Photoabsorption Oscillator Strengths Research Articles

Absolute oscillator strengths for hydrogen sulphide: II. Ionic photofragmentation and photoionization in the valence shell continuum regions (10–60 eV)

Absolute oscillator strengths (cross sections) of ionic photofragmentation and photoionization for hydrogen sulphide in the valence shell continuum regions have been determined using dipole (e,e+ion) coincidence spectroscopy (∼1 eV fwhm) at equivalent photon energies from the first ionization threshold to 60.2 eV. These have been determined from the recently published absolute photoabsorption oscillator strengths [Feng et al., Chem. Phys. 244 (1999) 127] together with the photoionization efficiency and ionic photofragmentation branching ratios obtained from time-of-flight mass spectra reported in the present work. Consideration of the presently reported data together with the photoelectron branching ratios for H 2S and ionization potentials obtained from previously reported photoelectron and dipole (e,2e) spectroscopies yields quantitative information on the breakdown pathways of H 2S following absorption of radiation in the VUV and soft X-ray regions. A new photofragmentation product (H 2 +) and the doubly charged molecular ion (H 2S 2+) from hydrogen sulphide have been found in the present work. Partial photoionization oscillator strengths for production of the four valence shell electronic states of H 2S + have also been derived from the molecular and dissociative partial photoionization oscillator strengths over the entire energy range up to 60.2 eV.

High‐Resolution Oscillator Strength Measurements of the COB \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $^{1}$ \end{document} \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $\Sigma ^{+}$ \end{document} –X \documentclass{aastex}

Large discrepancies in the published photoabsorption oscillator strengths of the vacuum-ultraviolet (VUV) bands of CO hamper the interpretation of VUV astronomical observations. We report new oscillator strength measurements of the (0, 0) and (1, 0) bands of the CO B1Σ+-X1Σ+ electronic system determined from high-resolution (resolving power ≈ 750,000) absorption spectra recorded with a tunable VUV laser system. The instrumental bandwidth (~ 0.14 cm-1 FWHM) was significantly less than the widths of the Doppler-broadened CO lines (~ 0.20 cm-1 FWHM). The B(0)-X(0) and B(1)-X(0) band oscillator strengths, derived from measurements of the photoabsorption cross sections of 36 individual rotational lines, are (6.5 ± 0.6) × 10-3 and (1.1 ± 0.1) × 10-3, respectively. Our results are compared with other recent laboratory measurements and with ab initio calculations.

Absolute oscillator strengths for hydrogen sulphide:: I. Photoabsorption in the valence-shell and the S 2p and 2s inner-shell regions (4–260 eV)

Absolute photoabsorption oscillator strengths (cross-sections) for the valence-shell discrete and continuum regions of hydrogen sulphide from 4 to 30 eV have been measured using high-resolution (∼0.05 eV fwhm) dipole (e, e) spectroscopy. A wide-range spectrum, covering both the valence shell and the S 2p and 2s inner shells, has also been obtained from 5 to 260 eV at low resolution (∼1 eV fwhm), and this has been used to determine the absolute oscillator strength scale using valence-shell TRK (i.e., S(0)) sum-rule normalization. The presently reported high- and low-resolution absolute photoabsorption oscillator strengths are compared with previously published data from direct photoabsorption measurements. In addition, a dipole sum-rule analysis on the present photoabsorption data has been performed. The static dipole polarizability for hydrogen sulphide determined from the S(−2) sum-rule using the presently reported oscillator strengths is compared with previously reported polarizability values. Other dipole sums S( u) ( u=−1, −3 to −6, −8, −10) and logarithmic dipole sums L( u) ( u=−1 to −6) are also determined from the presently reported absolute photoabsorption differential oscillator strengths.

Absolute photoabsorption oscillator strengths by electron energy loss methods: the valence and S 2p and 2s inner shells of sulphur dioxide in the discrete and continuum regions (3.5–260 eV)

Absolute photoabsorption oscillator strengths (cross-sections) for the valence shell discrete and continuum regions of sulphur dioxide from 3.5 to 51 eV have been measured using high resolution (∼0.05 eV FWHM) dipole ( e, e) spectroscopy. A wide-range spectrum, covering both the valence shell and the S 2p and 2s inner shells, has also been obtained from 5 to 260 eV at low resolution (∼1 eV FWHM), and this has been used to determine the absolute oscillator strength scale using valence shell TRK (i.e., S(0)) sum-rule normalization. The present measurements have been undertaken in order to investigate the recently discovered significant quantitative errors in our previously published low resolution dipole ( e, e) work on sulphur dioxide (Cooper et al., Chem. Phys. 150 (1991) 237; 150 (1991) 251). These earlier measurements were also in poor agreement with other previously published direct photoabsorption measurements. We now report new absolute photoabsorption oscillator strengths using both high and low resolution dipole ( e, e) spectroscopies. These new measurements cover a wider energy range and are much more consistent with the previously published direct photoabsorption measurements. The accuracy of our new measurements is confirmed by an S(−2) dipole sum-rule analysis which gives a static dipole polarizability for sulphur dioxide in excellent agreement (within 3.5%) with previously reported polarizability values. Other dipole sums S( u) ( u=−1,−3 to −6,−8,−10) and logarithmic dipole sums L( u) ( u=−1 to −6) are also determined from the presently reported absolute oscillator strength distributions.

Recurrence spectroscopy of atoms in electric fields: Scattering in the presence of bifurcations

Closed-orbit theory gives a semiclassical formula for the photoabsorption oscillator strength density of atoms in external fields. The oscillator strength can be calculated from the properties of the classical orbits of the highly excited electron moving in the combined Coulomb and electric field. The deviation from the Coulomb potential due to an alkali-metal atom core causes scattering between the classical orbits when a closed orbit returns to the origin. Bifurcations of closed orbits happen when a focus moves through the origin and we present a theory that describes the scattering of the electron waves by the alkali-metal core for atoms in external electric fields in the presence of a bifurcation. @S1050-2947~98!03211-9# Highly excited electronic state atoms in external fields have become good testing grounds for the connection between quantum and semiclassical mechanics. They are amenable to both theoretical calculations and experimental measurement @1‐5#. Closed-orbit theory is a semiclassical theory which predicts the positions and amplitudes of peaks in the Fourier transform of the photoabsorption spectrum: The peaks are at the periods of classical orbits that go out and return to the nucleus; the amplitude depends on the divergence rate of the neighbors of the orbits @6,7#. Closed-orbit theory was developed for hydrogen in a magnetic field by Du and Delos @7#. It was applied to alkali-metal atoms in an electric field by Gao and Delos @8#. The general picture of closed-orbit theory, in which waves excited by the laser go out and are turned around in the external fields, was simple. There were, however, the usual problems that occur in any primitive semiclassical formula. The semiclassical approximation for the returning wave near the core could, and would, become infinite as a focus or caustic passed through the origin. These failures occur at the bifurcation energies where closed orbits are created or destroyed as the parameters controlling the classical dynamics vary @9‐12#. Uniform approximations to semiclassical wave functions which repair these failures have been developed in the chemical physics and mathematical literature @13‐15# and have become better known in atomic physics @16‐19#. The nonhydrogenic core of an alkali-metal atom can be treated semiclassically by either propagating trajectories through a model core potential @20# or by a scattering expansion in terms of hydrogenic closed orbits that are coupled together by the core @21#. The closed-orbit approach in Ref. @21# works well for highly excited states where the effective size of is small and one can partially avoid the neighborhood of bifurcations. It is an open question how to apply this theory near a bifurcation. We present a closed-orbit theory for scattering in alkali-metal atoms in the presence of bifurcations that occur in static electric fields. The theory can be generalized to handle other types of bifurcations in other static fields.

Angular distributions for photodissociation of O2 in the Herzberg continuum

Photodissociation in the Herzberg continuum of molecular oxygen has been studied at 236, 226 and 204 nm. Using ion-imaging and monitoring of O(3Pj), j=0, 1, and 2 product-atom angular distributions, the amount of parallel character of the transition was measured. In order to interpret these data, analyses of the photoabsorption oscillator strengths and the parallel-perpendicular nature of the Herzberg I, II and III bands, and extrapolation of these properties into the Herzberg-continuum region have been performed. Our measured fine-structure-averaged angular distributions are found to be consistent with this photoabsorption model. In addition, the dynamics of the dissociation process is discussed, based on the O-atom fine-structure distributions.

Absolute oscillator strengths for the valence and inner (P 2p,2s) shell photoabsorption, photoionization, and ionic photofragmentation of PF 3

Absolute oscillator strengths (cross-sections) for the photoabsorption of phosphorus pentafluoride (PF 5) have been measured for the first time in the valence and phosphorus 2p discrete regions using high-resolution (0.0–0.1 eV fwhm), dipole ( e, e) spectroscopy. Long-range data (10–300 eV) have also been obtained at lower resolution (1 eV fwhm), from which the absolute oscillator strength scale has been determined using the valence-shell Thomas-Reiche-Kuhn sum-rule. The accuracy of the present measurement has been tested using the S(−2) sum rule normalization. Evaluation of the S(−2) sum using the presently reported absolute photoabsorption oscillator strength data gives a dipole polarizabilit for PF 5 in good agreement with the experimental value. The photoionization efficiencies, photoion branching ratios, and absolute partial oscillator strengths for molecular and dissociative photoionization have also been determined for PF 5 by dipole ( e, e+ion) coincidence spectroscopy from the first ionization threshold up to and above the phosphorus 2p edge.

Quantitative studies of the photoabsorption and photoionization of PCl 3 in the valence and inner (P 2p,2s; Cl 2p,2s) shell regions

Electronic excitation spectra and absolute photoabsorption oscillator strengths (cross sections) have been measured in the vacuum ultraviolet and soft X-ray energy regions for the valence and inner (P 2p,2s; Cl 2p,2s) shell photoabsorption of phosphorus trichloride (PCl 3) from 5 to 350 eV (1 eV fwhm) using dipole (e,e) spectroscopy. The discrete structures in the valence region and in the vicinity of the phosphorus 2p and chlorine 2p inner shells have also been studied at higher resolution (0.05–0.1 eV fwhm). Evaluation of the S(−2) sum using the presently reported absolute photoabsorption oscillator strength data gives a dipole polarizability for PCl 3 within 1% of the experimental value. The photoionization efficiency, ionic photofragmentation branching ratios, and absolute partial oscillator strengths for molecular and dissociative photoionization have also been determined for PCl 3 by dipole (e,e+ion) coincidence spectroscopy from the first ionization threshold up to the chlorine 2s edge.

Photoabsorption and photoionization of the valence and inner (P 2p, 2s) shells of PF 3: Absolute oscillator strengths and dipole-induced breakdown pathways

Absolute photoabsorption oscillator strengths (cross sections) for the valence and inner (P 2p, 2s) shells of phosphorus trifluoride (PF 3) have been measured using dipole ( e, e) spectroscopy in the 5–300 eV equivalent photon energy region (1 eV FWHM). The discrete spectral structures in the valence region and in the vicinity of the phosphorus 2p inner shell have also been studied at higher resolution (0.05 and 0.1 eV FWHM, respectively). Using these data and the S(−2) sum rule, the electric-dipole polarizability for PF 3 has been determined for the first time. In addition, dipole ( e, e+ion) coincidence spectroscopy has been used to obtain the photoionization efficiencies, photoion branching ratios, and absolute partial oscillator strengths for the molecular and dissociative photoionization channels of PF 3 from the first ionization threshold up to and above the phosphorus L shell edges to 175 eV. A consideration of the photoabsorption and photoionization measurement together with thermochemical data and results from previously published photoelectron branching ratios and photoelectron-photoion coincidence (PEPICO) studies provides information on the dipole-induced breakdown pathways of PF 3 in the photon region below 100 eV.

Ionic photofragmentation (11.5–160 eV) and PIPICO spectroscopy (40–130 eV) of BrCN in the valence shell and bromine 3d regions

Molecular and dissociative photoionization branching ratios and photofragment appearance potentials of BrCN have been determined using dipole (e, e + ion) spectroscopy at equivalent photon energies from the first ionization threshold up to 160 eV. Absolute partial photoionization oscillator strengths (cross sections) for the molecular and dissociative photoions have been obtained from the triple product of the photofragment branching ratio, the photoionization efficiency, and the previously reported absolute photoabsorption oscillator strength [Olney et al., Chem. Phys. 201 (1995) 505]. Information on the Coulomb explosion decay channels of doubly and triply charged molecular ions has been obtained from photoion-photoion coincidence (PIPICO) spectroscopy using synchrotron radiation as a light source in the 40–130 eV photon energy range. While stable doubly charged ions are formed in both the valence and the Br 3d regions no stable triply charged ions are observed. However, the PIPICO measurements detect time correlated singly and doubly charged fragment species resulting from Coulomb explosion of triply charged ions which are first formed at the Br 3d excitation threshold and throughout the ionization continuum by triple autoionization and double Auger type processes. The experimental results provide information on the dipole induced breakdown pathways resulting from valence shell and Br 3d ionization processes in BrCN.

Absolute photoabsorption of BrCN in the valence shell and the bromine M, carbon K and nitrogen K shell regions (5–450 eV)

Absolute oscillator strengths (cross sections) for photoabsorption by BrCN have been measured throughout the VUV and soft X-ray regions (5–451 eV) using dipole (e,e) spectroscopy at both high (0.05–0.10 eV fwhm) and low (1 eV fwhm) resolution. Measurement of the valence shell oscillator strengths are compared with the very limited direct optical data in the literature. For the sharper (Rydberg) bands and the presently determined dipole (e,e) oscillator strengths are considerably larger indicating that significant line saturation (bandwidth) errors are occurring in the previously published direct optical (Beer-Lambert law) measurements. The first absolute measurements and inner shell photoabsorption spectra are reported in the carbon K (1s), nitrogen K (1s) and bromine M (3d, 3p and 3s) regions of BrCN. The carbon and nitrogen 1s spectra show vibrational resolution in the respective, strongly resonance enhanced, 3π(π∗) ← 1s bands. The Br 3d spectrum of BrCN shows clear evidence of ligand field splittings in the 3d52(δ, π and gS) and 3d32(δ and π) excitations to the 5p Rydberg states. The first estimates of the inner shell ionization potentials for the C 1s and N 1s core orbitals of BrCN are obtained from density functional theory calculations. The Br 3d52,32, ligand field inner shell ionization energies are estimated using the 5p←Br 3d excitation energies and considerations of the (transferable) 5p Rydberg term values from the C 1s, N 1s and valence shell spectra.

Absolute UV and soft X-ray photoabsorption of acetylene by high resolution dipole (e,e) spectroscopy

Abstract Absolute photoabsorption oscillator strengths (cross sections) for the discrete electronic transitions of acetylene from 5.5 to 11.2 eV have been measured using high resolution ≈0.05 eV FWHM) dipole (e,e) spectroscopy. This experimental resolution enabled absolute oscillator strengths for most of the individual vibronic transitions to be obtained. A broader range spectrum, obtained from 5.5 to 200 eV at a resolution of ≈1 eV FWHM, was used to establish to absolute oscillator strength scale via TRK sum-rule normalization. The absolute oscillator strengths for the Rydberg transitions are in many cases significantly higher than previously reported values obtained using direct optical photoabsorption methods.

Absolute oscillator strengths for the photoabsorption of silane in the valence and Si 2p and 2s regions (7.5–350 eV)

Abstract Absolute photoabsorption oscillator strengths (cross sections) for the valence and Si 2p discrete regions of silane have been measured using high resolution (∼ 0.05–0.1 eV fwhm) dipole (e, e) spectroscopy. Long range (7.5–350 eV) lower resolution data (1 eV fwhm) have also been obtained, from which the absolute oscillator strength scale has been determined using TRK (i.e. S (0)) sum-rule normalization. The accuracy of the presently reported measurements has been tested using the S (−2) sum-rule: Evaluation of the S (−2) sum using the presently reported data gives a dipole polarizability for silane within 0.2% of the experimental value. The present valence shell measurements were undertaken in order to investigate the differences between earlier low resolution dipole (e, e) work (Cooper et al., Chem. Phys. 140 (1990) 133) and subsequent valence shell synchrotron radiation photoabsorption measurements reported by Kameta et al. (J. Chem. Phys. 95 (1991) 1456). The presently reported high and low resolution absolute phtoabsorption oscillator strengths are much more consistent with the direct photoabsorption measurements than the earlier dipole (e, e) work (within ∼ 15%). The resolution of the present high resolution data is sufficient to allow absolute photoabsorption oscillator strengths to be determined for many of the individual electronic transitions in the Si 2p discrete spectrum.

Absolute UV and Soft X-ray photoabsorption of ethylene by high resolution dipole (e, e) spectroscopy

Abstract Absolute photoabsorption oscillator strengths (cross sections) for the valence shell discrete region of ethylene from 6 to 10.7 eV have been measured using high resolution (∼ 0.05 eV fwhm) dipole (e, e) spectroscopy. A long-range spectrum was also obtained from 6 to 200 eV at low resolution ( ∼ 1 eV fwhm), from which the absolute oscillator strength scale was obtained via valence-shell TRK sum-rule normalization. The presently determined absolute oscillator strengths were found to be more consistent with the (exact) theoretical value of the total S (0) TRK sum-rule than previously published data. In addition, the electric dipole polarizability of ethylene determined from the total S (−2) sum-rule incorporating the presently reported oscillator strengths is in very good agreement with experimentally measured polarizability values.

Quantitative studies of the photoabsorption, photoionization, and ionic photofragmentation of methyl fluoride at VUV and soft X-ray energies (7–250 eV) using dipole electron scattering and synchrotron radiation

Absolute oscillator strengths (cross sections) for the valence shell photoabsorption of CH3F have been measured using low resolution (1 eV fwhm) dipole (e, e) spectroscopy in the equivalent photon energy range from 7 to 250 eV. In addition, high resolution (0.048 eV fwhm) dipole (e, e) spectroscopy has been used to study the valence shell region from 8 to 50 eV in more detail. The photoionization efficiency, ionic photofragmentation branching ratios and absolute partial oscillator strengths for molecular and dissociative photoionization have been determined for CH3F by dipole (e, e+ion) spectroscopy from the first ionization threshold to 100 eV. The major pathways of the ionic dipole induced breakdown scheme are predicted from these results. The electronic ion state branching ratios for the photoionization of CH3F were determined from photoelectron spectra recorded using monochromated synchrotron radiation at photon energies from 21 to 72 eV. The partial photoionization oscillator strengths for production of the electronic states of CH3F+ derived from the PES electronic ion state branching ratios and the present low resolution photoabsorption measurements are compared with estimates derived from the dipole induced breakdown scheme and the molecular and dissociative photoionization partial oscillator strengths. The two estimates of electronic state partial photoionization oscillator strengths are in good agreement only at higher photon energies. The differences at lower photon energies arise from errors in the photoelectron branching ratios due to the difficulties of assessing the steeply rising non-spectral background in the photoelectron spectra, particularly in the (1a1)−1 many-body region. Suggestions are made for improving the quantitative accuracy of PES measurements.

An evaluation of atomic and molecular mixture rules and group additivity concepts for the estimation of radiation absorption by long-chained, saturated hydrocarbons at vacuum UV and soft X-ray energies

The feasibility of using atomic and molecular mixture rules as well as group additivity concepts for predicting valence shell photoabsorption oscillator strengths (cross sections) for long-chained alkane molecules has been investigated over a wide energy range from 18 to 220 eV. The predictions are discussed with reference to recently reported experimental measurements (Chem. Phys. 173 (1993) 209) for normal alkanes, C n H 2 n+2 ( n=1–8). Atomic mixture rules based on either theoretical or experimental atomic oscillator strength sums are found to be unsatisfactory, giving very large errors at most photon energies. A wide range of molecular mixture rules based on linear combinations of measured oscillator strength values for small ‘component’ alkane molecules and molecular hydrogen have also been evaluated. Although good agreement with experiment is obtained with some linear combinations, many others result in substantial errors. Molecular mixture rules constructed using oscillator strength for larger component alkanes generally give better estimates of the experimentally measured data; however, since no other a priori physical or chemical reasons can be advanced for any particular choice of molecular mixture rule, this procedure is unsatisfactory for general application. In contrast, a group additivity procedure based on oscillator strength estimates for the methylene (CH 2) and methyl (CH 3) alkane group fragments, derived entirely from the photoabsorption measurements for lower alkanes, provides excellent agreement with the measured oscillator strengths for C 8H 18 over the entire energy range studied (18–220 eV). The absolute photoabsorption group oscillator strengths derived for the CH 2 and CH 3 fragments should be applicable to assessing the contributions from saturated hydrocarbon groupings to vacuum UV and soft X-ray absorption in larger chemical and biochemical systems.

Valence shell absolute photoabsorption oscillator strengths, constrained dipole oscillator strength distributions, and dipole properties for CH3NH2, (CH3)2NH, and (CH3)3N

Dipole (e,e) spectroscopy has been used to measure the absolute photoabsorption oscillator strengths (cross sections) for the valence shells of CH3NH2, (CH3)2NH, and (CH3)3N from the photoabsorption threshold to 250 eV at low resolution (∼1 eV fwhm) and to 31 eV at high resolution (0.048 eV fwhm). The observed peaks in the photoabsorption spectra of the methylamines have been assigned to transitions to Rydberg orbital upper states. Our measured photoabsorption data, augmented by mixture rule estimates for high photon energies, have been used in conjunction with Thomas–Reiche–Kuhn sum rule and molar refractivity constraints, to construct constrained dipole oscillator strength distributions for each of the methylamines. From these constrained dipole oscillator strength distributions a wide range of related dipole properties have been calculated for each of the methylamines, and in most cases the results so obtained represent the first (reliable) determination of these properties.

Discrete and continuum photoabsorption oscillator strengths for the electronic spectrum of nitrous oxide (5.5–203 eV)

The electronic excitation spectrum and the associated absolute optical oscillator strengths for the photoabsorption of nitrous oxide in the energy region 7.4–203 eV have been obtained using low-resolution dipole (e, e) spectroscopy and TRK sum-rule normalization. High-resolution dipole (e, e) spectroscopy (0.048 fwhm) has been used to measure the absolute photoabsorption oscillator strengths in the valence shell discrete region in the energy region 5.5–30 eV. The present results are compared with previously reported experimental and theoretical data.

The electronic spectrum of carbon dioxide. Discrete and continuum photoabsorption oscillator strengths (6–203 eV)

The recently developed high resolution dipole (e,e) method, which is free of Beer—Lambert law “line saturation” errors, has been used to determine absolute photoabsorption oscillator strengths for the discrete electronic excitation of carbon dioxide in the energy region 6–30 eV. Low resolution dipole (e,e) measurements (1 eV fwhm) have also been made in the equivalent photon energy range 8.5–203 eV. The absolute scale of the present measurements was obtained by TRK sum-rule normalization.

The electronic spectrum of water in the discrete and continuum regions. Absolute optical oscillator strengths for photoabsorption (6–200 eV)

The electronic excitation spectrum and the associated absolute optical oscillator strengths for the photoabsorption of water have been determined in the energy region 6–200 eV using low resolution dipole (e, e) spectroscopy and TRK sum-rule normalization. In addition, detailed studies of the absolute photoabsorption oscillator strengths for the valence shell discrete electronic transitions of water have been made using high resolution dipole (e, e) spectroscopy (0.048 eV fwhm), from the first excitation threshold up to 30 eV. The present results are free of “line saturation” (i.e. bandwidth/linewidth interaction) effects which can lead to serious errors when absolute intensity measurements are made using conventional Beer-Lambert law photoabsorption methods.