Benjamin Downing Day

Benjamin Downing Day died on July 13, 2013, in New Bedford, Massachusetts, at age 76. He was a leading member, a pillar, of the community of nuclear matter researchers. A student of Hans Bethe at Cornell University, he had post-doctoral experience at UCLA, and then a career in the low-energy nuclear physics theory group at Argonne National Laboratory.

Nuclear matter is a model for the interior of large atomic nuclei. Its study has had major significance, advancing theoretical physics in several ways: (1) There was much excitement when, in the early 1950s, Keith Brueckner introduced the concept of calculating the pairwise interaction of two nucleons interacting within the soup of all the other nucleons, using a two-body wave equation to deal with the very strong repulsion between any pair of nucleons at short distances (much shorter than the average separation between the nucleons). Hans Bethe and Jeffrey Goldstone modified this wave equation to include effects of the surrounding nucleons, and Goldstone provided a sound basis for understanding the concepts and approximations: he presented the first general derivation of a linked-cluster perturbation expansion for the ground state of a Fermi liquid, using Feynman-like diagrams. (2) The combination of this formal framework, Brueckner’s encouraging numerical results, and the contemporary successes of the BCS theory of superconductivity, the “random phase” or RPA and He-3, served to establish quantum many-body theory as a respectable discipline. (3) The resulting effective interaction between the nucleons in the nuclear matter was well-behaved at short distances, in spite of the bare interaction’s very strong short-range repulsion. This opened the way for a proper justification of the successful shell model of nuclear physics, along the lines of the Hartree−Fock theory of atomic structure. It also raised hope for ab initio determination of the parameters used in shell-model calculations. For all of these reasons, nuclear matter theory was cutting-edge physics.

Starting in the late 1950s, Hans Bethe assembled a team of grad students to carefully examine and refine the treatment of nuclear matter. Ben and I were among these students. Ben’s assignment was to apply the refined methods to the nuclear surface region, and specifically to calculate the surface-energy term of the Weiszacker statistical model of nuclear binding energies. This was a great challenge, requiring a tour de force of insight and numerical work. Using a realistic nucleon−nucleon interaction, he succeeded in obtaining reasonable agreement with the empirical nuclear surface energy. His next contribution was pedagogical: a widely respected “primer” article in Reviews of Modern Physics, which explained the concepts of nuclear-matter theory and its use of the Goldstone diagrams. By that time the frontier of this research had turned to three-body cluster terms, the three-body analog of the Brueckner effective two-body interaction. In this and later papers, Ben focused on these terms, presenting detailed calculations and clear explanations, and he later extended this to four-body cluster terms. He was not alone and not the first in the three-body calculations, but his clarity and sound analysis of the state of the art was much appreciated and relied on. He was also doing complete and definitive nuclear-matter calculations for a variety of empirical “bare” nucleon−nucleon interactions that were appearing from various groups. He became the principal scorekeeper for this research, regularly publishing review articles that detailed the successes and shortcomings of the various current calculations.

There was a second and later many-body technique for studying nuclear matter, a variational method developed by Vijay Pandharipande. (This was also encouraged by Bethe. It easily included higher-order cluster terms, advantageous for the study of neutron star matter, which is more dense than ordinary nuclear interiors.) This method was also undergoing continuous refinement. For years there had been significant quantitative discrepancy between these competing methods, but eventually they reached a reasonable agreement. This was demonstrated in a review by Ben Day and Robert Wiringa, a practitioner of the variational method. It was therefore considered significant that neither of these carefully refined methods provided agreement with experiment (the bulk density and binding energy deduced from nuclear data). This was accepted as evidence that some meson or quark-produced three-nucleon interaction must be playing a significant role. Indeed, such an interaction had been proposed, but it has taken many years to clarity the nature of this interaction (and agreement with bulk nuclear properties is still poor).

Not long after this plateau, a culmination of many years of excellent work, Ben was laid off from Argonne National Laboratory due to reduced funding for nuclear theory. He had been there twenty years. He found employment nearby, in a branch laboratory of Bell Telephone Laboratories, but he missed the satisfaction he found in basic research. After five years he retired. He did have the satisfaction of having played a central role in a significant arena of many-body and nuclear physics. Along the way he had extended institutional visits at MIT, at the Niels Bohr Institute in Copenhagen, Denmark, and at Los Alamos National Laboratory.

As an epilog, it should be added that nuclear-matter techniques have indeed been adapted and applied successfully in studies of real nuclei. This was a separate effort, begun by Brueckner but led mainly by Gerry Brown at the Niels Bohr Institute in Copenhagen and later at Princeton and at SUNY in Stony Brook.

Ben was known and respected for tackling really hard problems, seeing them through in a conscientious manner, and explaining it all very clearly. It would not be surprising if such a high standard was accompanied by a high-strung temperament, but Ben was always calm and uncommonly modest, a true gentleman. At Argonne he is fondly remembered for his assistance and advice, both socially and professionally, to younger staff members and postdocs in the Physics Division.

Benjamin Downing Day was born July 19, 1936, in Nassawadox, Virginia. He grew up in Newark, Delaware, where his father was a professor of Elizabethan English at the University of Delaware. His mother was an artist. In high school he excelled in golf and became the runner-up Junior State Golf Champion. His bachelor’s degree in 1958 was from Wesleyan University, Middletown, Connecticut, where he played golf and basketball. His Ph.D. from Cornell was gained in 1963. After two years of postdoctoral research at UCLA he obtained his position at Argonne National Laboratory. In retirement he settled in Indianapolis, Indiana, where his wife Holly was appointed Curator of Modern Art at the Indianapolis Museum of Art. He played golf quite frequently at a course near their home, in spite of having a weak heart in his later years. Another passion was sailing. They had a house and sailboat at South Dartmouth, Massachusetts, where in summers they sailed and raced on Buzzard’s Bay, enjoying this until his last days.

Baird Brandow