Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.

An experimental study of the mobility of edge dislocations in pure copper single crystals

The velocity of selectively-introduced edge dislocations in 99.999 percent pure copper crystals has been measured as a function of stress at temperatures from 66°K to 373°K by means of a torsion technique. The range of resolved shear stress was 0 to 15 megadynes/ cm^2 for seven temperatures (66°K, 74°K, 83°K, 123°K, 173°K, 296°K, 296°K, 373°K.

Dislocation mobility is characterized by two distinct features; (a) relatively high velocity at low stress (maximum velocities of about 9000 em/sec were realized at low temperatures), and (b) increasing velocity with decreasing temperature at constant stress.

The relation between dislocation velocity and resolved shear stress is:

v = v_o(τ_r/τ_o)^n

where v is the dislocation velocity at resolved shear stress τ_r, v_o is a constant velocity chosen equal to 2000 cm/ sec, τ_o is the resolved shear stress required to maintain velocity v_o, and n is the mobility coefficient. The experimental results indicate that τ_o decreases from 16.3 x 10^6 to 3.3 x 10^6 dynes/cm^2 and n increases from about 0.9 to 1.1 as the temperature is lowered from 296°K to 66°K.

The experimental dislocation behavior is consistent with an interpretation on the basis of phonon drag. However, the complete temperature dependence of dislocation mobility could not be closely approximated by the predictions of one or a combination of mechanisms.

Commercial testing of concrete

The material included within this report is the result of a series of tests of concrete specimens taken during the construction of various buildings in the cities of Pasadena and Los Angeles over a period of eight months.

The object of the problem is to determine the effect of the water ratio on the ultimate strength of the concrete as obtained from data observed and recorded from specimens taken from actual building practice rather than that from laboratory specimens made under ideal, or at least more nearly standard conditions.

The influence of the NN* channel on elastic NN scattering

The problem of two channels NN and NN*, coupled through unitarity, is studied to see whether sizable peaks can be produced in elastic nucleon-nucleon scattering due to the opening of a strongly coupled inelastic channel. One-pion-exchange (OPE) interactions are calculated to estimate the NN*→NN* and NN→NN* amplitudes. The OPE production amplitudes are used as the sole dynamical input to drive the multichannel ND^-1 equations in the determinental approximation, and the effect on the J = 2+ (¹D₂) elastic NN scattering amplitude is studied as the width of the unstable N* and strength of coupling to the inelastic channel are varied. A cusp-type enhancement appears in the NN channel near the NN* threshold but for the known value of the N* width the cusp is so “wooly” that any resulting elastic peak is likely to be too broad and diminished in height to be experimentally prominent. A brief survey of current experimental knowledge of the real part of the ¹D₂ NN phase shift near the NN* threshold is given, and the values are found to be much smaller than the nearly “resonant” phase shifts predicted by the coupled channel model.

Investigations into electronic stopping regime sputtering of uranium tetrafluoride

Yields were measured for ²³⁵U sputtered from UF₄ by ¹⁶O, ¹⁹F, and ³⁵Cl over the energy range ~.12 to 1.5 MeV/ amu sing a charge equilibrated beam in the stripped beam arrangement for all the incident ions and in the transmission arrangement for ¹⁹F and ³⁵Cl. In addition, yields were measured for ¹⁹F incident in a wide range of discrete charge states. The angular dependence of all the measured yields were consistent with cosʋ. The stripped beam and transmission data were well fit by the form (Az²eqln(BƐ)/Ɛ)⁴ (where Ɛ was the ion energy in MeV/amu and z_eq(Ɛ) was taken from Zeigler(80). The fitted values of B for the various sets of data were consistent with a constant B₀, equal to 36.3 ± 2.7, independent of incident ion. The fitted values of A show no consistent variation with incident ion although a difference can be noted between the stripped beam and transmission values, the transmission values being higher.

The incident charge data were well fit by the assumptions that the sputtering yield depended locally on a power of the incident ion charge and that the sputtering from the surface is exponentially correlated to conditions in the bulk. The equilibrated sputtering yields derived from these data are in agreement with the stripped beam yields.

In addition, to aid in the understanding of these data, the data of Hakansson(80,81a,81b) were examined and contrasted with the UF₄ results. The thermal models of Seiberling(80) and Watson(81) were discussed and compared to the data.