Kenneth M. Watson

Collective excitations of nuclear matter

Abstract A study of the collective motions of nuclear matter has been made. We first give a purely classical macroscopic description of hydrodynamic waves in nuclear matter, and suggest some experimental consequences of their excitation. Next a quantum mechanical study of the collective eigenstates of nuclear matter is taken up. The starting point of this discussion is the theory of the nuclear ground state as given by Brueckner and his collaborators. The excited states are described by means of the method developed by Sawada to apply to an electron gas. We generalize this method so as to include the internal degrees of freedom associated with spin and i-spin and to handle the momentum dependence of the level-shift operator K used by Brueckner. The connection between the quantum-mechanical eigenstates and the classical hydrodynamic motion is established. As a consequence of the internal degrees of freedom, there exist not only the usual compressive waves, but spin, i-spin, and coupled spin-i-spin waves. The i-spin waves can be associated with the Goldhaber-Teller oscillations. We have investigated the corrections to the Sawada theory. This gives rise to the damping of the stable Sawada collective eigenmodes, analogous to the viscous damping of a plasma oscillation. The spin and i-spin waves are only slightly damped, whereas the compressional mode is unstable in an exponentially growing sense.

A Transport Equation Description of Non-Linear Ocean Surface Wave Interactions

Abstract : The evolution of the power spectrum of surface gravity waves is described by means of a transport equation. The effects of a slowly varying, prescribed ocean current and nonlinear wave-wave interactions are included. A definition due to Wigner of a localized power spectrum is used to derive the transport equation from the dynamical equations describing surface wave motion.

Coupling of surface and internal gravity waves: a mode coupling model

A surface-wave/internal-wave mode coupled model is constructed to describe the energy transfer from a linear surface wave field on the ocean to a linear internal wave field. Expressed in terms of action-angle variables the dynamic equations have a particularly useful form and are solved both numerically and in some analytic approximations. The growth time for internal waves generated by the resonant interaction of surface waves is calculated for an equilibrium spectrum of surface waves and for both the Garrett-Munk and two-layer models of the undersea environment. We find energy transfer rates as a function of undersea parameters which are much faster than those based on the constant Brunt-ViiisSila model used by Kenyon (1968) and which are consistent with the experiments of Joyce (1974). The modulation of the surface-wave spectrum by internal waves is also calculated, yielding a ‘mottled’ appearance of the ocean surface similar to that observed in photographs taken from an ERTS1 satellite (Ape1 et al. 1975b).

Effects of the Pauli principle on the scattering of high-energy electrons by atoms☆

Abstract Some consequences of the Pauli principle for the elastic scattering of electrons by atoms are studied. The contributions both from the exchange integrals and from the Hartree-Fock condition that the scattered wave be orthogonal to the bound-state wave functions are expressed in a simple approximate form. For high-energy electrons these corrections are very small.

Radiation Transport along Curved Ray Paths

The transport of radiation in a turbulent, refracting medium is studied. It is shown that the conventional transport equation must be generalized. Path integrals are taken along curved ray trajectories. When these ray paths have torsion, a rotation of the polarization vectors needs to be taken into account. Two derivations of the transport equation are given. One is phenomenological and one is based on Maxwells equations. Some discussion is given of cross polarization of radar backscatter.

Some properties of deep water solitons

Envelope solitons for surface waves in deep water are studied using the coupled equation for the Fourier amplitudes of the surface displacement. Comparison is made with some wave‐tank experiments of Feir. A linear stability analysis is made for an imposed transverse ripple. A slowly growing instability is found at wavelengths comparable to, or longer than, the length of the soliton. A slowly developing instability is also found for a soliton propagating through a train of waves of wavelength appreciably smaller than that of the soliton. A soliton propagating through a train of waves with wavelength much larger than that of the soliton exhibits gross distortion due to the orbital fluid velocity of the wavetrain. This distortion is to some extent reversible, as the soliton tends to ’’recover’’ when the wavetrain is damped to zero amplitude. Some comments are given concerning the statistics of a wave field containing solitons.

Two‐Stream Instability in Finite Beams

The streaming instabilities of a finite beam of charged particles passing through a zero‐temperature plasma are studied. It is shown that there are no eigenmodes associated with the instabilities. Nevertheless, by constructing wave‐packet disturbances one is led to instabilities similar to those for a beam of infinite extent.

DOPPLER SHIFT IN FREQUENCY IN THE TRANSPORT OF ELECTROMAGNETIC WAVES THROUGH AN UNDERDENSE PLASMA

In an earlier publication, the validity of the radiation transport theory was studied for the calculation of multiple scattering of electromagnetic waves by a turbulent plasma. In the present paper, we extend the transport theory to include a description of the Doppler shift in frequency caused by electron motion.

The quasi-elastic scattering of fast particles by atomic nuclei

Abstract The scattering of fast particles by atomic nuclei for large momentum transfers and small energy loss is studied. The cross sections may be expanded in inverse powers of the energy of the incident particle, using methods due to Placzek and Wick. The resulting cross sections, when applied to analysis of experiments, may be used to study short range order in nuclei. An analysis of electron, pion and proton experiments shows consistent results and also shows in a striking way the effects of the “repulsive core” in two body forces.

Internal-wave interactions in the induced-diffusion approximation

Dynamical equations for the interaction of high-wavenumber, high-frequency internal waves with a prescribed, linear, large-scale internal-wave field are obtained from the Boussinesq–Euler equations. The relationship of these ‘induced-diffusion’ interactions to the Taylor–Goldstein equation is discussed. Exact equations are derived in the induced-diffusion limit of McComas & Bretherton (1977) for the evolution of the first and second moments of the small-scale flow when the large-scale flow is assumed random. Estimates of corrections to the induced-diffusion approximation for the Garrett–Munk internal-wave model indicate the domain of applicability of these equations. Computations of the autocorrelation function and action transport in wavenumber and physical space are presented. Severe limitations are found on the applicability of two-time perturbation theory and the resonant-interaction approximation. The high transfer rates found by McComas & Bretherton in the induceddiffusion regime are reduced significantly in the present calculations.