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Bremsstrahlung emission accompanying ternary fission of \isotope[252]{Cf}

This paper presents a new quantum model demonstrating that bremsstrahlung emission in the ternary fission of $^{252}$ Cf is highly sensitive to the process's geometry and dynamics, particularly the relative motion of heavy fragments, with theoretical predictions aligning well with preliminary experimental data.

Original authors: Sergei P. Maydanyuk, Ju-Jun Xie, Sergei O. Omelchenko

Published 2026-08-14

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CC BY 4.0

Original authors: Sergei P. Maydanyuk, Ju-Jun Xie, Sergei O. Omelchenko

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

Imagine the atomic nucleus not as a static marble, but as a squishy, energetic blob of dough. Sometimes, this dough gets so excited that it snaps apart. Usually, it splits cleanly into two big chunks, a process scientists call "binary fission." But occasionally, the dough is so restless that it doesn't just split in two; it launches a tiny, fast-moving piece (like a little marble of helium) out the side while the two big chunks fly apart. This rare event is called "ternary fission." It's like a trampoline act where two acrobats jump apart, but a third, smaller acrobat is launched into the air at the exact same moment.

When these charged particles zip away from each other at incredible speeds, they don't just move; they scream. In the world of physics, accelerating electric charges emit light, but because these particles are moving so fast and changing direction so violently, they emit a special kind of light called "bremsstrahlung." The name is German for "braking radiation," which is a perfect description: as the particles brake or swerve, they shed energy in the form of photons (packets of light). While scientists have studied this "screaming light" in other nuclear reactions for decades, no one had ever really figured out exactly what this light looks like when it comes from the chaotic, three-way split of ternary fission. Understanding this glow is like listening to the specific sound of a car crash to figure out exactly how the cars were moving and how hard they hit each other; it reveals hidden details about the crash that you can't see with your eyes.

In this paper, the authors build a brand-new quantum model to listen to that light. They focus on the most common type of ternary fission, where a heavy nucleus (specifically Californium-252) splits into two heavy fragments and shoots out an alpha particle (a helium nucleus). Using their new mathematical "ears," they simulate the entire process to predict the spectrum—the specific colors and intensities—of the braking radiation. They find that the light emitted is incredibly sensitive to the geometry and speed of the split. For instance, the light is brightest when the alpha particle shoots out sideways, perpendicular to the path of the two heavy fragments. Most importantly, they discover that the biggest contributor to this light isn't the alpha particle itself, but the relative motion between the two heavy fragments as they fly apart. The faster those two heavy chunks move away from each other, the more intense the light becomes.

The authors also tested their model against some preliminary experimental data that was already available. Their simulation, which accounts for the complex dance of the three fragments and the changing shape of the nuclear "neck" where they separate, matches the early data surprisingly well. They suggest that by refining their model with better experimental measurements, scientists could use this "braking light" to map out the exact dynamics of the fission process, essentially using the photons to see the invisible mechanics of how the nucleus tears itself apart. The study confirms that the motion of the heavy fragments is the dominant factor in creating this radiation, a finding that adds a new layer of understanding to how these rare nuclear events unfold.

Technical Summary: Bremsstrahlung Emission Accompanying Ternary Fission of $^{252}\text{Cf}$

Problem Statement
Ternary fission, a rare decay process where a heavy nucleus splits into three fragments (typically two heavy fragments and a light charged particle, LCP), is accompanied by the emission of bremsstrahlung photons. While bremsstrahlung has been extensively studied in other nuclear reactions and binary fission, its emission specifically accompanying ternary fission has not been investigated theoretically or experimentally until now. The primary objective of this work is to clarify what new information regarding the geometry and dynamics of ternary fission can be extracted from the study of these bremsstrahlung spectra, specifically for the $^{252}\text{Cf}$ nucleus with an $\alpha$ -particle as the LCP.

Methodology
The authors developed a new quantum mechanical model to describe bremsstrahlung emission in ternary fission. The methodology involves several key steps:

Geometric Modeling: The nuclear system is modeled as three fragments (two heavy fragments and an $\alpha$ -particle) connected by necks. The surface geometry is defined using a set of parameters describing the separation distances and angles. The model assumes the $\alpha$ -particle separates from the neck region, moving perpendicular to the fission axis in the most probable configuration.
Interaction Potential: A total interaction potential ( $V_{total}$ ) between the $\alpha$ -particle and the binary nucleus (composed of the two heavy fragments) is calculated. This potential includes nuclear and Coulomb components. To handle the complexity of the three-body geometry, the authors introduce an equivalent charge ( $Z_{eq}$ ) for the binary nucleus at large distances to ensure calculation stability. The potential depends on the relative distance ( $r$ ) between the $\alpha$ and the binary nucleus, the distance between the two heavy fragments ( $R_{12}$ ), and the angle ( $\phi$ ) between the fragment separation axis and the $\alpha$ -particle's motion.
Matrix Element Formulation: The bremsstrahlung matrix element is derived by considering the photon emission operator acting on the system of nucleons. The calculation separates the contribution from the relative motion of the $\alpha$ -particle against the binary nucleus and the contribution from the relative motion of the two heavy fragments themselves.
Probability Calculation: The differential probability of photon emission is calculated by integrating over the final states. The model accounts for different mass separations of the heavy fragments, various angular geometries ( $\phi$ ), and the dynamics of the relative motion (parameterized by a coefficient $C_1$ relating $R_{12}$ to $r$ ).
Dynamical Approximation: To address the difficulty in calculating the matrix element for the relative motion of the heavy fragments, the authors introduce an approximation involving a function $F[k, \cos(k, r)]$ . This function is tuned to match preliminary experimental data, distinguishing between low-energy emission (dominated by the $\alpha$ -particle in the field of the unseparated binary nucleus) and high-energy emission (dominated by the accelerating heavy fragments).

Key Results
The theoretical calculations yield the following findings regarding bremsstrahlung in the ternary fission of $^{252}\text{Cf}$ :

Angular Dependence: The intensity of bremsstrahlung emission is highest when the $\alpha$ -particle moves perpendicular to the fission axis ( $\phi = 90^\circ$ ). This aligns with the most probable emission direction observed in ternary fission literature.
Source of Emission: The relative motion between the two heavy fragments provides the most significant contribution to the total bremsstrahlung spectrum. The emission resulting from the $\alpha$ -particle leaving the system of heavy fragments is significantly less intense.
Dynamics and Intensity: The intensity of bremsstrahlung increases with the speed of the relative motion between the two heavy fragments. Faster separation leads to more intensive radiation.
Mass Separation: The spectra show sensitivity to the mass separation of the binary nucleus into two fragments. The calculated spectra generally agree with the shape of preliminary experimental data, though discrepancies exist in the 200–400 keV photon energy range.
Neck Geometry: The model establishes a small dependence of the bremsstrahlung spectrum on the initial distance ( $R_{12,0}$ ) between the heavy fragments at the moment of $\alpha$ -particle separation, provided the distance remains within the applicability of the model's approximations.

Significance and Claims
The paper claims that the theoretical study demonstrates a high sensitivity of bremsstrahlung spectra to the specific geometry and dynamics of the ternary fission process. The authors assert that:

This is the first theoretical study of bremsstrahlung specifically in ternary fission, noting that such emission has never been studied experimentally for this process prior to this work.
The developed model describes the mechanisms of the ternary fission process and shows good agreement with preliminary experimental data for $^{252}\text{Cf}$ , particularly when using the improved dynamical approximation, though some disagreement remains in the 200–400 keV range.
The bremsstrahlung spectrum serves as a probe for the ternary fission mechanism, particularly the dynamics of the heavy fragment separation and the geometry of the $\alpha$ -particle emission.
Future, more precise experimental measurements of bremsstrahlung in $^{252}\text{Cf}$ ternary fission will allow the model to extract new, specific information about the fission process, such as optimal separation distances and detailed dynamical parameters.

The work concludes that while current results show agreement with preliminary data trends, the full potential of the model to reveal new nuclear physics information depends on the availability of reliable, high-precision experimental data.

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