Session E01: Advances in Predictive Nuclear Reaction Theory

New studies and predictions for nuclear reactions in the extit{ab initio} symmetry-adapted framework

Recent advances in low-energy nuclear physics have opened several possibilities to unify nuclear structure and reaction dynamics. 

Various promising approaches, such as deriving effective optical potentials from microscopic calculations or using fully microscopic coupled-channel formalism, continue to be explored. 

Combined with first-principles calculations, these developments are enabling unprecedented insights into the atomic nuclei, especially those near drip lines, with far reaching consequences for nuclear astrophysics. 

While first-principles calculations offer reliable predictions but are constrained to few-particle systems, the Symmetry-Adapted No Core Shell Model (SA-NCSM) tackles this limitation. 

Leveraging near-perfect symmetries key to collective nuclear phenomena like deformation and vibrations, SA-NCSM employs a tailored basis to extend ab initio studies to nuclei as complex as those in the calcium region.

In this talk, I will introduce how SA-NCSM is playing a major role in unifying nuclear structure and reactions, and how it contributes to the advancement of first-principles microscopic approaches to nuclear reactions. 

The discussion will particularly focus on the employment of ab initio symmetry-adapted wave functions to capture the internal structure of the reaction components. 

I will showcase calculations of effective nucleon-nucleus "optical" potentials using Green's function formalism for reactions involving light nuclei. 

Additionally, I will introduce a coupled-channel framework, reformulated within the SA-NCSM basis, as an initial step toward achieving a comprehensive microscopic approach to nuclear reactions extending to the calcium region.   

Microscopic Estimation of Nuclear Reaction Rate in Astrophysical Phenomena

Nuclear reactions are the energy source for various astrophysical phenomena: 12C+12C and 12C+16O fusion reactions play a significant role in explosive astrophysical phenomena such as X-ray bursts and superbursts, and type Ia supernovae, where nuclear reaction rates determine recurrence times and the abundance of the produced elements.

The astrophysical is low energy for nuclear physics, and the contribution of resonances to nuclear reactions is significant. Direct measurement of low-energy resonances by accelerator experiments is challenging because of the tiny cross section due to the thick Coulomb barrier. Therefore, experimentally determined reaction rates at low temperatures are uncertain and need to be estimated by theory. However, the accuracy of theoretical evaluations is also still insufficient. In particular, heavy-ion fusion reactions are multinucleon rearrangement reactions, and it is necessary to clarify the properties of the resonance state, treating the effects of entrance and exit channel coupling. However, in the current situation where general coupling potentials have not been developed, it is not possible to treat the coupling phenomenologically.

We use a microscopic model, antisymmetrized molecular dynamics, to evaluate the nuclear reaction rate. Using the microscopic model, we can, in principle, treat the coupling of any channels from the nucleon-nucleon interactions. By treating the couplings of the entrance and exit channels and deformed structures using the generator coordinate method, the wave functions of the resonances are calculated. Then, their contribution to the fusion reaction is evaluated from the properties of the resonances.

In 24Mg, the resonances are obtained near the threshold of 12C+12C. They are essentially 12C+12C molecular resonance states, and the fragments that appear due to the coupling with the exit channels, a+20Ne and p+23Na channels, are distributed close to the threshold. They increase the 12C+12C fusion reaction rate in the typical temperature of X-ray superbursts. In 28Si, 12C+16O resonances are obtained close to the threshold through coupling with 12C+16O, a+24Mg, and other channels.   

The Optical Potential: From Structure to Reactions and Back Again

Nuclear reaction theory describes collisions between two or more nuclear species and plays an important twofold role in the context of low -energy nuclear physics. First, it connects experimental observables obtained at accelerated-beam facilities with specific aspects of nuclear structure. Second, it addresses processes that are essential for a variety of applications in nuclear astrophysics, nuclear energy, medicine, security, and industry. In its first role, it is essential to unlock the full discovery potential of FRIB, ATLAS, and the ARUNA labs; in the latter, it is at the basis of a successful implementation of the corresponding applications. Within this context, the nucleon-nucleus effective interaction, a.k.a the Optical Potential (OP) plays a pivotal role, being an essential ingredient of most theoretical accounts of nuclear reactions. Therefore, establishing the connection between the OP and the underlying nuclear structure will contribute significantly to achieve an important goal of nuclear physics: the unification of structure and reactions theory.   

Density functional approach to radiative neutron capture reactions on r-process nuclei

Radiative neutron capture is one of the key reactions in the r-process nucleosynthesis, which takes place in the neutron star mergers and in the supernova explosions. Quantitative prediction of the cross section is required as the direct experimental measurement is difficult for very neutron-rich nuclei along the r-process path. The neutron capture reactions are usually described in terms of two different mechanisms, the compound nuclear (CN) process and the direct capture (DC) process. The CN process is assumed to proceed via compound states with high level density, as described by means of the Hauser and Feshbach statistical model. However, the statistical model may not be appropriate for neutron-rich nuclei along the r-process path due to small level density at entrance. The direct capture (DC) models assuming single-particle transition is alternatively adopted, but they neglect many-body correlations such as the pairing, the collective vibrations, and their influences.

 

Aiming at overcoming the above problems, we are developing a microscopic theory to calculate cross section of the radiative neutron capture reaction on neutron-rich nuclei using the continuum quasiparticle random-phase approximation(cQRPA) based on the time-dependent density functional theory (TDDFT). This new approach makes it possible to describe various excitation modes present in the doorway states of the (n,¥gamma) reaction, including soft dipole excitation, the giant resonances as well as  non-collective excitations and the single-particle resonances. Furthermore, it enables us to describe the reaction where the final states of the gamma transition are low-lying surface vibrational states. Using numerical results obtained for the neutron-rich Sn isotopes, e.g. ¹³⁹Sn (n,¥gamma) ¹⁴⁰Sn, we discuss various new features which are beyond the single-particle model; presence of narrow and wide resonances originating from non-collective and collective excitations and roles of the pairing, low-lying quadrupole and octupole vibrational states.