ARTICLE IN PRESS

Journal of Quantitative Spectroscopy &

0022-4073/$ - se

doi:10.1016/j.jq

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Radiative Transfer 109 (2008) 863–872

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Measurements of photoionization cross sections fromthe 4p, 5d and 7s excited states of potassium

Nasir Amina,b, S. Mahmooda,c, S.U. Haqa, M.A. Kalyara, M. Rafiqa, M.A. Baiga,�

aAtomic and Molecular Physics Laboratory, Department of Physics, Quaid-i-Azam University, Islamabad 45320, PakistanbDepartment of Physics, University of Agriculture, Faisalabad, Pakistan

cDepartment of Physics, UAJ&K, Muzaffarabad, Pakistan

Received 22 June 2007; received in revised form 15 September 2007; accepted 24 September 2007

Abstract

New measurements of the photoionization cross sections from the 4p 2P1/2,3/2, 5d2D5/2,3/2 and 7s 2S1/2 excited states of

potassium are presented. The cross sections have been measured by two-step excitation and ionization using a Nd:YAG

laser in conjunction with a thermionic diode ion detector. By applying the saturation technique, the absolute values of the

cross sections from the 4p 2P3/2 and 4p 2P1/2 states at 355 nm are determined as 7.271.1 and 5.670.8Mb, respectively. The

photoionization cross section from the 5d 2D5/2,3/2 excited state has been measured using two excitation paths, two-step

excitation and two-photon excitation from the ground state. The measured values of the cross sections from the 5d 2D5/2

state by two-photon excitation from the ground state is 28.974.3Mb, whereas in the two-step excitation, the cross section

from the 5d 2D3/2 state via the 4p 2P1/2 state and from the 5d 2D5/2,3/2 states via the 4p 2P3/2 state are determined as

25.173.8 and 30.274.5Mb, respectively. Besides, we have measured the photoionization cross sections from the 7s 2S1/2excited state using the two-photon excitation from the ground state as 0.6170.09Mb.

r 2007 Elsevier Ltd. All rights reserved.

PACS: 32.30.Jc; 32.80.Rm

Keywords: Photoionization cross section; Excited states of potassium; Multi-photon excitation and ionization

1. Introduction

Laser photoionization spectroscopy is based on resonance ionization of atoms and molecules as a result ofsuccessive absorption of several laser photons. The high intensity of lasers, their narrow band width andtunable radiation have been playing a major role for selective excitation of some atomic state, and subsequentionization from the excited states enables one to measure the photoionization cross section of the pertinentexcited states. Photoionization cross sections have a number of utilities in the applied areas of science andtechnology such as space and astrophysics, radiation protection and laser designing. The interaction ofelectromagnetic radiation with matter is one of the most basic processes in nature; therefore, the study of

e front matter r 2007 Elsevier Ltd. All rights reserved.

srt.2007.09.008

ing author. Tel.: +9251 2278692; fax: +92 51 9210256.

ess: baig@qau.edu.pk (M.A. Baig).

ARTICLE IN PRESSN. Amin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 863–872864

photoionization cross sections has great significance. Although the measurements of photoionization crosssection from the ground states of the alkali metals are well documented, it is very rare for the excited states.Nygaard et al. [1] pioneered the measurements of the photoionization cross section of potassium from the 4pexcited state using the two-step photoionization process. The derived photoionization cross section wascompared with the values of Moskvin [2] who used the quantum defect method for calculating thephotoionization cross section. Aymar et al. [3] computed the photoionization cross section near the thresholdfor the s, p and d Rydberg states of Li, Na and K in the framework of a single-electron model using aparametric central potential. An atomic beam and laser saturation technique have been used to measure thephotoionization cross sections of the excited alkali atoms [1–7]. Huang and Wang [8] reported the oscillatorstrength for the principal series of potassium and at the series limit the photoionization cross section wasmeasured as 0.52Mb. Barrientos and Martin [9] obtained the oscillator strength distribution between thediscrete and continuous regions of the spectrum of Li, Na, K, Rb and Cs using the quantum defect orbitalprocedure. They also reported the photoionization cross section of these elements at the first ionizationthreshold. Burkhardt et al. [10] formulated an empirical relation to determine the photoionization crosssection of the excited state of barium 6p 1P1, potassium 4p 2P3/2 and sodium 3p 2P3/2. Subsequently, thisrelation was used by He et al. [11], Willke and Kock [12] and Mende et al. [13] to determine the absolute valuesof cross section. Mende et al. [13] studied the spatial distribution of photons in the laser pulse with a CCD andapplied in the evaluation procedure as a Gaussian profile. Kupliauskiene [14] calculated the single and shake-up photoionization cross section of sodium and potassium atoms from the ground and first excited statesusing the relaxed-orbital MCH approach. Petrov et al. [15] reported the partial and total photoionization ofpotassium using configuration interaction technique with Pauli-Fock orbitals. They also discussed the effectof polarization of the atomic core with the valence electron. The relative photoionization cross section ofpotassium 4p 2P3/2 over the photoelectron energy range 0–0.22 eV for parallel and perpendicular linearpolarizations of the two laser beams was also reported. Absolute cross section was determined at three selectedphotoelectron energies. More recently, Meyer et al. [16] performed high-resolution photoelectron experimentson laser-excited potassium and observed fine-structure resolved spectra in the region of the KII 3p54p stateand it was inferred that the relative intensities of the 3p54p fine structure lines depend on the initial excitationto one of the 4p spin-orbit components. Schulz et al. [17] studied the 3p shakedown spectra of laser-excitedpotassium as well as direct 3p photoionization of ground-state potassium. It was revealed that these twoexcitation schemes led to the same final state. They also determined the character of the final states that wereweakly excited in the direct photoemission but had much higher intensities in the shakedown spectrum. Janklaet al. [18] studied laser excitation combined with 2p photoionization and Auger decay of potassium bothexperimentally and theoretically and also resolved the shake-up structure of the 2p photoelectron ofpotassium.

In this paper, we report the measurements of the photoionization cross sections from the 4p 2P1/2,3/2,5d 2D5/2,3/2 and 7 s 2S1/2 excited states of potassium. The photoionization cross section from the 5d 2D5/2,3/2

states is determined through two different paths: two-photon excitation from the ground state and two-stepexcitation through an intermediate state. Our results for the photoionization cross section from the 4p 2P3/2

state are in good agreement with the known values, whereas the corresponding photoionization cross sections

from the 4p 2P1/2, 5d2D5/2 ð4s

2S1=2�!2_o

5d 2D5=2Þ, 5d2D5/2,3/2 ð4s

2S1=2�!2_o1

4p 2P3=2�!2_o2

5d 2D5=2;3=2Þ, 5d2D3/2

ð4s 2S1=2�!_o1

4p 2P1=2�!_o2

5d 2D3=2Þ and 7s 2S1/2 ð4s2S1=2�!

2_o7s 2S1=2Þ states are reported for the first time.

2. Experimental setup

The experimental arrangements to study the photoionization from the excited states of potassium is similaras described in earlier work [19–21], which comprises a Nd:YAG laser system, operated in the Q-switchedmode, and locally made Hanna-type dye laser [22]. The potassium vapor was produced in a cylindrical heatpipe tube 48 cm long, 3 cm in diameter and 1mm wall thickness, operating as a thermionic diode ion detectorworking in the space charge limited mode. About 2 g of pure potassium sample was placed in the centralheating zone. The cell was evacuated up to 10�6 Torr and an argon gas at a pressure of 1–2Torr was used as abuffer gas. The buffer gas provided a uniform column of vapors, and also protected the quartz windows from

ARTICLE IN PRESSN. Amin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 863–872 865

the chemical attack of the hot vapors. The thermionic diode was then heated up to 540K temperaturecorresponding to a potassium vapor pressure of 0.2 Torr.

In the first set of experiments, we measure the photoionization cross section from the 4p 2P1/2,3/2 states ofpotassium and used a two-step excitation technique. The first dye laser, charged with the pyridine-2 dyedissolved in propylene carbonate and pumped by the SHG (532 nm) of the Nd:YAG (Spectra, GCR-11) laser,works at 10Hz repetition rate, pulse duration E6 ns and energy 135mJ per pulse. The dye laser having linewidth p0.3 cm�1 was used to excite the atoms from the ground state to the 4p 2P3/2 state lying at 766.7 nm inthe first experiment and to the 4p 2P1/2 state lying at 770.1 nm in the second experiment. The THG (355 nm) ofthe same Nd:YAG laser was used as an ionizing laser beam. Both the laser beams were linearly polarized withthe polarization vectors in the same direction. The laser beams were spatially overlapped to achieve anoptimized ionization signal. The intensity of the exciting laser beam was fixed E0.5mJ, whereas the intensityof the ionizing laser beam was varied from a minimum value to E1mJ, using different neutral density filters,to register the corresponding ion signals.

In the second set of experiments, we measured the photoionization cross section from the 5d excited state,using a Q-switched pulsed Nd:YAG laser (Quantel, Brilliant), 10Hz repetition rate, pulse duration E4 ns,energy 180mJ per pulse at 532 nm. The output of the SHG of the Nd:YAG laser was used to pump theQuanta-ray PDL-2 dye laser having line width p0.2 cm�1. We used two different excitation paths. In the firstset of experiments the output of the Quanta-ray, PDL-2 dye laser (lE662.58 nm) was split into two parts. Thefirst part was used for the selective two-photon excitation to the 5d state and the second portion of the dyelaser beam was focused into the excitation region to ionize the excited atoms. In the second experiment, weused the two-step excitation scheme to populate the 5d excited state. The first dye laser (Quanta-Ray, PDL-2)charged with the pyridine-2 dye and pumped by the SHG (532 nm) was used to excite the atoms from theground state to the 4p 2P1/2 or 4p 2P3/2 intermediate states lying at 770.1 and 766.7 nm, respectively. Thesecond dye laser was tuned at 581.4 and 583.35 nm to access the 5d 2D5/2,3/2 state from the 4p 2P1/2 and 4p 2P3/2

intermediate states, respectively. This dye laser was home built with a cavity pioneered by Hanna et al. [22].The cavity was formed between a flat mirror and a 2400 linesmm�1 holographic grating and the wavelengthtuning was achieved by rotating the grating by a computer-controlled stepping motor.

In the third set of experiments, we measured the photoionization cross sections from the 7s 2S1/2 excitedstate of potassium which was populated via two-photon excitation from the ground state. Since the dye laseris linearly polarized, the accessible states from the 7s 2S1/2 are np 2P1/2,3/2 and the continuum states are epJ ¼ 1/2, 3/2 following the DmJ ¼ 0 selection rule. Ionization was achieved by the same dye laser output. In allthe above-mentioned experiments, the ion signal was taken across a 10 kO resistor through a 0.01 mF blockingcapacitor and was registered on a 100MHz storage oscilloscope.

3. Results and discussion

Alkali metals (Li, Na, K, Rb, Cs and Fr) are the elements of the first group of the periodic table, possessingms 2S1/2 ground-state electronic configuration, with a single valence electron outside a filled shell core. Thesemetals readily lose their outer electron to form stable positive ions. When an atom in the ground state of alkalimetals is excited, the last and loosely bound electron has the possibility of going to any of the higher statesaccording to the electric dipole selection rules D‘ ¼71, DJ ¼ 0,71, DS ¼ 0 (even2odd).

A schematic energy level diagram to measure the photoionization cross section from the 4p excited stateof potassium along with the relevant excitation paths is shown in Fig. 1. The atoms from the 4s 2S1/2 groundstate can be promoted to either 4p 2P1/2 or to 4p 2P3/2 state using a dye laser at 770.1 or 766.7 nm, respectively.The first dye laser is pumped by the second harmonic (532 nm) of a Nd:YAG laser and the laser light islinearly polarized with a polarization vector in the z-direction. The assessable transitions follow DmJ ¼ 0selection rules, the upper states possess mJ ¼+1/2 and �1/2. In the second step the atoms from either the2P1/2 or 2P3/2 level are ionized by the third harmonic (355 nm) of the Nd:YAG laser. The ionizing laser isalso linearly polarized and the polarization direction is parallel to that of the first step dye laser. Thecontinuum states are ed J ¼ 3/2, 5/2 and es J ¼ 1/2, with a dominating contribution from the ed channel.The ionizing laser beam is focused by a long focal length lens to ensure the spatial overlap of the excitingand the ionizing laser beams. The area of the overlap region in the confocal limit is calculated using the

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12985.17 cm-113042.89 cm-1

4p 2P1/2

4p 2P3/2

Continuum

355 nm

770.1 nm

4s 2S1/2

35009.82 cm-1

766.7 nm

Ground State

355 nm

Fig. 1. Energy-level diagram showing the two-step excitation and ionization paths.

N. Amin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 863–872866

equation [23,24]

A ¼ po20½1þ ðlz=po2

0Þ2�. (1)

Here o0 ¼ f l=pos is the beam waist and os is the spot size of the beam on the focusing lens. The cross-sectional area corresponding to 355 nm is calculated as 0.0017 (1) cm2 using the spot size of 0.115 cm at a focallength of 50 cm and Z is taken as effective length of the heating zone.

In the present work the absolute photoionization cross sections are determined using the saturation method[11]. Burkhardt et al. [10] applied the two-step ionization technique to measure the absolute cross section fromthe excited states of sodium, potassium and barium. These experiments were performed with certainassumptions that the intensity of the ionizing laser is higher, i.e., in excess to that required for saturating theresonance transitions and that the spontaneous emission is ignored during the 10 ns laser pulse. In addition,the transitions remain saturated during the laser pulse and the laser beam is uniform and linearly polarized.Under these assumptions the total charge per pulse is given by

Q ¼ eN0V vol 1� expsU

2_oA

� �� �, (2)

where e (coulomb) is the electronic charge, N0 (cm�3) is the density of the excited atoms, A (cm2) is the cross-

sectional area of the ionizing laser beam, U (joule) is the total energy per ionizing laser pulse, _o (joule) is theenergy per photon of the ionizing laser beam, Vvol (cm

3) is the laser interaction volume and s (cm2) is theabsolute cross section for photoionization. Subsequently, He et al. [11] reported the absolute photoionizationcross section of the 6s6p 1P1 excited state of barium. Their method for determining the photoionization crosssection is an extension of the saturation technique described by Burkhardt et al. [10] and accounting theeffects for the Gaussian laser intensity distribution. Recently, this technique has been used to determinethe photoionization cross section of lithium [25–27], helium [28], sodium [19,20,29], magnesium [30] andbarium [31].

We have recorded the signal intensity versus the pulse energy of the ionizing laser beam by inserting theneutral-density filters in the optical path of the ionizing laser. The ion signal is registered on a storageoscilloscope and on a computer for further processing. The measured data points, ionization signal versuslaser energy, are shown in Fig. 2. The solid line that passes through the experimental data points is a least-square fitting to Eq. (2). It is evident from these figures that as the intensity of the ionizing laser increases, theion signal increases up to a certain value very swiftly and then changes slowly. The multi-step photoionizationdepends on the flux of the ionizing laser pulse, which enables the absolute measurement of the photoionizationcross section. At saturation ionization the photon flux of the ionizing laser equalizes the population of theintermediate states. Fitting of the experimental data for the 4p 2P3/2 state yields the cross sections ¼ 7.271.1Mb. The photoionization cross sections extracted in the present work and in that of Burkhardtet al. [10] as 7.6Mb were achieved at the same ionizing laser wavelength and both these values are in excellentagreement within the experimental uncertainties. We have extended our studies to determine the

ARTICLE IN PRESS

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4p 2P3/2σ = 7.2 ± 1.1 Mb

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4p 2P1/2σ = 5.6 ± 0.8 Mb

Fig. 2. Photoionization data for the (a) K (4p 2P3/2) and the (b) K (4p 2P1/2) states. The solid line shown is the least-square fit of Eq. (2) to

the observed data for extracting the values of cross -section s (Mb).

0 2 3 4 50

2

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6

8

Cro

ss-s

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b)

Photoelectron energy (eV)

Petrov et al. [15]Petrov et al. [15]Burkhardt et al. [10]Present work

1

Fig. 3. A comparison of the photoionization cross sections of the present and previous work for the 4p 2P3/2 excited state of potassium.

N. Amin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 863–872 867

photoionization cross section from the 4p 2P1/2 state at 355 nm. The data presented in Fig. 2(b) yields ¼ 5.670.8Mb. It is worth mentioning that the absolute value of photoionization cross section for this stateis reported for the first time. Theoretical calculations to supplement these studies are desirable.

A comparison of experimental and calculated cross sections above the ionization threshold is shown inFig. 3. The solid line represents the calculated values of cross section of K(4p 2P3/2) excited state. The crosssections were computed using the configuration interaction Pauli-Fock with core polarization potentialapproximation [15]. It is evident from the theoretical curve that the photoionization cross section has strongestwavelength dependence above the first ionization threshold. The experimentally measured values (‘‘m’’ presentwork ‘‘J’’ and ‘‘W’’ taken from Petrov et al. [15] and Burkhardt et al. [10]) are also shown in the figure. Theexperimentally obtained cross sections are nearly 6% larger than the computed ones, which may be due to theuncertainties embedded in the experimental techniques.

In the next set of experiments, we have measured the photoionization cross section from the 5d 2D3/2,5/2

excited state of potassium. A schematic energy-level diagram and relevant transitions are shown in Fig. 4. Inthe two-photon excitation process, we have excited the atoms from the 4s 2S1/2 ground state to the 4d 2D5/2,3/2

states at 30185.18 and 30,185.69 cm�1, respectively [32]. Since the experiment has been conducted using two-photon excitation, the width of the observed line is expected to be nearly twice the dye laser line width i.e.E0.6 cm�1 [33], which is larger than the fine structure splitting in the 5d states (0.51 cm�1); therefore, both the

ARTICLE IN PRESS

4s 2S1/2

12985.17 cm-113042.89 cm-1

4p 2P1/2

4p 2P3/2

Continuum

581.4 nm

770.1 nm

35009.82 cm-1

766.7 nm

Ground State

5d 2D5/2

5d 2D3/2 30185.69 cm-1

30185.18 cm-1

662.58 nm

583.35 nm

662.58 nm

Fig. 4. Excitation scheme for the measurement of photoionization cross section from the 5d 2D5/2,3/2 excited states of potassium using the

two-step and two-photon excitation from the ground state.

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4s 2S1/2 → 5d2D 5/2σ = 28.9 ± 4.3Mb

Sign

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Fig. 5. Photoionization data for the state 5d of potassium atoms corresponding to 4s 2S1/2-5d 2D5/2,3/2 transition. The solid line is the

least-squares fit to Eq. (2) for extracting the value of the photoionization cross-section s (Mb).

N. Amin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 863–872868

components are simultaneously populated. According to the two-photon excitation selection rules, D‘ ¼ 0,72, DJ ¼ 0, 72, DL ¼ 0, 72, DS ¼ 0 and odd2odd or even2even parity, the 5d 2D5/2 state can beaccessed from the ground state only. Therefore, the above-mentioned state can be ideally approached with thelaser light of known polarization, linear polarization in the present case. The dye laser is tuned to the 5d stateat 662.58 nm. A beam splitter is inserted in the optical path of the dye laser beam to split the beam into twoparts. One portion of the laser beam (about 30%) is passed through the thermionic diode, which is used toexcite the atoms. The excitation laser beam has a spot diameter �2mm. The energy of the first (exciting) laserwas adjusted such that the excitation signal from the 5d state can easily be saturated. The remaining secondportion of the dye laser beam (about 70%) acts as an ionizing laser beam, which is delayed by a few nano-seconds and directed through the thermionic diode. The intensity of the exciting laser beam is kept fixed, while

ARTICLE IN PRESSN. Amin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 863–872 869

the intensity of the ionizing laser beam is varied by using different neutral-density filters (Edmond OpticsUSA). The experimentally observed data for the photoionization of 5d 2D5/2 are shown in Fig. 5. The least-squares fit to Eq. (2) gives the photoionization cross section of this state as 28.974.3Mb. The dominatingcontribution in the photoionization cross section is from the ef continuum channels.

In the next experiment, we have excited the potassium atoms from the 4s 2S1/2 ground state to the5d 2D5/2,3/2 state via the 4p

2P1/2 and 4p 2P3/2 intermediate states using the two-step excitation scheme. The firstlaser excites the atoms from the 4s 2S1/2 ground state to the 4p 2P3/2 state. From the 4p 2P3/2 intermediate state,the 5d 2D5/2,3/2 states are populated via single-photon excitation at 583.35 nm. The second dye laser beam isfurther divided into two parts. One part of the dye laser beam acts as an exciting laser beam while the secondpart of the dye laser beam is delayed by a few nano-seconds and act as ionizing laser. Both the dye laser beamsare spatially overlapped during the experiment. By varying the intensity of the ionizing laser beam, we haveregistered the ion signal at each point. The experimentally observed data for the photoionization of 5d 2D5/2,3/2

are shown in Fig. 6(a) together with the curve obtained by fitting Eq. (2). The best fit yields thephotoionization cross section s ¼ 30.274.5Mb.

In the third experiment, we have excited the potassium atoms from the 4s 2S1/2 ground state to the 5d 2D3/2

state via the 4p 2P1/2 intermediate state using the two-step excitation technique. According to the alloweddipole selection rules, only the 5d 2D3/2 state can be accessed from the 4p 2P1/2 intermediate state. In this casethe ionizing laser beam is adjusted at 581.4 nm and the corresponding data are presented in Fig. 6(b), whichyields the absolute value of the photoionization cross section from the 5d 2D3/2 excited state ass ¼ 25.173.8Mb.

From the comparison of Figs. 6(a) and (b) we have observed that the cross section of the 5d 2D5/2,3/2 states,accessed from the 4s 2S1/2 ground state via a two-step excitation though the 4p 2P3/2 intermediate state, isslightly higher than the photoionization cross section determined from the 4s 2S1/2 ground state via the two-step excitation though the 4p 2P1/2 intermediate state. Since via two-step excitation from the 4p 2P3/2

intermediate state both the 5d 2D3/2 and 5d 2D5/2 fine structure components are populated, therefore thephotoionization cross section (30.2Mb) is the combined cross section of these states. From Fig. 6(b) it isevident that the cross section 25.1Mb from the 2D3/2 state is lower than the combined cross section 30.2Mb of5d 2D5/2,3/2. The polarization effects do influence the results for the photoionization cross section. The linearlypolarized laser induces an alignment in the electron cloud of the intermediate level, which influences the crosssection for the ionizing step in a way that depends on the angle between the electric vectors of the two lasersand on the ratio of the relevant electric dipole matrix. Petrov et al. [15] predicted that for parallel linearlypolarized light the cross section from Na(2P3/2) level should be higher than that from the Na(2P1/2). Indeed inpotassium, the measured cross section from the 4p 2P3/2 is higher than that from the 4p 2P1/2 states. However,a meaningful comparison for the 5d cross sections could be made if the photoionization cross sections were

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4s 2S1/2 → 4p 2P1/2 → 5d 2D3/2σ = 25.1 ± 3.8 Mb

4s 2S1/2 → 4p 2P3/2 → 5d 2D5/2, 3/2σ = 30.2 ± 4.5 Mb

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Fig. 6. Photoionization data for the state 5d of potassium atoms corresponding to (a) 4s 2S1/2-4p 2P3/2-5d 2D5/2,3/2 and (b) 4s 2S1/2-4p2P1/2-5d 2D3/2 transitions. The solid line is the least-squares fit to Eq. (2) in each graph.

ARTICLE IN PRESSN. Amin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 863–872870

determined from the 5d 2D5/2,3/2 and 5d 2D3/2 excited states at the same ionizing laser. In the present studiesthe ionizing lasers are slightly different, 583.35 and 581.4 nm. The comparison of photoionization cross sectionof two-photon excitation, from the 5d 2D5/2 ð3s

2S1=2�!2_o

5d 2D5=2Þ at 662.58 nm ionizing laser wavelengthcannot be made with the two-step excitation due to different mechanisms of populating the 5d state anddifferent ionizing laser wavelengths as the photoionization cross section has the strongest wavelengthdependence above the first ionization threshold.

In the third set of experiments, we have measured the photoionization cross section from the 7s 2S1/2 excitedstate of potassium. A schematic energy-level diagram and the relevant transitions are shown in Fig. 7. In thetwo-photon excitation process, we have excited the atoms from the 4s 2S1/2 ground state to the 7s 2S1/2 excitedstate lying at 30,274.26 cm�1 [32] using a linearly polarized dye laser tuned at 660.6 nm. As the process is non-linear, high intensity is necessary to excite the atoms, which is achieved by focusing the laser beam in theinteraction volume. The efficiency of ionization from the excited state is further enhanced by adding a seconddye laser beam of the same wavelength (660.6 nm), which brings the atoms to 10,402 cm�1 above the firstionization threshold. The original dye laser beam is split into two parts by a 30:70 beam splitter. One portionof the laser beam acts as an exciting laser and the remaining portion acts as an ionizing laser. The measureddata points, ionization signal verses laser energy, are shown in Fig. 8. The solid line that passes through theexperimental data points is the least-square fitting to Eq. (2), which yields the value of photoionization fromthe 7s 2S1/2 state as s ¼ 0.6170.09Mb.

4s 2S1/2 Ground State

660.6 nm

30274.26 cm-17s 2S1/2

35009.82 cm-1

660.6 nm

Continuum

Fig. 7. Energy-level diagram showing the two-step excitation and ionization paths.

0 1 2 4

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4s 2S1/2 → 7s 2S1/2σ = 0.61 ± 0.09 Mb

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Fig. 8. Photoionization data for the state 7s of potassium atoms corresponding to 4s 2S1/2-7s 2S1/2 transition.

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Table 1

Photoionization cross-sections from the 4p excited states of potassium

Transitions Present work Previous work

Cross section s (Mb)

718%

Ionizing laser (nm) Cross section s (Mb) Ionizing laser (nm)

Measured Calculated

4s 2S1/2-4p 2P3/2 7.2 355 7.6 [10] 355

6.8 [15] 6.2 [15] 453

7.3 [15] 6.7 [15] 422

7.0 [15] 6.9 [15] 351

4s 2S1/2-4p 2P1/2 5.35 [3] At threshold

4.80 [2] At threshold

5.6 355 – – –

Table 2

Photoionization cross sections from the 5d and 7s excited states of potassium

Transitions Present work Previous work

Cross section s(Mb) 718%

Ionizing laser

(nm)

Cross section s (Mb) Ionizing laser

(nm)Measured Calculated

4s 2S1/2-5d 2D5/2 (two-photon) 28.9 662.6 – 55.6 [1] At threshold

4s 2S1/2-4p 2P3/2-5d 2D3/2, 5/2 30.2 583.4 – – –

4s 2S1/2-4p 2P1/2-5d 2D3/2 25.1 581.4 – – –

4s 2S1/2-7s 2S1/2 0.61 660.6 – 1.75 [1] At threshold

N. Amin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 863–872 871

The experimental and the theoretical results of photoionization cross sections are presented in Tables 1and 2. The measured value of the cross section for 4p 2P3/2 in the present work is in general agreement withthose obtained in both theoretical and experimental work but comparatively little information is availableabout the cross sections from the 5d and 7s excited states of potassium. The overall uncertainty in all theresults is about 18%, which is attributed to errors in the measurement of the cross-sectional area of the laserbeam, the laser energy and the calibration of the detection system.

In conclusion, we have been able to report the absolute values of the photoionization cross sections from the4p 2P1/2,3/2, 5d

2D3/2,5/2 and 7s 2S1/2 excited states above the ionization threshold of potassium. It will beinteresting to have some theoretical calculations to compare with the experimental data.

Acknowledgments

The present work was financially supported by the Higher Education Commission (HEC), Pakistan ScienceFoundation (PSF-120), ICTP, Trieste, Italy, under the ICAC-affiliated centre scheme and the Quaid-i-AzamUniversity, Islamabad, Pakistan. Nasir Amin S.U. Haq, M.A. Kalyar and M. Rafiq are grateful to the HigherEducation Commission of Pakistan (HEC) for the grant of Ph.D. scholarship under the Indigenous scheme.

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