Journal of Physics A: General Physics

Spin states analogous to the coherent states of the linear harmonic oscillator are defined and their properties discussed. They are used to discuss some simple problems (a single spin in a field, a spin wave, two spin ¹/₂ particles with Heisenberg coupling) and it is shown that their use may often give increased physical insight.

The author presents here a generalization of an already known solution, given by Kramer (1972).

The asymptotic form of Hirota's N soliton solution of the Korteweg-de Vries equation is derived. The phase shifts of the N solitons caused by a general collision are found to be linear sums of two soliton terms.

The author derives a spin hamiltonian V(S) for the g fold degenerate level of a system perturbed in first order by a physical perturbation V; the derivation explicitly relates the coefficients a, b, c,... of V(S) to the matrix elements V_MM' of V between the zero order physical basis functions psi _M. He shows how the symmetry of V and time reversal affect V(S), and considers three often treated examples as an illustration of the power and unity of his method.

An algebraic approach to the solution of the Klein-Gordon equation is described for the case of a charged particle in the presence of plane-wave electromagnetic radiation. From an examination of the commutation relations between P_mu =-i( delta / delta x_mu ) and A_nu , P.A A.A, etc. one finds a new set of 'translation' operators Pi _mu which commute with the total 'Hamiltonian'. The authors then construct a representation of the Poincare group out of the Pi _mu and their canonically conjugate 'coordinates' Q_nu . The solutions are shown to correspond to the spin zero mass m representation of the restricted Poincare group. Applications of the technique to other quantum-mechanical problems are also briefly discussed.

A Monte Carlo technique is described for estimating the number of tadpoles of a given size, which are weakly embeddable in a given lattice. Data are reported for the square lattice for tadpoles with up to twenty edges in the head and up to fifty edges in the tail. These data are combined with good self-avoiding walk extrapolants to yield estimates of the limiting probability (p_k) of forming a head with k edges, and it is suggested that p_k approximately k^{- alpha} where alpha approximately=2.13.

The hyperfine interaction of excited nuclear levels with deeply ionized atoms is discussed. A measurement is reported for ¹⁸O(2⁺) at 1.98 MeV, interacting with 7⁺ ions in the 1s state. Limits for the g factor of this level are reported as: 0.2< mod g mod <0.36. The excitation pattern of highly stripped ions is considered and it is concluded that such ions are formed in two distinct patterns, one characterized by predominant ground state occupation and the other by prolific excitation. The feature which determines the pattern is the degree of isolation of the ground state of the ions.

The connection between single particle and collective motion is discussed on the basis of the generator coordinate method. Earlier and recent work on the subject is reviewed.

Vector mesons with the same quantum numbers as the photon are expected to play an important role in electromagnetic interactions. The study of the electromagnetic decays of these mesons and their production by photons has provided related information which can be used to understand this interaction. The experimental information which is currently available is presented and compared with existing theoretical ideas in this article.

The historical development of those fields of physics investigated using storage rings is traced. The paper is divided into three parts. The first is the use of storage rings to investigate the validity of quantum electrodynamics. Second is their use in investigating vector meson dominance and lastly new aspects and preliminary results at high energy is given.

A survey is given for recent experiments in electroproduction and a discussion of their results. For the resonance region the main results are that the ratio of longitudinal to transverse excitation is about as small as it was found for the deep inelastic continuum (about 0.2 or smaller). The excitation of the Delta (1236) in the pi ⁰ channel, as measured by coincidence techniques, is going mainly through M₁₊. However, other small contributions like S₁₊ and E₁₊ for the resonant part and E₀₊ and M_1- for the nonresonant part are not negligible. In the deep inelastic region coincidence measurements are reported. Single positive pion production on hydrogen shows a large longitudinal cross section, which can be explained quite well by vector meson dominance. Proton momentum spectra in the directions of the virtual photon do not show an unusually large flux of protons with high momenta as was expected from a specific parton model.