Fine-structure-resolved measurements of photoelectron angular ...

PHYSICAL REVIEW A, VOLUME 65, 024702

Fine-structure-resolved measurements of photoelectron angular distributions by single-photon detachment of SnÀ at visible wavelengths V. T. Davis Department of Physics, United States Military Academy, West Point, New York 10996

J. Ashokkumar and J. S. Thompson Department of Physics and Chemical Physics Program, University of Nevada, Reno, Nevada 89557-0058 共Received 14 March 2001; published 16 January 2002兲 The spectral dependence of the angular distributions of photoelectrons produced by the single-photon detachment of Sn⫺ 关 core, (5s 2 , 5p 3 ) 兴 ions has been measured at four discrete photon wavelengths ranging from 457.9 to 514.5 nm 共2.71–2.41 eV兲 using a crossed laser-ion beams apparatus. Values of the fine-structureresolved asymmetry parameters have been determined by fits to the photoelectron yield as a function of the angle between the photon polarization vector and the linear momentum vector of the collected photoelectrons. The measured asymmetry parameters for Sn⫺ are compared to previous asymmetry parameter measurements for negative ions with similar electronic configurations. The measurements were also fit to a previously reported model for photoelectron asymmetry parameters for photodetaching p-orbital electrons from negative ions. DOI: 10.1103/PhysRevA.65.024702

PACS number共s兲: 32.80.Gc, 32.10.⫺f, 33.60.⫺q

I. INTRODUCTION

Investigations of photon interactions with negative ions 关1– 4兴 provide information necessary to characterize the initial and final states of the target species, as well as dynamical information pertaining to the mutual interaction of collision partners 关5兴. Subtle interactions such as electron correlation in the initial and final states of the photon-negative ion collision, which might be overshadowed by the long-range Coulomb potential present in the photoionization of either neutral or positively charged ionic species, can be studied in photodetachment processes. The most general form of the angular distribution of a collision process for an unpolarized target was summarized by Yang 关6兴. Cooper and Zare 关7,8兴 developed a negative-ion specific form of the differential cross section for the production of photoelectrons detached from a randomly polarized

␤⫽

target by linearly polarized incident light. The differential cross section can be written in the dipole approximation as

冋

1050-2947/2002/65共2兲/024702共4兲/$20.00

共1兲

where ␴ is the total photodetachment cross section at a given photon energy, ␪ is the angle between the polarization vector of the photon and the momentum vector of the photodetached electron, and ␤ is the asymmetry parameter, which completely characterizes the shape of the photoelectron emission pattern. The differential cross section must be nonnegative, which restricts the range of the asymmetry parameter to ⫺1⭐ ␤ ⭐2. Within the independent-particle approximation, the asymmetry parameter for the photoejection of an electron from an unpolarized initial state with angular momentum l, is given by 关7兴

2 2 l 共 l⫹1 兲 R l⫺1 ⫹ 共 l⫹1 兲共 l⫹2 兲 R l⫹1 ⫺6l 共 l⫹1 兲 R l⫹1 R l⫺1 cos共 ␦ l⫹1 ⫺ ␦ l⫺1 兲 2 2 ⫹ 共 l⫹1 兲 R l⫹1 共 2l⫹1 兲关 lR l⫺1 兴

The asymmetry parameter is found to be most sensitive to the phase-shift differences ␦ l⫹1 ⫺ ␦ l⫺1 , though it also depends on the relative magnitudes of the radial dipole integrals R l⫹1 and R l⫺1 . Cooper and Zare 关7兴 also showed that Eq. 共2兲 is valid for LS coupling. A more detailed theoretical description of the photodetachment process, reported by Fano and Dill 关9兴 considered the final-state interaction between the photoelectron and its parent residual atom. The coupling of the outgoing electron

册

␴ ␤ d␴ 1⫹ 共 3 cos2 ␪ ⫺1 兲 , ⫽ d⍀ 4 ␲ 2

.

共2兲

partial waves to the residual atom can result in various photodetachment channels not allowed in the model of Cooper and Zare. The first detailed experimental study of angular distributions of photodetached electrons was conducted by Hall and Siegel 关10兴. Subsequent measurements of angular distributions have been reported 关2兴, but relatively few experiments have investigated the energy dependance of photoelectron angular distributions for negative ions 关10–17兴. This paper

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FIG. 1. Typical photoelectron kinetic-energy spectrum for photodetaching Sn⫺ 关 h ␯ ⫹Sn⫺ ( 4 S 3/2)→Sn( 3 P 2,1,0 )⫹e ⫺ 兴 . The ion-beam energy was 10 keV and the photon wavelength was 514.5 nm 共2.410 eV兲 for this spectrum. The data points are plotted with error bars representing counting statistics at one standard deviation.

presents an experimental study of photoelectron angular distributions of Sn⫺ at visible wavelengths, and, as such, represents an experimental study of the heaviest column 14 element to date. The results of this experiment demonstrate that the description of photoelectron angular distributions based on the independant particle approximation is adaquate for describing photodetachment processes for an ion as heavy as Sn⫺ . II. EXPERIMENT

The experimental apparatus and techniques used for photoelectron angular distribution measurements has been described previously 关14,15兴, therefore, only a brief description is presented. The experimental apparatus consisted of a commercial cesium-sputter negative-ion source 关18兴, accelerator and an interaction chamber in which photoelectrons were produced and analyzed. The source of the negative ions was a target pellet consisting of a mixture of tin oxide, sodium carbonate, and copper powder. The negative ions produced were accelerated by a 10 kV potential, mass selected by a 90° bending magnet, then focused and steered into the interaction chamber. Once inside the chamber, the ion beam intersected a linearly polarized photon beam at an intersection angle of 90°. The photon beam was produced by an argon-ion laser operating in single line mode. Electrons photodetached in the interaction region were energy analyzed using a spherical-sector, 160° electrostatic kinetic-energy analyzer operated in fixed pass-energy mode. The electron spectrometer was positioned below the plane which contained the laser and ion beams at a 45° declination angle. Electrons transmitted through the spherical-sector analyzer were detected with a channel electron multiplier. Analog outputs from the ion-beam current and the laser power meters were converted to frequencies by a voltage-tofrequency converter, and logged with counters for normalization of electron counts.

III. MEASUREMENTS AND RESULTS

A typical photoelectron energy spectrum of Sn⫺ is shown in Fig. 1. The ion-beam current was approximately 4 nA. The laser power was 4.0 W for the photoelectron spectrum in Fig. 1. The energy scale for the spectra were set using the known electron affinity of tin 关19兴. The photoelectron spectra contained three peaks from the fine-structure transitions h ␯ ⫹Sn⫺ ( 4 S 3/2)→Sn( 3 P 0,1,2 )⫹e ⫺ . Following collection, each of the photoelectron spectra were fitted to the superposition of three Gaussian functions with a linear background. The fits were done with a nonlinear leastsquares fitting routine that weighted each data point by its statistical uncertainty assuming a Poisson distribution. Once the fitting parameters were obtained, each Gaussian was integrated to determine the total photoelectron yield along with its uncertainty at each indicated angle of the double Fresnel Rhomb polarization rotator, ␣ , which corresponds to the angle between the laser polarization vector and the electron collection direction. After determining the yields and uncertainties of each of the individual spectra, the asymmetry parameter was determined by a least-squares fit of photoelectron yield-vs-linear polarization angle, with respect to electron collection direction to the general expression I( ␣ ) ⫽a 兵 1⫹ ␤ P 2 关 cos(␣-c) 兴 其 , where P 2 关 cos(␣)兴 is the secondorder Legendre polynomial and a, c, and ␤ are fitting parameters. Table I shows the fine-structure resolved asymmetry paTABLE I. Photoelectron asymmetry parameters for the process 关 h ␯ ⫹Sn⫺ ( 4 S 3/2)→Sn( 3 P 2,1,0 )⫹e ⫺ 兴 . The transitions are labeled by the final fine-structure level in tin. ␭ (nm) 457.9 488.0 496.5 514.5

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3

P2

⫺0.57⫾0.11 ⫺0.73⫾0.04 ⫺0.78⫾0.06 ⫺0.88⫾0.02

3

P1

⫺0.22⫾0.15 ⫺0.38⫾0.06 ⫺0.41⫾0.01 ⫺0.49⫾0.01

3

P0

⫺0.15⫾0.12 ⫺0.07⫾0.06 ⫺0.03⫾0.11 ⫺0.14⫾0.04

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TABLE II. Asymmetry parameters for the photodetachment of Sn⫺ 关 h ␯ ⫹Sn⫺ ( 4 S)→Sn( 3 P)⫹e ⫺ 兴 . ␭ (nm)

␤

457.9 488.0 496.5 514.5

⫺0.40⫾0.13 ⫺0.54⫾0.07 ⫺0.53⫾0.06 ⫺0.64⫾0.07

rameters for photodetaching Sn⫺ at the four visible wavelengths. Experimental uncertainties for all angular distribution measurements include statistical and estimated systematic errors summed in quadrature as discussed below. A Poisson distribution was assumed for counting statistics of each individual data point in each photoelectron spectrum. Consequently, the counting statistics of each photoelectron spectrum were reflected in the uncertainties in the Gaussian fitting parameters. Uncertainties in the Gaussian fitting parameters, in turn, provided upper and lower bounds in the subsequent integrations to determine the photoelectron yield at each polarization angle. Following integration, uncertainties in the photoelectron yields were reflected in uncertainties of the fits for the determination of the asymmetry parameter, and are included to one standard deviation. IV. DATA ANALYSIS

Within the framework of the independent electron approximation, the electron photodetached from Sn⫺ is described as a bound p-orbital electron. Therefore, the photodetached electron can be represented by outgoing s- and dpartial waves in the dipole approximation. Near the photodetachment threshold, the s- partial waves should dominate the behavior of the emission pattern due to the suppression of dpartial waves by the centrifugal barrier as described by the Wigner threshold law 关20兴, yielding an isotropic photoelectron emission pattern, or ␤ ⫽0. For the Sn⫺ measurements,

the photoelectron energies are far from threshold and, therefore, both s- and d- partial waves are present. The photoelectron asymmetry parameters for this case can be described by Eq. 共2兲. There has not been a theoretical prediction of the spectral dependence of the asymmetry parameter for photodetaching Sn⫺ reported. However, the measurements of the asymmetry parameters for photodetaching Sn⫺ can be compared with previous measurements for photodetaching C⫺ 关14兴, Si⫺ 关15兴, and Ge⫺ 关16兴 which have similar electronic configurations 关 core (ns 2 ,n p 3 ) 兴 . The measurements can also be fit to a model 关11兴 based on a theoretical description of the asymmetry parameter for photodetachment 关7,8兴. The previous measurements of the asymmetry parameters for the photodetachment of C⫺ and Si⫺ were not finestructure-resolved. In order to compare the Sn⫺ asymmetry parameters with the C⫺ and Si⫺ measurements, the relative photoelectron yields for fine-structure transitions for photodetaching Sn⫺ were measured at the ‘‘magic angle,’’ i.e., the angle where P 2 关 cos(␪)兴⫽0. The asymmetry parameters for each fine-structure transition were weighted by their normalized photoelectron yields, measured at the magic angle, and summed at each measured photon wavelength. The resultant asymmetry parameters for photodetaching Sn⫺ are listed in Table II. Hanstorp et al. 关11兴, using assunptions based on threshold behavior, developed a straightforward simplification of the Cooper-Zare model of the asymmetry parameter for photodetachment of p-orbital electrons,

␤共 ␧ 兲⫽

2A 2 ␧ 共 A 2 ␧⫺2c 兲 1⫹2A 22 ␧ 2

.

共3兲

In this formula, ␧ is the photoelectron energy and A 2 corresponds to the relative size of the two matrix elements. In addition, c is substituted in Eq. 共2兲 for the cosine of the differences in the phase shifts, cos(␦2⫺␦0).

FIG. 2. Plot of photoelectron experimental asymmetry parameters vs photoelectron energy for C⫺ 关diamonds 共Ref. 关14兴兲, inverted triangles 共Ref. 关10兴兲兴, Si⫺ 关squares 共Ref. 关15兴兲兴, Ge⫺ 关circles 共Ref. 关16兴兲兴, and Sn⫺ 共open triangles兲. The lines are least-squares fits to a model of the spectral dependence of the asymmetry parameter 共Ref. 关11兴兲. The short-dashed line is a fit to the asymmetry parameters for photodetaching C⫺ , the long-dashed line is a fit to the Si⫺ asymmetry parameters, the solid line is a fit to the Ge⫺ , and the dotted line is a fit to the Sn⫺ asymmetry parameters.

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TABLE III. Comparison of the fitting parameters A 2 and c for the spectral dependence of the asymmetry parameters for photodetaching C⫺ , Si⫺ , Ge⫺ , and Sn⫺ .

⫺

C Si⫺ Ge⫺ Sn⫺

A 2 (eV⫺1 )

c⫽cos(␦2⫺␦0)

0.64 0.79 0.64 0.91

0.93 0.92 0.87 0.92

simplification by Hanstorp et al. are valid for C⫺ , Si⫺ , Ge⫺ , and Sn⫺ over the photoelectron energy range investigated in this paper. This indicates that final-state interactions do not significantly contribute to the spectral dependence of the asymmetry parameter for photodetaching p-orbital electrons from C⫺ , Si⫺ , Ge⫺ , and Sn⫺ at visible photon wavelengths. V. SUMMARY AND CONCLUSIONS

This equation predicts the correct spectral dependence for the asymmetry parameter ␤ for photodetaching a p-orbital electron. The asymmetry parameter is zero at threshold, due to the dominance of s-wave photoelectrons, decreases to a minimum value when ␴ 2 / ␴ 0 ⫽0.5, and approaches a value of ␤ ⫽1 as the photoelectron energy becomes large. Hanstorp et al. 关11兴 showed that Eq. 共3兲 fit their measured spectral dependence of the asymmetry parameter data for photodetaching O⫺ , and was in good agreement with a calculation by Cooper and Zare 关8兴. Previous measurements for C⫺ , Si⫺ , and Ge⫺ 关14 –16兴 could also be fit to Eq. 共3兲. The spectral dependence of the asymmetry parameters for C⫺ , Si⫺ , Ge⫺ , and Si⫺ , along with the fits of the data to Eq. 共3兲 are shown in Fig. 2. As can be seen from Fig. 2, this expression for ␤ (␧) fits the asymmetry parameter data quite well. The values of A 2 and c for the fits are given in Table III. The fits yielded a difference in phase shifts c, near 0.9 for the four ions, and the fit values of c were nearly identical for C⫺ , Si⫺ , and Sn⫺ . The quality of the fits using Eq. 共3兲 to the C⫺ , Si⫺ , Ge⫺ , and Sn⫺ asymmetry parameter data indicate that the assumptions made in the Cooper-Zare model, and the subsequent

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Fine-structure-resolved photoelectron asymmetry parameters for photodetaching Sn⫺ have been measured at four visible wavelengths. The fine-structure-resolved asymmetry parameters were summed by weighting these asymmetry parameters by their relative contributions of the fine-structure photodetachment channels in the observed photoelectron spectrum. The Sn⫺ asymmetry parameter measurements were then compared to previous measurements for C⫺ , Si⫺ , and Ge⫺ , which have similar electronic configurations 关 core (ns 2 ,n p 3 ) 兴 . The spectral dependence of the asymmetry parameters for these negative ions were very similar. The asymmetry parameters were also fit to a model based on an independent particle approximation. The model fit the asymmetry parameter data well for the four ions. Since the model does not include final-state interactions of the photodetachment process, final-state interactions probably make a small contribution to the physical description of the photon-ion collision system. A theoretical investigation of the photodetachment process for C⫺ , Si⫺ , Ge⫺ , and Sn⫺ is needed to verify this conclusion. ACKNOWLEDGMENT

This work was supported by the National Science Foundation under Cooperative Agreement OSR-935227.

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