# Dr Esra Yuksel

## Academic and research departments

School of Mathematics and Physics, Theoretical Nuclear Physics Group.## About

### University roles and responsibilities

- Physics Department Demonstrator Coordinator (2023–present)

### My qualifications

### Previous roles

## Research

### Research interests

My research interests are focused on understanding the properties and dynamics of atomic nuclei under extreme conditions of isospin and temperature and extending these studies to the nuclear weak interaction processes. Starting from the properties of atomic nuclei, my research area extends through nuclear astrophysics and creates a bridge between nuclear physics and nuclear astrophysics.

From the theoretical point of view, calculation of the properties of an atomic nucleus either with an extreme proton-neutron ratio close to the drip lines or highly excited nuclei is quite challenging. For these calculations, the nuclear energy density functional (NEDF) theory is standing as the most prominent and successful theoretical tool with its capability to make calculations for nuclei throughout the nuclear chart. However, the nuclear energy density functional theory is not complete and needs to be developed to study the nuclear ground-state properties and the excited states of nuclei, especially for nuclei near the drip lines. Therefore, the development of the nuclear energy density functionals and the relevant theoretical methods to explore the nuclear properties under extreme conditions constitute the main framework of my research.

## Supervision

### Postgraduate research supervision

I am currently principal supervisor of PhD student:

- Miriam Davies

I have supervised the following MSc theses:

- Kishore Thirumoorthy (Completed, 2023)
- Aloma Silva
- Athina Strati
- Yung-Chun Chiang

## Teaching

- Module Leader of Essential Mathematics
- Small Group Tutorials for year 1 students
- Essential Mathematics Tutorials

## Publications

The exploration of nuclear mass or binding energy, a fundamental property of atomic nuclei, remains at the forefront of nuclear physics research due to limitations in experimental studies and uncertainties in model calculations, particularly when moving away from the stability line. In this work, we employ two machine learning (ML) models, support vector regression (SVR) and Gaussian process regression (GPR), to assess their performance in predicting nuclear mass excesses using available experimental data and a physics-based feature space. We also examine the extrapolation capabilities of these models using newly measured nuclei from AME2020 and by extending our calculations beyond the training and test set regions. Our results indicate that both SVR and GPR models perform quite well within the training and test regions when informed with a physics-based feature space. Furthermore, these ML models demonstrate the ability to make reasonable predictions away from the available experimental data, offering results comparable to the model calculations. Through further refinement, these models can be used as reliable and efficient ML tools for studying nuclear properties in the future.

The Sky3D code has been widely used to describe nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The approach is based on Skyrme forces or related energy density functionals. The static and dynamic equations are solved on a three-dimensional grid, and pairing is been implemented in the BCS approximation. This updated version of the code aims to facilitate the calculation of nuclear strength functions in the regime of linear response theory, while retaining all existing functionality and use cases. The strength functions are benchmarked against available RPA codes, and the user has the freedom of choice when selecting the nature of external excitation (from monopole to hexadecapole and more). Some utility programs are also provided that calculate the strength function from the time-dependent output of the dynamic calculations of the Sky3D code.

Recent advancements, such as measurements of dipole polarizability and experiments involving parity-violating electron scattering on 48Ca (CREX) and 208Pb (PREX-II), have opened new perspectives for our understanding of nuclear energy density functionals (EDF). In particular, these advancements shed light on the isovector channel of the EDFs, which plays a pivotal role in determining properties related to symmetry energy and the thickness of the neutron skin in nuclei. Recently, a novel relativistic EDF DD-PCX has been developed based on point coupling interaction, adjusted using not only the ground state properties of nuclei but also the properties of isoscalar giant monopole resonance and the dipole polarizability in 208Pb. The DD-PCX interaction describes well the nuclear ground state properties, including the thickness of the neutron skin, and provides reasonable descriptions of nuclear excited states. Furthermore, the symmetry energy and its slope are found to be consistent with previous studies. Moreover, by applying the relativistic EDF framework, the consequences of the CREX and PREX-II electron scattering data have been investigated for the symmetry energy of nuclear matter and the isovector properties of finite nuclei, such as neutron skin thickness and dipole polarizability. The weak-charge form factors extracted from the CREX and PREX-II experiments have been directly used to optimize the relativistic density-dependent point coupling EDFs. Notably, the EDF derived from the CREX data yields substantially smaller values for parameters associated with symmetry energy, neutron skin thickness, and dipole polarizability for both 48Ca and 208Pb, when compared to the EDF derived from the PREX-II data, as well as previously established EDFs. It has become evident that the CREX and PREX-II experiments have not yielded consistent investigations and experimental studies are required to clarify these discrepancies.

Finite-temperature effects in electromagnetic transitions in nuclei contribute to many aspects of nuclear structure and astrophysically relevant nuclear reactions. While electric dipole transitions have already been extensively studied, the temperature sensitivity of magnetic transitions remains largely unknown. This work comprises the study of isovector magnetic dipole excitations (M1) occurring between spin-orbit (SO) partner states using the recently developed self-consistent finite-temperature relativistic quasiparticle random-phase approximation (FT-RQRPA) in the temperature range from T = 0 to 2 MeV. The M1 strength distributions of 40-60Ca and 100-140Sn isotopic chains exhibit a considerable temperature dependence. The M1 strength peaks shift significantly towards the lower energies due to the decrease in SO splitting energies and weakening of the residual interaction, especially above the critical temperatures where the pairing correlations vanish. By exploring the relevant two-quasiparticle configurations contributing to the M1 strength of closed- and open-shell nuclei, new proton and neutron excitation channels between SO partners are observed in low- and high-energy regions due to the thermal unblocking effects around the Fermi level. At higher temperatures, we have noticed an interesting result in 40,60Ca nuclei, the appearance of M1 excitations, which are forbidden at zero temperature due to fully occupied (or fully vacant) spin-orbit partner states.

In stellar environments nuclei appear at finite temperatures, becoming extremely hot in core-collapse supernovae and neutron-star mergers. However, due to theoretical and computational complexity, most model calculations of nuclear properties are performed at zero temperature, while those existing at finite temperatures are limited only to selected regions of the nuclide chart. In this study we perform the global calculation of nuclear properties for even-even 8 104 nuclei at temperatures in range 0 T 2 MeV. Calculations are based on the finite-temperature relativistic Hartree-Bogoliubov model supplemented by the Bonche-Levit-Vautherin vapor subtraction procedure. We find that near the neutron-drip line the continuum states have significant contribution already at moderate temperature T ≈ 1 MeV, thus emphasizing the necessity of the vapor subtraction procedure. Results include neutron emission lifetimes, quadrupole deformations, neutron-skin thickness, proton and neutron pairing gaps, entropy and excitation energy. Up to the temperature T ≈ 1 MeV, the nuclear landscape is influenced only moderately by the finite-temperature effects, mainly by reducing the pairing correlations. As the temperature increases further, the effects on nuclear structures become pronounced, reducing both the deformations and the shell effects.

Finite temperature results in various effects on the properties of nuclear structure and excitations of relevance for nuclear processes in hot stellar environments. Here, we introduce the self-consistent finite temperature relativistic quasiparticle random phase approximation (FT-RQRPA) based on relativistic energy density functional with point coupling interaction for describing the temperature effects in electric dipole (E1) transitions. We perform a study of E1 excitations in the temperature range T = 0–2 MeV for the selected closed- and open-shell nuclei ranging from 40Ca to 60Ca and 100Sn to 140Sn by including both thermal and pairing effects. The isovector giant dipole resonance strength is slightly modified for the considered range of temperature, while new low-energy peaks emerge for E < 12 MeV with non-negligible strength in neutron-rich nuclei at high temperatures. The analysis of relevant two-quasiparticle configurations discloses how new excitation channels open due to thermal unblocking of states at finite temperature. The study also examines the isospin and temperature dependence of electric dipole polarizability (αD), resulting in systematic increase in the values of αD with increasing temperature, with a more pronounced effect observed in neutron-rich nuclei. The FT-RQRPA introduced in this work will open perspectives for microscopic calculation of γ -ray strength functions at finite temperatures relevant for nuclear reaction studies.

A clear connection can be established between properties of nuclear matter and finite-nuclei observables, such as the correlation between the slope of the symmetry energy and the dipole polarizability, or between compressibility and the isoscalar monopole giant resonance excitation energy. Establishing a connection between realistic atomic nuclei and an idealized infinite nuclear matter leads to a better understanding of underlying physical mechanisms that govern nuclear dynamics. In this work, we aim to study the dependence of the binding energies and related quantities (e.g., location of drip lines, the total number of bound even-even nuclei) on the symmetry energy S2(rho). The properties of finite nuclei are calculated by employing the relativistic Hartree-Bogoliubov model, assuming even-even axial and reflection symmetric nuclei. Calculations are performed by employing two families of relativistic energy density functionals, based on different effective Lagrangians, constrained to a specific symmetry energy at the saturation density J within the interval of 30-36 MeV. Nuclear binding energies and related quantities of bound nuclei are calculated between 8 Z 104 from the two-proton to the two-neutron drip line. As the neutron drip line is approached, the interactions with stiffer J tend to predict more bound nuclei, resulting in a systematic shift of the two-neutron drip line towards more neutron-rich nuclei. Consequentially, a correlation between the number of bound nuclei Nnucl and S2(rho) is established for a set of functionals constrained using the similar optimization procedures. The direction of the relationship between the number of bound nuclei and the symmetry energy highly depends on the density under consideration.

Recent precise parity-violating electron scattering experiments on 48Ca (CREX) and 208Pb (PREX-II) provide a new insight on the formation of neutron skin in nuclei. Within the energy density functional (EDF) framework, we investigate the implications of CREX and PREX-II data on nuclear matter symmetry energy and isovector properties of finite nuclei: neutron skin thickness and dipole polarizability. The weak-charge form factors from the CREX and PREX-II experiments are employed directly in constraining the relativistic density-dependent point coupling EDFs. The EDF established with the CREX data acquires considerably smaller values of the symmetry energy parameters, neutron skin thickness and dipole polarizability both for 48Ca and 208Pb, in comparison to the EDF obtained using the PREX-II data, and previously established EDFs. Presented analysis shows that CREX and PREX-II experiments could not provide consistent constraints for the isovector sector of the EDFs, and further theoretical and experimental studies are required.

Properties of nuclei in hot stellar environments such as supernovae or neutron star mergers are largely unexplored. Since it is poorly understood how many protons and neutrons can be bound together in hot nuclei, we investigate the limits of nuclear existence (drip lines) at finite temperature. Here, we present mapping of nuclear drip lines at temperatures up to around 20 billion kelvins using the relativistic energy density functional theory (REDF), including treatment of thermal scattering of nucleons in the continuum. With extensive computational effort, the drip lines are determined using several REDFs with different underlying interactions, demonstrating considerable alterations of the neutron drip line with temperature increase, especially near the magic numbers. At temperatures T ≲ 12 billion kelvins, the interplay between the properties of nuclear effective interaction, pairing, and temperature effects determines the nuclear binding. At higher temperatures, we find a surprizing result that the total number of bound nuclei increases with temperature due to thermal shell quenching. Our findings provide insight into nuclear landscape for hot nuclei, revealing that the nuclear drip lines should be viewed as limits that change dynamically with temperature. It is interesting and important to understand how the properties of nuclei and their stability change with temperature. Here the authors report their theoretical study of hot nuclei and the drip lines that limit the nuclear existence at finite temperature.

We investigate the localization and clustering features in 20 Ne ( N = Z ) and neutron-rich 32 Ne nuclei at zero and finite temperatures. The finite temperature Hartree-Bogoliubov theory is used with the relativistic density-dependent meson-nucleon coupling functional DD-ME2. It is shown that clustering features gradually weaken with increasing temperature and disappear when the shape phase transition occurs. Considering thermal fluctuations in the density profiles, the clustering features vanish at lower temperatures, compared to the case without thermal fluctuations. The effect of the pairing correlations on the nucleon localization and the formation of cluster structures are also studied at finite temperatures. Due to the inclusion of pairing in the calculations, cluster structures are preserved until the critical temperatures for the shape phase transition are reached. Above the critical temperature of the shape phase transition, the clustering features suddenly disappear, which differs from the results without pairing.