Absolute Values Of Cross Sections Research Articles

The 16O( 3H, p) 18O(g.s.) reaction cross section with velocity-dependent potentials

The absolute value of the differential cross section of the 16O( 3H, p) 18O(g.s.) reaction is determined using the DWBA method of Mathur and Rook. The nucleon-nucleon interactions are central velocity-dependent potentials of exponential form whilst the triton ground state is taken to contain S and S′ states only, whose spatial functions are of product form with short-range correlations. Our results are in good agreement with the hard-core calculations of Mathur and Rook and with experiment. We also obtain an independent evaluation of P S′, the probability of the S′ state in the triton.

Excitation of helium by 0.05–6 keV electrons and polarization of the resulting radiation

Absolute cross sections have been determined for excitation of helium to n 1S ( n = 3, 4, 5 and 6), n 1P ( n = 2, 3, 4 and 5), n 1D ( n = 3, 4, 5 and 6), n 3S ( n = 3, 4 and 5), n 3P ( n = 3, 4 and 5) and n 3D ( n = 3 and 4) levels by 0.05–6 keV electrons determining the light intensities of the resulting spectral lines. The measurements have been carried out at low gas pressures to avoid all the effects due to collisional excitation transfer and the absorption of resonance radiation. The polarization of the resulting radiation has also been measured. The same apparatus has been used as before in ionization experiments, where detailed attention has again been paid to the elimination of disturbing effects caused by secondary electrons. Only small modifications were necessary for the observation of light. As far as the relative energy dependence is concerned, the experimental singlet excitation cross sections obey the asymptotic energy dependence predicted by the Bethe or Born theory. For 1S and 1D levels deviations from the Born energy dependence start at impact energies below about 1000 eV and for 1P levels below about 400 eV or possibly lower energy. As far as the absolute values of the singlet excitation cross sections are concerned, in the energy region where the Born approximation is valid, the agreement between experiment and theory varies from a few percent to about 50%, dependent on the level. The experimental polarization of n 1P-2 1S is in reasonable agreement with the Born calculations; for n 1D-2 1P there is no agreement. Cross sections for singlet excitation of helium by electrons are compared with those for protons, also measured by our group. At large impact velocities they become almost equal. In the case of triplet excitation, no agreement has been obtained with the Ochkur approximation; our cross sections decrease slower with increase of impact energy than E -3 el, similar as in other optical experiments.

Absolutbestimmung der Gesamtanregungsquerschnitte der Edelgase durch Elektronenstoß

AbstractWith an improved Maier‐Leibnitz collision chamber absolute values of the total excitation cross sections of the rare gases were measured. The half width of energy distribution in the beam of exciting electrons was approximately 0.7 eV. The results for He and Ne are in reasonable agreement with the excitation functions given by Maier‐Leibnitz, if some necessary corrections (especially with regard to contact potentials) are made. Only the cross sections obtained by us are a little smaller. Furthermore the better fine structure yielded more favourable possibilities of comparison with other measurements published so far. The error should not be greater than 30%.

Absolute total collision cross sections for Maxwellian beams of H 2 and He scattered by room temperature H 2 and He

The absolute values of total collision cross sections for Maxwellian beams of H 2 and He scattered by room temperature H 2 and He are determined. The simple scattering chamber geometry adopted allows for an easy pressure calibration and avoids end corrections to the scattering length.

Resonant Broadening of Double-Resonance and Level-Crossing Signals: Application to theP13State in Mercury

A detailed calculation of the relaxation matrix of resonance atomic states by resonant collisions is carried out in the semiclassical impact theory. The validity of the different approximations is discussed. These results have been tested by observing self-broadening of level-crossing curves in high field and in zero field, in the $6^{3}P_{1}$ state in mercury. Observation of these signals at high pressures is very difficult with a pure isotope because of strong absorption and trapping of resonance light in the vapor; it is made very easy by observing level-crossing signals of one isotope in a very low concentration in the vapor of another isotope. Collisions between the different pairs of mercury isotopes have been thus systematically studied. Results are in excellent agreement (10%) with theory, both for the absolute value of cross sections and for the ratio of orientation broadening to alignment broadening.

Photoionisationsuntersuchungen an Atomstrahlen

An experiment to determine the absolute value of the photoionization cross section of atomic oxygen is described. The atoms are produced in an electrical discharge in oxygen gas with 1% hydrogen added. In order to prevent recombination a crossed beam technique is employed. The ions formed are detected by a time-of-flight mass spectrometer. The concentration of oxygen atoms in the beam is 57%.The measured photoionization cross section of atomic oxygen is compared with theoretical data. The results show the participation of autoionization processes in ionization. The cross section at the autoionizing levels detected is considerably higher than the absorption due to the unperturbed continuum. Except for wavelengths where autoionization occurs the measured ionization cross section is in fair agreement with theory. This holds up to 550 Å whereas for shorter wavelengths the theoretical values are much higher.

Trends in nuclear reaction cross sections (IV). Recalculated (n,p) cross sections for 14.5 MeV neutrons of nuclei in the range 6 ≦ Z ≦ 50

In 1962 rough estimates were published of the absolute values of (n,p) cross sections of all stable isotopes of most of the elements. In this work we compute the relative (n,p) cross sections for isotopes of elements in the range 6 ≦ Z ≦ 50 using an equation, derived previously with the statistical model approach, in which only the level density parameter Q-value, pairing energy, effective Coulomb barrier and the energy of the incident neutron appear. The relative cross sections are used to compute absolute cross sections with the aid of an empirical equation. The latter cross sections agree with experiment in over 80% of the cases. The present calculations are compared with the predictions of the empirical equations of Levkovskii, and possible sources of shell effects in the observed cross sections are discussed.

The absolute cross sections of the (t, p) and ( 3He, p) reactions

The absolute value of the differential cross section for the 16O(t, p) 18O (g.s.) reaction is calculated in the distorted wave approximation using Ohmura's hard-core wave function to describe the internal motion of the nucleons in the triton. A reasonable agreement with the observed value of the cross section is obtained while reproducing at the same time the observed binding energy and the size of the triton. Further, an explanation is offered for the equality of the absolute cross sections of the (p, t) and (p, 3He) reactions leading to analogue isobaric states, apart from factors depending on momentum and isospin transfer, in spite of a considerable difference in the rms charge radii of the triton and 3He.

Theory of Electron Collision Experiments at Intermediate and High Gas Densities

Abstract : By means of a two stream approximation an analytical solution is obtained to the equation of transfer governing the steady state concentration of monoenergetic electrons within a slab of gas bounded by two infinite planes, one of which emits a constant current density normal to its surface. The theory places no restriction on the gas pressure and includes the effects of inelastic collisions and partial reflection of scattered electrons at one or both boundaries. The results are applied to electron beam experiments at intermediate and high pressures where the mean free path of electrons is comparable to or less than the length of the collision chamber. Analytical expressions are obtained for the electron current transmitted through the gas and for the normalized ion currents to be expected in the case of total ion collection and in the case of sampling through a slit. The effect of elastic and inelastic collisions may be represented by an 'equivalent length factor' which modifies the equations normally applicable under low pressure conditions. The results of the present theory are compared with previous theories with particular reference to their use in interpreting experiments of the Maier-Leibnitz type, designed to measure absolute values of inelastic collision cross sections. (Author)

Measurement of absolute differential collision cross sections of Co 60 photons for the Compton effect

Absolute values of the differential collision cross sections of Co 60 photons (1.17 and 1.33 MeV) have been measured in the angular range of 13° to 140°. A uniform spectral sensitivity photon counter developed in the laboratory has been used in the measurement of relative values of the cross sections. Corrections have been made for the effects of self-absorption in the source, small deviations of the detector efficiency from uniformity, etc. Detailed analysis has been made of the multiple scattering and absorption phenomena occurring in the cylindrical copper scatters used in the experiment and an empirical procedure has been developed to eliminate errors caused by it. Accurate relative values obtained in this manner have been converted into absolute differential cross sections through an integral measurement in which the effects of photons scattered by angles smaller than 13° are automatically eliminated. The root mean square deviation of the experimental values from the corresponding Klein-Nishina cross section is 1.5% which is contained within the r.m.s. spread 3.5% of the probable error of the experimental points themselves. Experimental points completely rule out the distribution formulae of Breit, Gordon and Dirac.

The (d, α) reaction on F 19

Angular distributions and excitation functions of α particles from the reaction F 19(d, α)O 17 leading to the ground and first nine excited final states have been studied in the deuteron energy region from 1 to 2.5 MeV. The emitted α particles were detected with a semiconductor detector. Broad intensive maxima were observed at certain deuteron energies in the excitation function of all α groups. Angular distributions were measured at deuteron energies corresponding to the maxima and minima of excitation functions. In most cases angular distributions of different α groups show characteristic features of the compound nucleus mechanism. The absolute values of differential and integral cross-sections have been obtained for all α groups.

Effects of Sample Size and Statistical Weights on Fluctuations in theC12(C12, α)Ne20Reactions

Absolute values of the differential cross sections for the reaction ${\mathrm{C}}^{12}({\mathrm{C}}^{12}, \ensuremath{\alpha}){\mathrm{Ne}}^{20}$ to the ground and 1.63-MeV states are given at 100-keV energy intervals between 20.3- and 25.6-MeV bombarding energy at eight equally spaced angles between 3 and 73\ifmmode^\circ\else\textdegree\fi{} in the laboratory, as well as some more detailed angular distributions at selected energies. Both differential cross sections and angle-integrated data are shown to fluctuate strongly with energy. A quantitative comparison between the properties of the fluctuations and the predictions of the statistical theory of the compound nucleus (used in the spirit of Ericson) is presented. The effects of making observations on a sample of finite size are illustrated in detail and are shown in some cases to lead to results that are readily mistaken for evidence of direct interaction. Fluctuations of cross sections involving sums of several incoherent components of different weights are calculated and compared with experiment and with the usual estimates based on equal weights. The proper weight coefficients for the calculation are derived from the treatment of the average cross sections in an accompanying paper. Agreement is found in all cases between observations and the statistical compound-nucleus picture although the finite-sample effects allow a contribution to the cross sections from direct reactions of 30% or less.

Study of the reaction B 10(d, t 0) B 9

The absolute value of the differential cross section for the reaction B 10(d, t 0B 9 has been measured at a bombarding energy of 13.5±0.1 MeV. The tritons were identified by means of the thin detector method combined with the d E/d x technique. By fitting a Butler curve to the angular distribution data values r 0 = 5.4 fm and l n = 1 were obtained. The absolute value of dσ/ dΩ yields a reduced stripping width of Θ 2 = 0.050±0.010. Within the accuracy of measurement this value agrees with the stripping width of the reaction B 10(n, d 0)B 9 and with the empirical single-particle width of B 10.

Energy and Angular Dependence of the Differential Cross Section for Production of Electrons by 50-100 keV Protons in Hydrogen Gas

Hydrogen gas in a rotatable scattering chamber was bombarded by 50, 75, and 100-kev protons. The resulting secondary electrons were analyzed in both direction and energy by a slit system and a cylindrical electrostatic analyzer and counted by an electron multiplier tube with suitable electronics. Relative values of the differential cross section for ejection of secondary electrons were measured for 4 to 300-ev electrons at angles of 23 un. Concent 85% , 45 un. Concent 85% , 67.5 un. Concent 85% , 90 un. Concent 85% , 112.5 un. Concent 85% , 135 un. Concent 85% , and 152 un. Concent 85% from Absolute values for the differential cross sections were obtained by integration of the 50-kev results over all angles and energies and normalizing to the total ionization cross section measured by Schwirzke. As a function of electron energy, at a fixed angle, the differential cross sections show a broad peak at 4 to 8 ev with a monotonic decrease at higher electron energies. As a function of angle, for fixed electron energy, most of the differential cross sections are largest at 23 un. Concent more » 85% , drop off rapidly to about 100 un. Concent 85% , and are then relatively constant. The differential cross sections were integrated in various ways to obtain cross sections differential only in energy and in angle, total cross sections for ionization, average energies of the ejected electrons, and the stopping cross section due to ionization. Comparisons are made wlth other experimental results and with Born approximation calculations. (auth) « less

A study of the reaction of potassium with CH 3Br in crossed molecular beams

The reaction K +; CH3Br → KBr +; CH3 has been studied by measurements on the scattering of a velocity selected K beam by a crossed thermal beam of CH3Br. Although KBr could not be detected directly, information about the reaction could be obtained from the measurements of the elastic scattering in the reactive system. An analysis based on the assumption that the interaction of the reactants can be represented by a spherically symmetric potential led to: (1) potential parameters for an assumed analytic form of interaction; (2) the threshold of the reaction cross section, 0.24 kcal/mole; (3) the probability of reaction as a function of relative initial kinetic energy at the distance of closest approach; (4) the energy dependence of the total reaction cross section; and (5) an estimate of the absolute value of the total reaction cross section, 21 a2, at 1.93 kcal/mole.

An investigation of the energy levels of A 38 and K 38

The energy levels of A 38 and K 38 have been investigated by means of the reaction K 39 (t, α)A 38 at an incident triton energy of 5.48 MeV and the reaction Ca 40(d, α)K 38 at an incident deuteron energy of 5.46 MeV. The reaction products have been analysed using a broad range magnetic spectrograph. Eleven energy levels have been assigned to A 38 up to an excitation energy of 6.06 MeV, and twelve energy levels have been assigned to K 38 up to an excitation energy of 3.98 MeV. Absolute values of differential cross sections have been determined. The observed energy level spectra have been compared with the spectrum predicted from a recent intermediate coupling calculation of the mass-38 system.

Velocity Dependence of the Differential Cross Sections for the Scattering of Atomic Beams of K and Cs by Hg

Measurements of the velocity dependence of the angular intensity distribution of potassium and cesium beams scattered by a crossed beam of mercury are presented. The alkali beam was velocity selected, with a triangular velocity distribution (half-intensity width 4.7% of peak velocity); the velocity was varied over the range 185–1000 m/sec. The Hg beam had a thermal distribution; the average Hg speed was ∼235 meters per second. The scattering data have been converted to the center-of-mass system. The angular distributions show the expected strong forward scattering and evidence the phenomenon of rainbow scattering. The energy dependence of the rainbow angle is used to evaluate the interatomic potential well depth, interpreted as the dissociation energy De of the 2Σ+ molecular ground state. Values (in erg×1014) thus obtained (±5%) are 7.46 for KHg and 7.72 for CsHg. Absolute values of differential cross sections could not be obtained; only relative cross sections D(θ) are reported. The observed low-angle behavior D(θ) ∝θ- 7/3 serves as direct experimental confirmation of the r—6 dependence of the long-range attractive potential for K–Hg and Cs–Hg systems.

Ta 181(p, n)W 181 and Au 197(p, n)Hg 197 excitation functions between 4 and 13 MeV

The excitation functions for the Ta 181(p, n)W 181 and Au 197(p, n)Hg 197 reactions have been measured for incident proton energies from 4 to 13 MeV. The stacked foil method was used. The activity of the foils was measured by counting the gamma rays and X-rays emitted when the product nuclei decay by electron capture. Absolute values of the cross sections were measured at several energies for these reactions and were compared with the cross sections for compound nucleus formation given by Shapiro. Threshold energies for the (p, 2n) reactions were obtained by comparing the present data with neutron yields obtained from long counter measurements. The (p, 2n) thresholds are 7.5 MeV for Ta 181 and 8.3 MeV for Au 197. The absolute (p, 2n) cross section values have also been obtained. The total reaction cross sections above 7 MeV are compared with the optical model calculations of Bjorklund and Fernbach. The present results confirm the assumption of a surface absorption potential.

Disintegration of K 39 by fast neutrons

The nuclear reactions K 39(n, p)A 39 and K 39(n, α)Cl 36 have been studied by bombarding a KI(Tl) crystal with mono-energetic fast neutrons and observing scintillations due to emitted protons and α particles. Using good energy resolution (less than 10 keV) a yield curve has been obtained for the p 0-group for neutron energies from 1.46 to 3.05 MeV, which exhibits 60 narrow resonances. Measurements with poorer energy resolution, varying between 70 and 150 keV, have been made in the neutron energy region from 2.3 to 8.7 MeV. From these absolute values of the reaction cross sections for the p 0-group ( E n = 2.3 to 8.7 MeV), the α 0-group ( E n = 2.3 to 3.8 MeV) and the p 1-group ( E n = 2.5 to 3.5 MeV) have been extracted. Fourteen proton groups are seen in the pulse-height spectra, and from an analysis of the associated pulse-heights as a function of neutron energy, ten new excited states of A 39 have been derived. The measured cross sections are compared with values obtained by other groups and with theoretical predictions.

Disintegration of K 39 by fast neutrons

The nuclear reactions K 39(n, p)A 39 and K 39(n, α)Cl 36 have been studied by bombarding a KI(Tl) crystal with mono-energetic fast neutrons and observing scintillations due to emitted protons and α particles. Using good energy resolution (less than 10 keV) a yield curve has been obtained for the P 0-group for neutron energies from 1.46 to 3.05 MeV, which exhibits 60 narrow resonances. Measurements with poorer energy resolution, varying between 70 and 150 keV, have been made in the neutron energy region from 2.3 to 8.7 MeV. From these absolute values of the reaction cross sections for the p 0-group ( E n = 2.3 to 8.7 MeV), the α 0- group ( E n = 2.3 to 3.8 MeV) and the p 1-group ( E n = 2.5 to 3.5 MeV) have been extracted. Fourteen proton groups are seen in the pulse-height spectra, and from an analysis of the associated pulse-heights as a function of neutron energy, ten new excited states of A 39 have been derived. The measured cross sections are compared with values obtained by other groups and with theoretical predictions.