^{1}, B. Kafle

^{1}, V. Chandrasekaran

^{1}, O. Heber

^{1}, M. L. Rappaport

^{1}, H. Rubinstein

^{1}, D. Schwalm

^{1,2}, D. Strasser

^{3}, Y. Toker

^{1}and D. Zajfman

^{1}

### Abstract

We describe a technique to measure absolute photo-induced cross sections for cluster anions stored in an electrostatic ion beam trap (EIBT) with a central deflector. The setup allows determination of total photo-destruction cross sections as well as partial cross sections for fragmentation and electron detachment. The unique properties of this special EIBT setup are investigated and illustrated using small clusters.

This work has been supported by the Israeli Science Foundation (Grant No. 124/09), and by a research grant from the estate of David Turner. D.Sch. acknowledges support by the Weizmann Institute of Science through the Joseph Meyerhoff program.

I. INTRODUCTION

II. EXPERIMENTAL ISSUES

A. Experimental setup

B. Ion density

C. Laser beam profile

D. Detection efficiencies

1. Collection efficiency of parent clusters

2. Collection efficiency of fragments

E. Dead times

III. ABSOLUTE PHOTO-DESTRUCTION CROSS SECTIONS BY DEPLETION

IV. TOTAL PHOTO-INDUCED FRAGMENTATION CROSS SECTIONS

A. Monomer fragmentation

B. Dimer fragmentation

C. Total fragmentation and detachment cross sections

V. CONCLUSION

### Key Topics

- Photons
- 29.0
- Laser beams
- 17.0
- Mirrors
- 16.0
- Electrostatics
- 12.0
- Photon absorption
- 12.0

## Figures

Schematic view of the experimental setup.

Schematic view of the experimental setup.

Main panel: Projection of the volume density of stored ions derived by Monte Carlo simulations onto the trap axis. Inset: r-dependence of the simulated volume density for three different z-regions; inside the deflector (black circles), inside the Einzel lens (blue squares), and inside the outer mirror electrodes (red triangles). The radius of the deflector hole (1.5 mm) is indicated by the dashed gray line.

Main panel: Projection of the volume density of stored ions derived by Monte Carlo simulations onto the trap axis. Inset: r-dependence of the simulated volume density for three different z-regions; inside the deflector (black circles), inside the Einzel lens (blue squares), and inside the outer mirror electrodes (red triangles). The radius of the deflector hole (1.5 mm) is indicated by the dashed gray line.

A typical laser beam profile at the center of the trap, obtained by projecting the two-dimensional intensity distribution measured with the CCD camera for a single laser shot onto the x axis (left panel) and onto the y axis (right panel), respectively. The solid (red) lines are Gaussian fits assuming a variance of σ l = 0.7 mm, which corresponds to a FWHM of 1.65 mm.

A typical laser beam profile at the center of the trap, obtained by projecting the two-dimensional intensity distribution measured with the CCD camera for a single laser shot onto the x axis (left panel) and onto the y axis (right panel), respectively. The solid (red) lines are Gaussian fits assuming a variance of σ l = 0.7 mm, which corresponds to a FWHM of 1.65 mm.

Upper panel: Definition of the positions to used in the schematic model approach to the collection efficiencies. At and , ions are leaving and re-entering the grounded shield of the deflector, while at and they are entering and leaving the inner grounded electrode of the Einzel lens of the entrance mirror, respectively. Within this model approach clusters stored between and at the moment the deflector voltage is switched (thick (green) line) can be deflected towards the MCP, while only fragments created between and (dashed (red) line) can be detected by the MCP. Lower panel: Collection efficiencies for parent clusters (black dots) and daughter fragments (blue squares) as a function of cluster number n. For parent clusters, the efficiencies are derived from measured spill times using Eq. (5) while the fragment efficiencies were determined by Monte Carlo simulations. Also shown are the collection efficiencies expected within the schematic model (Eqs. (6) and (7) ; dashed lines).

Upper panel: Definition of the positions to used in the schematic model approach to the collection efficiencies. At and , ions are leaving and re-entering the grounded shield of the deflector, while at and they are entering and leaving the inner grounded electrode of the Einzel lens of the entrance mirror, respectively. Within this model approach clusters stored between and at the moment the deflector voltage is switched (thick (green) line) can be deflected towards the MCP, while only fragments created between and (dashed (red) line) can be detected by the MCP. Lower panel: Collection efficiencies for parent clusters (black dots) and daughter fragments (blue squares) as a function of cluster number n. For parent clusters, the efficiencies are derived from measured spill times using Eq. (5) while the fragment efficiencies were determined by Monte Carlo simulations. Also shown are the collection efficiencies expected within the schematic model (Eqs. (6) and (7) ; dashed lines).

Number of (n − 1) photo-fragments of (black squares, left panel) and (black dots, right panel) as a function of the time difference t between the onset of the deflector voltage and the time of the laser pulse (normalized to 1 at t = t p ≈ −2.5 μs). Also shown are the expected relative collection efficiencies resulting from the schematic model (dashed red lines) and from Monte Carlo simulations (solid blue lines).

Number of (n − 1) photo-fragments of (black squares, left panel) and (black dots, right panel) as a function of the time difference t between the onset of the deflector voltage and the time of the laser pulse (normalized to 1 at t = t p ≈ −2.5 μs). Also shown are the expected relative collection efficiencies resulting from the schematic model (dashed red lines) and from Monte Carlo simulations (solid blue lines).

Depletion curves observed for and clusters that were exposed to photons of 550 nm contained in 9 ns long laser pulses with pulse energies of up to 1.5 mJ (dots with statistical error bars). The clusters were stored for 90 ms before they were subjected to the laser pulse. The solid (red) curves are the result of a fit of the experimental data with Eq. (11) by varying the photo-destruction cross section σ0. The results for σ0 are given with their statistical errors.

Depletion curves observed for and clusters that were exposed to photons of 550 nm contained in 9 ns long laser pulses with pulse energies of up to 1.5 mJ (dots with statistical error bars). The clusters were stored for 90 ms before they were subjected to the laser pulse. The solid (red) curves are the result of a fit of the experimental data with Eq. (11) by varying the photo-destruction cross section σ0. The results for σ0 are given with their statistical errors.

Measured pulse energy dependence (symbols with statistical error bars) of the depletion probability D(U) of and the appearance probability P f 1(U) of (upper panel), and of the corresponding branching function B f 1(U) (lower panel). The data were observed when illuminating clusters after 90 ms of storage by a short laser pulse with λ = 550 nm photons. The solid (red) lines are calculated probabilities including the destruction of the nascent by the absorption of a photon from the same laser pulse (see main text). The thick dashed lines indicate the expected pulse energy dependences of P f 1(U) and B f 1(U) in the absence of the daughter destruction channel. The dotted (green) curve is an exponential fit of B f 1(U) to extrapolate the data to U = 0.

Measured pulse energy dependence (symbols with statistical error bars) of the depletion probability D(U) of and the appearance probability P f 1(U) of (upper panel), and of the corresponding branching function B f 1(U) (lower panel). The data were observed when illuminating clusters after 90 ms of storage by a short laser pulse with λ = 550 nm photons. The solid (red) lines are calculated probabilities including the destruction of the nascent by the absorption of a photon from the same laser pulse (see main text). The thick dashed lines indicate the expected pulse energy dependences of P f 1(U) and B f 1(U) in the absence of the daughter destruction channel. The dotted (green) curve is an exponential fit of B f 1(U) to extrapolate the data to U = 0.

Appearance probability of observed relative to that of when subjecting after 90 ms of storage to a 9 ns long pulse of 550 nm photons (full circles, with error bars reflecting statistical uncertainties). The (green) dashed and (green) dashed-dotted lines are expected pulse energy dependences of the probability ratio in case the appearance of would be solely due to a one-photon induced dimer decay of , assuming two extreme values for the secondary destruction cross section σ d2 of . The (red) solid curve is obtained by allowing also for the production of by the photo-induced fragmentation of the nascent (for more details see main text).

Appearance probability of observed relative to that of when subjecting after 90 ms of storage to a 9 ns long pulse of 550 nm photons (full circles, with error bars reflecting statistical uncertainties). The (green) dashed and (green) dashed-dotted lines are expected pulse energy dependences of the probability ratio in case the appearance of would be solely due to a one-photon induced dimer decay of , assuming two extreme values for the secondary destruction cross section σ d2 of . The (red) solid curve is obtained by allowing also for the production of by the photo-induced fragmentation of the nascent (for more details see main text).

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