sentence

This paper redrew the map of a tiny atomic world, discovering that the "traffic jams" inside Neon-19 are more complex than we thought, which suggests that the radioactive fuel for nova explosions might last longer than expected, potentially making these cosmic fireworks visible to our telescopes for the first time.

Technical Summary

1. Problem Statement

The detection of the 511-keV positron-annihilation line from classical novae is a critical goal for upcoming gamma-ray missions like COSI. This emission is primarily driven by the $\beta^+$ decay of $^{18}$F ($t_{1/2} \approx 110$ min). However, the abundance of $^{18}$F in a nova envelope is highly sensitive to its destruction rate via the $^{18}$F(p, $\alpha$)$^{15}$O reaction.

This reaction proceeds through resonances in the compound nucleus $^{19}$Ne. Previous studies have attempted to constrain the reaction rate by identifying proton s-wave ($L_p=0$) states near the proton threshold ($S_p = 6410$ keV) in $^{19}$Ne. However, significant uncertainties remain due to:

• Ambiguities in the spin-parity ($J^\pi$) assignments of near-threshold states.
• Uncertainties in the Asymptotic Normalization Coefficients (ANCs) for bound states.
• Complex interference effects between multiple resonances (specifically $J^\pi = 1/2^+$ and $3/2^+$ states) which were previously underestimated.

2. Methodology

The authors employed a combination of experimental nuclear physics and ab initio theoretical modeling to resolve these uncertainties.

Experimental Approach:

• Reaction: The study utilized the $^{19}$F($^3$He, t)$^{19}$Ne transfer reaction to populate excited states in $^{19}$Ne.
• Facility: Experiments were conducted at the John D. Fox Superconducting Linear Accelerator Laboratory (Florida State University) using a 24-MeV $^3$He beam on a CaF$_2$ target.
• Detection:
  • Tritons: Detected using the Super Enge Split-Pole Spectrograph (SE-SPS) to identify the excitation energy of $^{19}$Ne states.
  • Decay Products: The SABRE (Silicon Array for Branching Ratio Experiments) detector, placed at backward angles, detected light ions (protons and $\alpha$ particles) from the decay of unbound states in coincidence with tritons.
• Analysis:
  • Angular distributions of decay products were measured to determine orbital angular momentum transfers ($L_\alpha$ and $L_p$).
  • Fits using Legendre polynomials were used to extract $L$-values and branching ratios ($\Gamma_x/\Gamma$).
  • R-matrix Analysis: The AZURE2 code was used to calculate the astrophysical S-factor and reaction rate, incorporating the new experimental data and varying parameters (ANCs, reduced partial widths) within their uncertainties.

Theoretical Approach:

• SA-NCSM: The authors used the Symmetry-Adapted No-Core Shell Model with Continuum (SA-NCSM) to calculate proton ANCs for states where experimental data was unavailable.
• Calculations: Overlap functions $\langle ^{19}\text{Ne} | p + ^{18}\text{F}(\text{g.s.}) \rangle$ were computed using the NNLO$_{\text{opt}}$ chiral potential.

3. Key Contributions and Results

A. Identification of Six Proton s-Wave States
The study identified six critical proton s-wave ($L_p=0$) levels between 5 and 7 MeV in $^{19}$Ne:

• Five sub-threshold (bound) states: 5.548, 5.826, 6.067, 6.133, and 6.285 MeV.
• One proton-unbound resonance: 7.074 MeV.

B. Resolution of State Assignments

• 5.486 MeV vs. 5.548 MeV: Contradicting previous work (Kahl et al.) that identified a candidate at 5.486 MeV, this study's $\alpha$-angular distribution analysis ($L_\alpha=2$) suggests the 5.491 MeV state is not an s-wave. Instead, a state at 5.548 MeV is identified as the proton s-wave ($J^\pi = 1/2^+, 3/2^+$).
• 6.285 MeV State: While previous studies suggested a doublet structure, the current data (angular distributions and width of 33 keV FWHM) favors a single state with $L_\alpha=1$ ($J^\pi = 1/2^+, 3/2^+$). Even if a higher-spin doublet exists, only the $1/2^+, 3/2^+$ component significantly impacts the reaction rate.
• 6.459 MeV Region: The region contains narrow resonances and a broad state. The authors found that while $L_\alpha=2$ fits the 6.459 MeV state best, contamination from lower-energy states cannot be ruled out; thus, an $L_p=0$ assignment remains statistically possible.
• High-Energy Resonances: Two new s-wave candidates were identified at 7.615 MeV ($L_p=0$) and 7.795 MeV (mixed $L_p$, but $J^\pi=1/2^+, 3/2^+$ adopted).

C. Reaction Rate and Uncertainty Analysis

• Interference Effects: The R-matrix calculations revealed that interference between the identified s-wave states creates a significantly broader range of possible reaction rates than previously estimated.
• Impact of ANCs: The reaction rate at nova-relevant energies (0.1–0.4 GK) is highly sensitive to the ANCs of the bound s-wave states.
• Comparison to Previous Work:
  • The new analysis shows that earlier studies (e.g., Portillo et al.) significantly underestimated uncertainties.
  • The results imply the $^{18}$F(p, $\alpha$)$^{15}$O reaction rate could be significantly lower than recent determinations.
  • A lower destruction rate leads to a higher predicted abundance of $^{18}$F, and consequently, a higher flux of 511-keV gamma rays.

4. Significance

• Astrophysical Implications: The finding that the reaction rate may be lower than previously thought increases the likelihood of detecting the 511-keV line from classical novae. This makes the detection of fainter novae via gamma-ray telescopes (like COSI) more feasible.
• Nuclear Physics Constraints: The work highlights that accurate reaction rates require precise knowledge of:
  1. Spin-parity assignments for sub-threshold and near-threshold states.
  2. Proton ANCs for these states.
  3. The complex interference patterns between multiple resonances, which cannot be constrained by a limited subset of states.
• Methodological Advance: The successful integration of experimental transfer reaction data with ab initio SA-NCSM calculations provides a robust framework for reducing uncertainties in nuclear astrophysics reaction rates.

In conclusion, this paper refines the nuclear physics inputs for the $^{18}$F(p, $\alpha$)$^{15}$O reaction, demonstrating that current uncertainties are larger than previously believed and suggesting a higher potential for $^{18}$F survival in novae, which is crucial for interpreting future gamma-ray observations.