13. Copenhagen 1974-86

Dr. Herdal. “You began as a poor country lad, and here you are the top man in your profession. Oh, yes, Mr. Solness, you‘ve had the luck on your side all right.”

Halvard Solness. “My luck will change, I know it. And I feel it will happen soon. Someone will stand up and demand : ‘Make way for me !’ And then all the others will storm after him shaking their fists and shouting : ‘Make way ! Make way !’ Just you wait, Doctor. One fine day, youth will come and bang on that door.”
– Henrik Ibsen, The Master Builder.

‘Electromagnetic Corrections to Hadron-Hadron Scattering’ with Bjarne Tromborg (Nucl. Phys. B76, p.483) was published in 1974. This work extends the work done with Ingjald Øverbø and Bjarne Tromborg in ‘Coulomb Corrections in Non-Relativistic Scattering’. In contrast to non-relativistic Coulomb corrections, the electromagnetic corrections are relativistic. The work uses Yennie’s factorisation device to obtain a dispersion relation which gives the full electromagnetic corrections to meson-baryon scattering. As with ‘Coulomb Corrections in Non-Relativistic Scattering’ there is reference to contemporary work by Oades and Rasche, also to work by Auvil, who had been at Imperial College during Jim’s UCL years. The paper carries an acknowledgement to Ingjald Øverbø.

Jim and Bjarne write : “The ultimate motivation for trying to estimate the electromagnetic effects is the hope that we shall be able to prove with precision the charge independence of the hadronic interactions. If, however, this turns out to be too ambitious, we wish to emphasize that the corrections we make in this paper are essential to give amplitudes which have the analytic properties that are commonly assumed for hadronic amplitudes. In other words these corrections must be made if we are to make intelligent use of the experimental data on hadron scattering which are available.”

Bjarne Tromborg’s recollection is that this paper took a long time to complete, mainly because he kept taking more and more electromagnetic effects into account : “In a dispersion relation analysis of experimental data it is necessary to take into account the effects of infra-red divergences and the singularities due to the long-range electromagnetic forces. This was our first objective and I think that was a manageable though complicated project. But we also wanted to show that if we correct for all electromagnetic effects we end up with scattering amplitudes which are isospin (global SU2) invariant. The latter objective is in fact only meaningful within certain approximations but that was not clear to us at the time. As an example, SU2 invariance implies that neutrons and protons have the same mass. With the knowledge of today we explain the actual mass difference as arising from Coulomb energy plus the mass difference between u and d quarks, so SU2 invariance only holds in the limit of equal u and d quark masses.” The slow progress was frustrating for Jim : on reflection Tromborg agrees that the 58-page paper should have been divided into a number of shorter publications.

The 1975 review article ‘Electromagnetic Corrections to Hadron Scattering’ (Fortschritte der Physik 23, p.211; also published as Nordita Publications no. 602) was based on a lecture given by Jim on this topic at Gleiszellen (Rhein-Pfalz) in June 1974. The electromagnetic corrections are described in four categories : emission corrections, radiative corrections, removal of infinite range interactions and implicit electromagnetic corrections.

The review article also discusses applications of this work “The methods surveyed here can form a basis for studying the breaking of SU(2). For this it is necessary to determine from the data the breaking of the important coupling constants. Also new coupling constants have to be found…There are deeper problems such as the p-n mass difference. The Coulomb effects would require n to be lighter than p, and it is important to know whether the splitting of the hadronic coupling constants will counteract this and give the correct sign and value for the mass difference…Another deep use of the theory is that the determination of the electromagnetic corrections can give valuable checks to our understanding of the hadron structure and interactions…”

The final results of the electromagnetic correction work Jim pioneered at Nordita appeared in 1976-8 (under the names Tromborg, Waldenstrøm and Øverbø) and came to be called the ‘Nordita method for treating electromagnetic corrections’ or the ‘Nordita corrections’ (1976, Ann. Phys. 100, p.1; 1977, Phys. Rev. D15, p.725; 1978, Helvetica Physica Acta, 51, p.584). Tromborg comments : “Jim wrote a review article on the collected work in Fortschritte der Physik [above], but otherwise I think that from then on he was only involved in occasional discussions of the project. He may have thought that it was time for us to be on our own.”

Tromborg was to leave particle physics, for lack of positions, after his NBI fellowship ended in 1977, but it was not long before he embarked on a successful career in optical communications and semiconductor technology. Looking again at his work from the 1970s he says : “I am surprised to see how relatively well the papers are cited, taking into account that it is a narrow topic far from main stream interests.” The title of a paper from 2001, ‘Towards an Understanding of Isospin Violation in Pion-Nucleon Scattering’ (Phys. Rev. C63, 045201), and also more recent articles, indicate that the topic is still alive and active 30 years on.

Reference in Jim’s work on electromagnetic corrections to the SU(2) symmetry group should be explained. S-matrix theorists would use SU(2) and SU(3) as global groups, often referred to as isospin groups. Jim was primarily interested in the isospin symmetry of SU(2).

During the 1970s there was an increasing interest in gauge symmetry which involved using the SU(2) and SU(3) groups in a different way. In the 1940s Wolfgang Pauli had introduced ‘gauge theory’. This was the idea that symmetry transformations can be performed locally as well as globally. In 1954, Chen Ning Yang and Robert Mills (Phys. Rev. 96, p.191), and separately Ron Shaw (in his Ph.D. thesis whilst working under Abdus Salam at Cambridge), had introduced ‘non-abelian’ gauge theories as models to understand the strong interaction (non-abelian means non-commutative, commutativity being the ability to change the order of something without changing the end result). In 1969 Iosif Khriplovich (published only in Russian) had discovered what later became known as ‘asymptotic freedom’ in the SU(2) gauge theory and in 1972 Gerardus ‘t Hooft had observed the same effect, although the significance of these findings was not immediately recognised.

Also almost unnoticed at the time, Steven Weinberg had in 1967 (Phys. Rev. Lett. 19, p.1264) formulated a very strange theory partially unifying the electromagnetic and the weak interactions into a (electroweak) theory he hoped could be consistent with quantum theory. Soon it was recognised that sketches of the theory had been formulated earlier by Sheldon Glashow and that also Abdus Salam had had similar ideas. In time the theory came to be known as the Glashow-Salam-Weinberg, or GSW, model.

Then, in 1970, Glashow, Iliopoulos and Maiani (Phys. Rev. D2, p.1285) had tried to combine the electroweak theory with the strong interaction, based on a version of Gell-Mann’s concept of quarks, but requiring a fourth quark, the ‘charm-quark’ (the names of quarks have no intrinsic significance) proposing what became known as the GIM mechanism. At the time this work was considered speculative – there was no experimental proof of the existence of a charm-quark. At the 1974 International Conference in London, Iliopoulos predicted that the charm-quark would be discovered prior to the next conference, in two years time. In fact he flamboyantly offered a bet of a box of good wine on it. Many in the audience were sceptical and the prediction was largely ignored, yet the charm-quark was identified that November, being a component of the J/psi meson discovered simultaneously by research groups at Stanford and Brookhaven.

In 1973, David Gross and Frank Wilczek (Phys. Rev. Letters 30 (26), p.1343 and Phys. Rev. D8, p.3633), and separately David Politzer (Phys. Rev. Letters 30 (26), p.1346 and Phys. Rep. 14, p.129), had attempted some technical calculations for non-abelian gauge theories and obtained similar results to those obtained earlier by Khriplovich and ‘t Hooft. The more recent work went further, in recognising the enormous significance of the results. Asymptotic freedom explained qualitatively why quarks acted as if they were free inside hadrons and also explained a fundamental property of deep inelastic scattering of electrons on hadrons. Out of this work was born the theory of quantum chromodynamics (QCD), a non-linear theory to explain the strong interactions binding quarks and gluons to form hadrons. The ‘Standard Model’ of particle physics which followed was a relativistic unification of the GSW model of quantum field theory and QCD. It provided an internally consistent theory of three of the four known fundamental interactions between elementary particles (electromagnetic, strong, weak), falling short of being a comprehensive theory of fundamental interactions only because it did not incorporate gravity.

Whereas quantum field theory had held that interactions between particles became increasingly strong, tending to infinitely strong, over shorter distances – this was known as a ‘Landau pole’, a considerable problem for QFT theorists – asymptotic freedom allows for the interaction to become arbitrarily weaker at ever shorter distances (it should be mentioned that a pole can be encountered even under asymptotic freedom : in QCD the pole indicates that interactions grow stronger at large distances, suggesting an effect of quark ‘confinement’ within hadrons).

Jim was again at Karlsruhe for a week at the end of June 1975 for a meeting with Gerhard Höhler’s group, prior to spending a week at CERN. It was at about this time that Jim became more actively involved in work at DESY and establishing links between Hamburg and Nordita. Certainly, if one wanted an introduction to the people and set-up at DESY, Höhler would have been able to provide much assistance. One of the people at Hamburg who Jim got to know well was Harry Lehmann, who had himself spent a year in Copenhagen during the 1950s. Jim visited DESY later in the year, in October. It should be added that there was at this time also an interest at NBI to establish co-operation with DESY, and that Aage Bohr had initiated this independently.

In April 1976 Jim, Glen and Patrick spent a few days in Venice before going on to Trieste where Jim worked for ten days at the Abdus Salam Centre. There is a recollection that Jim attended at least one of the Adriatic Summer Meetings on particle physics, which were held at two- or three-yearly intervals in Dubrovnik. His 1984 collaboration with Geoff Oades ‘The Short-Range Nucleon-Nucleon Repulsion’ (Nucl. Phys. A424, p.447) refers to Gerhard Höhler’s report ‘II Adriatic Summer Meeting on particle physics’ – it is a guess that Jim was back in the Adriatic for eleven days at the end of August.

‘The Theory of P-Wave States’, a collaboration with Bjarne Tromborg, (Nuovo Cimento 33A, p.605) was published in June 1976. The results of their work on ‘Partial Wave Amplitudes and Resonance Poles’ had led Jim and Tromborg to a simple model calculation to describe relativistic P-wave meson-baryon systems. The paper outlines the properties of a relativistic meson-baryon P-wave amplitude subject to a single driving pole, and examines various stability effects. Gösta Gustafson is acknowledged for his suggested representation of the variation of resonance position.

Two other papers would be published in 1977. The first was ‘Baryon Decays and SU(3) Breaking’ (Physica Scripta 15, p.289), a collaboration between Jim, Gösta Gustafson, Henry Nielsen, Geoff Oades and Bjarne Tromborg. The paper was an amended version of ‘The Exchange Picture, the Strange Quark and SU(3) Symmetry’ which had been a Nordita preprint a year earlier. Many of the Nordita research group had been involved in work on the dynamics of baryon resonances and ‘Baryon Decays and SU(3) Breaking’ presented a concerted attempt to deal more directly, using dispersion relations, with the dynamics of the decays than had been achieved previously. The paper also gave valuable data on how SU(3) breaking applied to various baryon couplings and on the values of the leading couplings. A good deal of work in this area was done by the members of Jim’s group (and others) : a general survey of this is provided by Nordita Lectures (1978) ‘New Developments in Dispersion Theory’, Vols. 2A, 2B by Jim and Geoff Oades (Oades made a considerable contribution to these).

The second was Jim’s paper ‘Discrepancy Analysis for SU(3)’ with Geoff Oades (Phys. Rev. D16, p.2295) which refers to several published works, the most recent by Horgan and Dalitz in 1974 (Nucl. Phys. B71, p.546), describing low- and medium-energy baryon bound states and resonances in terms of the SU(3) gauge group. The paper asks, and answers, two questions. Can SU(3) properties be observed in the scattering amplitudes away from the resonances ? Answer – “…one can indeed see SU(3) properties at nonresonant energies by using the discrepancy functions [developed in Jim’s 1961 paper with David Spearman : ‘Low Energy Pion Scattering’ (Annals of Physics, 12, p.172)] but only in the amplitudes where there is a strong attraction.” The second question asked is whether there is any trace of SU(3) in scattering states where there is a repulsion between the particles, and the answer given is “Probably not.” In ‘On Mesons and Methods’ Jim later states : “Geoff Oades and I found to our surprise that a discrepancy analysis (a discrepancy matrix)…gives a clear distinction between eigenamplitudes for which SU(3) holds well, and the remaining eigenamplitudes from which the symmetry has mostly disappeared. The former have large positive eigenvalues of the discrepancy matrix. This distinction may be one of the most important features of the partially broken symmetry. The dispersion theory of exchange interactions in two-body hadron scattering is well defined, and it can often be made precise. It may not be particularly easy for the quark-gluon approach to do as well in this field.”

In the years following the 1973 work by Gross, Wilczek and Politzer, many particle physicists abandoned S-matrix theory in favour of QCD. David Gross was a former student of Geoffrey Chew, one of those who, like Jim, had favoured the S-matrix approach. There were aspects of S-matrix theory which had led to the new developments and the mathematics involved in the theory would prove to be useful for a long time to come, but it seemed that the strong interaction could not be understood on the basis of S-matrix theory alone.

During the early 1970s Jim had encouraged the members of his research group at Nordita to continue working on topics associated with S-matrix theory. Jim’s view seems to have been clear : that further progress on understanding the strong interaction would most likely be made through the phenomenological study of scattering. Through his use of dispersion relations he could be predictive : at low and medium energies, dispersion relations were still the only viable framework for matching theory of the strong interaction against experimental data. He was not satisfied with following a new theory which merely appeared explanatory. In addition, it would have reflected poorly on him had Jim encouraged his fellows and visiting researchers to follow a promising, but speculative new line of research had it abruptly failed. Of course there is a fine line. If a scientist were always to wait until there is conclusive evidence for a new idea, he would miss the opportunity to be involved in exciting early work. It seems that Jim’s conscientious supervision of research ultimately may have worked against him here.

One evening during the summer of 1976, when the writer had telephoned Jim and Glen in Copenhagen, Jim was really not very talkative. A few minutes later Glen quietly explained that he was unhappy about some difficulties at work, though nothing specific was said. It later became clear that a few of the younger Scandinavian scientists (who were not at that time participants in Jim’s Nordita research group) had, away from Jim’s presence, been very critical about Nordita’s lack of involvement in any of the newer developments of GSW or QCD during the previous few years. They had indicated that Jim was responsible for this situation. When Jim learned about this, it upset him a good deal.

It was one thing to have a disagreement with a person face-to-face, but it was quite another to be talking in such a way in the person’s absence. In fairness, it should be said that face-to-face discussion with Jim on the direction of Nordita research could be inhibited. The father-son, or mentor-scholar, dynamic of Jim’s relationships with his research fellows was now more exaggerated than had been the case at Cambridge or UCL. Jim was now 58, most of the fellows in their 20s. An initial enquiry to Jim about the new topics of GSW and QCD may well have elicited a discouraging reply, along the lines that there were any number of strange-looking theories on the market. To pursue the matter further without appearing disrespectful, the questioner would need to be sure of his ground, and choose his words carefully. Reportedly there was one occasion when a young man at one of Jim’s seminars accused him of “prejudice”. Which likely didn’t go down too well.

At least until the mid-1970s, there were many eminent physicists equally sceptical of some of the new work. Even one of the architects of GSW, Steven Weinberg, was very wary : “In my own first work on the unification of weak and electromagnetic forces, I limited myself to particles like electrons and neutrinos that don’t feel the strong interactions, because I had no faith in the quark theory or any other existing theory of these interactions. Only later was I willing to bring quarks into the theory, though without much confidence. All this changed with the discovery in 1973 that there is a theory of quarks and strong forces in which quarks cannot in principle be seen in isolation.”

In 1988 Nordita set up an evaluation group of three Nordic and two non-Nordic researchers with the purpose of assessing Nordita’s performance, recommending improvements and reporting to the Nordic Science Policy Council (an organ of the Nordic Council of Ministers). Much of the performance assessment was derived from the responses of Nordita fellows to a questionnaire – it was, in effect, a self-assessment. Relating to elementary particle physics the report reads : “During the 1960s and the 1970s the research on particle theory at Nordita was led by James Hamilton as professor. This effort was centred on phenomenological amplitude analysis and the exploitation of dispersion relations and causality constraints for scattering amplitudes. Several of the stipendiates at the institute worked in this field as students and associates of J. Hamilton. This activity was useful in particular from the point of view of nuclear physics but missed out on the rapid developments of the 1970s in the areas of field theory and quantum chromodynamics…” Going on to comment on Jim’s successor as professor from 1986, Paolo di Vecchia, the report adds “…The complete concentration on superstring theory is associated with a considerable risk that the effort may in future, with hindsight, be viewed as having been misdirected if the field develops in another direction.”

After the event, the people at Nordita seemed to be saying they had wanted to follow the most recent trends but not to be involved in the risk necessarily involved. One way to achieve this would be to appoint more than one professor for particle physics and ‘lay off’ the risk. Various people who have assisted with this biography have indicated the close cooperation between Nordita and NBI. So how close was this relationship ? Close enough for the senior people, on learning that theoretical particle physics was rapidly becoming two distinct schools, to plan accordingly ? Perhaps. It would certainly make sense : with emphasis on S-matrix theory at Nordita and emphasis on the newer schools of thought at NBI, one might think that Copenhagen was assured to remain in the forefront of particle physics, whichever school ultimately yielded the hoped for results (this would also be a pragmatic approach in view of budget constraints). ¹

The eldest of Jim’s children, Elizabeth, was married in Copenhagen in May 1977 and the writer visited for the occasion. Following the ceremony, guests were all invited back to the house at Soldalen for a reception. There were photographs to be taken, and necessarily a considerable delay before the guests could enter the house. The writer found himself talking to one of Jim’s Nordita associates and enquired as to the nature of the difficulties there had been at Nordita. The man replied that some young people were unhappy that they were not allowed to pursue their preferred topics of research. The writer enquired as to the reason for this restriction on them and the man carefully responded : “Well, the two institutes [Nordita and NBI] aren’t as independent as you might imagine…” This answer, because of its seemingly non-sequitur nature, stayed lodged in the writer’s memory. There is recollection also that on many occasions, throughout his time at Nordita, Jim mentioned having meetings with some of the senior people at NBI.

It should be added that Jim was not the only senior scientist in Copenhagen to attract criticism for continuing to put emphasis on a subject which was being abandoned elsewhere. In 1975 Aage Bohr, Ben Mottelson and James Rainwater had jointly been awarded the Nobel Prize for their work in nuclear physics, determining the non-spherical geometry of atomic nuclei. Later Aage Bohr was criticised for continuing to emphasise the importance of nuclear physics. In Jim’s case it’s important to note that at Nordita, where there had been only limited focus on particle physics prior to Jim’s arrival in 1964, there had since grown a considerable interest in the subject.

The lack of early focus on QCD by Jim’s Nordita research group does not appear to have been a particular hindrance to its participants. Gösta Gustafson went on to play a leading role in developing the world-famous Lund string model of QCD, a phenomenological model which predicted particle jets forming along the paths of two separating quarks and a hadron ‘spray’ produced between the jets. Esko Pietarinen got involved in the industry of massive computer simulations of low energy QCD and later, with his son, went on to set up a highly successful company providing electronics for synchrotron facilities; Geoff Oades would pursue a very active career at Aarhus University; and Jens Lyng Petersen would also be prolific at NBI, having many collaborations with di Vecchia. Bjarne Tromborg would eventually leave high energy physics but developed a spectacularly successful career as an optical physicist.

It was perhaps during the winter of 1976-7 that Jim started an evening-class in navigation and seamanship, with a view to obtaining his Master’s certificate. One evening each week he would drive down to the harbour to attend the course, which was delivered entirely in Danish. Typically another evening of the week was spent with study at home, his desk covered with charts, pencil and dividers. When asked if he had plans to acquire a boat of some description, maybe upon his retirement, Jim replied to the effect : “Well, maybe, but the course was just something I wanted to do.” Jim seemed to enjoy the course immensely, many of his class-mates were men of about the same age, and most had a good many years experience of the sea. He enjoyed the company of these men and would talk of their different sea-faring experiences when he returned home. It was no surprise to learn that he passed the examinations (again entirely in Danish) and obtained his Master’s certificate.

During the same time it appears that Jim made his own thorough evaluation of the situation at Nordita and how everybody’s interests could be best served. In no small part due to his efforts, research on elementary particle theory was now well established and vigorously pursued throughout Scandinavia, but perhaps now was a suitable time for him relinquish the full-time professorship of particle physics. His own research interests were varied and not limited to work on particle physics; he wanted time to work more actively on problems of coherent radiation (laser light : whereas most light sources emit incoherent light, light that varies randomly with time and position, laser light is characteristically low-divergence, that is spatially coherent) and he had also become interested in examining the nucleon-nucleon interaction (in part this may have been a shift initiated through discussions with his friend Gerry Brown, whose field was nuclear physics).

There were also family considerations : Glen had on several occasions stated that she would prefer to be living back in the UK, closer to family (both the elder children had settled in the UK) and friends, while younger son Patrick would be eligible to go to university in 1978 and there had been the suggestion of Cambridge (two years previously Patrick had left his Danish School and enrolled in a French school in Copenhagen : his studies had gone well and he now enjoyed the prospect of obtaining results sufficient to gain him entry at a top university). Not insignificant, though maybe low on Jim’s list of considerations, he would reach the age of 60 in January 1978.

Jim’s evaluation process culminated with a formal request to the Nordita board in May 1977. The letter requests 6 months’ leave of absence from October 1978 to March 1979 (Jim had taken little leave of absence during the previous 13 years – just the occasional week or two at CERN – and the request certainly wasn’t creating a costly precedent) in order to spend time studying specified topics outwith particle physics. Also Jim asks the Nordita board to consider whether he could work a part-time contract from October 1979, working just 6 months of each year at Nordita.

There has been suggestion that Jim investigated the possibility of taking up a professorship in the UK at about this time. There were two visits to Cambridge, one in October 1977 and the second in March 1978. Sandwiched between these visits to Cambridge was a short stay in Hamburg, at the end of January 1978. As described earlier, Jim had been instrumental in establishing co-operation between DESY and Nordita during the early 1970s, and the role continued. The visit spanned 29th January, his 60th birthday, and this was not coincidence. Gerhard Höhler and Jim had for many years enjoyed a close friendship. In 1972 Jim had honoured Gerhard’s 50th birthday through his dedication of ‘The Dynamics of Some Pion-N Resonances’. Now Gerhard was involved in returning the favour. In fact this was not the first time Jim had happened to be in Hamburg for his birthday – he had also been there in January 1977.

Jim’s leave of absence was agreed by Nordita. It had also been agreed with Nordita that he would work 6 months of each year (1979 to 1985) from approximately late-April through to the end of October, though in practice Jim would usually be in Copenhagen for part of November also. Patrick had enrolled in Christ’s College in 1978, and with the other two children already living in the UK, the house at Soldalen was now more than Jim and Glen required. In the autumn of 1978 there was a lot of work to do at home, arranging the sale of the house, packing boxes to be subsequently freighted to the UK, other boxes to be put into storage until a flat in Copenhagen could be found which would be suitable for their use over the next few summers. At the end of September Jim and Glen left the house at Soldalen. They had been there for over 13 years, the longest time they had spent together at any one place.

In Cambridge they soon found a reasonable place to move into, in Lantree Crescent, a quiet residential cul-de-sac of Trumpington. Almost immediately DAMTP made provision for Jim to share an office in the department. This was a kind offer and proved to be a very useful one, as Jim often went into the department during the six months of the year he was in Cambridge. John C. Taylor recalls Jim coming into the coffee room at DAMTP most days and having interesting discussions with him. Even after his full retirement, in 1986, he would usually visit the department at least once a week, up until about 1997. It must have seemed quite a contrast to his early Cambridge days, when as a full-time lecturer he had no office.

The part-time arrangement seemed to suit Jim well. He had become interested in making an X-ray laser and would travel from Cambridge to London quite regularly in order to visit Dan Bradley, professor at Imperial College. Bill Woolcock recollects that in October 1978 he was coming to the end of a sabbatical year (spent mostly at Cambridge) and was fitting in a few weeks at UCL. He recalls meeting Jim for lunch one day at ICL where the two of them talked a lot about physics and had a very enjoyable time together. That night, or perhaps the night after, Bill ran into Jim and Glen at the Royal Festival Hall and remembers walking together with them across the Hungerford Bridge. He observes that both Jim and Glen seemed in very good spirits.

In the early spring of 1979 Jim, now 61,  was admitted to Addenbrooke’s Hospital where tests revealed that there was an irregularity with his heart, and he was transferred to intensive care for two or three days. A further two weeks were spent in hospital while he recovered, and finally it was considered safe for him to go home, although initially he would return to hospital every day for a check-up. Jim took cardioversion medication for the rest of his life.

He was advised to do very little for the remainder of the year. Physical and mental stress was to be avoided in case the heartbeat should revert to its irregular pattern. After a few weeks had passed without event, the check-ups became weekly, then fortnightly. An immediate return to Copenhagen was out of the question. The enforced period of idleness was all very well, for a while, but there were a number of issues in Denmark which he wanted to attend to. Not least of these was a feeling of responsibility for the work at Nordita – he should have been in Copenhagen during the months April to October. There were also the matters of upkeep of the summerhouse in Gilleleje, and finding a flat to use in Copenhagen.

Eventually he satisfied the medics, and travelled with Glen and Patrick to Denmark in September. Patrick needed to return to Christ’s College at the beginning of October for the second year of his undergraduate course, but Jim and Glen remained in Denmark for a further few weeks. Bjarne Tromborg remembers that he visited Jim in his office during this period and that this was the last occasion he saw him. He recalls that it was a very enjoyable meeting : “I shall forever remain very grateful for the support I had from Jim and for all I learned under his guidance.”

Jim still took a keen interest in Danish current affairs. A letter to Patrick during October referred to a Danish general election : “The election is more boring than usual. My father would say that they should let the cows vote : they might understand what the candidates say…” This doesn’t imply any general criticism : at various times Jim expressed that the Scandinavian social democracies were probably the best systems currently on offer. He was highly complimentary about the Scandinavian welfare models, in particular Swedish PM Tage Erlander’s ‘Strong Society’ (when Erlander stepped down in 1969, Jim was also complimentary about his successor, Olof Palme). Jim’s interest in European politics extended further. He’d been a great admirer of Willy Brandt (Chancellor of West Germany from 1969 to 1974) and his ‘Ostpolitik’ initiatives.

For Jim and Glen, the spring of 1980 went a little more according to plan than had the previous spring, and they arrived back in Copenhagen towards the end of April. Jim had secured a flat near the centre of Copenhagen (probably this was achieved during the previous autumn’s visit), on Rosenørns Alle in Vesterbro, close by to the lakes Skt Jørgens Sø and Peblinge Sø. The flat was comfortable, warm and within easy walking distance of Blegdamsvej : they retained it until 1986.

During 1980-1 Jim was much involved in setting up the first formal summer school to be held by Nordita. This initiative allowed further opportunity for young Nordic physicists to get together, also for dialogue between theoreticians and experimentalists. Nordita summer schools have since become frequent and popular, the participants favouring the more relaxed, seminar-based approach.

In 1981 Jim’s paper ‘Uncorrelated and Enhanced 3 Pion-Exchange in NN->NN’ appeared as a Nordita Preprint (81/45), but was not published elsewhere. His direction of research had changed, now examining the nucleon-nucleon interaction. The paper arose “…from the puzzle that existed, and still may exist, about the [omega]NN coupling” and acknowledges “…Andy Jackson, and especially Geoff Oades, for help in the early stages in safely penetrating the jungle of NN formulae…” Jim also thanks Gerry Brown “for much instruction and numerous discussions on the particle theory approach to NN interactions.”

Gerry Brown’s book with Andy Jackson, ‘The Nucleon-Nucleon Interaction’ (North Holland, 1976) describes one of the problems with use of dispersion relations in particle physics : “On the whole, dispersion theoretical approaches have not enjoyed much success in giving quantitative description of phenomena in particle physics. The usual trouble is that intermediate states of higher and higher energy must be included, in a way that gives little hope of convergence.” Brown and Jackson go on : “One can ask why such an approach appears to be suitable for the nucleon-nucleon problem. Our grounds for optimism stem from the strong repulsion obtained from [omega-] meson exchange…”

Jim’s summary refers to the ‘Quark Model’ and asks when, in nucleon-nucleon interactions at short distances, does one need to consider that the three quark structures have coalesced into a six quark structure ? “The discontinuities and sharp changes associated with such a transition should be clear, but there is no sign of them in the region we cover, namely 3 pion states…However if we contemplate 4 pion states, the number of states, and the number of different enhancements, becomes so large that a qualitative change may have set in. This means…one may begin to see the transition to quark matter. In this connection we point out that there cannot be any conflict between the quark model and dispersion relation methods; the only debate can be about which gives the simpler physical structure, in a given situation.”

At the beginning of March 1982 Jim and Glen would have been giving some thought to the coming six months in Copenhagen. There was travel to be arranged and always the matter of planning carefully what things from Cambridge they would need with them in Copenhagen. Then there was the issue of the summerhouse at Gilleleje : now that the children had all left home and gone their separate ways, it was not being used very much yet there were still the demands of the upkeep of the place. One afternoon there was a knock at the door. It was the police, with the news that Patrick, at age 21, had died in an accident. The following day Jim and Glen travelled to Brussels, where Patrick had been working.

Patrick had been awarded his BA in biochemistry from Cambridge only the previous June. Being fluently trilingual, he had readily found work with the European Commission in Brussels and was very successful in his work as an interpreter. He had made many friends there, as he had during his time at Christ’s. It was a terrible time for Jim and Glen, but they got on with things – what choice is there ? In April they were again back in Copenhagen and Jim’s Nordita work continued, one miserable summer day after another. Then there was a contact from Inge Johansen, professor at Trondheim University – Trondheim wished to award Jim an honorary doctorate, bestowed for Jim’s contributions over the years to Trondheim and its students – would he be able to attend a ceremony in September ?

The tribute to him published in Trondheim University News No 6, September 1982 (with apologies for this writer’s approximate translation) reads : “Professor James Hamilton’s scientific area is theoretical elementary particle physics. He is one of the world’s leading experts in theoretical meson physics and to a large degree he has shaped the subject over the last twenty years. Meson physics has found a central place in modern physics, both in lower energy – in nuclear physics – and in high energy physics. Professor Hamilton’s scientific contribution has stamped this field of physics. He became a Professor at Nordita in 1964. He is the only professor in elementary particle physics there and he has built up the research activities from nothing. His contribution has allowed Nordic research students to acquire a very good further education in theoretical elementary particle physics. Since he arrived at Nordita, he has had a close affinity to the department of theoretical physics at the University of Trondheim, and his work with Nordita has allowed greater understanding of elementary particle physics at Trondheim. The University honours him with a Ph.D. degree.”

There was also a short summary for the benefit of those attending the ceremony : “Professor James Hamilton works at Nordita in Copenhagen and through his teaching has made a great contribution to Norwegian particle physics. A large number of Norwegians have benefited from his lectures at Nordita.” Jim’s letter of 7th September to Johansen reads “…My wife and I would also like to thank you and your colleagues for the very pleasant time we spent in Trondheim. Our visit will be a happy memory.”

In Denmark that summer, Jim and Glen arranged the sale of the summer house in Gilleleje. It had served as a valuable retreat for them for a period of ten years, more than a retreat even, for it had been their principle place of residence during their autumn 1979 visit. The children had all enjoyed the place, but now Patrick was gone and the elder two had been visiting Denmark only rarely during the previous few years.

In 1983 Jim was asked to take on the office of Nordita director, to be effective from January 1984. This was a job that required familiarity with the organization and its personnel, which he carried out with great conscientiousness. Glen’s letter to the writer from July 1983 records that Jim was “finding himself in much demand now – even though his term of office is not due to start until January. He is having to attend many meetings, both scientific and administrative, and of course there are always the canvassers for support in various projects, who take up his time. He needs to hear all points of view before he can form an opinion on the course he should take. It is natural that after a period of having…a ruling dynasty, people are wondering what line the new man is going to take.”

The demands of directorship required more time spent at Nordita and Jim and Glen travelled to Copenhagen in early January 1984. Jim’s pre-occupation with matters of administration largely precluded his active participation in research over the following two years, but there were two further publications in 1984 from his research during the previous year.

‘The Short-Range Nucleon-Nucleon Repulsion’ (Nucl. Phys. A424, p.447), was a collaboration with Geoff Oades. The paper investigates the nature and the cause of the strong short-range repulsion (‘the hard-core interaction’, in the range of 0.2 to 0.4 fm) between nucleons : “It is believed that this interaction is relevant for obtaining a sufficiently low density of nucleons in the nucleus, and it is believed to be rather important for the state of matter in neutron stars where densities 10 to 50 times that in nuclei may occur. Clearly this short-range repulsion can also be relevant in determining the conditions under which nucleon matter goes over into a quark-gluon plasma (or indeed, determining if that can happen).” The opposing effects of omega meson exchange and sigma meson are investigated, and the relation to Regge behaviour is demonstrated using fixed-s dispersion relations. The energy dependence of the short-range interaction is emphasized, and experimental data on polarization in elastic nucleon-nucleon scattering at high energy are used to give the necessary coupling constant.

Also in 1984 ‘Two Techniques in NN Elastic Scattering’ was published (Nucl. Phys. A426, p. 477). This paper addresses two technical features which arose during the course of the work on ‘Uncorrelated and Enhanced 3 Pion-Exchange in NN->NN’ and ‘The Short-Range Nucleon-Nucleon Repulsion’. The first topic relates to the description of elastic nucleon-nucleon scattering in terms of meson exchanges, and how unique this description is apt to be in practice : “One may of course ask why it is not adequate to use quarks, gluons, bags etc. to study the short-range NN interactions. The answer is that the techniques of QCD have not so far been developed sufficiently to give a well-defined and precise method for this problem. The various treatments proposed so far all have difficulties in the case of NN interactions (cf. ‘The Short-Range Nucleon-Nucleon Repulsion’). Also we have to demand much of the theory; it is clear that the short-range interaction varies with energy, and probably also with momentum transfer, so that a low-energy calculation is insufficient. The theory has to be predictive and not merely explanatory.” The second topic relates to the derivation of the nucleon-nucleon partial-wave dispersion relations and refers to considerable progress achieved by the Paris group (1973, W.N. Cottingham et al., Phys. Rev. D8, p.800) and by the Stony Brook group (G.E. Brown and A.E. Jackson, ‘The Nucleon-Nucleon Interaction’) in describing the medium-range (0.4 to 0.9 fm) nucleon-nucleon interaction in terms of meson theory and also makes it clear that the nucleon-nucleon interaction is not to be described by a static potential “however much one likes the convenience of a static potential.”

One detects more than a hint of frustration here. However much success had been enjoyed by QCD in the previous few years (and however much some people had indicated that Jim’s own work had failed to fully explain the strong interaction), the new theory couldn’t be used in all areas. It was relatively easy to make calculations which could be tested against experiments at high energies, but at lower energies QCD was so complicated to deal with mathematically that no analytic tools existed for matching the theory with experiment. The only strategy employed was to perform massive computer simulations, though the accuracy of these fell a long way short of what was required for the theory to be predictive.

It had been agreed with Nordita that Jim’s term in office as Nordita director would finish at the end of 1985, and that his professorship would terminate at the end of January 1986. Jim would then be free to retire. A letter from Glen to the writer from late 1985 states that Jim was “still heavily involved in administration : e.g. trying to avoid pitfalls regarding arrangement for continued co-operation with [a Russian] physics institute; and trying to get the final suggestions for an order of computers for Nordita – he has permission to use the budget surplus for this (achieving a budget surplus is unusual in itself)…I hope the pressure on him will soon let up. However, he has achieved so much for Nordita that they keep thinking of things they would like to push through while he’s still in the chair.”

Glen’s letter also describes a recent three day break she had arranged for them both in Berlin : “Since we came back, the most frequent questions from friends have involved the idea that we would be restricted in our movements, that the population [of East Berlin] would look miserable, and the whole place would look dull and dreary. So far as we could see in such a short time, none of this is true. There are a few things which make it obvious that you are on the east side of the wall. For instance : there are many fewer cars and nearly all of these are of Eastern European manufacture…Another sure sign is that there is no litter…” Glen went on to report “People say that for many years the total effort of reconstruction was put into providing houses for the homeless…The other side from the foregoing was evident at various times…we observed the elderly women and men going through the checkpoint to West Berlin on Sunday morning. They were mostly alone, and nearly all carried a bunch of flowers or a carefully wrapped cake.” (People over 65 were permitted to cross the border for the day to visit relatives in the western sector.) In later discussion, Jim would be complimentary about DDR; the very low rate of unemployment (compared to some slumping western nations), and good social conditions generally. Of all the eastern bloc states (he had seen most, if not all, at first hand) he thought that DDR had achieved the best for its citizens, but he didn’t overlook that people were free neither to dissent nor to leave.

The move from Copenhagen back to Cambridge was considerably easier than that of 1978. There was not the business of selling their accommodation in Copenhagen – the flat in Rosenørns Alle had been rented, and most of their possessions were already in Cambridge. Jim and Glen arrived back in Cambridge in February 1986, but returned briefly to Scandinavia a few months later.

Early in the new year Jim had received a letter from Bengt Svensson, Professor at Lund University, informing him that he had been listed to receive an honorary doctorate. Jim and Glen travelled to Lund at the end of May in order for Jim to attend the ceremony. The tribute to Jim reads : “James Hamilton, Copenhagen, born 1918, professor. During the period in the 1950s and 1960s, when theoretical elementary particle physics established itself as an individual branch of science, Hamilton was one of the foremost figures. In 1963 he became Professor at Nordita, a post from which he has recently retired with pension. During the last two years Hamilton was also director of Nordita. Hamilton has been of very great importance for theoretical particle physics in the Nordic countries. His highly appreciated way of supporting the Nordic fellows visiting Nordita has meant a lot, not least for many young researchers from Lund. Hamilton was the initiator for and leader of ‘the Nordic dispersion theory group’, a fruitful collaboration during a large part of the 1970s between present and past Nordita fellows, and through this group the fellows found opportunities for continuing research and collaboration after their Copenhagen years, in the same and other Nordic seats of learning. Through his central role in Nordita, Hamilton has also contributed greatly in stimulating research on elementary particle theory in Lund and getting Lund researchers involved in Nordita’s high-grade international atmosphere.”

At the promotion ceremony, which took place in the cathedral, Jim received a laurel wreath, a ring and his diploma. The artillery outside the cathedral then fired a salute (honorary doctors are still saluted by an individual shot), and Jim was asked whether he wished to keep the spent 77mm shell. The empty cartridge made ideal protection for the recently received diploma, which very much appealed to Jim’s humour. There was no opportunity to enjoy Lund’s hospitality further : he was due to travel on to Finland the following day, to attend a one-day symposium at Helsinki which had been organized in his honour.

Esko Pietarinen recalls that there were 40-50 people at the symposium (which he also participated in) : “many considering the size of our small theory community.” From the Helsinki symposium, a tribute to Jim by Stig Stenholm (Stenholm was professor at the Institute for Theoretical Physics of the University of Helsinki) was later reproduced in Arkhimedes, a publication of the Finnish Physical Societies and the Finnish Mathematical Society, (Arkhimedes, 38. vsk, p.116) :

“Professor James Hamilton has been a professor of theoretical physics at the Nordic institute for theoretical physics NORDITA in Copenhagen since the year 1964. He also acted as the director from 1984 until the end of 1985, when he retired to England. Many Finnish theorists as NORDITA fellows in Copenhagen have come to know him as a kind and widely experienced teacher or collaborator. Jim Hamilton was born in Ireland in 1918. He undertook his basic education in Belfast and Dublin, and worked during the war in scientific tasks in the British Services. After the war he worked at the universities of Manchester, Cambridge and London before moving to Copenhagen. Hamilton’s research topics have been the interaction of quantized electromagnetic fields with atoms, properties of elementary particles, quantum mechanical scattering theory and in particular the application of causality and dispersion relations in the scattering analysis. This last mentioned topic became his long time research interest, through which he made an outstanding and permanent contribution to theoretical physics. During the earlier part of his research he collaborated with several well known physicists, among others Massey, Heitler, Salam and Bethe. At Copenhagen he collaborated with several younger Nordic scientists.”

Stenholm finishes up : “Following Hamilton’s retirement at the beginning of 1986, a one day symposium was arranged in his honour on 29th May in Helsinki. During this meeting Hamilton gave a lecture on the development of his research topics, their connections to current physics questions, and their status related to NORDITA and the physics in Nordic countries. This lecture is published here [‘On Mesons and Methods‘ (Arkhimedes, 38. vsk, p.118)] in its original English version as a personal description commenting the history of physics.”

In characteristic self-deprecating style, Jim’s lecture begins “I have kindly been asked to give some account of my research interests over the years and their relation to my activities during the very interesting years when I was at Nordita and had close contacts with many Nordic physicists. It could be that such a lecture would become a boring catalogue of topics studied, and it is probably more sensible to concentrate on a few subjects from when I was young, or moderately young, which seem to have influenced the work I did at Nordita.”

Bibliography.

Brown, G.E. & Jackson, A.D., The Nucleon-Nucleon Interaction, North-Holland 1976
Weinberg, S., Facing Up, Harvard University Press 2001

¹ In February 2009 word was received that Ben Mottelson would like to talk if the occasion arose for the writer to visit Copenhagen. Regrettably the writer couldn’t visit at the time, and the opportunity was missed. It’s entirely possible that Mottelson could have provided another perspective on these matters.