Nigel R. Badnell (1958–2024): A Legacy in Atomic Astrophysics

[Figure omitted. See PDF]

Nigel Robert Badnell was born on the 27th of October 1958 and grew up in Swindon where he lived with his parents, Dave and Patricia, and his wee sister, Hilary. Nigel would later become a brother-in-law of Ian and an uncle of Rachel and Shaun. Hilary recalls that Nigel was a ‘typical’ big brother, who played football with his friends.

Nigel always did very well at school, particularly in maths and science. After obtaining a First Class Honours in Mathematics at the University of Durham in 1980, Nigel went to Cambridge to study Part III Mathematics Tripos in 1981. He then obtained his PhD during 1981–1984 at DAMTP under the supervision of Alan Burgess on ‘Exchange Distorted-Wave approximations for electron-atom collisions’. Alan started the Atomic Astrophysics group at Cambridge in 1965, after obtaining his PhD in 1959 at University College London (UCL) under the supervision of Mike Seaton and after a few more years at UCL. Nigel stayed at DAMTP as a Post-doctoral Research Assistant for a further three years. Whilst in Cambridge he interacted closely with other former students, post-docs, and collaborators of Alan Burgess. These included, for example, Hugh Summers (who completed his PhD under the supervision of Alan Burgess in 1970) and Helen Mason (a former PhD student of Mike Seaton, who moved to DAMTP as a post-doc to work with Alan in 1976).

Those years in Cambridge had a profound influence on Nigel’s career and personal character. As many great scientists Cambridge has hosted over time, he was very bright and had a sharp sense of humour. He would always answer any deep scientific questions honestly with just a few words, normally adjusting the details of his answers depending on the knowledge and character of the person posing the questions. Often, he would avoid answering an ill-posed question with comments such as “How long is a piece of string?”. Manfred von Hellermann, a colleague of Nigel, wrote, “I still remember his kindness, and even more importantly, I never met somebody like him who lived in a universe which was (and still is) a complete mystery to me, and I simply couldn’t understand a single word of his. A fascinating man, I liked him a lot.”

Nigel used to say that Alan Burgess left him primarily alone and free to pursue his own research, but clearly Alan did have a huge impact on the way Nigel carried out his research. Indeed, Alan’s approach was to allow his students to grow and develop, but he was always there to guide and support them. Helen recalls many animated scientific discussions in the DAMTP common room at coffee and tea time. In a similar way to Mike Seaton and Alan Burgess, Nigel was mainly interested in pure atomic physics theory, but with relevance for astrophysical applications. He was an avid member of the Opacity and Iron Projects, initially led by Mike Seaton and later by David Hummer. He also produced important contributions to fusion plasma research as part of the ADAS team led by Hugh Summers, although this huge body of work is not reviewed here. As with Mike and Alan, Nigel was also very meticulous in coding programs in FORTRAN, which are still widely used. For those who did not know Nigel and Alan, it would be very surprising to learn that they never published a joint paper, especially considering that they always had the greatest regard for each other. However, Alan was keen for his students to take full credit for their work.

Helen Mason at DAMTP shared an office first with Hugh Summers and then with Nigel and introduced them to the use of the UCL codes, in particular superstructure, which was originally developed during 1967–1974 by Werner Eissner and Harry Nussbaumer under the supervision of Mike Seaton at UCL and later further developed by several researchers who were in Seaton’s group (e.g., Michael Jones, Pete Storey, Claude Zeippen). By 1985, Nigel had already developed the first version of autostructure, a non-relativistic atomic structure program, inheriting a large part of superstructure. As the change of name indicates, a key early extension was to enable the calculation of autoionisation probabilities. A code originally designed for the calculation of bound state energies and radiative data then became able to treat resonance phenomena, both in electron-impact excitation processes but also in dielectronic recombination.

Nigel continued to develop autostructure until his last few days (the physics was updated in Badnell and Zhang [1] while the development version 31.4.3 was edited at the end of July 2024), including a lot of physics, options, and processes. This code became the workhorse for large-scale calculations of dielectronic recombination (DR), photo-ionisation cross-sections, radiative recombination (RR), distorted wave scattering calculations, and excitation–autoionisation, as described in many papers. Unlike all other atomic physics codes, autostructure was Nigel’s own creation. It was like his own child—he was very quick to take care of any problems that were found with it. He treated it as though it had a life of its own: when asked what it would carry out in a certain calculation, he would talk about all the options that might be available to it and try to guess how it would go about the calculation. Despite his scientific stature, he was very happy to teach anybody who was interested how to use it, no matter their experience. His many years of lecturing obviously showed through in the clarity of his explanations and the patience he had with novice users. In the last few years, he expressed concern that nobody would be able to carry on future developments of the code. Within his to-do list, Nigel was planning further additions (such as collisional ionisation via an EPSRC grant led by GDZ, but which was not funded). However, autostructure already has a huge range of options, as he recently discussed in [1].

Alan Burgess made seminal contributions to the theory of dielectronic recombination for high-temperature plasma in the early 1960s, so it was natural that Nigel would become involved. In early 1986 (see, e.g., [2]) he started a long series of papers on calculating DR (see, e.g., the DR project [3]), becoming the world’s authority. During his last few weeks, he continued to work on DR calculations for low-charge iron ions as part of the UK APAP collaboration (see below).

Aside from spending some time as a Senior Scientific Officer at AWE (Aldermaston, UK) during 1988–1989, Nigel spent his post-Cambridge period between 1987 and 1992 at Auburn University (Auburn, USA), where he formed a long-lasting collaboration with Don Griffin and Mitch Pindzola on a wide range of topics, from extending his work on DR to developing improved ways to calculate electron-impact excitation (see, e.g., [4,5,6]) and ionisation (see, e.g., [7,8]). Together, they developed a theory that would allow the application of Multi-Channel Quantum Defect theory in intermediate coupling, which led to some lively debates with Mike Seaton, an acknowledged expert in the field, who had reservations about their work at first. Nigel convinced Mike eventually, and in the late 1990s they published together on the theory. The so-called Intermediate Coupling Frame Transformation (ICFT) method was the result which allowed the much faster calculation of electron scattering cross-sections in intermediate coupling than the full Breit–Pauli R-matrix method and became the workhorse for most of the subsequent scattering calculations by Nigel and his many collaborators.

During the Auburn period, Nigel also started to produce atomic data for modelling magnetic fusion plasma (see, e.g., [9]), collaborating closely with Hugh Summers, who was at the University of Strathclyde (Glasgow, UK) from 1979 and who also had a position at the Joint European Torus (JET). In the 1980s, Hugh formed the Atomic Data and Analysis Structure (ADAS) consortium of which Nigel was an enthusiastic member. In 1992 Nigel was appointed as Lecturer at the Department of Physics, University of Strathclyde, working alongside Hugh Summers. He later became a professor and stayed at Strathclyde for the rest of his life. He taught a variety of subjects, including Atomic Physics, Astrophysics, and Cosmology, which he recalled were largely based on his Cambridge academic studies. Nigel was an enthusiastic lecturer, tutor, and supervisor. Whilst at Strathclyde, he trained, together with Hugh Summers, many students and post-docs. He continued to produce a large amount of atomic data needed for ADAS, as, e.g., described in [10].

In the 1990s Nigel continued to improve autostructure with the inclusion of two-body non-fine-structure operators in the Breit–Pauli Hamiltonian [11]. He also continued to provide contributions on close-coupling calculations for the electron-impact excitation of ions, as well as DR, but he also started to collaborate with experimentalists who were measuring DR rates (see, e.g., [12]). During this period, he also started a close collaboration with Mike Seaton (UCL) (cf. [13]). Mike Seaton and his large atomic physics group, in collaboration with Phil Burke (QUB) and his group, developed the set of codes used for the Opacity Project (OP) (see [14]) and Iron Project (IP) (see, e.g., [15]) and following papers.

These sets of codes were the result of a large team effort over nearly 30 years. The codes for the R-matrix method, modified for the calculations of electron scattering by ions [16], were initially developed at QUB [17], but later the UCL and QUB teams joined forces to develop the codes for the OP [18], which were further modified for the IP. Nigel contributed to these projects and codes (cf. [19]), and autostructure became the standard program to calculate wavefunctions and radiative data. Over time, with the retirement of other parties involved, Nigel kept the main repository of all the codes at Strathclyde. A copy of all the codes has been made available by GDZ through ZENODO at https://zenodo.org/records/14946146 (accessed on 5 June 2025).

In the early 2000s, Nigel provided an important update to the results of the OP (see [20]) and continued to work in that field, especially when the calculated opacities became in doubt, first with the substantial revision of solar photospheric abundances [21] and then with the Sandia National Laboratory measurements by [22].

All this threw into doubt the standard solar model, a pillar for astrophysics, and caused a flurry in the literature on the subject. Nigel’s last published contribution on the subject was [23], but he continued working until 2023 on this topic, mainly collaborating with Franck Delahaye and Connor Ballance. Nigel stood firmly with the belief that his calculations could not be as wrong as indicated by the experiment and was very pleased when recent measurements [24] cast doubt on the results of the Sandia National Laboratory experiment.

During the early 2000s, he also started to contribute to a series of Iron Project papers to calculate electron-impact excitation (EIE) cross-sections, firstly with Marita Chidichimo [25], also a former PhD student of Alan Burgess, and then with others including GDZ [26]. Nigel obtained funding for astrophysical applications from PPARC/STFC/UKRI via the UK APAP (Atomic Processes for Astrophysical Plasmas) collaboration, formed originally by Nigel, Pete Storey (UCL), Giulio Del Zanna and Helen Mason (DAMTP) and later by Alessandra Giunta (RAL). The APAP team met frequently in Cambridge and Glasgow, and the collaboration continued despite the restructuring of the grant system by STFC. The APAP collaboration resulted in extensive and systematic production of many datasets, in particular the radiative and EIE data with the ICFT method by Mike Witthoef, Guiyun Liang, Luis Fernández Menchero, Junjie Mao, Giulio Del Zanna, and others. This resulted in complete datasets for all the ions from the H-like to the Al-like isoelectronic sequences, plus many other ions, including almost all the iron ions. Most of the calculations are still unsurpassed; see the earlier review given in [27]. Nigel attached great importance to the wide distribution of the codes and the results of these calculations to the wider astronomical community through his web pages (http://www.apap-network.org/codes.html (accessed on 5 June 2025)) and was keen that they were included in the ADAS and CHIANTI databases. Several problems in the EIE data have been found, and the corrected data, together with bin-averaged collision strengths (for modelling non-thermal electrons) for most of the sequences/ions have been made available by GDZ [28] through ZENODO: https://zenodo.org/records/14946146 (accessed on 5 June 2025).

The EIE and radiative data for many ions have been included over the years in the CHIANTI database by GDZ (cf. [29]). The CHIANTI team recently won, in 2024, the NASA group achievement award “for outstanding contributions to the scientific productivity of NASA missions and the creation of a uniquely valuable tool for spectroscopic scientists worldwide”. Much of the credit should go to Nigel and his collaborators as they produced the bulk of the atomic data. The same is true of many other codes used for astrophysical applications, which are too numerous to be listed here.

Nigel was interested in applying his results to astrophysical problems. The astronomy community is much larger than that of atomic physics, and astronomers enjoy a much higher citation rate as a result. In the early 2000s, he began collaborating with Gary Ferland, the developer of the spectral synthesis code Cloudy (https://ui.adsabs.harvard.edu/public-libraries/JRuqmRUrSnmRy1U-OR1pRw, accessed on 5 June 2025). Their work initially centered on DR [30], research that showed how Nigel’s updated results changed the stability of clouds near supermassive black holes. Nigel often took the approach of computing entire iso-electronic sequences, resulting in large quantities of high-quality data. Cloudy, like CHIANTI, uses as much of Nigel’s data as possible. It is a measure of both the importance of Nigel’s work and the relative sizes of the atomic physics and astronomy communities that Nigel’s three most cited papers [20,31,32] are centred on astronomical applications.

Nigel became interested in understanding differences in the l-changing collision theories of [33,34], a question of cosmological importance since it can affect precision measurements of primordial helium abundance [35]. The first of the series of papers was [36]; the last one deals with an original study of quadrupolar l-changing collisions [37].

With the launch of new solar and astrophysical missions in X-rays, it was clear that improved atomic data for satellite lines was needed. Nigel was happy to collaborate in this area with GDZ [38] and Adam Foster, a former PhD student of Strathclyde, now working with Randall Smith on ATOMDB developments.

Nigel was always enthusiastic to start working on new areas. The discovery of gravitational waves arising from a binary neutron star merger in 2017 led to a flurry of efforts to model the associated kilonova emission. Nigel’s pioneering work on opacities [32] before the discovery demonstrated that lanthanide opacities were orders of magnitude larger than typical iron-dominated supernova opacities and so are fundamental to model kilonova expansion. Nigel realised that a lot of data for opacities and recombination were needed, so he set up a plan to tackle this void.

In summary, Nigel became the leading scientist in the world with regards to the amount of atomic data he produced for astrophysics and fusion research. His contributions cannot be overstated and were recognised when he became a Fellow of the Institute of Physics and a Fellow of the American Physical Society. Nigel had a wide range of academic interests, from quantum electrodynamics to cosmology.

Nigel was truly prolific. He could have easily published ten times the number of papers he did but preferred not to. It is hard to summarise the many areas of research that his work touched. Hence, the number of published papers and direct citations (286 refereed and 10,618 according to ADS) are not a true measure of his scientific standing.

Citations alone do not indicate the influence of scientists upon their field. Practitioners can be separated into two groups: facility users, who utilise telescopes or code created by others, and facility creators, the people who make this possible. The former receive far higher publication and citation rates because the work is relatively easy while the hard work of the latter forms the foundation of our science. Nigel’s work created the framework that makes modern astrophysical spectroscopy possible.

As a scientist with great integrity, Nigel always wanted to get close to the truth and to the bottom of why different calculations or approaches were producing different results, often uncovering mistakes or incorrect interpretations provided by many authors, an approach that we will sorely miss. He was keen to learn about new fields of research. He would ask many questions and treat researchers as experts and peers, regardless of their career level. Claude Zeippen wrote: “Nigel was a remarkable physicist. He was competent, serious, dedicated, reliable. He played a crucial role in the Opacity Project. His autostructure has been and still is a precious tool for members of our community. His scientific work deserves a lot of praise. In the experience of many of us, it was a privilege to benefit from his scientific cooperation and his sense of friendship”.

Nigel influenced many scientists through his rigorous work. For example, Zikri Altun (Marmara University), a close collaborator in the past 20 years, regarded him as a “generous colleague and wise counselor”. Franck Delahaye wrote, “it took me a while to past the rough ‘façade’ but what a chance to have been able to go past it. He was so patient and so pedagogical with all my questions during so many years and so friendly all at once”. Manuel Bautista recalls: “Nigel was also a good and generous person in his own peculiar way. I enjoyed sharing with him some of his cinema collection when he hosted me and John Tully at his house”. Patrick Palmeri wrote: “I will miss him and his frank and clever discussions, and also his peculiar sense of humor”.

Within his private life, Nigel had several hobbies. Nigel found enjoyment and relaxation in occasionally going out sailing on Castle Semple Loch, camping at the Crinan Canal, fishing at the River Leven, and going on various other adventures. He liked driving the car south to Cambridge, going out for dinner with friends, and having long walks. He had a vast collection of DVDs of movies to watch at home and was an enthusiastic stamp collector, particularly of those from administrative regions in India before 1915. He always enjoyed Indian meals and was fond of many types of beers, including ginger beer. He was old-school, he did not even own a mobile phone, and he preferred cash and cheques. GDZ recalls several group meals where he became really upset when various colleagues put down what they thought was their fair share of cash, but the sum invariably was lacking the odd pound or two. Nigel was very meticulous about everything, even with his garden: the stripes on the grass had to be perfect!

He originally planned to retire in 2025 and move south to live again in Cambridge, where he used to visit about twice a year. In 2023 he decided instead to stay on at Strathclyde University in Glasgow for a few more years, as he had a new PhD student (Niamh Ferguson) and a post-doc (Chunyu Zhang), which he was very happy about. He had also applied for further funding for his research, in particular on kilonovae.

Nigel devoted his entire life to science, a unique case for his generation. His family were the young researchers he supervised: he would invite them to his house, drive them to places, take them to dinners and international conferences, and help them in their careers. Chunyu, the last of the UK APAP post-docs, wrote: “Nigel played a significant role in my growth path, and it is still difficult to accept the loss of such a guiding light. Even in his final days, he continued to support my work. His firm attitude in pursuing scientific truth and his tenacious spirit in fighting cancer will impress me profoundly and lastingly”.

Junjie, the previous UK APAP researcher working with Nigel during the pandemic, recalls: “with decades of experience, he was perceptive in many aspects yet remained unflappable, steering us toward the correct direction. Prior to the pandemic, he had already talked about his aspirations for retirement in Cambridge during our weekly coffee/tea time (the pandemic hardly impacted Nigel)”.

Guiyun Liang, a former UK APAP post-doc in 2008–2011, wrote: “Nigel was very kind and patient to guide me on how to use the R-matrix program and explain its principles. He used to drive me to Cambridge University for the UK APAP meetings with his BMW car. In 2017 we climbed the Great Wall together, and attended the ICPEAC conference in Australia”.

Simon Preval was also a post-doc. He wrote, “Nigel was kind and nurturing towards me, allowing me to continue studying white dwarf stars while I worked on the DR of tungsten ions for the upcoming ITER experiment. He was patient, dedicated to his craft, and was always happy to discuss atomic physics until the Sun went down. I will be forever thankful for his wisdom and kindness. His guidance allowed me to be the best scientist I could be. I will miss him terribly”.

Mike Witthoeft, a former UK APAP post-doc, wrote: “my first post-doc was with Nigel. He was very welcoming when I moved to Glasgow; I stayed at his place (awed by his movie collection!) for a couple weeks until I found my own. He was very patient and generous with his time, not only teaching me autostructure and R-matrix, but encouraging me to pursue my own research interests (and making those projects better). I couldn’t have asked for a better mentor”.

Connor Ballance, a former post-doc, wrote: “ he allowed his post-docs such a high degree of freedom to follow what their interest were, just as long as some aspects of the underlying grant were completed. Years later, if you still had questions, not many of us had to wait more than a couple of days for an answer to our emails. He will be missed, as mentor and friend”.

Bad news struck in April 2024, with a cancer diagnosis. In spite of this, he continued to work whilst having treatment until the last few days, passing away on 3 September 2024, at the age of 65. He was very stoic and did not disclose his condition to very many people. Stefan Kuhr recalls Nigel saying, when offered to pause his teaching duties: “Why should I stop? My body is ailing, but my mind is as sharp as ever!”

We lost not only a great colleague and friend but also one of the last among the greatest atomic physicists. His legacy is a large set of well-organised atomic data and codes used by a large community of physicists and astronomers. Nigel was always keen that they should be publicly available, putting into practice a central ideal of science. Most of all, his legacy is the students and post-docs he trained during his long career at the University of Strathclyde. He is greatly missed by all—his colleagues, collaborators, family, and friends.

Ad astra, Nigel

Acknowledgments

We would like to thank Nigel’s sister Hilary and all the colleagues that provided comments and contributions.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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