Coulomb Cross Section Research Articles

Effect of Resonant Charge Exchange on Heat Conduction in Plasmas

Estimates are made of cross sections for symmetric resonant charge exchange between ions differing by one electronic charge. At thermal energies and electron densities of interest, these cross sections are negligible compared to the elastic screened Coulomb cross section for diffusion. It is concluded that resonant charge exchange between ions cannot affect heat conduction in plasmas by controlling the rate of diffusive transport of ionization energy, in contrast to ion-neutral exchange in partially ionized gases.

Theory of Coulomb excitation in the collision of identical nuclei

A theory of Coulomb excitation in collisions of identical nuclei is developed. It is shown that under the usual quasi-classical conditions the differential cross sections for Coulomb excitation of nuclei (just as the Mott cross section for elastic Coulomb scattering of identical particles) display considerable oscillations with respect to the scattering angle. If the level excitation energy is sufficiently small as compared with the energy of colliding particles these oscillations are described by a simple modification of the exchange term in the Mott formula for elastic scattering. The character of oscillations in the neighbourhood of 90° (c.m.s.) proves essentially dependent on the multiple moment of the transition which points to a possible use of this relation for the unambiguous determination of multipole moments of the transitions.

The effects of multiple scattering in small-angle nuclear scattering experiments

The Molière theory of multiple scattering by a screened Coulomb field is applied to typical data from varioys laboratories on p-nucleus scattering at small angles, and it is shown that in many cases the systematic errors due to multiple scattering are much larger than the published errors at the smallest scattering angles. A brief account of the Molière theory is given, with an extension to take into account the effects of beam size, beam divergence and counter size, provided that, together, these can be represented by a Gaussian. The Moliére theory is extended to take into account deviations from the screened Coulomb field cross section caused by nuclear effects, provided that these deviations can be expressed as an additive correction to the screened Coulomb field cross section. Finally, a method is outlined for extracting single scattering cross sections from data containing contributions from multiple scattering, the method being based on the validity of the Molière theory as a first approximation.

Coulomb Interactions in a Strong Magnetic Field. II. Nonadiabatic Case. Line Profile of Cyclotron Radiation

Using the generalized quantum treatment of pressure broadening by Anderson, we derive an expression including the effects of both adiabatic and nonadiabatic transitions for the emission spectrum of cyclotron radiation from free-charged particles undergoing Coulomb interactions with fixed scatterers in typical plasma situations. After adapting the formalism to account for the continuous nature of the energy states parallel to the magnetic field, and after including the energy dependence of the dipole matrix element, one obtains half-width values for the cyclotron line in the case of a strong magnetic field. Extension to the weak field case can then be made in a plausible manner, resulting in the ordinary Coulomb cross section for vanishing magnetic field strength.

Collective interactions and the production of a high-temperature plasma

Turbulent heating appears to be a simple method for obtaining a plasma with a high electron temperature. Based on the use of collective motion in the plasma, it has certain advantages compared with heating methods based on binary Coulomb collisions. This advantage is especially important when the temperature is increased, in which case the Coulomb cross section becomes smaller.

Electrical Conductivities of Lithium and Helium Gases

Electrical conductivities of a multicomponent system in a uniform temperature, density, pressure, and magnetic field are obtained by using the transfer equations obtained by Burgers. The resulting formulas give the zero-order contribution to electrical conductivities by elastic scattering of colliding particles as a function of temperature and density. These formulas are applied to lithium and helium gases. The screened Coulomb cross sections and geometrical cross sections are used, respectively, for collisions involving charged particles and for collisions involving a charged particle and a neutral atom. The relative abundances of various species are obtained by using the Saha formulas. The limitations associated with the uses of the electrical conductivities are discussed.

Elastic Scattering of Heavy Ions from Several Gas Targets

The absolute differential cross section for the elastic scattering of oxygen by gaseous targets of helium, nitrogen, and neon and of carbon by nitrogen were measured from about 4 to \ensuremath{\sim}20 degrees in the center-of-mass system. The energy of the incident heavy ions was \ensuremath{\sim}10 Mev per atomic mass unit. The ratio of the elastic cross section to the Coulomb cross section exhibits diffraction-like oscillations which damp out as $\ensuremath{\eta}=\frac{{Z}_{1}{Z}_{2}{e}^{2}}{\ensuremath{\hbar}v}$ increases from \ensuremath{\sim}1 to \ensuremath{\sim}4. The results are compared with the predictions of a simple diffraction model, a sharp-cutoff model, and a modified-cutoff model. Reasonably good agreement is obtained in predicting the angular position of the maxima and minima, but not the absolute cross section. The modified-cutoff model appears to apply only if $\ensuremath{\eta}$ is greater than about 2.5. The value of ${r}_{0}$ found for the ${\mathrm{O}}^{16}$-Ne scattering is 25% greater than for the remaining three reactions.

Photostar cross-section from coulomb disintegrations of high energy heavy primaries

The photostar production process in nuclear emulsions is studied. Heavy primary cosmic nuclei at energies of approximately 1012 ev/nucleon may undergo reactions in emulsion that are similar to photostar production processes at energies of 0.2 to 25 Bev. The Coulomb disintegration cross section is calculated under various assumptions as to the photostar production cross section and as functions of primary size and energy. It is noted that a study of the Coulomb disintegration cross section of heavy primaries above 1012 ev/nucleon provides information concerning the photostar production cross section above 1.1 Bev.

The Elastic Scattering of3He by C, Mg, Al and Cu

Angular distributions of 5.5 Mev 3He particles elastically scattered by C, Mg, A1 and Cu have been measured by magnetic analysis at angles of observation between 20° and 132.5°. The curves of the ratio of observed cross section to calculated Coulomb cross section show a decrease with angle for C, Mg and A1 and an increase at large angles for Cu. The curves also show maxima and minima.

Nitrogen-Aluminium elastic scattering

The differential cross section for elastic scattering of 27.3-MeV nitrogen ions from aluminium was measured from 36° to 134° in the centre-of-mass system. A coincidence system detecting both the nitrogen and the aluminium ions was used to identify the elastic events. The angular resolution was about ±1 degree. The ratio of the elastic cross section to the Coulomb cross section exhibits a small rise above unity near 50° (c.m.), then drops almost exponentially from 60° to 134° (c.m.), where it has a value of 0.0265. The results of the experiment are compared with the predictions of a sharp cutoff calculation. Reasonably good agreement is obtained from 36° to 96° (c.m.) with an interaction radius R = 9.07 × 10 −13 cm. If we define R = r 0( A 1 ⅓+( A 2 ⅓), the value of r 0 is 1.68 × 10 −13 cm. Beyond 96° (c.m.) the sharp cutoff calculation displays increasing oscillations and no longer fits the data. The results of a semi-classical scattering theory due to Ford and Wheeler are also compared with the experimental data. The best fit is obtained for a rainbow angle θ r = 94°, corresponding to r 0 = 1.59 × 10 −13 cm, and a surface thickness parameter ΔR = 0.83 × 10 −13 cm. Quite good agreement between this theory and experiment is obtained from about 94° to 134° (c.m.).

Scattering of 18.7-Mev Alpha Particles from Al, Cu, and Ag

The scattering of 18.7-Mev alpha particles from Ag, Cu, and Al was studied from 10\ifmmode^\circ\else\textdegree\fi{} to 170\ifmmode^\circ\else\textdegree\fi{} with rms angular resolutions of 0.4\ifmmode^\circ\else\textdegree\fi{} to 0.85\ifmmode^\circ\else\textdegree\fi{}. The scattered alpha particles were separated from singly charged reaction products with the aid of a proportional counter, and their energies were measured with a CsI(Tl) scintillation spectrometer. The elastic scattering for Ag shows the "exponential" dropoff from the Coulomb cross section, without any pronounced structure at large angles. For Cu, definite changes in the slope of the dropoff are observed up to 120\ifmmode^\circ\else\textdegree\fi{}, followed by a shallow minimum near 130\ifmmode^\circ\else\textdegree\fi{} and a very deep, narrow minimum at 162\ifmmode^\circ\else\textdegree\fi{} (c.m.). The interaction radii deduced from the strong-absorption model agree with those found at higher energies. From the diffraction-like pattern found for Al, an interaction radius of 6.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm is derived, appreciably larger than the one obtained at 40 Mev (5.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm). There are indications that a direct-process interpretation of the inelastic scattering from Al is possible.

A new possible theory of the μ-meson

The paper presents a theory of the μ-meson as a particle with spin 1/2 described by anomalous equations differing from the Dirac equations. Calculation is carried out of the intrinsic magnetic moment of the μ-meson, the cross-section for Coulomb and Compton scattering, the self-energy and the electrodynamic correction to the magnetic moment of the μ-meson. An explanation is given of the similarity of the μ-meson and electron at low energies and their dissimilarity at very high energies in electromagnetic interaction. The difference in the masses of the electron and μ-meson is determined by means of the same electromagnetic cut-off for both particles.

C13(p, p)C13: Experiment and Analysis

The differential cross sections for the ${\mathrm{C}}^{13}(p, p){\mathrm{C}}^{13}$ elastic scattering interactions were measured over an energy range from 1.5 to 3.4 Mev (incident proton energy) at scattering angles of 45.0\ifmmode^\circ\else\textdegree\fi{}, 54.4\ifmmode^\circ\else\textdegree\fi{}, 74.1\ifmmode^\circ\else\textdegree\fi{}, 90.0\ifmmode^\circ\else\textdegree\fi{}, 106.4\ifmmode^\circ\else\textdegree\fi{}, 127.8\ifmmode^\circ\else\textdegree\fi{}, 148.9\ifmmode^\circ\else\textdegree\fi{} in the center-of-mass system. Methane gas, enriched to 72.5% in ${\mathrm{C}}^{13}$, was used as a target material. The absolute differential cross sections computed through this experiment were accurate to about 6% in the nonresonant energy regions. The measured nonresonant cross sections at about 2 Mev were essentially equal to those for Coulomb scattering at $\ensuremath{\theta}=45\ifmmode^\circ\else\textdegree\fi{}$ and increased to about seven times Coulomb cross section at $\ensuremath{\theta}=148.9\ifmmode^\circ\else\textdegree\fi{}$. There was also an increase in measured cross section relative to the Rutherford cross section at all scattering angles as the proton energy was increased. Maxima in the cross sections were observed at incident proton energies of 2.00, 2.12, 2.33, 2.90, and 3.12 Mev. A phase-shift analysis of the resonances at 2.00, 2.12, and 2.33 Mev yielded assignments for $J$ and $\ensuremath{\pi}$ of ${1}^{\ensuremath{-}}$, ${3}^{\ensuremath{-}}$, and ${1}^{+}$, respectively, and reduced widths relative to single-particle reduced widths of 0.10, 0.11, and 0.005, respectively.

Elastic Scattering of Nitrogen by Nitrogen

The differential cross section for the elastic scattering of nitrogen from nitrogen was measured for incident nitrogen laboratory energies of 15.0, 17.7, 19.2, and 21.7 Mev and laboratory angles from 15\ifmmode^\circ\else\textdegree\fi{} to 55\ifmmode^\circ\else\textdegree\fi{}. The scattering occurred in nitrogen gas and the particles were detected with a nuclear emulsion placed in a one-slit camera. At 15 Mev, the scattering is entirely due to the Coulomb potential. The interference term in the Mott scattering cross section of two identical particles can be seen as a rise in the cross section near 45\ifmmode^\circ\else\textdegree\fi{}, illustrating the fact that nitrogen is a Bose-Einstein particle. The angular resolution is not sufficient to enable the precise measurement of the spin. At the higher energies the cross section drops below the Mott cross section at angles greater than 30\ifmmode^\circ\else\textdegree\fi{}, due to the nuclear absorption of the particles as the apsidal distance approaches the sum of the two nuclear radii. At an energy of 21.7 Mev and an angle of 45\ifmmode^\circ\else\textdegree\fi{}, the cross section is $\frac{1}{5}$ of the Mott cross section. A calculation which uses the strong absorption model of Blair, fits the differential cross section at 21.7 Mev quite well. In order to fit the data, the contributions from values of $l$ up to 6 must be subtracted from the Coulomb cross section; this indicates that the nuclear radius of nitrogen is 4.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ ${\mathrm{cm}}^{2}$. From this calculation the total nuclear absorption cross section for 21.7-Mev nitrogen on nitrogen is inferred to be 3.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}25}$ ${\mathrm{cm}}^{2}$.

Elastic Scattering of Protons, Deuterons, and Alpha Particles from Heavy Elements

The elastic scattering of 7.8-Mev protons from ${\mathrm{Au}}^{197}$, 27.5-Mev alpha particles from ${\mathrm{Au}}^{197}$, and 15.2-Mev deuterons from ${\mathrm{Pb}}^{208}$ and ${\mathrm{Bi}}^{209}$ has been measured as a function of angle. Except for the proton scattering which bears a constant ratio to Coulomb scattering, the cross sections when plotted as a ratio to the Coulomb cross sections fall sharply below unity at an angle of about 50\ifmmode^\circ\else\textdegree\fi{} for the alpha particles on gold and about 30\ifmmode^\circ\else\textdegree\fi{} for the deuterons on lead and bismuth. The absolute cross section for elastic scattering of 15.2-Mev deuterons from gold at 30\ifmmode^\circ\else\textdegree\fi{} is equal to the Coulomb value within 20%, the energy variation is proportional to ${E}^{\ensuremath{-}2}$ from 15.2 to 8.5 Mev to within 6%, also at 30\ifmmode^\circ\else\textdegree\fi{}.

Elastic Scattering of 40-Mev Alpha Particles from Heavy Elements

Angular distributions have been measured for the elastic scattering of 40-Mev alpha particles from Ta, Au, Pb, and Th in the angular range 21\ifmmode^\circ\else\textdegree\fi{} to 155\ifmmode^\circ\else\textdegree\fi{}. If the ratios of the measured cross sections to the Coulomb cross section are assumed equal to 1.0 at small angles, they increase slightly with increasing angle, and in the vicinity of 30\ifmmode^\circ\else\textdegree\fi{} decrease exponentially with increasing angle to values less than 0.001. These data are compared with the semiclassical, strong absorption model of Blair and with the recent model of Ford and Wheeler.