Physical Review A

Angular Distributions from Resonant Two-Photon Ionization

Melissa Lambropoulos, R. Stephen Berry

Published Aug 1, 1973• 36 citations

Abstract

A general theory is developed to treat two-photon ionization through a single intermediate state in which an arbitrary degree of relaxation may occur. The method is set up to probe the parameters governing the relaxation, by determination of the angular distribution of photoelectrons. The method is applied to the ionization of Na atoms, through the $3p^{2}P_{\frac{1}{2}}$ and $3p^{2}P_{\frac{3}{2}}$ intermediate states.

DOI: 10.1103/physreva.8.855

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Physical Review A

Angular Distributions from Resonant Two-Photon Ionization

Melissa Lambropoulos, R. Stephen Berry

Published Aug 1, 1973• 36 citations

Publisher

Abstract

3p^{2}P_{\frac{1}{2}}

and

3p^{2}P_{\frac{3}{2}}

intermediate states.

DOI: 10.1103/physreva.8.855

Related papers

Photoelectron angular distributions from multiphoton ionization of cesium atoms

R. N. Compton, John A. D. Stockdale, C. Dewey Cooper +2 more

We present both experimental and theoretical studies of resonantly enhanced multiphoton ionization of cesium atoms. Photoelectron angular distributions for two-photon ionization via the one-photon-allowed $7p^{2}P_{\frac{1}{2},\frac{3}{2}}$ and $8p^{2}P_{\frac{1}{2},\frac{3}{2}}$ intermediate states and three-photon ionization via the two-photon-allowed $8d^{2}D_{\frac{5}{2},\frac{3}{2}}$ resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the $^{2}P_{\frac{1}{2}}$ states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the $^{2}P_{\frac{3}{2}}$ resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the $^{2}P_{\frac{3}{2}}$ data.We present both experimental and theoretical studies of resonantly enhanced multiphoton ionization of cesium atoms. Photoelectron angular distributions for two-photon ionization via the one-photon-allowed $7p^{2}P_{\frac{1}{2},\frac{3}{2}}$ and $8p^{2}P_{\frac{1}{2},\frac{3}{2}}$ intermediate states and three-photon ionization via the two-photon-allowed $8d^{2}D_{\frac{5}{2},\frac{3}{2}}$ resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the $^{2}P_{\frac{1}{2}}$ states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the $^{2}P_{\frac{3}{2}}$ resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the $^{2}P_{\frac{3}{2}}$ data.

Physical Review AOct 1, 198437 citations

Angular distribution of electrons from two-photon ionization of Ti atoms

S. A. Edelstein, Melissa Lambropoulos, John A. Duncanson +1 more

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Physical Review AJun 1, 197432 citations

Polarization phenomena in multiphoton ionization of atoms

V. L. Jacobs

The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.

Journal of Physics B Atomic and Molecular PhysicsAug 1, 197328 citations

Intensity-dependent electron angular distributions in resonant multiphoton ionization

S. Geltman, Gerd Leuchs

A theoretical investigation has been carried out on the dependence of the photoelectron angular distributions on laser intensity for the case of two-photon-resonant three-photon ionization of sodium. Good overall agreement is obtained with the experimental anisotropy parameters for ionization via the 4 ${D}_{3/2}$ and 4 ${D}_{5/2}$ intermediate states. The comparison of the theoretical results with the experimental data also clearly shows that the hyperfine splitting of the ground state has to be taken into account at high laser intensities although the low-intensity angular distributions do not depend on the initial ground hyperfine state.A theoretical investigation has been carried out on the dependence of the photoelectron angular distributions on laser intensity for the case of two-photon-resonant three-photon ionization of sodium. Good overall agreement is obtained with the experimental anisotropy parameters for ionization via the 4${D}_{3/2}$ and 4${D}_{5/2}$ intermediate states. The comparison of the theoretical results with the experimental data also clearly shows that the hyperfine splitting of the ground state has to be taken into account at high laser intensities although the low-intensity angular distributions do not depend on the initial ground hyperfine state.

Physical Review AMar 1, 19858 citations

Two-photon resonant three-photon ionization of the nd D2 states of cesium, rubidium, and sodium: Photoelectron angular distributions

Adila Dodhy, John A. D. Stockdale, R. N. Compton +3 more

Energy-resolved photoelectron angular distributions have been measured for the nd ${}^{2}$ D states (n=11--23) in cesium and rubidium atoms for two-photon resonant, three-photon ionization under conditions where the spin-orbit fine structure was not resolved. The photoelectron angular distributions reveal strong fine-structure mixing effects when the time duration of the laser pulse is longer than the time corresponding to the inverse of the fine-structure splitting of the nd states involved. Three-photon ionization photoelectron angular distributions for sodium atoms have been studied both experimentally and theoretically for laser frequencies in which resonance enhancement occurs via the two-photon excited nd ${}^{2}$ D states (n=5--9). The laser pulse duration is \ensuremath{\sim}6 ns which is comparable to or less than the fine-structure mixing time for the unperturbed fine-structure nd ${}^{2}$ ${D}_{5/2}$ ,3/2 levels. In addition, the high laser powers \ensuremath{\sim} ${10}^{8}$ W/ ${\mathrm{cm}}^{2}$ employed result in alterations of the energy separations of the fine-structure levels (and cause corresponding changes in the mixing times) due to the ac Stark effect. A detailed theoretical analysis is presented and good agreement is obtained with the experimental results.Energy-resolved photoelectron angular distributions have been measured for the nd ${}^{2}$D states (n=11--23) in cesium and rubidium atoms for two-photon resonant, three-photon ionization under conditions where the spin-orbit fine structure was not resolved. The photoelectron angular distributions reveal strong fine-structure mixing effects when the time duration of the laser pulse is longer than the time corresponding to the inverse of the fine-structure splitting of the nd states involved. Three-photon ionization photoelectron angular distributions for sodium atoms have been studied both experimentally and theoretically for laser frequencies in which resonance enhancement occurs via the two-photon excited nd ${}^{2}$D states (n=5--9). The laser pulse duration is \ensuremath{\sim}6 ns which is comparable to or less than the fine-structure mixing time for the unperturbed fine-structure nd ${}^{2}$${D}_{5/2}$,3/2 levels. In addition, the high laser powers \ensuremath{\sim}${10}^{8}$ W/${\mathrm{cm}}^{2}$ employed result in alterations of the energy separations of the fine-structure levels (and cause corresponding changes in the mixing times) due to the ac Stark effect. A detailed theoretical analysis is presented and good agreement is obtained with the experimental results.

Physical Review AApr 1, 19879 citations

Angular distributions of photoelectrons from resonant two-photon ionization: A graphical approach

Ring‐Ling Chien

The Liouville representation is a formalism that describes quantum mechanical problems by using the space of density operators as kets and the space of observable operators as bras. It is useful for problems with complicated angular momentum coupling because it gives directly the probabilities and expectation values rather than probability amplitudes, so that some of the extended and tedious steps of the angular momentum algebra are eliminated. The graphical representation of angular momentum coupling has proved itself as another way to simplify and clarify calculations; graphical representation helps one to visualize the physics and simplifies and organizes the computations. By combining the graphical method and Liouville representation, we introduce a simple, transparent method to deal with problems of many coupled angular momenta. We use this formalism to derive the analytic expression for the angular distributions of photoelectrons. The angular distributions are represented by diagrams of density matrix and detector operators and a diagram of the transition matrix. The analytic expressions are then obtained from the diagrams by following simple general rules for the graphical reduction. A specific example, angular distributions of photoelectrons from resonant two-photon ionization of alkali atoms with hyperfine interaction, is also given.The Liouville representation is a formalism that describes quantum mechanical problems by using the space of density operators as kets and the space of observable operators as bras. It is useful for problems with complicated angular momentum coupling because it gives directly the probabilities and expectation values rather than probability amplitudes, so that some of the extended and tedious steps of the angular momentum algebra are eliminated. The graphical representation of angular momentum coupling has proved itself as another way to simplify and clarify calculations; graphical representation helps one to visualize the physics and simplifies and organizes the computations. By combining the graphical method and Liouville representation, we introduce a simple, transparent method to deal with problems of many coupled angular momenta. We use this formalism to derive the analytic expression for the angular distributions of photoelectrons. The angular distributions are represented by diagrams of density matrix and detector operators and a diagram of the transition matrix. The analytic expressions are then obtained from the diagrams by following simple general rules for the graphical reduction. A specific example, angular distributions of photoelectrons from resonant two-photon ionization of alkali atoms with hyperfine interaction, is also given.

The Journal of Chemical PhysicsNov 1, 19845 citations

3p^{2}P_{\frac{1}{2}}

and

3p^{2}P_{\frac{3}{2}}

intermediate states.

7p^{2}P_{\frac{1}{2},\frac{3}{2}}

and

8p^{2}P_{\frac{1}{2},\frac{3}{2}}

intermediate states and three-photon ionization via the two-photon-allowed

8d^{2}D_{\frac{5}{2},\frac{3}{2}}

resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the

^{2}P_{\frac{1}{2}}

states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the

^{2}P_{\frac{3}{2}}

resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the

^{2}P_{\frac{3}{2}}

data.

Titanium atoms are excited by light from a nitrogen laser from the

a^{3}F_{4}

state, near the ground state, through the

x^{3}G_{5}

state, to become

^{4}F

ions plus free electrons. The angular distribution of photoelectrons from the process gives limits on the ratio of amplitudes for transitions from the intermediate

4p

orbital to the final continuum

s

and

d

channels. The total number of photoelectrons indicates that the total ionization cross section for the

^{3}G_{5}

state is 1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}18}$

{\mathrm{cm}}^{2}

. While the method can, in principle, provide relaxation times for angular momentum reorientation (an application of the methods of perturbed angular correlations in atomic processes), the present measurements have been carried out under conditions in which no relaxation occurs.

{D}_{3/2}

and 4

{D}_{5/2}

intermediate states. The comparison of the theoretical results with the experimental data also clearly shows that the hyperfine splitting of the ground state has to be taken into account at high laser intensities although the low-intensity angular distributions do not depend on the initial ground hyperfine state.

Energy-resolved photoelectron angular distributions have been measured for the nd

{}^{2}

D states (n=11--23) in cesium and rubidium atoms for two-photon resonant, three-photon ionization under conditions where the spin-orbit fine structure was not resolved. The photoelectron angular distributions reveal strong fine-structure mixing effects when the time duration of the laser pulse is longer than the time corresponding to the inverse of the fine-structure splitting of the nd states involved. Three-photon ionization photoelectron angular distributions for sodium atoms have been studied both experimentally and theoretically for laser frequencies in which resonance enhancement occurs via the two-photon excited nd

{}^{2}

D states (n=5--9). The laser pulse duration is \ensuremath{\sim}6 ns which is comparable to or less than the fine-structure mixing time for the unperturbed fine-structure nd

{}^{2}

{D}_{5/2}

,3/2 levels. In addition, the high laser powers \ensuremath{\sim}

{10}^{8}

{\mathrm{cm}}^{2}

employed result in alterations of the energy separations of the fine-structure levels (and cause corresponding changes in the mixing times) due to the ac Stark effect. A detailed theoretical analysis is presented and good agreement is obtained with the experimental results.