Excited-state Cross Sections Research Articles

Femtosecond to nanosecond dynamics in fullerenes: Implications for excitedstate optical nonlinearities

We compared detailed dynamics of the excited-state absorption for C60 in solution, thin films, and entrapped in an inorganic sol-gel glass matrix. Our results demonstrate that the microscopic morphology of the C60 molecules plays a crucial role in determining the relaxation dynamics. This is a key factor for applications in optical limiting for nanosecond pulses using reverse saturable absorption. We find that the dynamics of our C60-glass composites occur on long (ns) timescales, comparable to those in solution; thin film samples, by contrast, show rapid decay (<20 picoseconds). These results demonstrate that C60-sol-gel glass composites contain C60 in a molecular dispersion, and are suitable candidates for solid-state optical limiting. Multispectral analysis of the decay dynamics in solution allows accurate determination of both the intersystem crossing time (600±100ps) and the relative strengths of the singlet and triplet excited-state cross sections as a function of wavelength from 450–950 nm. The triplet excited-state cross section is greater than that for the singlet excited-state over the range from 620–810 nm.

Optical limiting in short chain basket handle porphyrins

Optical limiting under picosecond excitation at 532 nm is reported in a set of recently synthesized basket handle porphyrins. The effect is attributed to reverse saturable absorption. Theoretical simulations using a rate equation model satisfactorily reproduce the measurements and establish values for excited state cross-sections and lifetimes.

6Li-vector+12C inelastic scattering at 30 and 50 MeV.

A complete set of analyzing powers (AP`s), {ital iT}{sub 11}, {ital T}{sub 20}, {ital T}{sub 21}, and {ital T}{sub 22}, for 50 MeV {sup 12}C({sup 6}Li(vector),{sup 6}Li) elastic scattering and inelastic scattering to the {sup 12}C(2{sup +}, 4.44 MeV), {sup 12}C(0{sup +}, 7.65 MeV), and {sup 12}C(3{sup {minus}}, 9.64 MeV) states over the center-of-mass (c.m.) angular range 10{degree}{endash}115{degree} is reported. In addition, cross sections for the excited states 3{sup +}(2.18 MeV), 2{sup +}(4.31 MeV), and 1{sup +}(5.65 MeV) of {sup 6}Li were measured by using the inverse-kinematics reaction {sup 6}Li({sup 12}C,{sup 12}C) at 100 MeV. A combined analysis of the new 50 MeV data and previous 30 MeV data has been carried out using the coupled-channels (CC) code FRESCO. The CC calculations use an optical potential with double-folded (DF) real central, Woods-Saxon imaginary central, and Thomas real spin-orbit (SO) potentials. Calculations include reorientation terms and coupling to the first three excited states of {sup 6}Li and the first two nonzerospin states of {sup 12}C. The {sup 6}Li coupling strengths were fixed by the measured {sup 6}Li excited-state cross sections. The elastic-scattering cross sections and A.P.`s are described well. The need for an explicit SO potential is apparent in the elasticmore » and inelastic-scattering AP`s {ital iT}{sub 11}, more so at 30 MeV than at 50 MeV. The rank-2 AP`s up to 50{degree} c.m. arise mainly from ground-state reorientation effects. The DF potential normalization constant {ital N} approaches unity for the 50 MeV data. At both energies, the {sup 12}C(2{sup +}) cross sections are underestimated at large angles, and the description of the {sup 12}C(3{sup {minus}}) cross sections is poor in detail. The {sup 12}C(3{sup {minus}}) AP`s and the {sup 12}C(2{sup +}) {ital iT}{sub 11} are not reproduced at either energy. {copyright} {ital 1996 The American Physical Society.}« less

Investigation of tetrabenzporphyrin by the Z-scan technique

The nonlinear transmission of tetrabenzporphyrin dissolved in tetrahydrofuran was measured with the Z-scan technique at 532 nm with nanosecond pulses. The excited-state absorption cross section, the excited-state refractive-index cross section, and the linear and nonlinear absorption contributing to a thermal index change have been determined. To our knowledge, the excited-state cross section and its effective ratio to the ground-state cross section are the largest values reported to date.

Formation of antihydrogen in the ground state and n=2 level.

The cross sections of antihydrogen formation in the ground state and {ital n}=2 level by the impact of antiprotons on the ground state of positronium have been calculated under the framework of the eikonal approximation for incident energy of 30--1000 keV. The excited-state capture cross sections are quite appreciable and are even larger than the ground-state cross sections for impact energies {le}75 keV. The total eikonal cross sections ({sigma}={sigma}{sub 1{ital s}}+{sigma}{sub 2{ital s}}+{sigma}{sub 2{ital p}}) are always higher than the corresponding first-order Born approximation cross section throughout the present energy span.

Nonlinear Optical Properties of Tetrabenzporphyrins

AbstractOptical limiting in a solution of tetrabenzporphyrin (TBP) dissolved in tetrahydrofuran (THF) was measured in an f/5 optical focusing arrangement using 532 nm wavelength laser light with a 9 ns pulse duration. The performance of this solution was compared to a variety of other materials. In order to better understand the nonlinear behavior of this material, apertured and unapertured Z-scans were performed. From these measurements it was determined that the excited-state cross section and its ratio to ground-state cross section were large. The nonlinear refraction of this material is made up of contributions from thermal density change and population redistribution. Limiter performance was modeled in an f/64 limiter. The limiter behavior of a slightly modified compound and an additional solvent were measured.

Solvent Effects on C60 Excited State Cross Sections

AbstractA survey study of solvent effects on the linear and nonlinear absorption properties of C60 has been done. The nonlinear absorption measurements are done at 694 nm with a Q-switched Nd:YAG pumped dye laser. In conjunction with this study a three level rate equation system has been solved analytically and the model results used to extract effective excited state cross sections. A difference and a ratio are calculated from the effective excited state cross section and the ground state cross section. The analysis demonstrates that it is this difference and the initial transmission which determine the critical fluence for the onset of nonlinear absorption. The saturation behavior is determined by the ratio of the cross sections and the initial transmission. Based on these findings C60 is shown to have some of the highest reported nonlinear absorption properties at 694 nm. The effective excited state cross sections at 694 nm are reported for the solutions and correlations to the solvent types demonstrated.

Optimization of Reverse Saturable Absorber Limiters: Material Requirements and Design Considerations

AbstractWe present numerical beam-propagation simulations of optimized reverse-saturable absorption (RSA) based optical limiters where the depth of focus of the input beam is much smaller than the thickness of the nonlinear material. The optimization is achieved by allowing the molecular concentration to vary along the propagation path, allowing the entire length of the limiter to reach the maximum possible nonlinear absorption before eventual damage to the limiter. We review in detail the analytic model originally derived by Miles [1] to determine the design and performance of such limiters. This model requires the usual 5-level model used in the numerical solution to be approximated by a quasi-three-level system. We show that this effective 3-level excited-state cross section is both pulsewidth and fluence dependent. The numerical propagation output shows that there is considerable diffractive beam distortion, which cannot be accounted for in the analytic model. The end result is that while there is qualitative agreement with numerical results, the magnitude of the limited output can be an order-of-magnitude underestimated. We determine that the fluence level at all parts of the limiter must be at least ten times the saturation fluence to efficiently utilize the nonlinear absorption. We further describe how the optimized distribution of molecular density is the limit of the multi-element tandem limiter for an infinite number of elements. By carefully accounting for saturation over the entire length of each individual element, we show how a multi-element limiter may be designed to closely approach the performance of the optimized distribution for as few as four elements. With current materials technology the damage threshold of solid hosts needed to vary the molecular density is much lower than that of glass cuvettes used for liquid based limiters. Therefore, a multi-element liquid based tandem limiter can be used in full saturation so that better limiter performance should be obtained. Ultimately, however, the operation of all RSA-based limiters involves a strict trade-off between performance and linear transmittance.

Picosecond investigations of the excited-state transition at 532 nm in King's complex [(C5H5)Fe(CO)]4 and synthesized analogs

Variations of the organometallic cluster known as King's complex, [(C 5 H 5 )Fe(CO)] 4 , have been synthesized to study the excited-state transition responsible for reverse saturable absorption observed at 532 nm in this molecule. Picosecond pump-probe measurements have been used to measure the excited-state cross sections and lifetimes in King's complex and the analogs methyl-King's complex, [CH 3 (C 5 H 4 )Fe(CO) 4 ] and triethylaluminum King's complex, [(C 5 H 5 )Fe{COAl(C 2 H 5 ) 3 }] 4

Momentum transport cross sections for excited and ground state potassium with rare gases by light-induced diffusive pulling

The authors have used the light-induced diffusive pulling (LDP) method to measure the ground state momentum transport cross sections and the relative difference of the excited and ground state cross sections with respect to the ground state for potassium with several inert gas atoms. For the LDP measurements, the excited state cross section is a weighted average of the potassium 42P3/2 and 42P1/2 fine structure levels, which are mixed by collisions with the inert gas atoms. The authors have also used a light-induced drift (LID) experiment to measure the ratio of the differences in the excited and ground state cross sections for the individual fine structure levels ( Delta sigma /J=3/2): Delta sigma (J=ff) for potassium-Ne and potassium-Ar. For the case of potassium-Ar, the authors have combined this ratio with the results from the LDP measurements to obtain absolute transport cross sections for the individual 42S1/2, 42P1/2 and 42P3/2 levels.

Abundance anomalies in stars: atomic physics at play II

By reviewing recent progress in the models used to explain abundance anomalies in stars, a number of problems involving atomic physics are identified, in particular: the collision cross-sections for excited states, the constitution of large atomic physics data banks, the angular distribution of electrons after photoionization and the identification of broad absorption features.

Populations of excited states and reaction mechanisms in the emission of complex fragments for collisions of 58Ni+58Ni at 11 MeV/nucleon.

Cross sections for emission of complex fragments ({ital Z}{gt}2) in their ground and excited states are presented for the reaction {sup 58}Ni+{sup 58}Ni at a bombarding energy of 630 MeV. Measurements of energy spectra, angular distributions, and angle-integrated cross sections were made for fragments of {ital Z}=4 to 20. {gamma} rays emitted in coincidence with the fragments were measured in a 4{pi} geometry using 62 NaI detectors and 8 Compton-suppressed germanium detectors. Data presented are mostly for the cross sections extracted by {gamma}-ray techniques. A simple statistical approach to associate the ratio of cross sections for excited states and ground states to the temperature of the emitter fails to give the expected temperatures. However, it is shown that this is mostly due to the fact that the fragments that {gamma} decay are secondary fragments produced by particle decay of the primary fragments. A Hauser-Feshbach analysis accounts well for the fragment cross sections, energy spectra, and extracted temperatures, provided that evaporation from the primary fragments is included.

Threshold law for electron-atom impact ionization: towards the inside contribution of the Coulomb-dipole theory

The author has previously derived an ionization threshold law on the basis of the Coulomb-dipole theory, but including only the contribution from the outer (semi-asymptotic) region of configuration space to the relevant matrix element. Here the author initiates a study of the (overwhelmingly dominant) inside contribution. The main part of this paper is devoted to a detailed analysis of the asymptotic form to which the inside function must be attached. The author returns to an older approach of deriving the ionization yield by extrapolating excitation cross sections of excited states (N) (because the asymptotic form there is known to be dipole configurations of degenerate (l) states for each N excited by the incoming electron) into the continuum. Here the author concentrates on the dipole matrix from which the dipole configurations are obtained; it is derived analytically; its eigenfunctions and eigenvalues are evaluated numerically to very high N (for several of the lower partial waves L). A key parameter emerges, JC(N,L), which specifies the number of coherent, attractive, dipole states as a function of N and L.

A high-resolution study of the 12C(γ,p) reaction with 49–78.5 MeV tagged photons

We present tabulated cross-section measurements for the reaction 12C(γ, p) leading to resolved, low-lying, excited states of 11B. The measurements were obtained using tagged photons of 49–78.5 MeV and for mean laboratory proton emission angles from 65° to 115°. The proton excitation energy spectra are dominated by the ground state ( 3 2 − ), 2.13 MeV ( 1 2 − ), 5.02 MeV ( 3 2 − ) and doublet ( 7 2 − , 1 2 + ) states of 11B. No evidence is found for the population of the 4.45 MeV ( 5 2 − ) state. Our analysis demonstrates that both the ground-state and excited-state cross-section data scale with momentum mismatch. The data are qualitatively discussed within the context of the existing (e, e'p) data and direct knockout and quasideuteron models. A consistent and quantitative understanding of the data will require more sophisticated models than are currently available.

Correlation enhancement of the electron-impact ionization cross section for excited-state Ne-like ions.

The electron-impact ionization cross section is calculated in the distorted-wave approximation for the Ne-like ions ${\mathrm{Ar}}^{8+}$, ${\mathrm{Ti}}^{12+}$, ${\mathrm{Fe}}^{16+}$, ${\mathrm{Zn}}^{20+}$, and ${\mathrm{Se}}^{24+}$. For ionization from the 2${p}^{6}$ ground state, the contributions from inner-shell excitation followed by autoionization are negligible. However, when these ions are initially in the 2${p}^{5}$3s excited configuration, contributions arising from the inner-shell excitations 2${p}^{5}$3s\ensuremath{\rightarrow}2${p}^{4}$3snl and 2${p}^{5}$3s\ensuremath{\rightarrow}2s2${p}^{5}$3snl are large. The overall branching ratio for autoionization of the 2${p}^{4}$3snl and 2s2${p}^{5}$3snl levels increases when the atomic-structure calculations are extended beyond the single-configuration approximation to include the configuration interaction. The resulting correlation enhancement of the excited-state ionization cross section is found to increase as a function of Z. For ${\mathrm{Se}}^{24+}$ the correlation enhancement of the total ionization cross section is found to be 42%.

Absolute photoionization cross sections of the Cs 7D3/2 level measured by use of fluorescence reduction.

A simple technique for measuring absolute photoionization cross sections \ensuremath{\sigma} of excited atoms has been applied to the 7${D}_{3/2}$ level in Cs. Past experiments on excited-state cross sections have relied on measurements of the total number of ions or photoelectrons produced by photoionization to deduce \ensuremath{\sigma}. Our technique is novel in that it utilizes the simple measurement of the reduction in the excited-atom fluorescence due to photoionization to find \ensuremath{\sigma}. We report measurements of cross sections at six different photon energies.

Photoionization of excited atomic oxygen: Theory and calculations.

The variational R-matrix approach for photoionization has been modified in two ways to treat Rydberg excited states of large radius: (1) the large residual contributions to dipole transition and normalization integrals outside the R-matrix radius are treated analytically, and (2) the amplitude of Rydberg functions on the boundary is considered explicitly. Photoionization cross sections as a function of energy are reported for 2${p}^{4}$ O${(}^{3}$P) ground-state atomic oxygen and for ${\mathrm{O}}^{+}$${(}^{4}$S)3p $^{3}\mathrm{P}$ excited-state oxygen and compared with previous work, where available. The excited-state cross section is in excellent agreement with limited experimental data. A Cooper minimum is predicted in the excited-state partial cross section to the ${\mathrm{O}}^{+}$${(}^{4}$S)\ensuremath{\epsilon}d continuum. A systematic study of the effect of electronic correlation in the configuration-interaction (CI) expansion of the wave function inside the R matrix is reported. The location of the Cooper minimum is the feature that is most sensitive to the CI representation used.

Electron scattering from vibrationally excited CO2

The total cross section for electron scattering from vibrationally excited (principally 010) CO2 molecules has been measured in the energy range 0.12-2.0 eV with a time of flight electron spectrometer. The vibrationally excited molecules were produced by thermal excitation of the gas contained in a scattering cell at a temperature of 300 degrees C. The cross section for scattering from these excited molecules was deduced by comparison with similar measurements performed at room temperature. At energies below 2 eV the excited-state cross section is considerably larger than that for scattering from ground-state CO2. The ground-state measurements are in excellent agreement with other recent experimental and theoretical work. No other experimental or theoretical data exist for the excited-state cross section.

Possible narrow and deep minima in the photoionization cross sections of excited states.

Hartree-Fock-Slater calculations of the photoionization cross section of the 6 ${\mathrm{}}^{2}$${D}_{3/2}$ excited state of cesium predicted a sharp minimum near threshold. The properties of such an unusually narrow and deep minimum are examined. The narrowness arises from the large spatial extension of the bound excited-state function and the strong threshold region energy dependence of the inner lobes of a high-angular-momentum continuum state. The depth is caused by the near coincidence in position of the zeros of the two dominant dipole matrix elements. This coincidence can be fine tuned as a function of atomic number. Consequences of changes in the atomic model or the atomic number for the properties of the minimum are also examined.

Anharmonic forced Rayleigh scattering: A technique for study of saturated absorption in liquids

The technique of anharmonic forced Rayleigh scattering is developed and applied to the study of saturated absorption in liquids. Isobaric heating following saturated absorption at a crossed beam interference pattern creates an anharmonic transient thermal grating containing harmonics of the single spatial frequency present in the intensity. Diffraction observed for a probe beam incident at the Bragg angle for the second harmonic grating component provides a zero-background measurement of a deviation from linear absorption. Gaussian spatial and temporal beam profiles are taken into account and the angular sensitivity of the grating is measured and compared with theory. Transient decay rates are also measured and found to be in good agreement with the theory. A four-level saturation model is developed, and the saturation parameter Isat is related to kinetic parameters for the two dominant causes of saturation in liquids: intermediate state ‘‘bottlenecking’’ and photochemical change. The lack of second order diffraction from azulene in CCl4 allows us to put limits on the saturation intensity, photochemical yield, excited state cross section, and two-photon cross section of this molecule. The relative diffraction efficiency and dependence on excitation intensity of two diffraction orders are used to determine the nonrecombinant dissociation yields of I2 (excited at 532 nm) in hexadecane and hexane. The dissociation yields are 0.038 and 0.153, respectively.