Atomic Photoabsorption Cross Sections Research Articles

Photon detection from stopped 87Rb atoms injected into superfluid helium for a new nuclear laser spectroscopy of rare radioisotopes

We have been developing a new nuclear laser spectroscopic method "OROCHI" for determining spins and moments of exotic RIs. This is a method based on the combination of superfluid helium as a stopper of radioactive isotope (RI) beam and in-situ laser spectroscopy of RI atoms. This unique method will enable us to measure nuclear spins and electromagnetic moments of extremely low yield RI (less than 1 particle per second). To confirm the feasibility of this method for rare radioisotopes, we carried out the first on-line experiment with a 87Rb beam, aiming at evaluating the minimum beam intensity required for the measurement. The LIF (Laser Induced Fluorescence) photons from the 87Rb atoms stopped in He II are successfully observed in the on-line experiment. The obtained LIF intensity is nearly consistent with the intensity calculated from the photo-absorption cross section of atoms in He II.

Transmission Measurement Using Extreme Ultraviolet Light for the Development of Extreme Ultraviolet Resist

A transmission measurement system with high accuracy was installed in the BL10 beamline of the NewSUBARU synchrotron facility. We measured the transmittance of a resist using extreme ultraviolet (EUV) light, and evaluated the relation between the E0 sensitivity and the transmittance of the resist under EUV exposure. The measured transmittance was almost the same as the calculated value obtained using from the table of Henke atomic scattering factors. Furthermore, it is confirmed that there is a correlation between the photoabsorption coefficient of the anion of PAG and the E0 sensitivity under EUV exposure at a wavelength of 13.5 nm. Thus, increasing the atomic photoabsorption cross section of the anion of PAG is effective in increasing the sensitivity of the chemically amplified resist in EUVL.

Macroscopic local-field effects on photoabsorption processes

The influence of the local-field effect on the photoabsorption cross sections of the atoms which are embedded in the macroscopic medium has been studied by a set of alternative expressions in detail. Some notes on the validity of some different local-field models used to study the photoabsorption cross sections of atoms in condensed matter have been given for the first time. Our results indicate that the local fields can have substantial and different influence on the photoabsorption cross section of atoms in condensed matter for different models. Clausius–Mossotti model and Onsager model have proved to be more reasonable to describe the local field in gas, liquid, or even some simple solid, while Glauber–Lewenstein model probably is wrong in these conditions except for the ideal gas. A procedure which can avoid the errors introduced by Kramers–Kronig transformation has been implemented in this work. This procedure can guarantee that the theoretical studies on the local field effects will not be influenced by the integral instability of the Kramers–Kronig transformation.

Theory of x-ray absorption by laser-dressed atoms

An ab initio theory is devised for the x-ray photoabsorption cross section of atoms in the field of a moderately intense optical laser (800nm, 10^13 W/cm^2). The laser dresses the core-excited atomic states, which introduces a dependence of the cross section on the angle between the polarization vectors of the two linearly polarized radiation sources. We use the Hartree-Fock-Slater approximation to describe the atomic many-particle problem in conjunction with a nonrelativistic quantum-electrodynamic approach to treat the photon-electron interaction. The continuum wave functions of ejected electrons are treated with a complex absorbing potential that is derived from smooth exterior complex scaling. The solution to the two-color (x-ray plus laser) problem is discussed in terms of a direct diagonalization of the complex symmetric matrix representation of the Hamiltonian. Alternative treatments with time-independent and time-dependent non-Hermitian perturbation theories are presented that exploit the weak interaction strength between x rays and atoms. We apply the theory to study the photoabsorption cross section of krypton atoms near the K edge. A pronounced modification of the cross section is found in the presence of the optical laser.

Semiclassical S-matrix theory for atomic fragmentation

A semiclassical scattering approach is developed which can handle long-range (Coulomb) forces without the knowledge of the asymptotic wave function for multiple charged fragments in the continuum. The classical cross section for potential and inelastic scattering including fragmentation (ionization) is derived from first principles in a form which allows for a simple extension to semiclassical scattering amplitudes as a sum over classical orbits and their associated actions. The object of primary importance is the classical deflection function which can show regular and chaotic behavior. Applications to electron impact ionization of hydrogen and electron–atom scattering in general are discussed in a reduced phase space, motivated by partial fixed points of the respective scattering systems. Special emphasis, also in connection with chaotic scattering, is put on threshold ionization. Finally, motivated by the reflection principle for molecules, a semiclassical hybrid approach is introduced for photoabsorption cross sections of atoms where the time-dependent propagator is approximated semiclassically in a short-time limit with the Baker–Hausdorff formula. Applications to one- and two-electron atoms are followed by a presentation of double photoionization of helium, treated in combination with the semiclassical S-matrix for scattering.

X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92

The primary interactions of low-energy x-rays within condensed matter, viz. photoabsorption and coherent scattering, have been described for photon energies outside the absorption threshold regions by using atomic scattering factors. The atomic scattering factors may be accurately determined from the atomic photoabsorption cross sections using modified Kramers-Kronig dispersion relations. From a synthesis of the currently available experimental data and recent theoretical calculations for photoabsorption, the angle-independent, forward-scattering components of the atomic scattering factors have been thus semiempirically determined and tabulated here for 92 elements and for the region 50-30,000 eV. Atomic scattering factors for all angles of coherent scattering and at the higher photon energies are obtained from these tabulated forward-scattering values by adding a simple angle-dependent form-factor correction. The incoherent scattering contributions that become significant for the light elements at the higher photon energies are similarly determined. The basic x-ray interaction relations that are used in applied x-ray physics are presented here in terms of the atomic scattering factors. The bulk optical constants are also related to the atomic scattering factors. These atomic and optical relations are applied to the detailed calculation of the reflectivity characteristics of a series of practical x-ray mirror, multilayer, and crystal monochromators. Comparisons of the results of this semiempirical, "atomic-like" description of x-ray interactions for the low-energy region with those of experiment and ab initio theory are presented.

Closed-orbit theory of oscillations in atomic photoabsorption cross sections in a strong electric field. I. Comparison between theory and experiments on hydrogen and sodium above threshold.

Using a simple analytic formula from closed-orbit theory, we calculate photoabsorption cross sections of hydrogen and sodium in a strong electric field. The theoretical spectra show good agreement with experimental results. A scaled variable measurement is also suggested.

Closed-orbit theory of oscillations in atomic photoabsorption cross sections in a strong electric field. II. Derivation of formulas.

A formula for photoabsorption cross sections of hydrogen and alkali-metal atoms in a static electric field is derived, based on the closed-orbit theory previously used to study hydrogen in a magnetic field. Electric fields are simpler than magnetic fields, because the classical motion is regular and closed orbits can be enumerated. In alkali metals the core modifies the relevant dipole matrix elements, and it produces additional phase shifts.

Nature of the dips in the atomic photoabsorption cross section.

It is shown that the appearance of the plateau on the atomic electron density n(r) gives rise to the dip in the photoabsorption cross section of a many-electron atom. The dip at frequency \ensuremath{\omega} is formed if (a) there is a point of plasma resonance ${\mathit{r}}_{0}$ where the local plasma frequency inside the atom is equal to \ensuremath{\omega} or (b) the derivative of electron density at this point equals zero: n'(${\mathit{r}}_{0}$)=0. Another result of the appearance of the plateau on electron-density distribution is the effect of complete screening of the external electric field inside the atom behind the resonance point ${\mathit{r}}_{0}$.

Charge oscillations and photoabsorption of the Thomas-Fermi-Dirac-Weizs�cker atom

Following the work of Bloch and Ball et al. the theory of linear response of a hydrodynamic Thomas-Fermi model is extended to a general density dependent energy functional. The theory is applied to the Thomas-Fermi-Dirac-Weizsacker atom. Normal mode solutions and the atomic photoabsorption cross section are calculated.

Calculation of Photoabsorption Cross Section of an Extended Thomas-Fermi Atom

Bloch's hydrodynamic approximation for treating the charge oscillation of an atom is applied to the Thomas-Fermi atom extended by introducing a modified Weizsäcker correction. Normal mode solutions of the oscillation are obtained and the atomic photoabsorption cross section and the logarithmic mean excitation energy are calculated. The differences of the results from those of the simple Thomas-Fermi atom are as follows: (1) The eigenfrequencies of the normal modes consist of one discrete value ω D (<ω C ) and continuous values between ω C and ∞, where ω C is a definite frequency characteristic for an individual atom. (2) The photoabsorption cross section has also a discrete value corresponding to the frequency ω D and continuous values for frequencies larger than ω C . (3) The logarithmic mean excitation energy becomes larger.

Photoabsorption and Charge Oscillation of the Thomas—Fermi Atom

The complications of calculating the photoabsorption cross section of atoms for frequencies in the far ultraviolet and soft x-ray regions motivate an analysis of this problem on the basis of the Bloch semiclassical model of hydrodynamic charge oscillation in the neutral Thomas-Fermi atom. The hydrodynamic modes of oscillation of the neutral Thomas-Fermi atom have a continuous frequency spectrum. The resulting photoabsorption cross section is a continuous function of frequency which scales with atomic number $Z$ and in this sense is a universal cross section, approximately applicable to all heavy atoms. Numerical solutions of the normal mode functions of dipole charge oscillation are used to calculate the photoabsorption cross section in a range of photon energies $0.816 \mathrm{Z}\mathrm{eV}l\ensuremath{\Elzxh}\ensuremath{\omega}l272 \mathrm{Z}\mathrm{eV}$, the range where the model is expected to be most realistic. In this range the semiclassical hydrodynamic cross section agrees with experimental data for the noble gases as well as could be expected for a cross section applicable to all atoms. The model cross section, extended to zero and infinite frequencies by analytical calculation, checks the sum rule to within 2%; but gives a value $I=4.95$ $Z$ eV for the logarithmic mean excitation energy of stopping power formulas. The unrealistically low value of $\frac{I}{Z}$ results because the Thomas-Fermi atom exaggerates the number of electrons which absorb at low frequencies. Use of the hydrodynamic cross section in the approximate range of validity of this model $\ensuremath{\Elzxh}\ensuremath{\omega}g0.816$ Z eV gives $I=12.4{e}^{\ensuremath{\beta}}$ Z eV, where $\ensuremath{\beta}$ depends upon the oscillator strength below $\ensuremath{\Elzxh}\ensuremath{\omega}=0.816$ Z eV which cannot be satisfactorily determined from the Bloch model. Used within its limitations the Bloch model of hydrodynamic oscillation in the statistical atom provides a useful method of estimating photoabsorption cross sections and could possibly be applied to other atomic processes.

Collective effects in the photoabsorption cross sections of atoms and molecules

The linear response of atoms and molecules to an external field is formulated in a self-consistent manner. The discussion centers on the collective effects in the spectral properties at frequencies higher than the first ionization edge, and their experimental manifestations. Photoabsorption and the photoelectric effect are shown to have distinct cross sections which happen to coincide only in certain approximations such as in the single-particle model. The line profile of autoionization levels is derived and compared with recent experimental observations.

Atomic photoabsorption cross sections

Results are reported of extensive calculations on atomic photoabsorption cross sections by the statistical method in various approximations, based on developments presented in previous papers. A closely spaced family of photoabsorption cross sections emerges which, on scaling with regard to atomic numbers, represents in an unified manner the absorption cross sections of all atoms over wide frequency ranges. A limited search into detailed spectral properties of atoms reveals everywhere some, and in certain instances strong evidence for collective effects in the response of atoms to external disturbances.