Measurement of the isoscalar giant monopole resonance in $^{86}$Kr via deuteron inelastic scattering using an active target CAT-M

Using deuteron inelastic scattering in inverse kinematics with the CAT-M active target, researchers measured the isoscalar giant monopole resonance in $^{86}$Kr at 17 $\pm$ 1 MeV to investigate the nuclear matter incompressibility and its isospin dependence.

The Gist

The Big Picture: Squeezing the Atomic Nucleus

Imagine an atomic nucleus not as a static ball of dust, but as a giant, bouncy water balloon filled with protons and neutrons. If you were to squeeze this balloon, it would resist, then bounce back. The measure of how hard it is to squeeze this "nuclear balloon" is called nuclear incompressibility.

Scientists want to know exactly how "squishy" or "stiff" this balloon is. Why? Because this property dictates how matter behaves in the most extreme places in the universe, like inside neutron stars (which are basically giant atomic nuclei). If we know how stiff the nucleus is, we can better understand how big neutron stars are and how they crash into each other.

The Problem: The "Thin Target" Dilemma

To measure this stiffness, scientists usually hit a nucleus with a particle (like a deuteron) and listen to how the nucleus "breathes" (expands and contracts). This breathing mode is called the Isoscalar Giant Monopole Resonance (ISGMR).

However, there was a major technical problem:

• The Trade-off: To hear the "breathing" clearly, you need to look at the particles bouncing off at very shallow angles (like a golf ball skimming the grass). But these particles have very low energy.
• The Catch: If you use a thick target (like a solid sheet of metal), the low-energy particles get stopped or lost before they can be detected. If you use a thin target (to let them through), you don't have enough atoms to hit, so you get very few data points (bad statistics).

It was like trying to hear a whisper in a noisy room: if you stand too far away (thick target), you can't hear it; if you stand close but the room is empty (thin target), there's no one whispering.

The Solution: The "Smart Cloud" (CAT-M)

The researchers solved this by building a special device called CAT-M. Instead of a solid sheet of metal, they used a cloud of gas (deuterium) as their target.

Think of CAT-M as a giant, 3D camera that is also the target.

1. The Cloud: They filled a chamber with deuterium gas. This acts as the target. Because it's gas, the "bouncing" particles can travel through it without getting stuck.
2. The Camera: The gas is inside a special detector (a Time Projection Chamber). When a particle hits a gas atom, it leaves a trail of electrons, like a plane leaving a contrail in the sky. The detector maps this trail in 3D.
3. The Magnet: They put a magnet inside the cloud to sort the particles, acting like a sieve to filter out the "noise" (unwanted particles) so they can focus on the "signal" (the breathing mode).

This allowed them to use a thick cloud (lots of atoms to hit) while still catching the low-energy particles that usually get lost.

The Experiment: Squeezing Krypton-86

They took a beam of heavy atoms (Krypton-86) and fired them through this gas cloud.

• The Collision: The Krypton atoms smashed into the gas atoms.
• The Breath: The Krypton nucleus got excited and started "breathing" (expanding and contracting).
• The Measurement: By tracking the debris from the collision, they could calculate exactly how much energy was needed to make the nucleus breathe.

The Result: They found that the "breathing" energy for Krypton-86 is 17 MeV (about 17 million electron volts).

Why This Matters: The "Recipe" for Neutron Stars

The paper isn't just about Krypton. It's about a specific mathematical recipe that scientists use to predict how stiff nuclear matter is. This recipe has two main ingredients:

1. The Base Stiffness ($K_0$): How stiff normal matter is.
2. The "Flavor" Adjustment ($K_\tau$): How the stiffness changes if the nucleus has a different mix of protons and neutrons (like a recipe that changes if you add more salt than sugar).

Most previous experiments only looked at stable, "normal" nuclei. This experiment looked at Krypton-86, which is a bit "unbalanced" (it has more neutrons than protons).

By adding this new data point to the recipe, the scientists could refine the value of the "Flavor Adjustment" ($K_\tau$). While their measurement had a large margin of error (because Krypton-86 is unstable and hard to study), it confirmed that previous theories were on the right track.

The Takeaway

• The Innovation: They built a "gas cloud camera" (CAT-M) that solved the old problem of needing thick targets but catching low-energy particles.
• The Discovery: They successfully measured the "breathing mode" of a rare, unstable nucleus (Krypton-86) for the first time using this new method.
• The Impact: This proves that we can now study the "stiffness" of unstable nuclei. This is a crucial step toward understanding the physics of neutron stars, helping us answer questions like: How big are they? How do they explode?

In short, they invented a new way to "listen" to the heartbeat of unstable atoms, giving us a clearer picture of the universe's most extreme matter.

Technical Summary

1. Problem Statement and Motivation

The primary goal of nuclear physics research in this domain is to determine the Equation of State (EoS) for nuclear matter, which governs the behavior of nucleons in nuclei and astrophysical objects like neutron stars. A critical parameter in the EoS is the nuclear incompressibility ($K_0$) and its isospin-dependent term ($K_\tau$).

• The Challenge: While $K_0$ is relatively well-constrained by measurements on stable nuclei (e.g., Pb, Sn, Zr), $K_\tau$ remains uncertain. Determining $K_\tau$ precisely requires measuring the Isoscalar Giant Monopole Resonance (ISGMR) in unstable nuclei with varying isospin asymmetry.
• The Technical Barrier: Measuring ISGMR in unstable nuclei via inelastic scattering (e.g., $(d, d')$) is difficult because the resonance strength is concentrated at very forward angles ($\theta_{CM} \approx 0^\circ$). In these kinematics, the recoil particles have extremely low energies (often < 1 MeV).
  • Traditional thin targets are required to detect these low-energy recoils, but thin targets suffer from poor statistics.
  • Thick targets provide statistics but stop the low-energy recoils before detection.
  • Previous attempts using active targets (e.g., MAYA) faced limitations: $\alpha$-scattering suffered from energy loss preventing forward-angle detection, and deuteron scattering suffered from background noise (break-up protons) and insufficient statistics.

2. Methodology and Experimental Setup

The authors addressed these challenges by performing an experiment at the Heavy Ion Medical Accelerator in Chiba (HIMAC) using a novel gaseous active target, CAT-M.

• Reaction: Inverse kinematics deuteron inelastic scattering: $^{86}\text{Kr} + d \rightarrow ^{86}\text{Kr}^* + d'$.
• Beam: $^{86}\text{Kr}$ beam at 115 MeV/u with an instantaneous intensity of ~600 kcps (average ~200 kcps).
• Detector System (CAT-M):
  • Active Target: Deuterium gas at 40 kPa serves as both the target and the detection medium.
  • Beam TPC: A Time Projection Chamber (TPC) upstream to track the incoming beam.
  • Recoil TPC: A large-volume TPC to detect low-energy recoil particles. It utilizes a Dual-Gain Multi-layer THGEM for amplification.
  • Dipole Magnet: Installed inside the Recoil TPC to bend charged particles. This separates the signal from background (delta electrons) and allows for momentum analysis.
  • Silicon Strip Detectors (SSDs): Placed at backward angles to detect high-energy particles that pass through the gas.
  • Veto System: Plastic scintillators and SR-PPACs (Strip-Readout Parallel-Plate Avalanche Counters) to filter beam particles that reacted upstream.
• Data Acquisition: A hybrid system using GET (General Electronics for TPCs) for the CAT-M and a standard RIKEN DAQ system. The system achieved a DAQ efficiency of 51%.

3. Data Analysis Techniques

The analysis involved complex reconstruction due to the reaction occurring inside a magnetic field.

1. Particle Identification (PID):
   • For particles stopping in the TPC: PID was based on $\chi^2$ fitting of the trajectory against proton and deuteron stopping powers.
   • For particles reaching the SSD: PID used the $\Delta E - E$ method (energy loss in TPC vs. total energy in SSD).
   • Efficiency: Tracking efficiency was 98% for TPC-stopped particles and 87% for SSD-reaching particles.
2. Vertex Reconstruction:
   • Since the reaction vertex was inside the dipole magnet, trajectories were extrapolated into the magnetic field.
   • Beam particles: Corrected using analytical solutions for uniform fields.
   • Recoil particles: Corrected by numerically solving equations of motion for slowing charged particles in a non-uniform magnetic field (using a measured field map). This reduced systematic shifts in excitation energy from >4 MeV to <400 keV.
3. Cross-Section Extraction:
   • Double-differential cross-sections were calculated using missing mass spectroscopy.
   • Corrections were applied for beam transmission, DAQ efficiency, and geometric acceptance (evaluated via GEANT4 simulations).
4. Multipole Decomposition Analysis (MDA):
   • The experimental cross-sections were decomposed into contributions from different angular momentum transfers ($\Delta L$) using Distorted Wave Born Approximation (DWBA) calculations.
   • The ISGMR corresponds to $\Delta L = 0$.

4. Key Results

• ISGMR Centroid Energy: The centroid energy of the ISGMR in $^{86}\text{Kr}$ was determined to be $E_0 = 17.1^{+0.7}_{-0.5}$ MeV.
• ISGQR Centroid Energy: The Isoscalar Giant Quadrupole Resonance (ISGQR) was found at $E_2 = 13.6^{+1.0}_{-2.9}$ MeV.
• Strength Distribution: The ISGMR strength function was successfully extracted, yielding an Energy-Weighted Sum Rule (EWSR) exhaustion of $174^{+40}_{-43}\%$.
• Systematics: The measured centroid energy is consistent with the systematics of $N=50$ isotones (specifically $^{90}\text{Zr}$ and $^{92}\text{Mo}$) and macroscopic scaling laws ($80A^{-1/3}$).

5. Discussion on Nuclear Incompressibility ($K_\tau$)

Using the derived ISGMR energy, the authors calculated the nuclear incompressibility ($K_A$) and extracted the isospin-dependent term ($K_\tau$).

• Method: They fitted the $K_A$ values of $N=50$ isotones (including the new $^{86}\text{Kr}$ data) against the isospin asymmetry $(N-Z)/A$ using the droplet model.
• Result: The derived $K_\tau$ value is $-1035 \pm 2577$ MeV (when combined with RCNP data).
• Significance of Uncertainty: While the uncertainty is larger than previous global fits (e.g., $-550 \pm 100$ MeV), this is the first determination of $K_\tau$ using an isotone perspective (fixed neutron number, varying proton number) rather than just isotopes. The analysis highlights that the precision of $K_\tau$ is heavily limited by the uncertainty in the zeroth-order term ($K_0$), suggesting that future measurements of $N=Z$ nuclei are crucial for pinning down $K_\tau$.

6. Significance and Conclusion

• Technological Breakthrough: This study successfully demonstrated that gaseous active targets (CAT-M) combined with inverse kinematics can overcome the traditional trade-off between target thickness and detection of low-energy forward-angle recoils.
• Beam Intensity Handling: The system handled beam intensities up to ~1 MHz, comparable to facilities providing unstable beams (like RIBF), proving the method's viability for future experiments on short-lived unstable nuclei.
• Scientific Impact: It established a robust methodology for measuring ISGMR in unstable nuclei, providing a new data point ($^{86}\text{Kr}$) that validates existing systematics and offers a new pathway to constrain the nuclear matter equation of state, specifically the isospin dependence of incompressibility.

In summary, the paper presents a successful proof-of-concept for using advanced active target technology to study collective nuclear modes in unstable nuclei, overcoming long-standing kinematic and statistical barriers.