Synthesis mechanism of superheavy element 120: a dinuclear system model approach with microscopic inputs

This paper employs a dinuclear system model with microscopic inputs derived from finite-temperature covariant density functional theory to successfully reproduce experimental cross-sections for known superheavy elements and predicts maximum synthesis cross-sections for four specific reaction pathways targeting element 120.

The Gist

Imagine the periodic table of elements as a vast, crowded city. Most of the buildings (elements) we know are stable and safe. But as you move to the very edge of the city, past the skyscrapers of Uranium and Plutonium, the ground gets shaky. The buildings there are so heavy and unstable that they crumble (fission) almost instantly.

However, physicists have a hunch that if you go even further out, there might be a hidden "Island of Stability"—a place where super-heavy buildings are surprisingly sturdy. The goal of this paper is to figure out how to build the very first skyscraper on that island: Element 120.

Here is a simple breakdown of how the authors tried to solve this puzzle.

1. The Problem: Building with Mismatched Blueprints

To predict how to build Element 120, scientists use a computer model called the Dinuclear System (DNS) model. Think of this model as a sophisticated recipe for a cake.

• The Recipe: You need to smash two smaller atoms (like a projectile and a target) together to fuse them into a giant new atom.
• The Ingredients: To get the recipe right, you need precise numbers for things like how heavy the atoms are, how much energy holds them together, and how likely they are to fall apart.

The Catch: In the past, scientists used ingredients from different bakeries. They might have used a mass measurement from one theory, a stability calculation from another, and an energy estimate from a third. It's like trying to bake a cake using flour from France, sugar from Brazil, and eggs from a different farm, all without checking if they mix well together. This leads to a cake that might not rise correctly.

2. The Solution: A Unified Kitchen

The authors of this paper decided to bake their cake using one single, consistent kitchen. They used a modern, high-tech theory called Covariant Density Functional Theory (CDFT) to generate all the necessary ingredients (masses, energy barriers, stability factors) from scratch.

• The Analogy: Instead of buying ingredients from different stores, they grew their own wheat, raised their own cows, and made their own sugar. This ensures that every part of the recipe is perfectly compatible with the others.
• The Result: They created a "self-consistent" model. Because the ingredients match perfectly, their predictions are much more reliable.

3. The Test Drive: Checking the Map

Before they tried to build the new, unknown Element 120, they had to make sure their new kitchen worked. They tested their recipe on elements they already knew existed: Nobelium (No) and Flerovium (Fl).

• The Result: They ran simulations of past experiments where these elements were successfully created. Their "unified kitchen" predictions matched the real-world experimental data very well. This proved their new, consistent ingredients were high quality.

4. The Grand Challenge: Hunting for Element 120

Now that they trusted their model, they looked at four different ways to build Element 120. Imagine you are trying to build a tower, and you have four different pairs of workers (projectile + target) to do the job:

1. Titanium + Californium
2. Vanadium + Berkelium
3. Chromium + Curium
4. Manganese + Americium

They ran the numbers to see which pair had the best chance of success.

The Findings:

• The Winner: The Titanium + Californium combination is the clear champion. It has the highest chance of success (about 48 "femtobarns"—a tiny unit of probability, but the biggest among the options).
• The Runner-up: Vanadium + Berkelium is the second best, but significantly harder to pull off.
• The Losers: The other two combinations are extremely difficult, with success rates dropping by huge margins.

Why does this happen?
Think of the fusion process like two dancers trying to merge into a single, complex routine.

• If the dancers are too different in size or style, they might bump into each other and bounce apart (quasi-fission) instead of merging.
• The Titanium + Californium pair is the best "dance match." They can merge smoothly, and the resulting "super-dancer" (the new atom) is stable enough to survive for a split second before evaporating a few neutrons and settling down.
• The other pairs are like mismatched dance partners; they struggle to merge, and the resulting atom is too shaky to survive.

5. The Conclusion: A Roadmap for the Future

The paper concludes with a clear instruction manual for experimentalists (the people with the giant particle accelerators).

They are saying: "If you want to find Element 120, stop guessing. Point your particle accelerator at a Californium target and shoot Titanium ions at it. Aim for a specific energy level (41 MeV), and you have the best possible chance of creating this new element."

In a nutshell:
This paper didn't just guess how to find Element 120. They built a better, more consistent computer model to simulate the physics, tested it on known elements to prove it works, and then used it to give scientists a precise "treasure map" for the next great discovery in nuclear physics.

Technical Summary

1. Problem Statement

The synthesis of new superheavy elements (SHEs), particularly those with atomic numbers $Z=119$ and $Z=120$, is a major frontier in nuclear physics, aiming to reach the predicted "island of stability." However, experimental production is extremely challenging due to vanishingly small reaction cross-sections (often in the femtobarn range) and high costs.

• Theoretical Gap: Existing theoretical models, such as the Dinuclear System (DNS) model, are powerful tools for predicting synthesis cross-sections. However, their predictive accuracy relies heavily on input physical quantities (nuclear masses, fission barriers, shell corrections, level density parameters).
• Inconsistency Issue: Traditionally, these inputs are derived from disparate theoretical models (e.g., Finite-Range Droplet Model for masses, macroscopic-microscopic models for fission barriers, Strutinsky method for shell corrections). This lack of a unified, self-consistent framework introduces uncertainties and potential redundancies in the treatment of physical factors.

2. Methodology

The authors propose a self-consistent theoretical framework where all essential input parameters for the DNS model are generated from a single microscopic source: Finite-Temperature Covariant Density Functional Theory (CDFT).

• Microscopic Foundation (Finite-Temperature CDFT):

  • Model: Utilizes the PC-PK1 energy density functional with zero-range point-coupling interactions.
  • Pairing: Treated via the BCS (Bardeen-Cooper-Schrieffer) approach at finite temperatures.
  • Calculations: Performed on the $(\beta_2, \gamma)$ deformation plane to generate free energy surfaces for compound nuclei.
  • Extracted Quantities: From these calculations, the authors derive:
    • Single neutron separation energies ($S_n$).
    • Fission barriers ($B_f$) as a function of excitation energy ($E^*$).
    • Shell correction energies ($E_{sh}$).
    • Asymptotic level density parameters ($\tilde{a}$) and shell damping factors ($E_D$).
  • Temperature Dependence: The study explicitly models how fission barriers and level densities evolve with temperature, identifying critical phase transitions (around $T \approx 0.4-0.5$ MeV) where shell effects begin to dampen.

• Reaction Dynamics (DNS Model):

  • The DNS model calculates the evaporation residue cross-section ($\sigma_{ER}$) as a product of three probabilities:
    1. Capture Probability ($T$): Passing the Coulomb barrier.
    2. Fusion Probability ($P_{CN}$): The probability of the dinuclear system evolving into a compound nucleus (surpassing the Businaro-Gallone point).
    3. Survival Probability ($W_{sur}$): The probability of the excited compound nucleus surviving fission by evaporating neutrons ($x$-neutron channels).
  • Validation: The model is first validated against experimental data for known isotopes of Nobelium (No, $Z=102$) and Flerovium (Fl, $Z=114$) using cold and hot fusion reactions.

3. Key Contributions

1. Unified Microscopic Input: The paper successfully demonstrates a self-consistent approach where all critical inputs for the DNS model are derived from a single CDFT framework (PC-PK1 + BCS), eliminating the need to mix parameters from different phenomenological models.
2. Validation of Method: By reproducing experimental excitation functions for $^{48}\text{Ca} + \text{Pb}$ (cold fusion) and $^{48}\text{Ca} + \text{Pu}$ (hot fusion) reactions, the authors validate that the microscopic inputs are compatible with the DNS model.
3. Identification of Optimal Level Density Extraction: The study compares three methods for extracting the level density parameter ($a$) from CDFT data ($a_1 = S/2T$, $a_2 = E^*/T^2$, $a_3 = \frac{1}{2}\partial S/\partial T$). It concludes that $a_3$ provides the best agreement with experimental data for the DNS model.
4. Prediction for Element 120: The framework is applied to predict the synthesis cross-sections for the unknown superheavy element 120 using four specific projectile-target combinations.

4. Key Results

A. Validation (No and Fl Isotopes):

• The calculated excitation functions for $^{48}\text{Ca} + ^{204,206-208}\text{Pb}$ (cold fusion) and $^{48}\text{Ca} + ^{239,240,242,244}\text{Pu}$ (hot fusion) show good agreement with experimental data, particularly near the Coulomb barrier.
• Discrepancy Note: At higher excitation energies, the theoretical cross-sections are slightly higher than experimental values. The authors attribute this to the microscopic fission barriers decreasing more slowly with excitation energy than observed experimentally.

B. Prediction for Element 120:
The study calculates the maximum evaporation residue cross-sections ($\sigma_{ER}$) for four potential reactions targeting Element 120. The results are summarized below:

Reaction System	Optimal Channel	Max Cross Section ($\sigma_{ER}$)	Optimal Excitation Energy ($E^*_{CN}$)
$^{50}\text{Ti} + ^{249}\text{Cf}$	$4n$ ($^{295}120$)	48.20 fb	41 MeV
$^{51}\text{V} + ^{249}\text{Bk}$	$3n$ ($^{297}120$)	12.33 fb	34 MeV
$^{54}\text{Cr} + ^{248}\text{Cm}$	$3n$ ($^{299}120$)	5.25 fb	32 MeV
$^{55}\text{Mn} + ^{243}\text{Am}$	$5n$ ($^{293}120$)	0.47 fb	53 MeV

• Trend Analysis: The cross-sections decrease significantly as the projectile mass increases (from Ti to Mn). This is attributed to the increased symmetry between the projectile and target, which reduces the fusion probability (quasi-fission competition).
• Most Promising Route: The $^{50}\text{Ti} + ^{249}\text{Cf}$ reaction is identified as the most viable path, offering the highest cross-section (48.20 fb) for the $4n$ evaporation channel.

5. Significance

• Experimental Guidance: The results provide concrete, theoretically grounded targets for experimentalists at facilities like JINR, GSI, RIKEN, and IMP. Specifically, it prioritizes the $^{50}\text{Ti} + ^{249}\text{Cf}$ reaction as the most promising candidate for synthesizing Element 120.
• Theoretical Advancement: By establishing a self-consistent link between CDFT and the DNS model, the paper sets a new standard for theoretical predictions in superheavy element research. It reduces the uncertainty associated with mixing different nuclear models and highlights the importance of temperature-dependent fission barriers and level densities.
• Insight into Shell Effects: The study reinforces the role of shell corrections in stabilizing superheavy nuclei and demonstrates how these effects dampen with increasing excitation energy, a critical factor in determining survival probabilities.

In conclusion, this work bridges the gap between microscopic nuclear structure theory and macroscopic reaction dynamics, offering a robust prediction for the synthesis of the next superheavy element.