The nuclear droplet model for arbitrary shapes

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Topics in the S-Matrix Theory of Massless Particles. S. P. AUERBACH. Department of Physics, University of California, Berkeley, California 94720, M. R. PENNINGTON. Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720, AND CARL ROSENZ~EIG. Department of Physics, University of California, Berkeley, California 94720. We discuss how massless particle reactions may be incorporated into standard S-matrix theory. The crucial element for doing so is a low energy zero. Examples of reactions where such zeros occur are weak interaction processes involving neutrinos, chirally symmetric massless pion scattering and two photon exchange between neutral systems. These zeros make two body unitarity a good approximation for sufficiently low energy despite the coalescence of multiparticle thresholds. Through two body unitarity, these zeros produce lines of zeros in the absorptive parts and double spectral functions. These lines of zeros are the S-matrix analog of the requirement of an infrared finite field theory. Not only do they produce finite total cross sections at finite energies, but they also allow both upper and lower bounds to be derived for these cross sections at high energies. This upper bound is our main result. If a plausible smoothness assumption is made, we find oror < fl (where B is arbitrarily small). In particular, the experimentally observed linear rise of the neutrino proton cross section cannot continue indefinitely. The Nuclear Droplet Model for Arbitrary Shapes. W. D. MYERS AND W. J. SWIATECKI. Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720. The droplet model of nuclear masses and density distributions for spherical configurations is generalized to arbitrary shapes. Equations in closed form are given for the neutron and proton density nonuniformities induced by the electric forces, and also for the dependence of the neutron skin thickness on position on the nuclear surface. The formular for the corrections to the nuclear energy associated with these effects are derived and this leads to a droplet model atomic mass formula which is presented with a preliminary set of coefficients adjusted to nuclear ground state masses and fission barriers. Relaxation, Amplification and the KMS Conditions. G. L. SEWELL. Department of Physics, Queen Mary College, London, El 4NS, England. We formulate the dynamics of an oscillator, 2, harmonically coupled to an infinite quasifree bose system Z, the initial states of Z and 2 being mutually uncorrelated and the initial state of X being quasifree, primary, and stationary. It is shown that, subject to certain regularity conditions, the oscillator 2 will either relax towards a terminal state, whose value is independent of the initial state of the oscillator, or else will become amplified, according to whether the energy quantum for 2 is positive or negative. In the former case, the weak-coupling limit for the terminal state of 2 is a Gibbs state, corresponding to a temperature which takes the same value for all Z-c-b couplings of the prescribed class, if and only if the initial state of C satisfies the KMS conditions for that temperature. We argue that this result provides an operational justification for identifying equilibrium conditions with KMS conditions, at least for the class of stationary states of Z that we consider. The Spin Dynamics of an Anisotropic Fermi Superfluid ($He?). A. J. LEGGETT. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14850 and School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton BNl 9QH, Sussex, UK, and Department of Physics, Faculty of Science, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan. In this paper we develop a general theory of the spin dynamics of anisotropic Fermi supertluids of the generalized BCS type, under conditions which should be realistic for any such phase of