Microscopic Simulation of Angular Momentum Transfer in Nuclear Reactions Using Time-Dependent Hartree-Fock Theory

Core Concepts

Time-dependent Hartree-Fock (TDHF) simulations reveal complex mechanisms of angular momentum transfer in nuclear reactions, challenging previous macroscopic models and highlighting the significant role of neck formation, nucleon transfer, and stochastic fluctuations.

Abstract

Bibliographic Information:

Scamps, G. (2024). Microscopic Study of Spin Transfer in Near-Barrier Nuclear Reactions. arXiv preprint arXiv:2409.15018v2.

Research Objective:

This study investigates the mechanisms of angular momentum transfer from the initial relative orbital angular momentum to the intrinsic spin of fragments in near-barrier nuclear reactions using microscopic time-dependent Hartree-Fock (TDHF) simulations. The research aims to clarify how the transferred spin is distributed between fragments, establish the timescales associated with different transfer mechanisms, and determine the influence of deformation on this process.

Methodology:

The study employs TDHF simulations within the TDHF-Skyrme framework to model several nuclear reactions at different impact parameters and with increasing complexity. The reactions studied include 40Ca + 40Ca, 208Pb + 208Pb, 40Ca + 208Pb, and 50Ca + 176Yb. A method is proposed to analyze the evolution of the fragments' total spin as a function of time and angular velocity.

Key Findings:

• The study reveals that the transfer of nucleons and neck formation significantly influence the transfer of spin through tangential friction, contradicting previous macroscopic calculations.
• Sliding friction is found to be approximately twice the rolling friction coefficient, contrary to earlier estimates suggesting an order of magnitude difference.
• The spin of the fragments does not always increase with time, challenging the notion of using spin as a "clock" to differentiate between deep-inelastic collisions and fusion-fission.
• The study highlights the stochastic nature of spin evolution in long contact time trajectories due to large excitation energy and random neck breaking.
• Coulomb torque at large distances and nucleon transfer are found to directly contribute to the angular momentum of fragments.

Main Conclusions:

The TDHF simulations provide a detailed microscopic understanding of angular momentum transfer in nuclear reactions, revealing limitations in previous macroscopic models. The findings emphasize the importance of considering neck formation, nucleon transfer, and stochastic fluctuations for accurately describing spin evolution in these reactions.

Significance:

This research significantly contributes to the field of nuclear physics by providing a more accurate and nuanced understanding of angular momentum transfer in nuclear reactions. The findings have implications for interpreting experimental data and developing more sophisticated theoretical models.

Limitations and Future Research:

The study acknowledges the potential impact of pairing interactions on the observed results and suggests further investigation using Time-dependent Hartree-Fock-Bogoliubov (TDHFB) calculations.

Stats

The initial relative orbital angular momentum in the 208Pb + 208Pb reaction at Ec.m. = 700 MeV and b = 4 fm is 236.9 ℏ, of which only 44 ℏ is transferred to the fragments' spin.
The time scale for angular momentum transfer in the 208Pb + 208Pb reaction is approximately 120 fm/c (0.4 zs).
The maximum spin observed in the fragments for the 40Ca + 40Ca reaction at Ec.m. = 70 MeV is around 3 ℏ.
The sticking equilibrium in the 40Ca + 208Pb reaction is achieved at an impact parameter of approximately 4 fm with a contact time of about 2 zs.
The rolling relaxation time in the 40Ca + 208Pb reaction is estimated to be around 1 zs.
The mass equilibrium in the 40Ca + 208Pb reaction is expected to occur on a timescale of approximately 20 zs.
The ratio of mass relaxation time to spin relaxation time (τM/τJ) in the 40Ca + 208Pb reaction is estimated to be 50.
The deformation parameter (β2) of the 176Yb nucleus in the 50Ca + 176Yb reaction is 0.196.

Quotes

"The spin of the fragments does not always increase during the collision which prevents it from being used to estimate the collision time of the reaction."
"Several mechanisms are in contradiction with previous macroscopic calculations."
"In particular, it is shown that the transfer of nucleons, and neck formation can significantly affect the transfer of spin through tangential friction."

Key Insights Distilled From

Microscopic Study of Spin Transfer in Near-Barrier Nuclear Reactions

by Guillaume Sc... at arxiv.org 11-19-2024

https://arxiv.org/pdf/2409.15018.pdf

Deeper Inquiries

How would the inclusion of pairing interactions in future TDHFB calculations potentially affect the observed spin transfer mechanisms and timescales?

Pairing interactions, which are not included in standard Time-Dependent Hartree-Fock (TDHF) calculations but can be incorporated in Time-Dependent Hartree-Fock-Bogoliubov (TDHFB) calculations, could significantly influence both the mechanisms and timescales of spin transfer in nuclear reactions. Here's how:

Reduced Dissipation: Pairing correlations are known to act as a "lubricant" in nuclear systems, reducing the effectiveness of energy dissipation mechanisms. This is because pairing leads to the formation of Cooper pairs, which are more resistant to breaking due to their binding energy. Consequently, the inclusion of pairing in TDHFB calculations could potentially lead to longer timescales for both rolling and sliding friction. This means that the transfer of angular momentum from the relative orbital motion to the intrinsic spin of the fragments could be slower compared to standard TDHF predictions.

Impact on Equilibration: The presence of pairing could also affect the final equilibrium values of the fragments' spins. Since pairing modifies the internal structure and collective excitations of nuclei, it can influence the moments of inertia of the fragments. This, in turn, would alter the expected equilibrium distribution of angular momentum between the relative motion and the intrinsic spins, as predicted by the sticking and rolling models.

Dependence on Pairing Strength: The magnitude of these effects would depend on the strength of the pairing interaction in the specific nuclear system under consideration. For nuclei with strong pairing correlations, the impact on spin transfer could be more pronounced.
In summary, incorporating pairing interactions in future TDHFB calculations is crucial for a more complete and realistic description of angular momentum transfer in nuclear reactions. It would enable us to assess the limitations of the simplified TDHF approach and gain a deeper understanding of the role of pairing in these complex dynamical processes.

Could the discrepancies between the TDHF simulations and previous macroscopic models be attributed to the simplified assumptions made in those models, such as neglecting neck formation and nucleon transfer?

Yes, the discrepancies observed between the microscopic TDHF simulations and previous macroscopic models regarding angular momentum transfer can be largely attributed to the simplified assumptions inherent in those models. Here's a breakdown of how neglecting neck formation and nucleon transfer contributes to these discrepancies:

Neck Formation: Macroscopic models often treat the colliding nuclei as rigid spheres, neglecting the dynamic formation and evolution of the neck region that connects the fragments during close contact. The neck introduces several complexities:

Modified Friction: The neck significantly alters the geometry and flow of nuclear matter between the fragments, directly impacting the tangential friction. The TDHF simulations clearly demonstrate that the presence of the neck enhances friction, leading to faster equilibration timescales compared to predictions based on rigid-sphere models.

Non-Rigid Behavior: The neck allows for non-rigid behavior, enabling energy and angular momentum exchange between the fragments that goes beyond simple rolling or sliding. This more complex dynamics is not captured in rigid-sphere models.

Nucleon Transfer: Macroscopic models often simplify or neglect the transfer of nucleons between the fragments during the collision. However, nucleon transfer has significant implications for angular momentum:

Direct Angular Momentum Transfer: As shown in the TDHF simulations, transferred nucleons carry angular momentum, directly influencing the spin of the receiving fragment. This mechanism is not accounted for in models that neglect transfer.

Modified Moments of Inertia: Nucleon transfer alters the mass distribution within the fragments, leading to changes in their moments of inertia. This, in turn, affects the equilibrium distribution of angular momentum.
In essence, the TDHF simulations, by incorporating the microscopic details of nucleon-nucleon interactions, provide a more realistic and nuanced picture of the collision dynamics. They highlight the limitations of macroscopic models that rely on simplified assumptions and emphasize the importance of considering neck formation and nucleon transfer for accurately describing angular momentum transfer in nuclear reactions.

What are the broader implications of understanding angular momentum transfer in nuclear reactions for fields such as astrophysics and energy production?

A deep understanding of angular momentum transfer in nuclear reactions has profound implications that extend far beyond nuclear physics, impacting fields like astrophysics and energy production:
Astrophysics:

Supernova Explosions: Angular momentum plays a crucial role in the dynamics of core-collapse supernovae, which are responsible for the creation of heavy elements. Accurate modeling of these explosions requires a detailed understanding of angular momentum transport within the collapsing stellar core and during the subsequent ejection of matter. Insights from nuclear reaction studies can help refine these models and improve our understanding of the element synthesis processes in the universe.

Neutron Star Mergers: The recent observation of gravitational waves from merging neutron stars has opened a new window into the study of these extreme environments. Angular momentum transfer during the merger process influences the properties of the resulting object, such as its spin and the potential formation of a black hole. Nuclear physics insights are essential for interpreting these observations and unraveling the mysteries of neutron star mergers.
Energy Production:

Nuclear Fusion Reactors: Achieving controlled nuclear fusion, the process that powers the sun, holds immense promise for clean energy production. In fusion reactors, understanding angular momentum transfer is crucial for confining and heating the plasma, which consists of extremely hot, charged particles. By controlling the angular momentum of the plasma, scientists aim to create the conditions necessary for sustained fusion reactions.

Nuclear Waste Transmutation: Angular momentum transfer also plays a role in the transmutation of nuclear waste, a process that aims to transform long-lived radioactive isotopes into shorter-lived or stable ones. By understanding the mechanisms of angular momentum transfer, scientists can optimize transmutation techniques and develop more efficient methods for reducing the hazards associated with nuclear waste.
In conclusion, unraveling the complexities of angular momentum transfer in nuclear reactions is not merely an academic exercise. It has far-reaching implications for our understanding of the cosmos, the development of future energy sources, and the management of nuclear waste. As we continue to refine our models and experimental techniques, we can expect even deeper insights and technological advancements in these critical areas.