We have measured the power spectrum of flicker noise in high-purity, single-crystal $n$-InSb at 76 K in the frequency range 0.1 Hz-10 kHz. The power spectrum can be interpreted as a superposition of two noise spectra. One of them is $\frac{1}{f}$ like at frequencies above a cutoff frequency ${f}_{0}$ which is on the order of a few hundred Hz, while at frequencies below ${f}_{0}$ it appears to level off to a constant value. The second spectrum is dominant at frequencies well below ${f}_{0}$ and behaves as $\frac{1}{f}$. Noise power much smaller than that predicted by the Hooge relation, ${S}_{\ensuremath{\delta}V}=\frac{\ensuremath{\alpha}{V}^{2}}{\mathrm{NF}}$, is observed. Also it is found that chemical treatments of the surface have a strong influence on the magnitude of the measured flicker noise.

A modified droplet optical-model method is developed for evaluating cross sections for short-lived (\ensuremath{\sim}${10}^{\ensuremath{-}23}$ sec) particles produced in two-body reactions. Using elastic-scattering and $\ensuremath{\rho}$-production differential cross sections for 1.7-BeV/c ${\ensuremath{\pi}}^{\ensuremath{-}}p$ interactions in this model, we estimate the total $\ensuremath{\rho}$-nucleon cross section as 12 mb.

We consider a self-coupled spinor model of elementary particles having $S{U}_{2}\ensuremath{\bigotimes}S{U}_{2}$ symmetry. We demonstrate that for the case of complete spontaneous breakdown of the isospin symmetry the bubble approximation gives a method for treating the meson states that is compatible with symmetries of the model in that it gives the Goldstone bosons and Goldberger-Treiman relations exactly. We also show that by a continuation in the parameter characterizing the isospin breakdown we can transform from a solution having isospin degeneracy to solutions in which the isospin, as well as the chiral symmetry is spontaneously broken. Calculational techniques for our approximation are explicitly given.

We consider the spontaneous breakdown of unitary octet symmetry in a nonlinear spinor model of elementary-particle theory. Our model is an adaptation to unitary octet symmetry of a model originated by Nambu and Jona-Lasinio and contains $S{U}_{3}\ensuremath{\bigotimes}S{U}_{3}$ symmetry in the same way that their model contained $S{U}_{2}\ensuremath{\bigotimes}S{U}_{2}$ symmetry. We derive an exact formula for the physical baryon mass that reduces to the usual superconductor-type formula in the lowest order approximation. Nonperturbative solutions that leave the physical $\ensuremath{\Lambda}$ and $\ensuremath{\Sigma}$ masses degenerate are obtained. We confirm the presence in our nonperturbative solutions of massless pseudoscalar and scalar mesons transforming as components of $F$-type octets as predicted by the Goldstone theorem. We also find massless pseudoscalar and scalar mesons that transform as components of unitary spin decimets. We explain that only the $F$ octets are Goldstone mesons associated with the spontaneous breakdown of octet symmetry in our model, whereas the massless decimets are associated with the invariance of a restricted part of our Lagrangian under a larger group and their masslessness is not a consequence of symmetry breakdown in our solutions.

The proton-size correction to the hyperfine structure in the ground state of atomic hydrogen is re-examined. It is shown by means of dispersion relations that this correction can be expressed as an integral over experimentally measurable cross sections for electron-proton scattering. This clarifies the physical nature of the correction, puts it on a rigorous basis and lends support to previous analyses. In the absence of experimental data, we give some theoretical estimates for the correction. They agree with previous estimates, and therefore we cannot explain the present experimental value for the hyperfine splitting. We discuss some possible implications of this disagreement and suggest some experiments which would clarify the situation.

A study is made of the depolarization of polarized, relativistic fermions (spin \textonehalf{}) passing through matter. The final polarization of the projectile shows two features, (i) a rotation of the polarization vector so that it does not have the same direction as the initial polarization with respect to the initial or final momenta: rotation; (ii) an unpolarized component so that the magnitude of the polarization has diminished: shrinkage. We consider the scattering of the incident polarized fermion off unpolarized target electrons and nuclei to lowest order in $\ensuremath{\alpha}$. Whereas to this order no polarization can be produced, i.e., the magnitude of the polarization vector cannot increase, the magnitude of the spin vector can decrease if the target has spin. General formulas are presented for the spin-\textonehalf{} particles scattered electromagnetically from an unpolarized target with arbitrary spin in terms of form factors. Numerical results are presented for processes (i) and (ii) in the cases of positrons and muons scattered by unpolarized electrons. Process (ii) is proportional to ${t}^{2}$ (for small momentum transfer $t$). If one expands the expressions for the polarization phenomena keeping only the linear term in $t$, then the shrinkage (ii) vanishes and the rotation effects (i) all reduce to those for the pure Coulomb scattering case. (As is well-known the depolarization due to Coulomb scattering is negligible for small-angle scattering.) However, if one is concerned with particles scattered into a sizeable solid angle, then (a) the rotation effects in, e.g., positron-electron scattering become enormously larger than that given by Coulomb scattering; (b) they become strongly dependent on the relative orientation of the incident polarization vector: much larger rotations occur for transversely polarized beams; (c) one cannot omit the contribution from the annihilation diagram compared to that from the direct one-photon exchange; (d) and most important the depolarization due to shrinkage is comparable to the rotational effects. In multiple scattering, the shrinkage is a cumulative effect whereas the rotational contribution to depolarization is a random walk process.

Using a static hyperon-nucleon potential, we calculate the fraction, $\frac{{\ensuremath{\Sigma}}^{0}}{({\ensuremath{\Sigma}}^{0}+\ensuremath{\Lambda})}$, for the low-energy reactions: ${\ensuremath{\Sigma}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}n+{\ensuremath{\Sigma}}^{0}$ or $\ensuremath{\Lambda}$ and ${\ensuremath{\Sigma}}^{\ensuremath{-}}+d\ensuremath{\rightarrow}2n+{\ensuremath{\Sigma}}^{0}$ or $\ensuremath{\Lambda}$. The parameters in this potential are the pion-hyperon coupling constants, ${f}_{\ensuremath{\Lambda}\ensuremath{\Sigma}}$ and ${f}_{\ensuremath{\Sigma}\ensuremath{\Sigma}}$, and the cores in the $^{3}S_{1}$ and $^{1}S_{0}$ states. We restrict these parameters to values which will reproduce the $\ensuremath{\Lambda}N$ scattering lengths. Both even and odd $\ensuremath{\Sigma}$ parity are considered. We cannot find agreement for global symmetry, but small ${f}_{\ensuremath{\Sigma}\ensuremath{\Sigma}}(\ensuremath{\lesssim}0.1)$, in particular unitary symmetry, agrees very well with experiment. Solutions can also be found for the case of odd $\ensuremath{\Sigma}$ parity.

We have obtained an approximate expression for the impedance function at all frequencies, temperatures, and coupling strengths of an electron coupled to a polar lattice (a system commonly called a polaron). The starting point for the calculation is the quantum mechanical expression for the expected current. The phonon coordinates are eliminated from this expression by well-known field-theory techniques. The resulting exact "influence functional" is then approximated by a corresponding quadratic "influence functional" which, it is hoped, imitates the real polaron. Correction terms are computed to account for the difference between the approximate impedance and the exact polaron impedance in a manner closely analogous to Feynman's treatment of the polaron self-energy. In fact, the analytic evaluation of the expression for the impedance obtained here is carried out using the approximate "influence functional" that was successfully employed in minimizing the binding (and free) energy of the polaron in earlier calculations. However, the accuracy obtained using this approximation, for the impedance calculation, is less satisfactory and its limitations are discussed. Nevertheless, beginning at intermediate coupling strengths, the approximate impedance produces a level structure of increasing complexity and narrowing resonances as the coupling strengthens. This suggests that further refinements may be fruitful. Methods for finding a better quadratic influence functional for use in our impedance expression as well as ways of improving the expression further are suggested. A comparison of our results with those of the Boltzmann equation points up interesting differences which arise from reversing the order of taking limits of zero frequency and coupling.

Using the prescription laid down by Brueckner and Watson, we have calculated the pion contribution to the hyperon-nucleon potentials for both even and odd $\ensuremath{\Sigma}$ parity. The coupled Schr\"odinger equations are solved numerically taking into account the $\ensuremath{\Lambda}\ensuremath{\Sigma}$ mass difference. Fitting the $\ensuremath{\Lambda}$-nucleon scattering lengths, as obtained from the hyperfragment data, we have determined the coupling constants. When we use the same core (${x}_{c}=0.35$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$) in all channels and ${{f}_{\mathrm{NN}}}^{2}=0.08125$, we find ${{f}_{\ensuremath{\Lambda}\ensuremath{\Sigma}}}^{2}={{f}_{\ensuremath{\Sigma}\ensuremath{\Sigma}}}^{2}=0.0841$ for the even $\ensuremath{\Sigma}$-parity case and ${{f}_{\ensuremath{\Sigma}\ensuremath{\Sigma}}}^{2}=0.0225$ (${f}_{\ensuremath{\Sigma}\ensuremath{\Sigma}}<0$) and ${{g}_{\ensuremath{\Lambda}\ensuremath{\Sigma}}}^{2}=0.578$ for the odd $\ensuremath{\Sigma}$-parity case. The rationalized pseudovector coupling constant we denote by $f$ and the rationalized scalar coupling constant by $g$. For these coupling constants and cores, we have calculated the cross sections for $\ensuremath{\Lambda}$-nucleon scattering below $\ensuremath{\Sigma}$ threshold. The results suggest the presence of attractive spin-orbit potentials.

Nonstatic corrections to the two-nucleon potential of Brueckner and Watson and of Gartenhaus are computed within the framework of the ${\ensuremath{\gamma}}_{5}$ theory. These terms appear as spin-orbit corrections of order $\frac{\ensuremath{\mu}}{M}$ to the static potentials.The $S$ matrix is calculated in second and fourth order for a reduced form of the relativistic theory. The potential is then chosen so as to duplicate this $S$ matrix to the required order in the coupling constant and $\frac{\ensuremath{\mu}}{M}$. We consider to what extent our reduction of the ${\ensuremath{\gamma}}_{5}$ theory changes its character.The resulting potentials are given in analytic form for no cutoff in momentum space and in numerical form for the Gaussian cutoff employed by Gartenhaus. We give also some additional static corrections to previous potentials. A qualitative comparison is made with the experimental observations in nucleon-nucleon scattering, the fine structure in the splitting of the ${\mathrm{He}}^{5}$ nucleus, and the contribution of the nonstatic potential to the magnetic moment of the deuteron.

The authors have previously shown that the form factor of the proton, measured by Hofstadter, implies an energy shift in the hyperfine structure of atomic hydrogen. Uncertainties in this method of applying the Hofstadter data, due to the effects of virtual mesons, are investigated in an approximate way and found to be small, on the order of one to two percent of the total correction. Under certain assumptions about the form of the amplitudes for various photoproduction processes, we conclude that the value of the fine-structure constant implied by the hyperfine structure (hfs) measurement of Kusch disagrees with the value obtained from the Lamb shift by 34\ifmmode\pm\else\textpm\fi{}21 ppm.

In previous papers, corrections to the hyperfine structure (hfs) in hydrogen of relative order $\frac{\ensuremath{\alpha}m}{M}$ have been calculated by treating the proton as a point particle with an anomalous magnetic moment in addition to its Dirac moment. In this paper the proton is treated as a particle with structure by making use of the high-energy electron-proton-scattering data. Corrections of the previous work in which only a point particle was considered are calculated by using the Feynman formulation of quantum electrodynamics. It is also shown that exactly the same terms may be obtained by using the covariant Bethe-Salpeter equation.The calculated shift of -35 parts per million (including the "recoil corrections") is not in agreement with the combined results of several experiments (-1.4\ifmmode\pm\else\textpm\fi{}18 parts per million). A possible source of this difference is meson corrections to a two-photon form-factor which is taken here as the product of two (Hofstadter) single-photon form-factors.