Total Excitation Cross Sections Research Articles

Total cross section for proton excitation of H-atoms

In this letter we give a simple expression for the total cross section for excitation to all discrete states of a hydrogen atom by a fast proton. This asymptotic expression is applicable for protons of energy equal to or greater than 25 keV.

Total inelastic cross sections for slow electrons in xenon†

An electron beam of low energy enters a cubic wire gauze chamber in Xe at a pressure of about 10−2 torr. The scattered electrons escaping from the chamber are received by a collector kept at a retarding potential of frac13; of the accelerating voltage. When inelastic collisions duo to excitation sot in, the collector current decreases. In order to derive from this change the absolute cross section, the average number of electron collisions in the chamber must be known; this was determined in two ways. With this result and the observed variation of the collector current with the accelerating voltage the total excitation cross section is found between the lowest excitation potential of 8-2 v and the ionization potential of 12-1 v; multiple scattering, energy spread and closeness of energy levels of Xe prevent the appearance of a fine structure. For energies up to 15 v approximate cross-section values are obtained after allowing for the positive ion current and including the known ionization cross sections. Further analysis of the results suggests that the transparency of the gauze is smaller than its geometric value, that it varies with the energy of the electrons and positive ions and that the ion concentration in the chamber is relatively large. The electron emission from the collector by Xe ions and metastable atoms seems to be insignificant.

Rotational Excitation ofH2by Slow Electrons in a Beam Experiment

Rotational excitation and de-excitation ${J}_{f}\ensuremath{-}{J}_{i}=\ifmmode\pm\else\textpm\fi{}2$, ${J}_{i}=0,\ensuremath{\cdots},3$, of ${\mathrm{H}}_{2}$ by slow electrons with and without the simultaneous excitation of one vibrational quantum has been measured. The absolute total cross section for pure rotational excitation $J=3\ensuremath{\leftarrow}1$ in the energy range 1-10 eV is presented. The measurements of angular dependences indicate $s$-, $p$-, and $d$-wave scattering.

Resonances in the Total Cross Sections for Metastable Excitation of Noble Gases by Electron Impact

Total cross sections for excitation by electron impact of metastable states in the noble gases helium, neon, argon, krypton, and xenon have been measured as a function of impact energies. A 180\ifmmode^\circ\else\textdegree\fi{} spherical monochromator was used to obtain incident beams of electrons with energy resolutions between 0.035 and 0.050 eV. Metastable atoms were detected in the scattering chamber by electron ejection from a metal surface. The detector was biased negatively to repel scattered electrons, and was electrostatically shielded from the incident electron beam. The cross sections were measured for impact energies up to 5 eV above the metastable thresholds. Several narrow resonances associated with negative-ion states were observed, and where possible their shapes and positions on the energy scale were compared with similar results obtained by different techniques.

Total Cross Sections for Inelastic Scattering of Charged Particles by Atoms and Molecules. I. A Sum Rule for the Bethe Cross Sections and Its Application to the Helium Atom

The Bethe cross section for inelastic scattering of fast charged particles by an atom or molecule is shown to obey a sum rule which permits the calculation of the total inelastic scattering cross section from the optical oscillator strength distribution and certain ground-state expectation values. The sum rule can also be utilized as a requirement of compatibility among the individual inelastic scattering cross sections; for example, together with the experimental ionization cross section, it yields the total excitation cross section, which is very poorly known at the present time. An accurate evaluation is made for the helium atom. The resulting total inelastic scattering cross section, ${\ensuremath{\sigma}}_{\mathrm{tot}}=\frac{{z}^{2}}{{\ensuremath{\beta}}^{2}}\left\{1.410\left[\mathrm{ln}\left(\frac{{\ensuremath{\beta}}^{2}}{1\ensuremath{-}{\ensuremath{\beta}}^{2}}\right)\ensuremath{-}{\ensuremath{\beta}}^{2}\right]+15.118\right\}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20} {\mathrm{cm}}^{2},$ is in excellent agreement with experimental data.

Branching ratio of para- and ortho- helium in the electron impact excitation from the ground singlet state

The ratios of differential and total cross sections for electron-impact excitation of singlet- and triplet- states helium atoms from its ground state are studied both in the threshold and in the high energy regions.

Electron impact cross sections for atmospheric species: 1. Helium

The semi-empirical method for determining electron impact cross sections is used to determine sets of collision cross sections for helium. The parameters are evaluated using experimental angular distribution data, total cross section data, high-energy experimental generalized oscillator strengths, and theoretical optical oscillator strengths. The results for total excitation and ionization cross sections are also presented in a simplified empirical form that is more convenient for applications to electron loss calculations. The analysis points to remaining questions of consistency of data that will have to be resolved by future experiments or more refined theoretical calculations.

Remeasurement of the total cross section for excitation of the hydrogen 22S1/2state by electron impact

The cross section for excitation of the 2 2S1/2 state of atomic hydrogen by electron impact has been remeasured in the energy from the threshold (10.2 ev) to 500 ev. The shape of the σ(1s, 2s) cross section curve observed agrees with the earlier measurements. The absolute values of our σ(1s, 2s) cross section disagrees with those of Lichten and Schultz by about a factor of 3. The maximum of the cross section and its total error is σmax(1s, 2s) = (0 11 ± 0 025)πa02; this is somewhat smaller than that of Stebbings et al. which is (0.16 ± 0.01)πa02. Comparison has been made with theoretical results.

Direct and Resonance Rotational Excitation of Molecules by Slow Electrons

The theory of electron scattering by molecules is presented in terms of Feshbach's projection-operator formalism with special attention to the problem of molecular rotational excitation. The absolute orders of magnitude and the energy dependence of the cross section for resonance rotational excitation are calculated for the (${\mathrm{N}}_{2}$, $e$) system. The characteristic multipeak structure for resonance elastic scattering and vibrational excitation is again found for resonance rotational excitation. A comparison of the calculated results with experimental measurements is made for peak positions in the cross section for resonance elastic scattering, which may be considered as a special case of resonance rotational excitation (i.e., $\ensuremath{\Delta}{l}_{0}=0$). Cross sections for simultaneous rotational and vibrational excitation of ${\mathrm{N}}_{2}$ are also calculated. The total partial cross sections for resonance vibrational excitation are then obtained as a sum of all the corresponding partial cross sections with different allowed rotational transitions. The energy dependence of the newly obtained vibrational excitation cross section compares favorably with experimental observations.

Excitation ofn=2States in Helium by Electron Bombardment

Measurement of total cross section for excitation of metastable atoms of helium by electron bombardment

Multiple Coulomb excitation of nuclei

The excitation probabilities and the differential and total excitation cross sections for multiple Coulomb excitation of rotational states are evaluated without use of the approximation of instantaneous excitation.

The shape of the giant dipole resonance for light nuclei

A complete spectrum of the giant dipole resonance is calculated taking into account the finite depth of the single particle potential. The mixing of the one particle-one hole excitations because of residual interactions is treated in the time-dependent Hartree-Fock approximation. If the interaction is approximated by a separable potential a general formula can be derived, which gives the total dipole excitation cross section σ(E) in terms of the simple shell-model cross section σ0(E). Numerical results are given for O16 and C12 by evaluating σ0(E) in a square well potential.

Double Coulomb Excitation with Oxygen Ions

Total cross sections for Coulomb excitation of the first and second excited states of the ground-state rotational bands of eight even-even rare earth nuclei have been measured. Oxygen ions accelerated to energies in the range 14 to 50 MeV in the Wisconsin tandem accelerator produced the nuclear excitations. The transitions from the second excited state (${4}^{+}$) to the first (${2}^{+}$), and from the first to the ground state (${0}^{+}$), were detected by analyzing the emitted internal conversion electrons in a wedge-shaped magnetic beta-ray spectrometer. Cross sections for excitation of the ${2}^{+}$ levels yield $B(E2)$ values in satisfactory agreement with those obtained from lifetime measurements and from inelastic scattering of protons, deuterons, and alpha particles. Cross sections for double $E2$ excitation of the ${4}^{+}$ levels are in qualitative agreement with the multiple Coulomb excitation theory of Alder and Winther. The energies of the ${4}^{+}$ levels are ${\mathrm{Sm}}^{152}$, 366.2 keV; ${\mathrm{Sm}}^{154}$, 267.1 keV; ${\mathrm{Gd}}^{160}$, 248.6 keV; ${\mathrm{Dy}}^{162}$, 266.0 keV; ${\mathrm{Er}}^{170}$, 261.5 keV; ${\mathrm{Yb}}^{176}$, 271.9 keV; ${\mathrm{Hf}}^{180}$, 309.4 keV; and ${\mathrm{W}}^{184}$, 363.4 keV. In all cases the uncertainty is \ifmmode\pm\else\textpm\fi{}2 keV.

Transition Probabilities and Collisional Cross Sections for Ultraviolet Lines.

view Abstract Citations (1) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Transition Probabilities and Collisional Cross Sections for Ultraviolet Lines. Varsavsky, Carlos M. Abstract With the advent of rocket-born and satellite-born spectrographo it is becoming possible to study celestial objects in the hitherto inaccessible ultraviolet. The spectroscopic analysis will require the knowledge of the basic atomic parameters of the lines observed. To satisfy this need, a program for the computation of these parameters has been started at the University of Colorado. The nuclear-charge expansion method of Layzer and Varsavsky has been applied to the computation of the electric dipole matrix elements for many lines of interest. The method is particularly suitable for the treatment of a particular transition along an isoelectronic sequence. In a forthcoming publication we shall present the numerical results obtained for typical allowed transitions in the isoelectronic sequences from helium through chlorine (except neon), together with a detailed account of the mechanics of the method that will enable other investigators to calculate the matrix elements for any other transition of interest. The matrix elements for electric dipole transitions are easily related to optical transition probabilities and total excitation cross sections by electronic impact. In the first case we must make some assumptions about the coupling of the angular momenta. Our tables are based on the L-S coupling scheme. In the case of total cross sections, a simple relationship is obtained if we can make use of the Born approximation, and if the transition is optically allowed; these restrictions reduce, of course, the scope of the tables but allow the treatment of many transitions of interest in the solar corona. An attempt is made to evaluate our method by comparison with the available experimental and theoretical data. In the few cases where such data exist the agreement is satisfactory. Publication: The Astronomical Journal Pub Date: March 1960 DOI: 10.1086/108190 Bibcode: 1960AJ.....65...58V full text sources ADS |

Coulomb Excitation of Rare-Earth Nuclei with Alpha Particles

Using our doubly charged He beam at 6 Mev we have excited most low-lying (rotational) states in the nuclei between $Z=60$ and $Z=73$. Assignments were made with isotopically enriched targets where available. On the whole the predictions of the "strong coupling" approximation of the unified model are strikingly borne out by our observations. All ${2}^{+}$ first-excited states of even-even nuclei lying below \ensuremath{\sim}600 kev were observed, some of which were previously unknown. Two excited states were found in most odd-$A$ nuclei as revealed by direct and/or cascade radiation to the ground state as well as coincidence measurements. The positions of the first two rotational levels agree with the simple interval rule in all established cases within the experimental accuracy. The majority of these states are not found in beta-ray spectroscopy. The reduced electric-quadrupole transition probabilities for all these transitions were measured and found to be some 50 to 100 times greater than those expected for an independent particle. Good agreement was found with some values of these quantities available from direct lifetime observations, giving us confidence in the correctness of both the theoretical expression for the total excitation cross section, and the experimental approach for its determination. A systematic decrease in these transition probabilities is evident in even-even nuclei upon approaching the closed-neutron shell at $N=82$; a corresponding increase in the energy of the ${2}^{+}$ levels reflects the common origin of both phenomena, namely the decrease of the intrinsic deformation of the nuclei. However, the absolute magnitude derived for this deformation depends upon which manifestation is used.Some evidence for a difference in splitting constants $\frac{{\ensuremath{\hbar}}^{2}}{2\mathcal{I}}$ between even-even, even-odd, and odd-even nuclei is found. Within the rather large uncertainties the transition probabilities do not seem to show a corresponding variation.