Nils Paar obtained his Ph.D. in theoretical nuclear physics from Technical University Munich in 2003 under the supervision of Prof. Peter Ring. Following a postdoctoral position at Technical University Darmstadt until 2006, he joined the University of Zagreb Faculty of Science, where he is currently serving as a full professor. From 2014-2015 he was a Marie Curie research fellow at Universitaet Basel, Switzerland. His research activities in exotic nuclear structure and dynamics, astrophysically relevant weak-interaction processes and neutrino-induced reactions, resulted in publication record comprising over 137 papers in international scientific journals and conference proceedings, with over 4000 citations (WoS). Over the course of his career, he has overseen and mentored a multitude of scholars, guiding them through Master's, Ph.D., and postdoctoral research programs, in addition to hosting international guests. He has actively participated in international conferences and workshops, delivering more than 67 talks, including 34 invited presentations. Nils Paar served as the head of the Division for Theoretical Physics, the head of the Department of Physics at the Faculty of Science, and as a member of the Senate at the University of Zagreb.

Modern Theory of Nuclear Structure
and Nuclear Astrophysics


The field of nuclear structure theory is rapidly evolving from macroscopic and microscopic models applied to stable nuclei, toward modern density functional theory applied in the uncharted territories of nuclide map encompassing vast regions of short-lived and exotic nuclei away from the valley of beta-stability. Our primary aim is to achieve a comprehensive understanding of nuclei and their excited states, grounded in a fundamental understanding of the underlying nuclear interaction. The precise description of nuclear properties holds paramount importance in astrophysics, influencing critical processes such as stellar evolution and nucleosynthesis, with accurate global microscopic calculations serving as essential tools for astrophysical applications. Within the Eleven Science Questions for the New Century lies a compelling mystery: How were the elements from iron to uranium made? With a good chance of answering this question in the near future, nuclear structure and astrophysics find themselves on the threshold of the most exciting era in decades.

The Properties of Nuclei in Hot Stellar Environment

hot nuclei

One of the most important challenges in nuclear physics and nuclear astrophysics is the understanding how the nuclear chart and its limits - drip lines - evolve with increasing temperature, considering that nuclei participating in most of the processes in the Universe are hot. Therefore, it is essential to know how many protons and neutrons can be bound together in hot stellar environment. Therefore we aim to understand which nuclei can contribute to nuclear reactions and processes, especially in extremely hot stellar environments such as supernovae and neutron star mergers, where most of the chemical elements heavier than iron are produced. The knowledge about nuclear properties at finite temperature is largely unknown, since most of theoretical and experimental studies are restricted to zero temperature. Only recently, we have established a theory framework based on relativistic nuclear energy density functional that allowed us to map the position of nuclear drip lines at finite temperature for the first time (see Video Byte by Research Square).

Exotic Modes of Nuclear Excitations

Pygmy mode

The extreme isospin of nuclei far from stability and their weak binding reveal unique structure phenomena such as neutron halo and skin, which play a crucial role in understanding of the nuclear many-body problem at the limits of stability. The multipole response of nuclei far from the beta-stability line and the possible occurrence of new exotic modes of excitation presents a rapidly growing field of research. The properties of observed low-energy dipole excitations in nuclei with a pronounced neutron excess is currently very much under discussion due to their unique properties. A new excitation mode has been suggested by theory calculations to appear also in nuclei close to the proton drip-line: proton pygmy dipole resonance whose dynamics is governed by vibrations of protons from weakly bound orbits against the core composed of other nucleons. This exotic mode is currently awaiting for its experimental confirmation.

The exotic modes of excitation are interesting not only as new physical phenomena, but also because they could play an important role in astrophysically relevant processes. The description of multipole spin-flip and isospin-flip excitations is essential in calculations of beta-decay, electron capture and neutrino-nucleus interaction rates. The low-energy dipole transition strength in neutron-rich nuclei have a pronounced effect on the calculated r-process abundances, i.e. on the production of chemical elements and on the propagation of ultra-high energy cosmic rays. On the proton-rich side the proton pygmy dipole resonance could contribute to the nucleosynthesis in rapid proton capture processes, as well as in the two-proton capture in astrophysical conditions characteristic for explosive hydrogen burning in novae and x-ray bursts.

Neutrino-Nucleus Reactions and Weak Interaction Rates

Image of the Globe

Neutrino-nucleus reactions are of central importance in astrophysics where the transport of neutrinos determines the rate of cooling of many stellar objects, and their detection provides a unique way of looking at such fascinating astrophysical phenomena as the interior processes in our sun, supernovae explosions, and stellar nucleosynthesis. These reactions are also essentially connected to another of the Eleven Science Questions for the New Century: do neutrinos have mass? Since nuclei are used as neutrino detectors in solar experiments, supernova observatories and in neutrino oscillation measurements, it is of outmost importance to achieve a quantitative description of neutrino-nucleus reactions in a fully microscopic theory.

Description of a neutrino-nucleus cross section becomes increasingly complicated as the target mass number increases and novel accurate approaches based on relativistic energy density functionals must be developed and applied in calculations for all relevant neutrino-induced reactions. More generally, microscopic nuclear structure theory must be integrated into various astrophysical models of nucleosynthesis , supernova dynamics, and neutrino-induced reactions, by providing accurate global predictions for bulk nuclear properties and nuclear transitions. Understanding of the nucleosynthesis of heavier elements during the r-process necessitates systematic knowledge on the neutrino-nucleus cross sections not only in stable nuclei but also in nuclei away from the valley of beta stability.

The Key Research Methods

Relativistic density functional theory

Utilizing the most advanced energy density functionals, this approach provides a coherent, universally applicable, and quantitative description of nuclei. It allows studies of exotic nuclear structure and dynamics, extrapolations into uncharted territories of the nuclide map, extending towards the particle drip lines.

Theory of Nuclear Weak Interactions

The theory of nuclear weak interactions, formulated within the framework of the electroweak theory, describes the fundamental mechanism responsible for processes such as beta decay and electron capture in atomic nuclei or neutrino - nucleus interaction. It plays a crucial role in understanding the transformation of one type of elementary particle into another within the atomic nucleus.

Advanced Scientific Computing

It serves as an essential method for tackling the intricate challenges posed by the relativistic nuclear many-body problem, e.g., solving coupled systems of differential equations, vast numbers of nuclear matrix elements, and extensive eigenvalue problems. Notably, it is an indispensable method for large-scale calculations across the nuclide chart, contributing significantly to the advancement of nuclear physics research.

More details are available in the listed publications and references therein.

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University of Zagreb

Established on 23 September 1669 by Emperor and King Leopold I Habsburg, the University of Zagreb stands as one of the oldest universities in Europe. Its official inception occurred through a decree that bestowed university status and privileges upon the Jesuit Academy of the Royal Free City of Zagreb. In the realm of natural sciences, the university commenced its teachings in 1896, initiating with lectures in mineralogy and geology, followed by botany, physics, mathematics, chemistry, zoology, and geography. Presently, the University of Zagreb holds the distinction of being the largest university in Croatia, boasting an enrollment of over 70,000 full-time students.

Department of Physics

The Department of Physics at the University of Zagreb Faculty of Science, stands out as the regional center of excellence for both scientific research and university-level education in the field of physics. Each academic year, the department hosts around 700 students engaged in various theoretical, experimental, and educational physics study programs. Committed to fostering scientific excellence, the department actively participates in internationally relevant and competitive research, spanning fundamental and applied studies. At the forefront of theoretical physics, the Division of Theoretical Physics within the department specializes in diverse areas such as atomic and nuclear physics, optics and photonics, physics of condensed matter, and biophysics. Demonstrating a commitment to global impact, members of the division publish cutting-edge research in leading international scientific journals and take the lead on numerous competitive research projects, as well as engaging in agreements for international scientific cooperation.