Final Atomic States Research Articles

Relativistic R-matrix theory of photoionisation: application to neon

The R-matrix theory of atomic photoionisation using the Dirac Hamiltonian is formulated in a similar way to that used in the non-relativistic case. Both the initial atomic bound state and the final atomic continuum state are expanded in terms of R-matrix bases. The method is programmed for a general atomic system and then used to calculate the total photoionisation cross sections of ground-state neon atoms.

R-matrix theory of photoionization. Application to neon and argon

The R-matrix method, which has been used recently to calculate electron-atom and ion collision cross sections and atomic polarizabilities is extended to enable atomic photoionization processes to be studied. Both the initial atomic bound state and the final atomic continuum state are expanded in terms of R-matrix bases. The method is programmed for a general atomic system and then used to calculate the photoionization cross sections of ground state neon and argon atoms leaving the residual ions in their ground or first excited states. Good agreement is obtained with recent experiments using synchrotron radiation both in resonant and non-resonant regions, showing that the method has a wide range of applicability.

Parity violation induced by weak neutral currents in atomic physics. part II

The first part of this paper gives a detailed account of the evaluation of the electric dipole amplitude induced in alkali one-photon S-S transitions, by the parity violating electron-nucleus short range potential Vp.v. associated with the weak neutral currents. Two methods are presented : the first involves an explicit sum over the contributions of the P-states admixed with the S-states and incorporates the best information available on S-P electric dipole amplitudes. The second method, mathematically more elegant, avoids with the help of Green's function techniques any explicit sum over the P states, and, provided that some spin-orbit corrections are neglected, leads to a fairly simple formula involving Coulomb integrals tabulated in the literature and the interpolated quantum defects for S and P waves. The second part is devoted to a description of possible ways to detect parity violation induced in radiative S-S transitions, with a brief discussion of physical processes which could be a source of experimental difficulty. The last section of the paper deals with a theoretical analysis of the influence of a static electric field on the radiative S-S transitions. An evaluation of the induced electric dipole amplitude in the case of cesium indicates that it will compete with the magnetic dipole amplitude for electric fields larger than 10 V/cm. An interference effect between these two amplitudes gives rise to an electronic polarization in the final atomic state proportional to the vector product of the static electric field by the photon momentum which, in a typical case, could be as large as 64 %; the measurement of this interesting and rather peculiar effect will lead to a determination of the sign of the magnetic dipole amplitude. Moreover parity violation could manifest itself by a dependence of this electron polarization on the state of circular polarization of the incident photon.

High-Resolution Measurements of Auger-Electron and Photoelectron Structure in the Secondary-Electron Energy Distributions of Aluminum, Nickel, and Copper

Measurements are reported of selected structure in the secondary-electron energy distributions of evaporated aluminum, nickel, and copper. The specimens were bombarded with 3-keV electrons and the secondary structure was measured with a resolution of 0.1 eV. For each metal, it was hoped to measure Auger transitions involving two relatively narrow inner-shell levels and the valence band in order to obtain information on the valence-band density of states. Attempts were made to observe the Al $K{L}_{2,3}M$ Auger-electron energy distribution expected at about 1470 eV. Structure was, however, observed with a high-energy edge of 1485.9 \ifmmode\pm\else\textpm\fi{} 0.5 eV and a breadth of 8-9 eV. This structure was interpreted as being due to photoemission of valence electrons by internally generated $K\ensuremath{\alpha}$ x rays and was similar to uv photoelectron energy distributions and to the calculated density of states. Inelastic scattering of the photoelectrons obscures the expected Al $K{L}_{2,3}M$ structure. Auger-electron peaks in the ranges 730-800 and 820-865 eV were measured in the secondary-electron energy spectra for nickel and copper, respectively. Structure was observed in the ${L}_{3}{M}_{2,3}{M}_{4,5}$ Auger transition (over a range of about 20 eV) that could be associated in part with the final atomic states and in part with over-all features of the $3d$-band density of states as determined by soft-x-ray-emission spectroscopy and x-ray photoelectron spectroscopy. It is believed that Auger-electron spectra can yield useful data on changes of electronic structure (e.g., by alloying or by compounding) but, in general, density-of-states data cannot be derived from the Auger spectra without detailed knowledge of the final states expected after the Auger transition of interest.

On Some Atomic Effects in the Tritium β-Spectrum

The present work forms part of a detailed investigation of the upper end-point region of the tritium β-spectrum, aiming at improved information on neutrino mass, neutrino degeneracy and on the ft-value of the tritium β-decay, the latter being of interest for judging the applicacability of PCAC for obtaining the modification of the axial-vector matrix element due to pion exchange. By the application of high-efficient β-spectroscopic methods a considerable improvement in basic accuracy of data has been achieved, making it necessary to inspect in a more detailed way than previously done how the interplay between a β-decaying nucleus and its atomic surrounding affects the observed β-spectrum. The β-decay of an atom leads to a distribution in atomic final states; the present work is essentially concerned with the various quantitative consequences of this circumstance for the case of the tritium decay. The distribution in atomic final states is found to imply a mean square energy spread as large as (27 eV)2 in the end-point energy of the spectrum from the tritium atom. This inherent spread in end-point energy is comparable in magnitude with the experimental resolution width now reached in the investigation of the tritium β-spectrum and has to be considered when interpreting the exprimental data with respect to limits on neutrino mass and neutrino degeneracy. The spread in end-point energy found will present a severe inherent difficulty in any effort to improve further the experimental information on these two entities. The distribution in atomic final states also affects the interpretation of the extrapolated end-point energy in terms of the H3-He3 nuclear mass difference and further is found to imply that the proper screening potential to be employed in the Fermi function differs by no less than 50% from the value conventionally assumed. An approximate treatment of the β-decay of the T-H molecule indicates that no drastic change in the atomic effects on the tritium spectrum should result when the tritium atom is not free but chemically bound in some more complex atomic surrounding. Some consequences of a minor residual ambiguity in the magnitude of the atomic effects in this case are commented on.

Use of Electron Scattering Data to Obtain Accurate Born Cross Sections for Atom-Atom and Other Heavy-Particle Collisions. II. Breakup of FastH2+upon Collision with He

In an earlier paper it was suggested that, in Born calculations of total cross sections for heavy-particle collisions, it might be more practical, if accuracies of the order of 10% are acceptable, to obtain the necessary matrix elements by measuring differential electron-atom and electron-molecule cross sections than it would be to calculate the matrix elements from the wave functions of the initial and final atomic or molecular states. In this paper the foregoing idea is explored for ${\mathrm{H}}_{2}^{+}$-He collisions. Experimental electron cross sections are used only for He, theoretical ones being used for ${\mathrm{H}}_{2}^{+}$. Since Lassettre's electron-He measurements do not extend to large enough momentum transfers to allow calculation of the ${\mathrm{H}}_{2}^{+}$-He total cross sections for all transitions of interest, theory is introduced to provide quantitative extrapolations of the experimental data to larger momentum transfers. By this means the extent to which the ${\mathrm{H}}_{2}^{+}$-He total cross sections are determined by the unextrapolated electron-He measurements is examined. At the same time, ranges of momentum transfer are determined, over which the electron-He cross sections need to be measured if they are to be adequate for ${\mathrm{H}}_{2}^{+}$-He total cross-section calculations, without the use of quantitative extrapolation. By a generalization of the ${\mathrm{H}}_{2}^{+}$-He results, analogous ranges are determined for the electron scattering measurements relevant to most heavy-particle collisions of practical interest. The general results show that the most extensive of Lassettre's electron excitation measurements are adequate for heavy-particle collisions in which both collision partners undergo transitions to discrete excited states. Measurements of electron cross sections out to larger momentum transfers than this are required, however, for other combinations of the possible final states of the colliding particles. A table of the upper limits of the required ranges of momentum transfers is given in the hope that it may stimulate additional experimental work. Of particular importance is the measurement of differential electron ionization cross sections out to large values of momentum transfer and energy loss. From the ${\mathrm{H}}_{2}^{+}$-He cross sections, theoretical cross sections are obtained for the breakup of ${\mathrm{H}}_{2}^{+}$ via electronic excitation during collisions with He. These are compared with experiment.

Influence of Atomic Binding on the Recoil Distribution in Electron-Field Pair Production

The recoil-momentum distribution in high-energy triplet production in hydrogen, taking into account the initial atomic binding of the electron, is calculated. The method of Wheeler and Lamb is used, with the final atomic state specified to be an outgoing electron (Coulomb wave). Explicit recoil distributions for various photon energies from 84 to 2000 ${\mathit{mc}}^{2}$ are obtained, and a binding correction to the total triplet cross section of Borsellino is calculated.

Overlap and Exchange Effects in Beta Decay

The change in nuclear charge by one unit in beta decay causes initial and final atomic states to overlap imperfectly. The effect of this imperfect overlap on the shape of allowed electron and positron emission spectra is calculated. The calculated change in the spectrum shape can be simulated by including the average excitation energy of the final atom in the energy balance. The inhibition, due to imperfect atomic overlap, of electron-capture rates, as well as total electron and positron-emission rates, is also determined. In all known cases, imperfect atomic overlap increases beta-decay lifetimes by at most a few percent and usually by an amount less than a few tenths of one percent. Antisymmetrization between decay and bound atomic electrons, in conjunction with the change in nuclear charge, gives rise to exchange effects in electron emission and electron capture. Due to exchange terms, the usual allowed electron spectrum is multiplied by a quantity that is of the order of $1\ensuremath{-}2{Z}^{\ensuremath{-}1}$ for energies less than the binding energy of a $K$ electron in the initial atom. This exchange correction is negligible for higher energies of the emitted continuum electron. A simple approximate formula is derived that predicts the effect of exchange on $L$ to $K$ capture ratios; this formula predicts a 22% increase over the usual theoretical value for the $L$ to $K$ ratio of ${\mathrm{Ar}}^{37}$. The ${\mathrm{Ar}}^{37}$ prediction is in excellent agreement with recent experiments and with a more complicated calculation by Odiot and Daudel. Exchange effects change total electron emission and electron capture rates by at most a few percent.

Electron Capture and Nuclear Matrix Elements ofBe7

BS>The Be/sup 7/ electron capture rate from continuum orbits is calculated as a function of electron temperature and concentration, and the effect on the decay rate of the statistical distribution of electrons, the electron-nucleus Coulomb intetaction, relativistic and nuclear size corrections, the imperfect overlap between Initial and final atomic states, and electron screening in bound decay, is considered. Experimental information on Be/sup 7/ and Li/sup 7/ is analyzed to obtain accurate experimental Gamow-Teller matrix elements for both the ground- and excited-state transitions and compare these matrix elements with the predictions of some simple nuclear models. This comparison supports the conclusion that near the beginning of the 1p nuclear shell L-S coupling is better satisfied than j-j coupling. (auth)

Electron capture by a -particles in hydrogen

A non-resonance charge-transfer reaction for x -particles in hydrogen is investigated by the use of an expansion based on atomic eigenfunctions as in Bates (1958), full account being taken both of the non-orthogonality of the eigenfunctions of the initial and final atomic states and of the effect of distortion. Cross-section for the reaction have been computed for a range of incident particle energies from 50 to 1600 keV. The results indicate that the effect of distortion is considerable up to energies of 800 keV. Comparison is made with the results obtained w hen the effect of the non-orthogonality is ignored (with and without the inclusion of the nuclear-nuclear term in the interaction potential).

Calculation of the 1s-2s Electron Excitation Cross Section of Hydrogen

The zero order partial cross section for the excitation of hydrogen from the (1s) to the (2s) states by electron collision has been calculated by a numerical method. Full allowance has been made for electron exchange and all direct coupling between the initial and final atomic states has been retained. The cross sections obtained are compared with those that have been calculated by more approximate methods. In particular, the cross section near the threshold is found to be considerably smaller than that given by Erskine and Massey using the distorted wave approximation.

The Conversion of Metastable Helium from the Singlet to the Triplet State by Electron Collision

The zero-order partial cross section has been calculated for the conversion of He* (21S) metastable atoms to He* (23S) by superlastic collision with thermal electrons. A numerical method has been used, which retains all the direct-coupling terms between the initial and final atomic states. Full allowance has been made for electron exchange. A cross section of 5 × 10-15 cm2 was obtained at a temperature of 300°K, which is rather too small to account for the experimental value of 3 × 10-14 cm2 observed by Phelps.