Experimental Study of Bremsstrahlung Gamma Ray Emission and Short-Range Correlations in $^{124}$Sn+$^{124}$Sn Collisions at 25 MeV/u

This study presents a precision measurement of bremsstrahlung gamma rays in $^{124}$Sn+$^{124}$Sn collisions at 25 MeV/u using the CSHINE spectrometer, establishing a robust experimental framework to extract a high momentum tail fraction of $(20 \pm 3)\%$ and demonstrating the feasibility of probing short-range correlations in low-energy heavy-ion reactions.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Big Idea: Finding the "Secret Handshakes" Inside an Atom

Imagine an atom's nucleus as a crowded dance floor. Usually, we think of the dancers (protons and neutrons) moving around in a predictable, organized way, like people swaying gently to a slow song. This is the "standard model" of how atoms work.

But physicists suspect that sometimes, two dancers suddenly grab each other, spin wildly, and move incredibly fast, breaking away from the slow crowd. These are called Short-Range Correlations (SRCs). They are like secret handshakes between neighbors that happen for a split second but give those two dancers a massive burst of energy (high momentum).

The big question this paper answers is: How many of these "wild spin" pairs exist inside a specific atom (Tin-124), and how fast are they moving?

The Experiment: Smashing Atoms to See the Flash

To find these hidden pairs, the scientists didn't just look at the atom; they smashed two of them together.

1. The Setup: They took two heavy atoms of Tin-124 and smashed them together at a speed of 25 million electron volts per particle. Think of this as crashing two cars together at highway speeds, but on a microscopic scale.
2. The Flash: When these atoms collide, the protons and neutrons inside them crash into each other. If two neutrons and protons are already holding hands (an SRC pair) and moving super fast, their collision creates a bright flash of light—a Gamma Ray.
   • Analogy: Imagine two cars crashing. If they are moving normally, they make a loud crunch. But if they were already speeding down a ramp before the crash, the explosion is much brighter and hotter. That "brightness" is the Gamma Ray.
3. The Detector: They used a giant, high-tech camera called CSHINE (Compact Spectrometer for Heavy Ion Experiment). It's like a super-sensitive eye that can catch these flashes of light even if they are very faint or very fast.

The Challenge: Seeing the Signal in the Noise

The problem is that the "flash" from the wild, fast-moving pairs is very rare. Most of the time, the collision just makes a lot of "background noise" (like static on a radio or a crowd cheering in the background).

The scientists had to be like detectives filtering out the noise:

• The "Beam Off" Method: They ran the experiment with the particle beam turned off to see what the background noise looked like (just cosmic rays hitting the detector). Then they subtracted that from the "Beam On" data.
• The "Fast Coincidence" Method: They looked for flashes that happened at the exact same time as the particle crash, ignoring anything that happened a split second later (which is usually just random noise).

By using these two different detective techniques, they made sure their results weren't just a fluke.

The Result: The "High-Speed Tail"

After crunching the numbers and comparing their data to complex computer simulations (which act like a virtual reality test drive), they found the answer.

They discovered that about 20% of the nucleons (protons and neutrons) in the Tin-124 nucleus are part of these high-speed "wild spin" pairs.

• The Metaphor: Imagine a school of fish. Most fish swim at a steady, average speed. But this study proved that about 1 out of every 5 fish is actually a speedboat, zooming around much faster than the rest. This group of speedboats is what physicists call the High-Momentum Tail (HMT).

Why Does This Matter?

1. It's a New Way to Look: Usually, scientists study these fast pairs using electron beams (like shining a flashlight). This paper proves you can also find them by smashing atoms together and listening for the "flash" (Gamma rays). It's like proving you can hear a thunderstorm just as well by feeling the wind as by seeing the lightning.
2. Understanding the Universe: These fast-moving pairs are key to understanding how matter behaves under extreme pressure, like inside a neutron star (the core of a collapsed star). If we don't understand these "secret handshakes," our models of the universe are incomplete.
3. Precision: Previous experiments had a lot of uncertainty (like guessing the speed of a car from a blurry photo). This experiment used a brand-new, upgraded detector and better math to give a very precise answer: 20% ± 3%.

The Bottom Line

This paper is a success story of "smashing and listening." By smashing Tin atoms together and carefully listening for the specific "flash" of light that only high-speed pairs can make, the scientists confirmed that one-fifth of the matter inside these atoms is moving at extreme speeds due to short-range correlations. It's a major step forward in understanding the hidden, chaotic dance floor inside the heart of an atom.

Technical Summary

Here is a detailed technical summary of the paper "Experimental Study of Bremsstrahlung Gamma Ray Emission and Short-Range Correlations in 124Sn+124Sn Collisions at 25 MeV/u".

1. Problem Statement

The study addresses the challenge of quantifying Short-Range Correlations (SRC) in atomic nuclei. SRCs are transient, high-momentum nucleon pairs (predominantly neutron-proton) that exist beyond the Fermi surface, driven by the strong tensor component of the nucleon-nucleon interaction.

• Context: While electron scattering has been the primary tool for studying SRCs, hadronic reactions offer a complementary approach. High-energy bremsstrahlung $\gamma$-rays produced in heavy-ion collisions (HICs) are theoretically sensitive to the high-momentum tail (HMT) of the nucleon momentum distribution.
• Gap: Previous experiments (e.g., $^{86}\text{Kr} + ^{124}\text{Sn}$) provided preliminary evidence for SRC-induced HMT but suffered from limited energy coverage, restricted event reconstruction regions, and asymmetric reaction systems that prevented the isolation of SRC fractions for specific nuclei.
• Objective: To perform a high-precision, statistically robust measurement of bremsstrahlung $\gamma$-rays in a symmetric $^{124}\text{Sn} + ^{124}\text{Sn}$ collision system at 25 MeV/u to quantitatively extract the HMT fraction ($R_{\text{HMT}}$) and validate the feasibility of using low-energy HICs as a probe for SRCs.

2. Methodology

Experimental Setup

• Facility: The experiment was conducted at the Radioactive Ion Beam Line in Lanzhou (RIBLL-1) using the Compact Spectrometer for Heavy Ion Experiment (CSHINE).
• Reaction System: $^{124}\text{Sn} + ^{124}\text{Sn}$ at 25 MeV/u. The symmetric system allows for the determination of SRC fractions specific to the $^{124}\text{Sn}$ nucleus.
• Detection System:
  • $\gamma$-ray Detection: A CsI(Tl) hodoscope (CSHINE-Gamma) consisting of 15 units in a $4 \times 4$configuration (one corner vacant) located at$\theta_{\text{lab}} = 110^\circ$. It features improved high-energy detection efficiency and an extended energy range compared to previous setups.
  • Particle Identification: 8 Silicon-Strip Detector Telescopes (SSDTs) for light charged particles (LCPs) and a plastic scintillator array for neutrons.
  • Trigger: An FPGA-based logic system combining signals from SSDTs, the $\gamma$-hodoscope, and neutron arrays to select events with LCPs, high-energy $\gamma$s, and neutrons.
• Calibration: The CsI(Tl) response was calibrated using radioactive sources and tested for linearity at the Shanghai Laser Electron Gamma Source (SLEGS) using quasi-monochromatic $\gamma$-beams.

Theoretical Framework

• Model: The Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model with Momentum-Dependent Interactions (MDI).
• SRC Implementation: The initial nucleon momentum distribution incorporates SRC effects via a high-momentum tail parameterized as $C/k^4$ for momenta $k > k_F$. The fraction of nucleons in this tail is denoted as $R_{\text{HMT}}$.
• Bremsstrahlung Mechanism: The model simulates $\gamma$-ray production primarily via neutron-proton collisions ($np \to np\gamma$) using a neutral scalar $\sigma$ meson exchange model. The probability of photon emission is calculated perturbatively based on the relative velocity of colliding nucleons.

Data Analysis Techniques

The authors employed three distinct, complementary approaches to ensure robustness:

1. Slow Coincidence (Beam-Off Subtraction):
   • Used the entire dataset within a slow coincidence window.
   • Background was estimated using "beam-off" measurements (cosmic rays).
   • Systematic uncertainties were evaluated by varying calibration parameters and normalization energy ranges.
2. Fast Coincidence (Beam-On Subtraction):
   • Used a fast coincidence gate defined by the trigger.
   • Background was estimated from a time window of the same width but far from the main trigger (random coincidences).
   • Events with specific SSD triggers (SSD M2) were excluded to avoid timing jitter issues.
3. Inverse Problem Reconstruction (Richardson-Lucy Algorithm):
   • To compare directly with theory without detector response folding, the measured $\gamma$-spectrum was "unfolded" to reconstruct the original energy spectrum.
   • The Richardson-Lucy (RL) algorithm was used to solve the inverse problem, iteratively deconvolving the detector response matrix.

3. Key Contributions

• Precision Measurement: Achieved the first statistically high-precision extraction of the SRC fraction in low-energy heavy-ion collisions using bremsstrahlung $\gamma$-rays.
• Symmetric System: Utilized the $^{124}\text{Sn} + ^{124}\text{Sn}$ reaction to isolate the SRC properties of a specific nucleus, overcoming limitations of previous asymmetric systems.
• Methodological Validation: Established a comprehensive framework involving independent background subtraction methods (beam-off vs. beam-on) and an independent spectral reconstruction (unfolding) to cross-validate results.
• Theoretical Sensitivity Studies: Systematically demonstrated that the high-energy bremsstrahlung spectrum is sensitive to $R_{\text{HMT}}$ but largely insensitive to other model parameters (impact parameter, mean-field potential, symmetry energy), confirming the reliability of the extraction method.

4. Results

• High-Momentum Tail Fraction ($R_{\text{HMT}}$):
  • Slow Coincidence Analysis: $R_{\text{HMT}} = (20.1 \pm 0.4_{\text{stat}} \pm 2.1_{\text{syst}})\%$.
  • Fast Coincidence Analysis: $R_{\text{HMT}} = (18.0 \pm 2.8)\%$.
  • Unfolded Spectrum Analysis: $R_{\text{HMT}} = (20.8 \pm 1.8)\%$.
• Final Combined Result: The study concludes with a robust value of:
  $$R_{\text{HMT}} = (20 \pm 3)\%$$
  This result indicates that approximately 20% of nucleons in $^{124}\text{Sn}$ possess momenta beyond the Fermi surface due to SRCs.
• Spectral Shape: The experimental spectrum shows a smooth high-energy tail consistent with SRC models. Notably, the broad hump-like structure near 60 MeV observed in previous lower-statistics experiments was absent, suggesting the previous feature was likely a statistical fluctuation rather than a physical signal (e.g., from the $np \to d\gamma$ channel).
• Significance: The non-zero $R_{\text{HMT}}$ is confirmed with a significance level greater than $5\sigma$.

5. Significance

• New Probe for Nuclear Structure: This work validates bremsstrahlung $\gamma$-rays in low-energy heavy-ion collisions as a "clean" and sensitive probe for SRCs. Unlike hadronic probes, photons interact weakly with the nuclear medium, minimizing final-state interaction complications.
• Bridging Scales: The results provide crucial constraints on the high-momentum components of nucleon momentum distributions, linking nuclear many-body physics with quark-gluon dynamics (via the EMC effect connection).
• Methodological Benchmark: The paper sets a new standard for analyzing heavy-ion collision data by demonstrating how to rigorously handle systematic uncertainties, background subtraction, and detector unfolding to extract fundamental nuclear properties.
• Future Outlook: The established framework opens the door for future studies of SRCs in other nuclei and at different energies, potentially offering insights into the equation of state of dense nuclear matter and neutron star interiors.