# Dr Alexis Diaz-Torres

### Biography

I grew up in a small town in Cuba and competed in the Cuban Team at the 19th International Junior Physics Olympiad in Bad Ischl (Austria) in 1988. I studied Physics at KLTE in Debrecen (Hungary) and InSTEC in Havana (Cuba). I received my PhD in Theoretical Nuclear Physics from the Justus-Liebig-University Giessen (Germany) in 2000. I have worked as a researcher at Surrey (UK), Goethe-University in Frankfurt am Main (Germany), ANU (Australia) and the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) in Trento (Italy). I was a Humboldt Research Fellow at Goethe-University in Frankfurt (2003-2005) and a Senior Researcher at the ECT* (2011-2016). I was appointed as a Senior Lecturer at Surrey in 2016, and promoted to Reader in 2020. My research interests include quantum physics and the physics of nuclear reactions, which are crucial for our understanding of the creation of the chemical elements in the universe and is therefore at the core of science programmes at new generation nuclear research facilities. I use quantum dynamical methods for describing nuclear reactions and associated measurements. I am a fellow of the Institute of Physics and the Higher Education Academy. I am a member of the Editorial Board of The European Physical Journal A. Beside my research and teaching, I enjoy hiking, taking photos, and cooking.

### Areas of specialism

### University roles and responsibilities

- Leader of the Maths & Physics Programmes
- Module Leader of Mathematical and Computational Physics (PHY1038)
- Module Leader of Maths and Physics MPhys Project (PHYM060)

### Research

### Research interests

These include Quantum Dynamics; Theory of Open Quantum Systems; Nuclear Theory; Few-Body & Many-Body Physics; Super-Heavy Elements Research; Nuclear Molecules; Nuclear Astrophysics.

### Research projects

This project is founded by a Leverhulme Research Project Grant (£200k) over 36 months from 1 October 2020. New basic studies of chemical element creation in the universe is being carried out. I am leading a team [1 PDRA, 1 PhD student and myself in collaboration with Prof. Peter Saalfrank (University of Potsdam, Germany), Dr. Adriana Palffy (Max-Planck Institute for Nuclear Physics, Germany) and Dr. Gilbert Gosselin (CEA, France)] to develop a new model based on the theory of open quantum systems, allowing us to characterise quantum mechanically fusion reactions of atomic nuclei in dense stellar plasma for the first time. This will expand our knowledge of nucleosynthesis, as accelerator experiments on Earth cannot probe important effects on element creation caused by stellar plasma. The new model will provide a breakthrough in our understanding of the origin of the elements and, therefore, of life itself.

- *OWL: a code for the two-center shell model with spherical Woods-Saxon potentials*, A. Diaz-Torres, Computer Physics Communications **224** (2018) 381-386.

- *PLATYPUS: a code for reaction dynamics of weakly bound nuclei at near-barrier energies within a classical dynamical model*, A. Diaz-Torres, Computer Physics Communications **182** (2011) 1100-1104.

### Supervision

## Postgraduate research supervision

**Current PhD students (as primary supervisor):**

- Iain Lee (University of Surrey, UK, 2020-2023). Iain is working on an exciting research project about modelling fusion of atomic nuclei in dense stellar plasma using the theory of open quantum systems.

- Nicholas Thomson (University of Surrey, UK, 2021-2024). Nick is working on a very interesting research project about laser-assisted fusion of atomic nuclei using the theory of open quantum systems.

**Former PhD students (as primary supervisor):**

- Dr. Terence Vockerodt (University of Surrey, UK, 2017-2021). The thesis is entitled "Quantum dynamics of heavy-ion collisions at Coulomb energies using the time-dependent coupled-channels wave-packet method". Some chapters of the thesis have been published in Physical Review C [Vockerodt & Diaz-Torres, PRC 104, 064601 (2021); PRC 100 (2019) 034606].

- Dr. Rafael Van den Bossche (University of Surrey, UK, 2017-2021). Rafael's thesis is entitled "Modelling incomplete fusion dynamics of complex nuclei at Coulomb energies: Superheavy element formation". Some chapters of the thesis have been published in Physical Review C [Van den Bossche & Diaz-Torres, PRC 102 (2020) 064618; PRC 100 (2019) 044604].

- Dr. Maddalena Boselli (ECT* & University of Trento, Italy, 2012-2016). Maddalena's thesis is entitled "Fusion processes in low-energy collisions of weakly bound nuclei", and it can be downloaded from http://eprints-phd.biblio.unitn.it/1852/. Part of the content of the thesis is published in Physical Review C & Journal of Physics G [Boselli & Diaz-Torres, PRC 92 (2015) 044610; JPG 41 (2014) 094001].

**POSTDOCTORAL RESEARCH SUPERVISION:**

- Dr. Laura Moschini (University of Surrey, UK, 2020-2023). Laura has been working on a novel semi-classical, time-dependent coupled-channels reaction model for exotic nuclei using a two-center molecular continuum [Physics Letters B 820 (2021) 136513]. She is also investigating laser-driven quantum dynamics in low-energy nuclear collisions as well as the possibility of laser-assisted element creation in nuclear fusion reactions.

### My teaching

I am currently lecturing the Mathematical and Computational Physics module (PHY1038) in Semester 2 for year-1 students. I am also teaching the Python Computer Lab of the Essential Maths module (PHY1034) in Semester 1 for year-1 students as well as Computer Lab Projects of the modules PHY2071/73 in Semester 2 for year-2 students. Other teaching activities include small group tutorials for year-1 students in Semester 1 and the supervision of both BSc Final Year Projects (PHY3002) in Semester 2 and MSc Physics Dissertation Projects (PHYM021) over the summer.

Linking teaching and research is one of my main priorities. For instance, doing this, 3 BSc final year projects turned into peer-reviewed articles: e.g., Lenton, Lee & Diaz-Torres, Annals of Physics 434 (2021) 168624; Lee & Diaz-Torres, Journal of Physics G 47 (2020) 015101; Diaz-Torres & Quraishi, Physical Review C 97 (2018) 024611.

### My publications

### Highlights

Most of my publications can be downloaded from ResearchGate (https://www.researchgate.net/profile/Alexis_Diaz-Torres2). Please find below some ePrints at Surrey. A complete list of my publications can be found on ORCID (https://orcid.org/0000-0001-6234-9353).

### Publications

We investigate the fusion and scattering of a 16 O projectile on 152,154 Sm targets using the time-dependent coupled-channel wave-packet method. We benchmark calculations of the S-matrix elements, fusion cross sections and scattering differential cross sections with those from the time-independent coupled-channel method, and compare the results to experimental data. We find that our time-dependent method and the time-independent method produce quantitatively similar results for the S-matrix elements and fusion cross sections, but our method cannot quantitatively explain the experimental scattering differential cross sections, mainly due to the low maximum number of partial waves produced by the time-dependent method. Nevertheless, the strong agreements between our method and the time-independent method demonstrates that the time-dependent coupled-channel wave-packet method can be used to address fusion reactions for a wide range of energies, with the advantage of being able to extend to time-dependent Hamiltonians for more advanced modelling of nuclear reactions.

We investigate the fusion of 16O and 154Sm with excited states at Coulomb energies using a theoretical dynamical model. The two-body Schrödinger equation is solved using the time-dependent wave-packet coupled-channels method. The wave function of the collective motion and excitations are visualized in both position and momentum space, providing a detailed mechanism of the reaction. We benchmark our calculations of the energy-resolved fusion transmission coefficients with those from the time-independent coupled-channels method. The present results are in good agreement with the time-independent results for a wide range of energies and angular momenta, demonstrating both the reliability of the quantum wave-packet dynamical approach for fusion and its usefulness for providing additional insights into fusion dynamics.

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier.

Some of my recent works on the two-center shell model and its application to describing low-energy nuclear collisions within time-dependent approaches are reviewed and a perspective for their further use is given.

A novel quantum dynamical model based on the dissipative quantum dynamics of open quantum systems is presented. It allows the treatment of both deep-inelastic processes and quantum tunneling (fusion) within a fully quantum mechanical coupled-channels approach. Model calculations show the transition from pure state (coherent) to mixed state (decoherent and dissipative) dynamics during a near-barrier nuclear collision. Energy dissipation, due to irreversible decay of giant-dipole excitations of the interacting nuclei, results in hindrance of quantum tunneling

The mechanism of reactions with weakly-bound proton-rich nuclei at energies near the Coulomb barrier is a long-standing open question owing to the paucity of experimental data. In this study, a complete kinematics measurement was performed for the proton drip-line nucleus .sup.17F interacting with .sup.58Ni at four energies near the Coulomb barrier. Thanks to the powerful performance of the detector array, exhaustive information on the reaction channels, such as the differential cross sections for quasielastic scattering, exclusive and inclusive breakup, as well as for fusion-evaporation protons and alphas, was derived for the first time. The angular distributions of quasielastic scattering and exclusive breakup can be described reasonably well by the continuum-discretized coupled-channels calculations. The inclusive breakup was investigated using the three-body model proposed by Ichimura, Austern, and Vincent, and results indicate the non-elastic breakup is the dominant component. The total fusion cross sections were determined by the fusion-evaporation protons and alphas. Based on the measured exclusive breakup data, the analysis of the classical dynamical simulation code PLATYPUS demonstrates that the incomplete fusion plays a minor role. Moreover, compared with .sup.16O+.sup.58Ni, both the reaction and total fusion cross sections of .sup.17F+.sup.58Ni exhibit an enhancement in the sub-barrier energy region, which mainly arises from couplings to the continuum states. This work indicates that the information of full reaction channels is crucially important to comprehensively understand the reaction mechanisms of weakly bound nuclear systems.

Using a semiclassical dynamical model that combines a classical trajectory model with stochastic breakup with a dynamical fragmentation theory treatment of two-body clusterization and decay of a projectile, results are presented for 20 Ne-induced incomplete fusion reactions for the production of superheavy elements. Targets include 247,248,250 Cm and 251,252,254 Cf, and results include angular, excitation energy, and angular momentum distributions in addition to total integrated cross sections for heavy incomplete fusion products. The results show that at Coulomb energies, the studied Cf isotopes are generally the more favorable choice of target over the studied Cm isotopes for the production of 'colder' and more stable 263 Lr, 263,264,266 Rf, and 265 Db isotopes through the incomplete fusion mechanism. Also presented are evaporation residue cross sections for the dominant primary incomplete fusion products of each of the six reactions: 263,264,266 Rf and 267,268,270 Sg, as well as for the primary incomplete fusion products 269,270,272 Bh.

A Fortran-90 code for solving the two-center nuclear shell model problem is presented. The model is based on two spherical Wood-Saxon potentials and the potential separable expansion method. It describes the single-particle motion in low-energy nuclear collisions, and is useful for characterizing a broad range of phenomena from fusion to nuclear molecular structures.

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier.

Nuclear physicists all over the world are searching for new exotic nuclei. But their ambitions are being hindered by the lack of effective state-of-the-art methods for laboratory nucleosynthesis. Activities are ongoing in many places to find new pathways for production and detection of exotic nuclei. But how promising are these efforts? Here we give an overview of the ongoing worldwide activities. Objects of desire Figure 1. The current Karlsruhe Chart of Nuclides, issued in 2018, contains almost 3300 different isotopes of 118 elements. The expected limits of nuclear stability (driplines) are indicated by dashed lines. Toward the driplines, the nuclei become more and more exotic. How and where are the chemical elements created in the universe? Which nuclear reactions determine the evolution and destiny of stars? And what is the nature of the still obscure nuclear force? Such fundamental questions occupy nuclear physicists. The answers are mostly hidden in the properties of exotic nuclei, like their binding energy, half-life or shape. Exotic nuclei are unstable and do not occur in our natural environment on Earth, therefore we have to produce them artificially in the lab. This is what nuclear physicists have been doing for many decades. Meanwhile, we know of the existence of more than 3000 different isotopes of 118 elements (Fig.1), with about 90 percent of them being man-made [1]. Each nuclide has its own individual combination of protons and neutrons and is governed by the sensitive interplay between the attractive nuclear force and the repulsive Coulomb force which determines its properties. Model predictions indicate that another 4000 isotopes are still awaiting their discovery, with the vastest unexplored territory located on the neutron-rich side in the upper half of the nuclide chart. Most of the astrophysical rapid neutron capture process (r-process), which is assumed to be responsible for the production of the heavy elements in stellar explosions, proceeds through this unknown territory. By studying the properties of nuclei along the r-process path we can understand the astrophysical synthesis of the heavy elements and their abundances in nature. It is still obscure where the r-process ends in the upper part of the nuclide chart. Presumably it penetrates deep into the territory of neutron-rich superheavy nuclei. New magic neutron and proton numbers are predicted in this region at N=184, Z=114 or 120-126 creating an " island of stability ". Nuclei on this " island " are expected to have higher fission barriers, resulting in an enhanced stability against fission. Is the " island of stability " the endpoint of the r-process path?

Using a classical dynamical reaction model, angular momentum (____textit{L}) values of a compound nucleus due to incomplete fusion at energies near and above the Coulomb barrier are studied. In this model, a projectile consisting of two cluster nuclei is fired at a stationary target nucleus. After breakup of the projectile due to Coulombic and nuclear forces, an ____(____alpha____)-cluster fuses with a ____textsuperscript{208}Pb target, forming an excited ____textsuperscript{212}Po compound nucleus. Results show that all incomplete fusion reactions produced higher angular momentum in the compound nucleus compared to a direct beam of ____(____alpha____) particles at the same incident energy. The highest angular momentum values produced in ____textsuperscript{212}Po for near and above Coulomb barrier energies were obtained using a ____textsuperscript{20}Ne projectile, at 16____(____hbar____) and 40____(____hbar____) respectively. This produced 25____% and 50____% ____textit{L} values above the next highest-Z projectile used, ____textsuperscript{8}Be, respectively.

A modern two-center shell model and its usefulness for addressing low-energy reaction dynamics of light and heavy nuclei are presented. A perspective for further developments in nuclear reaction theory is given.

The incomplete fusion dynamics of 6Li + 209Bi collisions at energies above the Coulomb barrier is investigated. The classical dynamical model implemented in the {____sc platypus} code is used to understand and quantify the impact of both 6Li resonance states and transfer-triggered breakup modes (involving short-lived projectile-like nuclei such as 8Be and 5Li) on the formation of incomplete fusion products. Model calculations explain the experimental incomplete-fusion excitation function fairly well, indicating that (i) delayed direct breakup of 6Li reduces the incomplete fusion cross-sections, and (ii) the neutron-stripping channel practically determines those cross-sections.

^{184}Re from the

^{9}Be +

^{181}Ta reaction, In: Physical Review C99(5)054617pp. 054617-1 American Physical Society

The isomer yield ratios of 184R in the incomplete fusion of the 9Be + 181Ta system were measured at energies around the Coulomb barrier, using online activation followed by offline γ-ray spectroscopy method. The PLATYPUS code that is based on a classical dynamical model is employed to analyze the measurements. By applying a phenomenological approach, model calculation managed to fairly reproduce the order of magnitude of the yield ratios at above barrier energies. Through the study, it is shown that the PLATYPUS code in conjunction with a phenomenological analysis can provide a reasonable explanation of isomer yield ratios resulted from incomplete fusion of weakly bound projectiles.

The quantum dynamics of a particle in a one-dimensional box with an oscillating wall (the Fermi accelerator) is investigated. The model is applied to the motion of a single nucleon in the mean-field potential of a heavy atomic nucleus whose surface vibrates. By directly solving the time-dependent Schrödinger equation, both the state of the particle and its mean-energy are studied. The effects of the frequency of the wall oscillation on the nucleon’s energy are addressed. Its energy oscillates in phase with the moving wall for all frequencies, showing no chaotic behaviour. There is a large initial peak of the nucleon’s energy as the particle adjusts to the sudden change in the size of the box and a varying relaxation time as it plateaus towards lower energy and a partial equilibrium. Small oscillations in energy continue, since there cannot be a true equilibrium while the wall is moving. The quantum coherence between the different parts of the nucleon’s wave-function in real space is very much preserved. This research lays the foundation for future investigations into quantum tunnelling in the Fermi accelerator.

A quantitative study of the astrophysically important sub-barrier fusion of 12C+ 12C is reported. Lowenergy collisions are described in the body-fixed reference frame using wave-packet dynamics within a nuclear molecular picture. In contrast to conventional methods, such as the potential model and the coupled-channels approach, these new calculations reveal three resonant structures in the S-factor, explaining some structures observed in the data. The structures in the data that are not explained are possibly due to cluster effects in the nuclear molecule, which need to be included in the new approach.

Complete fusion (CF) cross section measurement for the weakly bound 9Be projectile interacting with the intermediate mass target 89Y has been extended to energies greater than the fusion barrier, by implementing off-line characteristic γ -ray detection techniques. The available experimental data for the 9Be + 89Y reaction system were compared with the theoretical predictions, using the PLATYPUS code that is based on a classical dynamical model. By introducing the breakup probability that deduced in the literature from the fitting of the experimental data, the model managed to reproduce the CF cross sections of 9Be beam with targets of different atomic mass. Through the study, it is revealed that the extended CF excitation function for the 9Be + 89Y system is consistent with the systematical behavior that the prompt-breakup probability at above-barrier energies is roughly independent of the target in the reactions induced by the same weakly bound projectiles.

Recent measurements of low-energy (quasi)elastic-scattering angular distribution of halo nuclei have shown a strong suppression of the Coulomb-nuclear interference peak. Examining the components of the elastic-scattering differential cross sections for 11Be + 64Zn and 6He + 208Pb at energies near the Coulomb barrier, this appears to be caused by a dramatic phase-change (destructive) of the reduced Coulomb-nuclear interference term due to continuum couplings.

The incomplete fusion dynamics of ²⁰₁₀Ne + ²⁰⁸₈₂Pb collisions at energies above the Coulomb barrier are investigated using a novel semiclassical dynamical model, which combines a classical trajectory model with stochastic breakup, as implemented in the platypus code, with a dynamical fragmentation theory treatment of two-body clusterization and decay of a projectile. A finite-difference method solution to the time-independent Schrödinger equation in the charge asymmetry coordinate is employed by way of diagonalizing a tridiagonal Hamiltonian matrix with periodic boundary conditions. Results are compared with published experimental values to indicate the success of this new model, and next steps for its development are detailed.

In the past 85 years the number of known nuclides increased by more than a factor of ten, resulting in 4000 presently known isotopes of 118 elements. This considerable progress we owe to the discovery of new reaction types along with the development of powerful accelerators and experimental techniques for separation and identification of reaction products. Model predictions indicate that still about 4000 further nuclides are waiting for their discovery. The vastest unexplored territory is located on the neutron-rich side in the upper half of the chart of nuclides and hides the answers to some of the most fundamental questions of nuclear physics like the limits of nuclear stability, element synthesis in the universe or stellar evolution. The access to these nuclei is presently limited by available beam intensities and/or the lack of appropriate methods for their production and identification. The latter concerns particularly new neutron-rich isotopes of transuranium and superheavy elements. To extend this area, the hope is presently based on multinucleon transfer reactions and on the application of fusion reactions with radioactive ion beams. But how promising are these approaches? Based on a survey of present-day knowledge, we will treat the questions where we currently are on our journey towards new territory on the chart of nuclides, how the chances are to gain new territory in the future and which challenges we will have to face.

We report on an isomer yield ratio study of biologically important 94 Tc following the fusion of the 9 Be + 89 Y system, carried out using the offline γ-ray spectroscopy in continuation to the online activation method. The incident beam energies considered are above the Coulomb barrier for the present study. The PLATYPUS model in conjunction with a potential model calculation was employed to analyze the data. An agreement in the order of magnitude between the experimental data and theoretical predictions has been achieved, by applying a phenomenological approach. The approach was further tested with isomer yield ratios of 94 Tc formed through 3 He + 93 Nb reactions. Possible factors that relate to the isomer yield ratios are also presented.

Predictions of energy-shifting formulae for partial reaction and capture probabilities are compared with coupled channels calculations. The quality of the agreement notably improves with increasing mass of the system and/or decreasing mass asymmetry in the heavy-ion collision. The formulae are reliable and useful for circumventing impracticable reaction calculations at low energies.

The competition among reaction processes of a weakly-bound projectile at intermediate times of a slow collision has been unraveled. This has been done using a two-center molecular continuum within a semiclassical, time-dependent coupled-channel reaction model. Dynamical probabilities of elastic scattering, transfer and breakup agree with those derived from the direct integration of the time-dependent Schrödinger equation, demonstrating the usefulness of a two-center molecular continuum for gaining insights into the reaction dynamics of exotic nuclei.

A systematic study of total fusion involving the weakly bound nuclei 6,7Li with several light to heavy mass targets at Coulomb energies is presented. Emphasis is given to the role of resonance states (l=2,Jπ=3+,2+,1+ of 6Li and l=3,Jπ=7/2−,5/2− of 7Li) on the total fusion excitation function. A comparative analysis of the effects of resonant breakup on total fusion is performed for both projectiles, using the Continuum-Discretized Coupled-Channel (CDCC) framework. The calculations demonstrate that (i) resonant breakup couplings play a more important role in total fusion than non-resonant couplings, (ii) resonance states with short half-lives are very important for total fusion, as incident energies decreases towards the Coulomb barrier energy where incomplete fusion dominates, and (iii) resonance states with long half-life act as quasi-bound inelastic states, playing a crucial role in complete fusion.

A quantitative study of the astrophysically important sub-barrier fusion of 12C+12C is presented. Low-energy collisions are described in the body-fixed reference frame using wave-packet dynamics within a nuclear molecular picture. A collective Hamiltonian drives the time propagation of the wave-packet through the collective potential-energy landscape. The fusion imaginary potential for specific dinuclear configurations is crucial for understanding the appearance of resonances in the fusion cross section. The theoretical sub-barrier fusion cross sections explain some observed resonant structures in the astrophysical S-factor. These cross sections monotonically decline towards stellar energies. The structures in the data that are not explained are possibly due to cluster effects in the nuclear molecule, which are to be included in the present approach.