Measurement of $^{144}$Sm(p,$γ$) cross-section at Gamow energies

This study presents the first measurement of the astrophysical S-factor for the $^{144}$Sm(p,$\gamma$)$^{145}$Eu reaction at Gamow window energies using the activation technique, demonstrating satisfactory agreement with theoretical predictions from TALYS and NON-SMOKER codes to facilitate the calculation of relevant astrophysical reaction rates.

The Gist

The Big Picture: Cooking the Universe's Ingredients

Imagine the universe is a giant cosmic kitchen. Most of the ingredients (elements) in our solar system are cooked up by two main chefs: the Slow Cooker (s-process) and the Explosive Chef (r-process). These chefs make things like iron, gold, and lead.

But there's a weird, rare group of ingredients called p-nuclei (proton-rich nuclei) that these two chefs can't make. They are like the "forbidden fruits" of the periodic table. To make them, you need a third, very intense chef: the Gamma Chef (the $\gamma$-process). This chef works in the super-hot, fiery hearts of exploding stars, blasting atoms with high-energy light (gamma rays) to knock pieces off them.

One of these rare ingredients is Samarium-144 ($^{144}\text{Sm}$). It's a "magic" ingredient because it's surprisingly abundant compared to its neighbors. Scientists want to know exactly how fast the Gamma Chef can make (or break) this ingredient.

The Problem: We Can't Build a Star in a Lab

To figure out how fast these reactions happen, scientists usually need to measure the "cross-section." Think of a cross-section as the target size of an atom. If you shoot a bullet (a proton) at a target (a Samarium atom), how likely is it to hit and stick?

The problem is that the "Gamma Chef" works at temperatures so high that we can't easily recreate them on Earth. We can't build a star in our basement.

The Trick: Instead of trying to blast Samarium with gamma rays (which is hard to do), the scientists decided to do the reverse. They shot protons at Samarium to see if they would stick and turn into a new element (Europium-145).

It's like trying to figure out how hard it is to break a vase by throwing a ball at it, versus trying to figure out how hard it is to glue a broken vase back together. If you know how well the glue works (the reverse reaction), you can use math to figure out how easily the vase breaks (the forward reaction). This is called the Reciprocity Theorem.

The Experiment: The "Stack of Pancakes" Technique

The scientists went to the VECC Cyclotron in Kolkata, India. This is a giant machine that accelerates particles to near the speed of light.

1. The Targets: They needed pure Samarium-144. Since it's rare, they used a special "molecular deposition" technique. Imagine spraying a very fine mist of Samarium onto a thin aluminum foil, like dusting a cake with powdered sugar, to create a target layer only a few atoms thick.
2. The Energy Problem: The machine they had could only shoot protons at a high speed (7 MeV). But they needed to test lower speeds (down to 2.6 MeV) to match the conditions inside stars.
3. The Solution (The Stack): They couldn't just slow the machine down, so they used a stack of foils.
   • Imagine throwing a ball at a stack of 10 pancakes.
   • The ball hits the first pancake and loses a little speed.
   • It hits the second and loses a bit more.
   • By the time it hits the 10th pancake, it's moving much slower.
   • By placing Samarium targets at different spots in the stack, they could measure the reaction at many different speeds (energies) in a single run.

The Measurement: Counting the "Ghost" Particles

After shooting the protons at the targets for hours or days, they didn't see the reaction happen immediately. Instead, the Samarium turned into Europium-145, which is radioactive.

• The Wait: They let the targets sit for a while.
• The Count: They put the targets near a super-sensitive detector (an HPGe detector). This machine is like a very picky bouncer at a club; it only lets specific "gamma ray" frequencies in.
• The Result: When the Europium-145 decayed, it emitted gamma rays. By counting these rays, they could calculate exactly how many Samarium atoms had been hit.

The Findings: A Perfect Match

The scientists measured the reaction rates at 11 different energy levels.

• The "Sweet Spot": They found the reaction rates in the "Gamow Window." Think of this as the Goldilocks Zone of stellar temperatures. It's the specific energy range where stars are most likely to cook these elements.
• The Comparison: They compared their real-world data with computer simulations (using a program called TALYS).
  • Imagine the computer is a weather forecast model.
  • The scientists' data was the actual weather report.
  • The result? The forecast was spot on. The computer models predicted the reaction rates very accurately.

Why Does This Matter?

1. Filling the Gaps: This is the first time they measured the reaction rate at the lowest energy (2.57 MeV). It's like finding the missing piece of a puzzle that explains how the universe makes heavy elements.
2. Star Models: Now, when astrophysicists simulate how stars explode or how elements are formed, they can use these new, precise numbers. It makes their models of the universe more accurate.
3. The Reverse Reaction: Because they measured the "gluing" (proton capture), they can now calculate the "breaking" (gamma-induced proton emission) rate. This tells us exactly how much Samarium-144 gets destroyed in the fiery hearts of stars.

Summary in One Sentence

Scientists used a "stack of pancakes" trick to slow down protons and shoot them at Samarium atoms, measuring how easily they stick together; this allowed them to calculate exactly how the universe cooks rare elements in the fiery hearts of stars, confirming that our computer models of the cosmos are working correctly.

Technical Summary

1. Problem Statement and Motivation

• Astrophysical Context: The study addresses the origin of p-nuclei (proton-rich isotopes), specifically 144Sm, which are bypassed by standard s- and r-process neutron capture. These nuclei are primarily produced via the $\gamma$-process (photodisintegration) in high-temperature stellar environments (supernovae or neutron star mergers).
• The Challenge: Direct measurement of the photodisintegration reaction $^{144}\text{Sm}(\gamma, p)$ is difficult due to the lack of high-intensity $\gamma$-beams.
• The Solution: The study utilizes the principle of detailed balance (reciprocity theorem) to measure the inverse reaction, $^{144}\text{Sm}(p, \gamma)^{145}\text{Eu}$, at astrophysically relevant energies.
• Specific Gap: Previous measurements (e.g., by Kinoshita et al.) covered the 2.8–7.5 MeV range but suffered from high energy uncertainty due to degrader foils. There was a lack of precise data near the Gamow window for stellar temperatures of $T_9 = 2, 3, 4$ (GK), particularly below 3 MeV. Additionally, 144Sm is a "magic" neutron shell nucleus with unusually high solar abundance, making its reaction rate critical for accurate nucleosynthesis models.

2. Methodology

The experiment was conducted at the VECC K130 Cyclotron in Kolkata, India, using the stacked foil activation technique followed by offline $\gamma$-ray spectroscopy.

• Target Preparation:
  • Material: Isotopically enriched $^{144}\text{Sm}_2\text{O}_3$ (67% enrichment).
  • Technique: Molecular deposition was used to create thin targets (100–350 $\mu\text{g/cm}^2$) on pure Aluminum backings. This involved dissolving the oxide in nitric acid, evaporating, re-dissolving in deionized water, and electrodepositing onto Al foils using a platinum wire anode (+500 V).
• Beam and Irradiation:
  • Beam: 7 MeV proton beam.
  • Energy Range: 2.6 to 6.8 MeV.
  • Energy Degradation: Since the accelerator minimum was 7 MeV, degrader foils (Aluminum) were used to lower the beam energy.
    • Stack 1 (S1): Irradiated for energies 5.1–6.8 MeV.
    • Stack 2 (S2): Irradiated for energies 4.2–4.7 MeV.
    • Single Target: Used with varying Al degraders for energies 2.6–4.1 MeV.
  • Beam Monitoring: Natural Copper foils were placed within the stacks to monitor beam intensity via the $^{65}\text{Cu}(p, n)^{65}\text{Zn}$ reaction.
• Detection and Analysis:
  • Spectroscopy: Irradiated targets were counted using a 40% relative efficiency HPGe detector (resolution ~1.8 keV at 1.33 MeV).
  • Corrections:
    • Coincidence Summing: Corrected using the EFFTRAN Monte Carlo code due to the close geometry (12.5 mm) required for low-activity samples.
    • Efficiency Calibration: Performed using a $^{152}\text{Eu}$ standard source, with corrections for finite sample geometry.
    • Energy Straggling: Calculated using LISE++ and GEANT4 simulations to determine the precise energy and uncertainty ($1\sigma$) at each foil position.
• Theoretical Modeling:
  • Data was compared with Hauser-Feshbach statistical model calculations using TALYS 1.96 and NON-SMOKER.
  • Sensitivity analysis was performed on optical potentials (OPM), nuclear level densities (NLD), and $\gamma$-ray strength functions ($\gamma$-SF).

3. Key Contributions

• First Measurement at Low Energy: This study reports the first measurement of the astrophysical S-factor at a center-of-mass energy of $E_{cm} = 2.57 \pm 0.13$ MeV, significantly extending the data into the Gamow window for $T_9 = 2$ and $3$.
• Improved Precision: By optimizing the molecular deposition technique and using precise simulation codes (GEANT4/LISE++) for energy degradation, the study reduced energy uncertainties compared to previous works.
• Comprehensive Sensitivity Study: The paper identifies that the proton width is the dominant factor influencing the cross-section in the astrophysically relevant energy regime (2.6–6.8 MeV), while $\gamma$-width and neutron width become relevant at higher energies.
• Reaction Rate Prediction: The study provides updated thermonuclear reaction rates for both the forward ($^{144}\text{Sm}(p, \gamma)$) and inverse ($^{145}\text{Eu}(\gamma, p)$) processes, which are essential inputs for stellar evolution codes.

4. Key Results

• Cross-Section Data: Measured cross-sections for 11 proton energies ranging from 2.6 to 6.8 MeV.
  • Uncertainties ranged from 25% to 45%, increasing at lower energies due to lower reaction yields.
  • The data showed satisfactory agreement with theoretical predictions from TALYS 1.96.
• S-Factor:
  • The S-factor increases as energy decreases, reaching $2.542 \pm 1.152 \times 10^{10}$ MeV-b at $E_{cm} = 2.57$ MeV.
  • The experimental data aligns well with TALYS predictions using specific parameter sets (OPM 1, ldmodel 5, and $\gamma$-SF 1 or 3).
• Theoretical Agreement:
  • The experimental data fell within the grey shaded region of TALYS calculations (representing 216 combinations of model parameters).
  • The best fit was achieved with OPM 1 (Koning-Delaroche local potential), ldmodel 5 (Gogny-Hartree-Fock-Bogoliubov), and $\gamma$-SF 3 (Hartree-Fock BCS tables).
• Reaction Rates:
  • Calculated reaction rates for $^{144}\text{Sm}(p, \gamma)$ were compared with the REACLIB database, showing good consistency.
  • Using the reciprocity theorem, the rates for the inverse reaction $^{145}\text{Eu}(\gamma, p)$ were derived, providing crucial data for modeling the destruction of 145Eu in the $\gamma$-process.

5. Significance

• Nucleosynthesis Modeling: The precise measurement of the $^{144}\text{Sm}(p, \gamma)$ cross-section and the derived S-factor directly improves the accuracy of astrophysical models predicting the abundance of p-nuclei, particularly 144Sm, which is the second most abundant p-nucleus after 92Mo.
• Validation of Nuclear Models: The agreement between experimental data and TALYS 1.96 validates the current nuclear physics inputs (optical potentials and level densities) used in statistical models for this mass region ($A \approx 145$).
• Methodological Advancement: The successful application of the molecular deposition technique for preparing thin, enriched targets demonstrates a robust method for future low-energy activation experiments where target thickness and uniformity are critical.
• Data Availability: The study provides a new dataset for the REACLIB database, reducing uncertainties in stellar reaction networks for temperatures between 2 and 4 GK.