Absolute Excitation Research Articles

A semi-empirical formula for calculation of absolute cross sections for ionization and excitation of atoms by electrons

A simple analytical expression for the absolute ionization and (optically allowed) excitation cross sections, as a function of the electron energy, is “derived”. In this expression there are two parameters. The first one is proportional to the optical oscillator strength and the second one is dependent on the shape of the differential cross section (generalized oscillator strength), for scattering of energetic electrons as a function of their (small) momentum loss. The analytical expression is exact for large energies of the impinging electron. For small energies of this electron, the expression gives good agreement with experiment. Ionization cross sections are calculated for H, He, Ne, Ar, Kr, Xe, H 2, N 2 and O 2. Excitation cross sections are calculated for H and He.

Excitation of helium by He + and polarization of the resulting radiation

Absolute excitation cross sections have been determined for He + incident on He by measuring the intensities of the singlet and triplet lines of the He I spectrum emitted by the target atom between 2900 Å and 6000 Å. The polarization of the photons has also been measured. The impact energy was between 5 and 100 keV. As a function of the energy the cross sections show a similar behaviour for different levels of a spectral series and the polarization of light tends to be the same for the corresponding emission lines. Generally more than one maximum is found in the cross section curves, and these maxima have a tendency to shift to higher impact energies for levels with increasing quantum number n, probably due to the corresponding increase of excitation energy. Moreover the energies of the cross section maxima decrease with increasing azimuthal quantum number l, which may be explained by means of electrical polarization of the target atom. Cross section results are compared with the theoretical calculations of Moiseiwitsch and Stewart, using Born approximation. A big discrepancy is present and it seems also probable that their neglection of the electron exchange process is in contradiction with our large experimental cross sections for excitation of triplet states. Comparing our results for He excitation by He +, H + and H impact, we find that levels with higher l values are relatively more excited if the effective charge of the impacting particle increases. This can be understood by taking into account a larger electrical polarization of the He target atom by projectiles with a larger effective charge.

Absolute cross-sections and excitation functions for α particles induced reactions on bromine between 10 and 24 MeV

Absolute cross-sections and excitation functions for α induced reactions have been measured, from 10 to 24 MeV, by activation and stacked foil techniques. The following reactions were seen: Br 79(α, n)Rb 82 6.3 h, Br 79(α, αn)Br 78 6.4 min, Br 79(α, 2n)Rb 81 31.5 min and 4.7 h, Br 81(α, αn)Br 80 18 min and 4.4 h, Br 81(α, n)Rb 84 23 min. The experimental results have been compared with theoretical predictions based on optical model and statistical analysis. It seems that the magnitude of the cross-sections is best predicted by optical model calculations. The shape of the excitation function for compound nucleus formation agrees best with the continuum theory, but the shapes of the individual cross-sections are not in agreement with evaporation calculations and some of the excitation functions are very peaked. Isomeric ratios seem to indicate that the (α, αn) reactions proceed through direct interaction and that there might be some admixture of compound nucleus and direct reaction on the high energy side of (α, 2n) reactions.

Excitation of helium by protons and hydrogen atoms and polarization of the resulting radiation

Absolute excitation cross sections have been determined for H + and H incident on He by measuring the intensities of the singlet and triplet lines of the He I spectrum. The energy range was mostly 5 to 35 keV, but for one 1D and one 1S level up to 100 keV. The polarization of the photons has also been determined. As a function of the energy the cross section shows a similar behaviour for different levels of a spectral series and decreases with increasing quantum number n. The polarization is almost the same for the emission lines of one series. These properties can be understood qualitatively by theory. Many maxima in the excitation cross sections are found at energies of about 15 keV for singlet and triplet excitation of helium. A tentative explanation is given in terms of formation of intermediate molecular states. Excitation of the 4 1D level by protons results into two maxima, one at 15 keV and the other at 55 keV. The excitation of the 3 1P level and the degree of polarization of the 3 1P-2 1S transition show an energy dependence which differs from the existing theoretical results. In agreement with the spin conservation rule of Wigner, we have measured that the 3 3P level is excited much more effectively by H atoms than by protons (at least a factor of 100).

Absolute Electron Excitation Cross Sections of Helium

The absolute apparent electron excitation functions of helium were measured for the 3/sup 1/S, 4/sup 1/S, 5/sup 1/S, 6/sup 1/S, 3/sup 1/P, 4/sup 1/ P, 3/sup 1/D, 4/sup 1/D, 5/sup 1/D, 6/sup 1/D, 3/sup 3/S, 4/sup 3/S, 5/sup 3/S, 3 /sup 3/P, 3/sup 3/D, 4/sup 3/D, 5/sup 3/D, and 6/sup 3/D states at pressures sufficiently low so that the effects of radiation imprisonnaent and collisional excitation transfer can be neglected. The data were corrected for polarization of the radiation and cascading from the upper excited states, and the true excitation functions obtained. The peak values and shape of these excitation functions are compared with results of other laboratories. Generally good agreement is found with previous works where the collisional excitation transfer was properly reduced and allowance made for the cascading effect. The experimental cross sections show satisfactory agreement with the theoretical values calculated by the Born approximation for the /sup 1/S and /sup 1/P states at high electron energies, but are about four times larger than the theoretical values for /sup 1/D states. For the triplet series, the experimental cross sections exceed the calculated values by factors of ten to one hundred or more. It is concluded that the populationmore » of the triplet states is produced mainly by processes other than direct excitation. (auth)« less

INTERACTION OF VANADIUM WITH PROTONS OF ENERGIES UP TO 84 MEV

Radiochemical techniques have been used to determine absolute excitation functions for 17 nuclides formed as spallation products from the irradiation of vanadium by protons of energy up to 84 Mev. The shape of the excitation functions and classical threshold calculations showed evidence of contribution of heavy-particle emission in the reactions of the type (p,3pxn), (p,5pxn), and (p,7pxn). The Barr method for analysis of the cross-section distribution was modified and applied at 60 and 80 Mev bombarding energies. The experimentally measured cross sections for 16 nuclides at 60 and 80 Mev bombarding energies were fitted to the four-parameter Rudstam equation σ (A,Z) = exp [PA−Q−R(Z−SA)2]. Comparison of the results obtained at 8 Mev bombarding energy with the predictions of the weak and strong absorption models showed better agreement with the predictions obtained by using the surface absorption Fernbach–Bjorklund potential.

Absolute Cross Sections and Excitation Functions for (d, p) and (d, 2n) Reactions onMn55,Cu63,Cu65,Zn66, andZn68Between 3 and 11.6 MeV

BS>Absolute cross sections and excitation functions for some (d,p) and (d,2n) reactions have been measured by activation and stacked-foil techniques. The cross sections for (d,p) reactions seem to indicate a direct mechanism, although there seems to be some compound nucleus admixture above the Coulomb barrier. A striking result is the great difference (a factor 3.5) between the (d,p) cross sections on the two Cu isotopes. This result is unexplained and requires confirmation. The (d,2n) reaction proceeds via compound-nucleus formation but the theoretical excitation functions, calculated on the basis of compound-nucleus formation followed by evaporation of particles, are not in agreement with the experimental ones. The isomeric ratio of the Zn/sup 69/ isomers is also discussed. (auth)

Excitation of Ne, Ar, and Kr Induced byH+andHe+Impact (5-35 keV)

Impact radiation from ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ in noble gases is studied in the wavelength region below 1250\AA{}. A vacuum spectrograph has been built and absolutely calibrated for this purpose, so that the measurements provided absolute excitation or emission cross sections. We observe strong maxima in the light intensities of some atom and ion lines of noble gases. These maxima appear at remarkably low energies of the impinging particles, and moreover, correspond with large absolute cross sections (\ensuremath{\sim}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$/atom). For instance, the excitation of the $n{p}^{6}^{2}S_{\frac{1}{2}}$ states of Ar II ($n=3$) and Kr II ($n=4$) induced by the ${\mathrm{He}}^{+}$ impact on Ar and Kr show maxima at 9 and 7 KeV, respectively. This can be predicted by the adiabatic criterion of Massey. However, for the $(n+1){s}^{\ensuremath{'}}^{2}D_{\frac{5}{2}}$ states of Ar II ($n=3$) and Kr II ($n=4$) the maxima lie below 5 keV, though more energy is needed for the excitation of these states than there is for the $^{2}S_{\frac{1}{2}}$ ones. Also for the excitation of the $2{p}^{5}3s$ state of Ne I induced by ${\mathrm{He}}^{+}$ impact on Ne, the maximum lies below 5 keV. There are indications that intermediate molecular states occur which contribute to the formation of these low-energy maxima.

Nuclear Excitation Functions:Ar40,Zn68(d,He3)

The (d,He/sup 3/) reaction was studied by radiochemical techniques. Absolute excitation functions were determined to 15 Mev for the reactions Ar/sup 40/(d,He/sup 3/)Cl/sup 39/ and Zn/sup 68/(d,He/s up 3/)Cu/sup 67/. The Ar/sup 40/ (d,He/sup 3/)Cl/sup 39/ cross section is 0.37 plus or minus 0.07 mb at 14.8 Mev and the Zn/sup 68/(d,He/sup 3/)Cu/sup 67/ cross section is 0.54 plus or minus 0.08 mb at 15.4 Mev. These cross sections are shown to be more than an order of magnitude greater than predicted by the statistical model of nuclear reactions. The energy dependence of the cross section appears to be governed by the Coulomb barrier felt by the outgoing He/sup 3/ particle, at least when the He/sup 3/ energy is less than the classical barrier height. The shape of the observed excitation functions may be reproduced moderately accurately by a very simple proton pickup model. (auth)

Excitation processes in helium and polarization of the resulting light induced by proton impact (5–35 keV)

Absolute excitation cross sections in proton-helium collisions have been determined by measuring n 1S → 2 1P and n 1D → 2 1P transitions of the He I spectrum and n 2F → 3 2D transitions of the He II spectrum. The excitation cross sections of the n 1D levels show maxima as a function of the energy. It is found that the emitted light is polarized in the n 1D → 2 1P He I transitions.

Inelastic scattering of heavy ions

Absolute inelastic excitation cross sections have been obtained in the reactions (C 12, C 12), (C 12, O 16), (O 16, O 16) and (N 14, C 12). The heavy ion beams used were the full energy (10.54 MeV per nucleon) beams from the Yale University heavy ion accelerator. The data were analysed with the diffraction model of inelastic scattering and interaction radii, deformation parameters and the parity of the transitions were determined. The results indicate that the inelastic radii are slightly larger than the corresponding elastic radii. The analysis also shows that the oxygen excitation is mainly one of odd parity and verifies the 2 +, 4.433 MeV excitation in C 12. In the N 14, C 12 reaction the 2.312 MeV level of N 14 is found to be strongly suppressed relative to other excitations seen.

Nuclear Reactions of Cobalt with Protons from 0- to 100-Mev Energy

Absolute excitation functions for 0- to 100-Mev protons on cobalt have been measured for 18 radioactive products from vanadium through nickel. Linear-accelerator bombardments in the 0- to 30-Mev region plus a scattered-beam cyclotron technique gave good energy resolution. The results are in qualitative agreement with the Bohr compound nucleus picture at low energies and a mixture of the Bohr and Serber mechanisms at higher energies. Evidence for high yields of alpha-particle emission was found. The influence of shell structure on yields was pronounced, with magic-number nuclei having especially low yields.

Fission and Total Reaction Cross Sections for 22-Mev Protons onTh232,U235, andU238

Absolute excitation functions for ($p, f$) reactions in ${\mathrm{Th}}^{232}$, ${\mathrm{U}}^{235}$, and ${\mathrm{U}}^{238}$ were measured by radiochemical techniques; at 21.5 Mev, the cross sections are 0.83, 1.31, and 1.28 barns, respectively (\ifmmode\pm\else\textpm\fi{}15 percent in each case). Cross sections for ($p, \mathrm{xn}$) reactions in ${\mathrm{U}}^{238}$ were found to be quite small. The total reaction cross sections correspond to a nuclear radius of $(1.55\ifmmode\pm\else\textpm\fi{}0.1){\mathrm{A}}^{\frac{1}{3}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm. Some advantages of determining the nuclear radius by total reaction cross sections are pointed out, and the discrepancy between electromagnetic and nuclear determinations of the nuclear radius is discussed.

Excitation Functions to 100 Mev

A method is described for obtaining excitation functions using the stacked foil technique with an internal cyclotron beam. The method, which utilizes multiple Coulomb scattering for deflection and 180\ifmmode^\circ\else\textdegree\fi{} focusing for energy separation, has the advantages of good energy resolution, high intensity, and low background. Equations are presented for the particle orbits from which are derived the energy resolution and efficiency attainable. Absolute excitation curves are given for the reactions, ${\mathrm{C}}^{12}(p,pn){\mathrm{C}}^{11}$; ${\mathrm{Na}}^{24}$, ${\mathrm{Na}}^{22}$, and ${\mathrm{F}}^{18}$ from ${\mathrm{Al}}^{27}$; ${\mathrm{B}}^{11}(p,n){\mathrm{C}}^{11}$; and ${\mathrm{S}}^{34}(p,n){\mathrm{Cl}}^{34}$. Absolute cross sections are determined using the monitor reaction, ${\mathrm{C}}^{12}(p,pn){\mathrm{C}}^{11}$, and the ratio of the $\ensuremath{\beta}$-counting rates. Various corrections to the relative and absolute excitation curves are discussed. A brief interpretation of the results is given in which it is argued that they are consistent with present ideas about high energy nuclear reactions.

Absolute Excitation Function of theBe9(d,t)Reaction

The gas counting technique used earlier for the absolute assay of natural waters for tritium has been applied to the reactions producing tritium by the deuteron bombardment of beryllium. Absolute yield measurements for both thick and thin beryllium targets with deuteron energies ranging from 350 kev to 7.7 Mev have shown that the reaction cross section rises rapidly at about 1.5 Mev to a flat plateau at 0.23\ifmmode\pm\else\textpm\fi{}0.01 barn, extending up to 7.7 Mev. From these results the tritium production appears to be about as prolific as the neutron production. In general one feels that the large magnitude of the ($d,t$) cross section must be associated with the low binding energy of the extra neutron in ${\mathrm{Be}}^{9}$.