# Dr Brian Buck dies aged 85

26 August 2020

It is with sadness that the Department of Physics announces the death of Dr Brian Buck on 24 July 2020, aged 85.

Brian was a University Lecturer in Theoretical Physics and a Fellow of Wolfson College from 1971 to 2002, and after that was active as an emeritus member of the Department of Physics. Following school in Middlesbrough, Brian was an undergraduate and graduate student at Jesus College, completing a DPhil in theoretical nuclear physics under the supervision of Roger Blin-Stoyle. He held positions at Oak Ridge and Brookhaven National Laboratories before joining the theoretical physics faculty in Oxford. Brian’s research interests extended across nuclear physics, quantum optics, and maximum entropy inference methods.

Dr Alan Merchant is a Lecturer in Physics at Christ Church, Oxford and started working with Brian as a DPhil student in 1976 before subsequently worked alongside him at Oxford: ‘Brian’s principal research interests were concentrated on the physics of the nucleus and over the years we co-authored – often together with Sandy Perez – 71 publications in refereed journals. He valued interactions with his experimental colleagues, particularly those of the Oxford group, and always wanted his work to make contact with experimental data. He had a knack of cutting through detailed formalism and replacing it with simplified but highly insightful approximations that went directly to the heart of the problem. Nevertheless, in the 1960s he was at the forefront of applications of “electronic computers” to calculations that could be taken no further by purely analytic methods.

‘At Oak Ridge and Brookhaven in the 1960’s he worked mainly on neutron, proton and alpha scattering. With Francis Perey^{1} he introduced an energy independent non-local optical potential for the elastic scattering of neutrons from nuclei and solved the wave-equation numerically in its full integro-differential form, employing a separable non-local kernel consisting of a potential form factor times a Gaussian non-locality – an article which has garnered well over 1,000 citations. He also pioneered the development of the coupled-channels formalism to include excitations of the nucleus in his scattering calculations^{2}. On top of this, he did ground-breaking work on photonuclear reactions^{3} and the variable moment of inertia model^{4}.

‘After his return to Oxford he worked tirelessly on the development of a local potential cluster model^{5} that could be applied across the Periodic Table of nuclei and was particularly successful in the first half of each nuclear shell^{6}. A key insight was to approximate antisymmetrization by restricting the relative motion quantum numbers to values compatible with the cluster being completely outside the core. As well as rotational energy spacings, smoking gun signatures of alpha-clustering straightforwardly described by the model included strongly enhanced electromagnetic transitions between the states (the whole cluster making the transition rather than a single nucleon), large charge radii, magnetic and electric moments that were simple combinations of the values of the core and cluster constituents together with contributions from their relative motion, and large alpha decay widths for those states above the emission threshold.

‘Unexpectedly, the model proved ideal for describing the exotic nuclear decay of ^{14}C from the ground state of ^{223}Ra, discovered by Rose and Jones in Oxford^{7} and gave a good account of the half-lives of all such subsequently observed exotic decays. Stimulated by this outcome, the model was belatedly applied to the 500+ known cases of alpha decay from nuclear ground states^{8}. Apart from generally excellent agreement with experiment, the procedure uncovered an unsuspected subtlety in those Geiger-Nuttall plots that consisted of isotopic sequences that crossed a neutron shell. They actually contained two straight lines displaced from one another, corresponding to nuclei above and below the neutron shell closure, naturally explained within the model as the promotion of the alpha cluster to a higher orbit to keep it out of the core. Finally, the model was easily turned to a successful description of proton emission from nuclear ground states of very proton rich nuclei, so that it gave a satisfying coherent account of all observed charged particle emissions from the nuclear ground state.

‘I remember one of Brian’s experimental collaborators (Aadu Pilt) once proclaiming that an ounce of physical intuition was worth a pound of mathematics. A neat summary of Brian’s research methods would be to observe that he certainly possessed that ounce but could supply the pound of mathematics as well when required.’

Dr C. Sukumar is Emeritus Fellow and Tutor in Physics at Wadham College, Oxford. He worked with Brian in the 1980’s and reflects on Brian’s legacy within the field of quantum optics: ‘Brian's interest in quantum optics was aroused in 1979 by a paper in Physical Review Letters on the possibility of periodic partial revivals of the excited state of the atom, despite initial decay, in certain models of atom-radiation interaction. His collaborative effort led to the development of a non-linear model which was exactly solvable and exhibited exact periodic revivals and decay^{9}. The exact solution of the model attracted much interest and became a test bed for many other calculations in quantum optics.'

Dr Vincent Macaulay is a Reader in the School of Mathematics and Statistics at the University of Glasgow, who started his DPhil with Brian in 1988. He writes: ‘While still working in the United States, Brian came across the work of the late Edwin T. Jaynes. A professor of physics at Washington University in St. Louis, Jaynes was perhaps the key figure in the rediscovery (from the 1960s onwards) of Bayesian inference in the physical sciences, building himself on the pioneering work of Richard Cox^{10}, who had shown in the 1940s that the rules of probability theory could be much more broadly viewed than was common at the time as an algebra of plausible inference, for reasoning consistently in the presence of uncertainty. Entropy (as already shown by Claude Shannon) was a measure of the uncertainty captured by a probability distribution and maximizing entropy (“MaxEnt”), subject to constraints, as Willard Gibbs had done, provided a way of assigning probability distributions given certain sorts of prior information. Brian was to use those ideas to approach a variety of applied inference problems in physics including to inverse scattering and to power spectrum analysis. He was a frequent contributor to the annual “MaxEnt” conferences in the eighties and nineties. He also edited a well-received collection of essays on the subject^{11}, which developed from a seminar series run in the Department of Theoretical Physics.

‘Brian was a fan of Jaynes and went to considerable lengths to obtain his latest writing (including an early incomplete typescript of the book Probability Theory: The Logic of Science^{12}, which remained unfinished at Jaynes’ death). Brian himself left a textbook applying Jaynes’ approach to the teaching of statistical mechanics unfinished after the death of his co-author Caroline Fraser in 1996. Brian was a hoarder of books and knew the second-hand bookshops of the UK better than almost anyone.’

[1] F.Perey and B.Buck (1962). A non-local potential model for the scattering of neutrons by nuclei, Nucl. Phys. 32 p.353

[2] B.Buck, A.P.Stamp and P.E.Hodgson (1963). The excitation of collective states by inelastic scattering the extended optical model, Phil Mag. 8 p.1805

[3] B.Buck and A.D.Hill (1967). Calculation of photonuclear resonance cross sections by coupled channel reaction theory, Nucl. Phys. A95 p.271

[4] M.A.J.Mariscotti, G.Scharff-Goldhaber and B.Buck (1968). Phenomenological analysis of ground-state bands in even-even nuclei, Phys. Rev. 178 p.1864

[5] B.Buck, H.Friedrich and C.J.Wheatley (1977). Local potential models for the scattering of complex nuclei, Nucl. Phys. A275 p.246

[6] B.Buck, A.C.Merchant and S.M.Perez (1995). Systematics of alpha-cluster states above double shell closures”, Physical Review C51 559.

[7] H.J. Rose and G.A. Jones (1984). A new kind of natural radioactivity, Nature (London) 307, p.245

[8] B.Buck, A.C.Merchant and S.M.Perez (1993). Half-lives of favoured alpha decays from nuclear ground states, Atomic Data and Nuclear Data Tables 54 p.53

[9] B.Buck and C.V.Sukumar , Physics Letters A81 132 (1981).

[10] Cox, R. T. (1946). Probability, frequency and reasonable expectation. American Journal of Physics, 14, 1-13.

[11] Buck, B. and Macaulay, V. A. (eds) (1991). Maximum Entropy in Action. Oxford University Press, Oxford.

[12] Jaynes, E. T. (2003). Probability Theory: The Logic of Science, Cambridge University Press, Cambridge.