Selected Papers, with Commentary, of Tony Hilton Royle Skyrme

The following sections are included:

• Pictures

• Preface

• Contents

Tony Hilton Royle Skyrme died unexpectedly on 25 June 1987, at the age of 64. In 1985 he received the Hughes Medal, which throughout this century has been the rarest honor conferred on British physicists by the Royal Society (election to Fellowship in the Society is common by comparison, so that Skyrme's status as a Medalist but not a Fellow must be nearly unique).

The list of Skyrme's publications presented at the end of this article contains 23 items. Of these, no fewer than 9 are related to the Skrmyion^{2, 3, 15–21}). Among his other notable works are several on many-body theory, particularly focused on applications in nuclear physics. The short- range "Skyrme forces" provided a physically sensible and computationally practical description of the residual interaction which must be added to the shell model to give a more accurate picture of nuclear structure ^12–14). This formulation is still used today, nearly 30 years after its introduction. A systematic method of isolating the degrees of freedom corresponding to center-of-mass motion of a many-body system was formulated ⁵). An analysis of nuclear surface dynamics was presented ⁶). These too are often cited today …

1922-43: Youth and Education - Tony Hilton Royle Skyrme was born on 5 December 1922 at 7 Blessington Road, Lewisham (Kent), London, the family house occupied by his maternal grandparents. His parents were John (sometimes Jack) Hilton Royle Skyrme, a bank clerk, and Muriel May née Roberts, who had been married at St. Margaret's Church in the parish of St. Margaret's and Eastney, in Portsmouth (Hants.), on 25 March 1922. Tony's paternal grandparents were James Henry Rowland Skyrme and Minnie née Hilton, the former being a schoolmaster at Combwitch, near Bridgewater (Somerset), when Tony's father was born in 1896. Tony's maternal grandfather was Herbert William Thomson Roberts, a tidal computer for the Admiralty by profession. The inclusion of Lord Kelvin's baptismal name (William Thomson) among his forenames reflects the professional contact which Tony's great - grandfather had with Lord Kelvin and the high regard in which he held the latter …

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It is shown that it is possible to write down α-particle wave functions for the ground states of ⁸Be, ¹²C and ¹⁶O, which become, when antisymmetrized, identical with shell-model wave functions. The α-particle functions are used to obtain potentials which can then be used to derive wave functions and energies of excited states. Most of the low-lying states of ¹⁶O are obtained in this way, qualitative agreement with experiment being found. The shell structure of the 0⁺ level at 6.06 Mev is analysed, and is found to consist largely of single-particle excitations. The lifetime for pair-production is calculated, and found to be comparable with the experimental value. The validity of the method is discussed, and comparison made with shell-model calculations.

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An empirical analysis is made of the mean effective internucleon potential required in the shell-model description of nuclei, allowing for the presence of many-body effects as suggested by current theory. A consistent description is found in which the effective two-body interaction acts almost entirely in even states, and the many-body effects are simulated by a repulsive three-body contact interaction. The strength of the two-body interaction is consistent with that expressed by the free scattering matrix of the two-nucleon system, and that of the three-body interaction with the ‘rearrangement energy’ calculated in the many-body theory.

Analysis of the nucleon–nucleon scattering around 100 Mev has determined the spin–orbit coupling part of the two-body scattering matrix at that energy, and a reasonable extrapolation to lower energies is possible. This scattering amplitude has been used, in the spirit of Brueckner's nuclear model, to estimate the resultant single-body spin–orbit coupling for a single nucleon interacting with a large nucleus. This resultant potential has a radial dependence approximately proportional to r⁻¹ dρ/dr, and with a magnitude in good agreement with that required to explain the doublet splittings in nuclei and the polarization of nucleons scattered elastically off nuclei.

The analysis previously made of the average nuclear potential has been extended to consideration of the spin-orbit interactions. It has not been possible to find a satisfactory two-body interaction consistent with all the data; that suggested by the phase-shift analysis of nucleon-nucleon scattering is just within the region of possible forms.

The different values obtained for nuclear radii from electromagnetic interactions as compared with specifically nuclear interactions suggest a model of nuclear matter in which the meson field is supposed to condense into an incompressible fluid and the nucleonic sources are confined to its interior by a strong interaction between the sources and the fluid as a whole. The sources are also coupled to spin and charge fluctuations in the fluid, whose exchange leads to further internucleonic forces. It is necessary to postulate that the fluid have a comparatively low density; as a result rotational levels of the fluid are high, leading to a small probability of exchange of angular momentum (and charge coupled to it) with the sources. The values of the anomalous electrical interactions of nucleons deduced are in rough agreement with the facts. The nuclear structure indicated is a shell model embedded in the mesic fluid whose oscillations, strongly coupled to the nucleons, give rise to the collective features of nuclear structure as in the theory of Bohr & Mottelson. It is suggested that this picture of the mesic field may indicate where to look for solutions of the meson field equations.

An attempt is made to justify the use of the concept of a ‘mesic fluid’ in connexion with the structure of nuclear matter. A transformation is made of the usual symmetric pseudo-scalar meson theory to bring into evidence certain saturation properties, which provide a natural basis for the use of a ‘self-consistent’ field in the discussion of nuclear structure. Fluctuations about this semi-classical saturated state will give rise to residual interparticle forces within the nucleus, and are also briefly considered in relation to electromagnetic interactions.

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I am very grateful to the organizers for inviting me to give a brief talk at this meeting, but I accepted only with some reluctance, as I have really very little new to say that would be of interest to a Workshop such as this. They explained that they wanted me to say a little, quite informally, about the history and philosophy of the origins of the model that lies behind the meeting. I will do this briefly, leaving recent developments to those who have been more closely associated with them than I have been. I shall finish by mentioning briefly some related ideas in which I have recently been interested …

Not widely known facts on the genesis of the Skyrme model are presented in a historical survey, based on Skyrme's earliest papers and on his own published remembrance. We consider the evolution of Skyrme's model description of nuclear matter from the “Mesonic Fluid” model up to its final version, known as the baryon model. We pay special tribute to some well-known ideas in contemporary particle physics which one can find in Skyrme's earlier papers, such as: Nuclear Democracy, the Solitonic Mechanism, the Nonlinear Realization of Chiral Symmetry, Topological Charges, Fermi–Bose Transmutations, etc. It is curious to note in the final version of the Skyrme model gleams of Kelvin's “Vortex Atoms” theory. In conclusion we make a brief analysis of the validity of Skyrme's conjectures in view of recent results and pinpoint some questions which still remain.

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ⁴ term; this destroys the continuous rotation group in the iso-space, leaving a ‘cubic’ symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to ‘strangeness’; one consequence is that, at least in elementary interactions, charge is only conserved modulo 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified-model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone.

On the foundation of an antecedent non-linear meson field theory it is suggested that the π-meson fields may be described in terms of collective motions of the K-meson fields. A particular model of the K-nucleon interaction is considered whose collective π-modes have symmetrical PV coupling with the nucleon system; parity is conserved to a great extent for the π-nucleon system in the absence of strange particles. The direct K-nucleon interactions do not conserve parity; their sign and symmetry are qualitatively acceptable. The masses and coupling constants of the meson fields are determinate in terms of one universal coupling constant and a cut-off. The structure of this model suggests a natural way for the introduction of the ‘spurion’, describing weak interactions that violate strangeness.

A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hyper-charge. The postulates include one constant of the dimensions of length, and another that is conjectured necessarily to have the value ℏc, or perhaps ½ℏc, in the quantized theory.

A simple non-linear field theory is considered as the model for a recently proposed classical field theory of mesons and their particle sources. Quantization may be made according to canonical procedures; the problem is to show the existence of quantum states corresponding with the particle-like solutions of the classical field equations. A plausible way to do this is suggested.

The classical solutions of a unified field theory in a two-dimensional space-time are considered. This system, a model of interacting mesons and baryons, illustrates how the particle can be built from a wave-packet of mesons and how reciprocally the meson appears as a tightly bound combination of particle and antiparticle.

In a model quantum theory of interacting mesons, the motion of certain conserved particlelike structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation.

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In this paper the existing results concerning mesons and glue states in the large-N limit of QCD are reviewed, and it is shown how to fit baryons into this picture.

A new mathematical framework for the Wess-Zumino chiral effective action is described. It is shown that this action obeys an a priori quantization law, analogous to Dirac's quantization of magnetic change. It incorporates in current algebra both perturbative and non-perturbative anomalies.

It is shown that ordinary baryons can be understood as solitons in current algebra effective lagrangians. The formation of color flux tubes can also be seen in current algebra, under certain conditions.

We compute static properties of baryons in an SU(2) × SU(2) chiral theory (the Skyrme model) whose solitons can be interpreted as the baryons of QCD. Our results are generally within about 30% of experimental values. We also derive some relations that hold generally in soliton models of baryons, and therefore, serve as tests of the 1/N expansion.

We introduce vector mesons in a chiral lagrangian. The ω meson stabilizes the chiral solitons. We compute the static properties of baryons in this model.

We review the recent developments on the Skyrme model in the context of OCD, and analyze their relevance to low-energy phenomenology. The fundamentals of chiral symmetry and PCAC are presented, and their importance in effective chiral models of the Skyrme type discussed. The nature and properties of skyrmions are thoroughly investigated, with particular stress on the basic role of the Wess–Zumino term. The conventional Skyrme model is extended to the low-lying vector meson resonances, and the rudiments of vector meson dominance are elucidated. A detailed account of the static and dynamical properties of nucleons and Δ-isobars is presented. The relevance of the Skyrme model to the nuclear many-body problem is outlined and its importance for boson exchange models stressed.