Impact of Detailed Nuclear Structure on Observables in High-Energy Collisions: Limitations of the Woods-Saxon Parameterization

Grunnleggende konsepter

Accurately modeling observables in high-energy isobar collisions requires moving beyond simplified Woods-Saxon descriptions of nuclear density to incorporate the detailed radial structure revealed by Density Functional Theory, especially for observables sensitive to the outer regions of nuclei.

Sammendrag

Yan, Z., Xu, J., & Jia, J. (2024). Impact of the radial profile of atomic nuclei on observables in high-energy collisions. arXiv preprint arXiv:2405.18318v2.

This study investigates the limitations of the commonly used Woods-Saxon (WS) parameterization in describing nuclear density distributions for high-energy heavy-ion collisions. The authors aim to quantify the impact of the detailed radial structure, as predicted by Density Functional Theory (DFT), on key observables in these collisions.

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Impact of the radial profile of atomic nuclei on observables in high-energy collisions

by Zhengxi Yan,... klokken arxiv.org 10-10-2024

https://arxiv.org/pdf/2405.18318.pdf

Dypere Spørsmål

How might the incorporation of DFT-calculated nuclear structures impact the interpretation of data from experiments designed to study the properties of the Quark-Gluon Plasma?

Incorporating DFT-calculated nuclear structures, which capture the nuanced radial profile of atomic nuclei, can significantly impact the interpretation of high-energy collision data used to study the Quark-Gluon Plasma (QGP). Here's how:

Improved Precision in Extracting QGP Properties: The paper demonstrates that using simplified Woods-Saxon (WS) distributions to model nuclei can lead to a few percent level deviations in observables like elliptic flow (v2), triangular flow (v3), and particle multiplicity (Nch) compared to more realistic DFT calculations. These observables are key indicators of the QGP's properties, such as its transport coefficients (like shear viscosity and bulk viscosity). By using DFT, we can reduce systematic uncertainties associated with the nuclear structure in the initial state, leading to a more precise extraction of these QGP properties.

Enhanced Sensitivity to Initial State Fluctuations: DFT calculations can capture the subtle wiggle structures in the nucleon density distribution arising from quantum effects. These structures can lead to event-by-event fluctuations in the initial state of the collision, which propagate through the hydrodynamic evolution of the QGP and influence the final-state observables. By incorporating DFT, we gain a better handle on these initial-state fluctuations, allowing for a more detailed understanding of their impact on the QGP evolution.

Deeper Understanding of Isobar Collisions: Isobar collisions, involving nuclei with the same mass number but different internal structures, are highly sensitive probes of both nuclear structure and QGP properties. The paper highlights that DFT calculations are crucial for accurately interpreting isobar data, as they can distinguish subtle differences in the neutron skin thickness and deformation parameters between the colliding nuclei. This, in turn, allows for a more precise determination of the QGP response to these initial-state differences.
In summary, incorporating DFT-calculated nuclear structures into the analysis of high-energy collision data can significantly enhance our understanding of the QGP. It allows for a more precise extraction of QGP properties, a better understanding of the role of initial-state fluctuations, and a more refined interpretation of isobar collision data.

Could the observed differences between DFT and WS be attributed to limitations in the Glauber model itself, rather than solely the nuclear density parameterization?

While the paper focuses on the impact of nuclear density parameterization on observables, it's certainly plausible that limitations within the Glauber model itself could also contribute to the observed differences between DFT and WS calculations. Here's why:

Simplified Nucleon Interactions: The Glauber model typically employs a simplified picture of nucleon-nucleon interactions, often treating them as binary collisions with a fixed cross-section. In reality, these interactions are more complex and can be influenced by factors like the nuclear medium and many-body effects, which are not fully captured in the standard Glauber approach.

Neglect of Nuclear Dynamics: The Glauber model primarily treats nuclei as static objects with a predefined density distribution. However, nuclei are dynamic systems of interacting nucleons, exhibiting collective excitations and internal motion. These dynamic aspects can influence the collision dynamics and potentially lead to deviations from the predictions of a static Glauber calculation.

Impact of Short-Range Correlations: The Glauber model often neglects short-range correlations between nucleons, which can impact the spatial distribution of nucleons within the nucleus. These correlations, arising from the repulsive core of the nuclear force, can lead to deviations from the smooth density profiles assumed in both WS and DFT calculations.
Therefore, it's essential to consider the limitations of the Glauber model itself when interpreting the observed differences between DFT and WS calculations. Further investigations using more sophisticated models that incorporate realistic nucleon-nucleon interactions, nuclear dynamics, and short-range correlations are necessary to disentangle the contributions from the nuclear density parameterization and the model's inherent limitations.

If we consider the nucleus not as a static object but as a dynamic system of interacting nucleons, how might our understanding of high-energy collisions and the information we can extract from them change?

Considering the nucleus as a dynamic system of interacting nucleons rather than a static object would profoundly impact our understanding of high-energy collisions and the information we can extract. Here's a glimpse into this shift:

Beyond Average Density Profiles: Instead of relying solely on average density profiles like WS or even DFT, we'd need to incorporate the dynamic nature of nucleons. This includes considering their momentum distributions (Fermi motion), nucleon-nucleon correlations, and the possibility of nucleon excitations within the nucleus before the collision.

Fluctuations and Correlations: The dynamic nature of the nucleus introduces event-by-event fluctuations in the positions and momenta of nucleons. These fluctuations can propagate to the initial state of the QGP, leading to a richer spectrum of initial conditions and potentially impacting observables like flow harmonics and particle production.

Emergence of Collective Phenomena: Treating the nucleus as a dynamic system allows for the emergence of collective phenomena, such as giant resonances or pre-clustering of nucleons, which can influence the collision dynamics. These collective effects can modify the energy and momentum deposition in the early stages of the collision, potentially impacting the QGP formation and evolution.

New Observables and Probes: A dynamic picture of the nucleus opens avenues for exploring new observables sensitive to the internal motion and correlations of nucleons. For instance, measuring the correlations between nucleons or fragments in the final state could provide insights into the initial-state dynamics of the colliding nuclei.

Theoretical Challenges and Opportunities: Modeling high-energy collisions with dynamic nuclei presents significant theoretical challenges. It demands developing sophisticated computational tools that can handle the many-body dynamics of nucleons within the colliding nuclei and their subsequent interactions in the hot and dense environment of the collision.
In conclusion, shifting from a static to a dynamic picture of the nucleus in high-energy collisions would revolutionize our understanding of these events. It would necessitate developing new theoretical frameworks and computational tools, but it would also unlock a wealth of information about the internal structure and dynamics of atomic nuclei and their influence on the formation and evolution of the QGP.