Appl Phys B (2011) 102: 841–849 DOI 10.1007/s00340-010-4194-4

Ionization yield of two-step photoionization process in an optically thick atomic medium of barium B. Jana · A. Majumder · P.T. Kathar · A.K. Das · V.K. Mago

Received: 7 May 2010 / Revised version: 21 July 2010 / Published online: 16 September 2010 © Springer-Verlag 2010

Abstract The kinetics of a two-step photoionization process in optically thick atomic medium of barium (Ba) is studied using the rate equation approach. In the first step, Ba atoms get resonantly excited by laser radiation from their ground state to an intermediate excited state and subsequently are ionized in the second step by another laser radiation. The absorption of exciting radiation is taken into account along its propagation direction (optically thick). However, the medium is assumed to be optically thin for the ionizing radiation. A numerical simulation is done to estimate the ionization yield for timevarying Gaussian shaped laser pulses. The required energy density of the laser pulse to saturate the excitation transition throughout the thick medium is calculated. The effect of optical delay between the laser beams on the ionization yield is simulated. The calculated ionization yield from the simulation is compared with the measured values.

1 Introduction The invention of lasers has provided tunable and intense monochromatic radiation in visible and ultraviolet range of electromagnetic spectrum. The resonant interaction of light and matter via electromagnetic dipole radiation leads to the technique of laser resonance ionization spectroscopy (RIS). In this method, two processes, namely excitation and ionization of atoms, are involved. Firstly, a laser pulse resonantly B. Jana () · A. Majumder · P.T. Kathar · A.K. Das · V.K. Mago Laser & Plasma Technology Division, Bhabha Atomic Research Centre, Mumbai 400085, India e-mail: [email protected] Fax: +91-22-25505151

excites an electron in an atom from an initial ground state to an intermediate excited state. Secondly, other photons, collisions or an electric field causes ionization of the excited atoms. So the RIS is a multi-step photon absorption process in which the final state is ionization continuum of an atom resulting in creation of an ion-electron pair from each atom. This enables the RIS technique [1, 2] to be highly sensitive (single atom/molecule detection) and extremely selective (1010 –1020 ). The RIS has widespread application in isotope separation [3] and metal purification [4] etc. It also makes it possible to measure on-line isotope shifts and hyperfine structures of short-lived radioactive isotopes. This generates knowledge of nuclear properties (nuclear spin, magnetic and quadrupole moment) of elements [5]. Two-step photoionization is the simplest of the multi-step photoionization schemes involving the excitation of a resonant intermediate electronic state and the subsequent ionization of the excited atom. It can be achieved using two different lasers, which simultaneously provide the advantages of individual tuning of wavelengths, fixing their intensities, pulse durations, spectral widths etc. The first two-step RIS experiment was performed on the ground state of rubidium atoms in a cell [6]. Since then the two-step isotope selective photoionization experiments were carried on various elements like uranium [7], samarium, europium, gadolinium [8], lithium [9–11], potassium [12], titanium [13], barium [14, 15] and palladium [16] etc. The motivation was to do the feasibility studies of isotope selectivity using cw and pulsed lasers and to separate the isotopes having application in the nuclear and medical industry. To quantify photoionization yield and isotope selectivity, the kinetics of the processes is described either by the density matrix [17, 18] or by the rate equations [14, 16, 19–21]. The applicability of the methods depends on the nature of laser-atom interaction (discussed latter). The rate equation approach is

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Fig. 1 (a) Low-lying singlet energy levels of BaI and (b) geometry for laser-atom interaction involved in two-step photoionization process

the simpler of the two. Letokhov et al. [19] have solved the rate equations of two-step ionization process analytically for synchronized rectangular laser pulses. The ionization yield has been calculated assuming equal statistical weights of the ground level and excited level [14, 16, 20]. The influences of laser line-width, laser pulse durations and charge-exchange processes during ion production and extraction on the isotope selectivity [21–23] have been studied for various elements. In all such calculations it is assumed that the medium is optically thin where the absorption of laser radiations is ignored. However, the effect of optically thick media needs to be accounted in situations where the media are dense and radiation is absorbed as it propagates through the medium. Such cases occur in laser beam propagation effects in atomic beams [24] and the X-ray emission from galaxies [25]. Our interest is to study the effect of electric field on a cylindrically shaped photoionized plasma (photoplasma). The plasma is produced by shining pulsed lasers on the atomic beam using the technique of two-step resonant photoionization [15]. We have chosen the barium (Ba) element for the following reasons: (i) It has reasonable vapor pressure (∼4.8 Pa at 1000 K), which implies that a high atom density can be obtained at low evaporating temperatures. (ii) It has several energy levels with large excitation cross sections that can easily be accessed with dye lasers having reasonable power densities for multistep ionization schemes. (iii) Further, it is our aim to study the role of condensable vapor and electrical conduction in photoion-extractors [26]. Ba satisfies the condition for being a conducting metal. In this paper we have described the kinetics of two-step resonant photoionization process of Ba in the formalism of rate equation for an optically thick atomic medium. The absorption of excitation radiation along propagation direction has been taken

into account whereas the medium is assumed to be optically thin for the ionizing radiation. A numerical simulation has been done to estimate the ionization yield for time-varying laser pulses. Different statistical weights of transition levels and the time delay between two pulses have been considered in the calculation. The calculated ionization yield has been compared with the experimental value.

2 Relevant atomic parameters of barium Neutral Ba is an alkaline earth element. It has atomic number 56 and atomic mass 137.327 amu (56 Ba138 ). In its ground state, 54 electrons are arranged in a closed xenon shell electronic structure with the remaining two 6s electrons available for optical excitation, [Xe] 6s2 . The partial energy-level diagram of few low-lying states of neutral atoms of barium, BaI, relevant for this study is schematically shown in Fig. 1. The first ionization potential of Ba atom is 5.210 eV. The ground state is designated 6s2 1 S0 , while the resonant state, 6s6p 1 P1 is at 18060 cm−1 [27]. The resonant transition of 6s2 1 S0 – 6s6p 1 P1 is at wavelength 553.5 nm, with its characteristic green color. The corresponding transition probability for spontaneous emission is about 1.19 × 108 sec−1 . The absorption oscillator strength of 6s6p 1 P1 is 1.59 [28] and its lifetime is 8.37 ns [29]. The degeneracy factor of ground state (g0 ) and resonant state (g1 ) are 1 and 3, respectively. The atoms from the 6s6p 1 P1 resonant state can decay to 6s5d 1 D2 (apart from ground state) with transition probability of 2.5 × 105 sec−1 [27]. The 6s5d 1 D2 at 11395 cm−1 is a metastable state. Decay from its metastable state to the ground state is for-

Ionization yield of two-step photoionization process in an optically thick atomic medium of barium

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Fig. 2 (a) Schematic of laser-atom interaction region. 1. Crucible, 2. Atomic beam, 3. Laser beams, 4. Photoplasma, 5. Parallel-plate electrodes. (b) Width view

bidden by parity but allowed by electric quadrupole transition [30]. This implies that the 1 D2 level has a long lifetime of ∼0.5 s [31]. Natural Ba has seven stable isotopes [32]. The heaviest isotope, 138 Ba is the most abundant (0.72). The shift in 553.5 nm resonant line of 138 Ba from other isotopes is in the range of 125–250 MHz [33]. There are three components in hyperfine structure of odd isotopes (135 Ba and 137 Ba), among them the signal strength of the first component is significant while others are negligible. The corresponding shift in resonant line of 138 Ba due to hyperfine structure of odd isotopes is nearly 300 MHz [33]. Laser-induced two-step, two-color resonant ionization scheme (Fig. 1) was used to ionize the atoms. Recourse was taken to the resonant transition because it has a large photoexcitation cross section, σ1 ∼ 3 × 10−16 m2 [34]. In the first step, Ba atoms were excited by 553.5 nm radiation and subsequently ionized by 355 nm radiation. The ionization cross section from 6s6p 1 P1 state to the continuum at 355 nm is σ2 ∼ 1.7 × 10−21 m2 [35].

3 Experimental details 3.1 Photoionization Photoionization process was performed in an atomic beam of Ba. It was configured in a manner such that the direction of vapor flow, combined laser beams and electric field were mutually orthogonal (Fig. 2). Details of the experimental systems were discussed elsewhere [15]. Here we describe in brief the salient features that were relevant to this study. The system consisted of a resistively heated furnace for atomic beam generation, laser systems for photoionization and parallel-plate electrodes for photoion collection. The furnace and the ion-collection setup were housed in a stainless steel vacuum chamber. Ba metal pieces were placed in a rectangular tungsten crucible, which was surrounded on its vertical sides by a tantalum filament. The filament was

Fig. 3 Temporal profile of 355 nm pulse of Nd:YAG laser and the dotted curve represents the fitted Gaussian shaped pulse

heated directly by passing current through it and radiation from it heated the crucible. The emanating vapor was collimated by a set of slits and this produced a vertically moving rectangular shaped atomic beam of Ba. Pulsed lasers were used for two-step, two-color resonant photoionization. The laser system consists of a Q-switched Nd:YAG laser operating at 20 Hz with its harmonic generation unit and a dye laser. The second harmonic of the Nd:YAG laser at 532 nm radiation pumped Rhodamine 6G dye in the dye laser which was tuned to provide the firststep excitation pulse at λ1 = 553.5 nm. The third harmonic of the Nd-YAG laser at λ2 = 355 nm radiation pulse was used as the second step to ionize the excited atoms. Although Ba has a lot of autoionization levels [19], we have used 355 nm radiation for the ionization step because it was easily available from the Nd:YAG laser and no further dye laser was required for the second step. Both the laser radiations co-propagated after combination in a beam combiner and overlapped with the atomic beam. Good temporal and spatial overlap of the two laser beams with the atomic beam was maintained for efficient ionization. The line-width (FWHM) was ∼9 GHz for 553.5 nm while it was ∼17 GHz for 355 nm. This implies that the excitation radiation was broadband and all isotopes of Ba were excited [15]. An optical delay of 4 ns (<8.37 ns, the lifetime of the 1 P1 state) was introduced between two laser beams such that the ionizing pulse arrived at the atomic beam after the exciting pulse and this increased the laser-atom interaction time. A measured temporal profile of 355 nm radiation is shown in Fig. 3. It was fitted with the Gaussian shaped pulse and the corresponding pulse duration (FWHM) was ∼9 ns. Similarly the dye laser radiation pulse of 553.5 nm had pulse duration of ∼7 ns. The ionization was carried at a height of ∼0.07 m (laser-atom interaction region) from the top of the crucible

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3.3 Atom density [36]

Fig. 4 Schematic circuit diagram for signal processing

lid. A cylindrically shaped Ba photoplasma with circular diameter of ∼0.01 m and length ∼0.1 m was produced. The average pulse energy in the laser-atom interaction zone was ∼2 J/m2 and ∼40 J/m2 for excitation and ionization steps, respectively. 3.2 Ion density The photoionization was carried out in between two parallelplate electrodes (Fig. 2). The electrode system was used to measure the photoion density. As charges move in an external electric field produced by the electrodes, they generate currents. The currents were recorded across series resistors connected to the electrodes. The schematic of the circuit for signal processing is shown in Fig. 4. The pulsed photoionization signal was measured by oscilloscope of 100 MHz bandwidth (M/s Tektronix, TDS 224). The Q switch pulse of Nd:YAG laser triggered it. The magnitude of the electric field (∼2.85 × 104 V/m) ensured that all photoions generated in one pulse were collected on the electrode (cathode). Maximum voltage applied was –1 kV. Since the photoions were produced in the center of the electrodes (Fig. 2(b)), the estimated mean free path of the electron-atom collision is ∼10 m (at electron energy ∼500 eV). It is much larger than the electron-atom interaction length (0.02 m) and inter-electrode separation (∼0.035 m). Hence the contribution to ionization of Ba atoms by electron-impact ionization was negligible. It was also verified that the effect of ioninduced secondary electron emission was insignificant [15] at these extraction voltages. The area of photoionization signal gave the total ions produced in photoplasma and its density was calculated from the knowledge of the interaction volume within 10% error. The photoion density for several values of atom density in the interaction zone was measured for fixed photon flux of the excitation and ionization pulses.

To measure atom density in the interaction region, separate experiments were performed. Measurements were carried out using the technique of absorption spectroscopy with Ba-hollow cathode lamp (Ba-HCL) as the emission source. The light emitted from Ba-HCL was divided into two parts, transmitted and reflected beams. The transmitted beam was sent through the Ba vapor and the reflected beam traveled outside the vacuum chamber and provided the reference signal. The intensities of transmitted and incident light of the resonant radiation (553.5 nm) were measured using monochromator (resolution 0.1 nm and focal length 1/4 meters) and photomultiplier tube combination. The signals were processed by a lock-in-amplifier, which was locked at reference frequency of the optical chopper. The atom density in ground state was estimated by the resonant absorption method of Mitchel-Zimansky [37]. In this method, the absorbed fraction A(= 1 − It /I0 ) of the spectral line along the absorption length (L0 ) was experimentally determined. Here, It and I0 are transmitted and incident line intensities emitted by the Ba-HCL. The I0 was measured when the atomic beam was absent. Since both the incident radiation from Ba-HCL and the atomic absorption coefficient have their corresponding frequency distribution, the absorbed fraction A was calculated by integrating the intensities over the line profile. In the calculation the emission and absorption line-widths are considered as different values. The integral depends on the absorption coefficient at center line and the ratio of the spectral width (half-intensity full widths) of the Ba-HCL source (∼1.2 × 109 Hz) and of the absorbing atoms. The width of the absorption profile is expressed as νABS (∼500 MHz) √ = {(νNL )2 + (νIS )2 + (νHF )2 + (νD )2 }. Here, νNL , νIS , νHF and νD are natural line-width, linewidth due to isotope shifts, hyperfine structure and Doppler width, respectively. From the linear relationship between the absorption coefficient at center line and the number density, the density of absorbing Ba atoms was estimated. Several values of atom density corresponding to various crucible temperatures were measured in the experiment.

4 Kinetics of two-step photoionization When laser photons interact with atoms, an atomic polarization is induced in atomic medium. Phase relation among the atomic dipoles decays in time and is defined by the phase relaxation time. Its value is nearly the inverse of the atomic absorption line-width expressed in frequency unit. If the relaxation time is less than the time of laser-atom interaction (∼laser pulse duration), the coherent atomic induced polarization decays spontaneously. This results in the interaction

Ionization yield of two-step photoionization process in an optically thick atomic medium of barium

to be incoherent. The opposite case is considered as coherent. When the interaction is incoherent, the photoionization process is described well by rate equations [38]. For coherent cases density matrix needs to be used. For our case, laser pulse duration (∼10 ns) is greater than the phase relaxation time (∼2 ns) and hence the kinetics of photoionization method has been described by the rate equations. 4.1 Formulation of rate equations The related transitions of the two-step two-color photoionization process in Ba are schematically shown in Fig. 1(a). When laser radiations interact with a vapor column of length L0 shown in Fig. 1(b), there is absorption of laser radiations, which depends on the product of neutral atom density (N0 ), absorption cross section (σi ) and the interaction length (L0 ). When their product is greater than or equal to unity (i.e. N0 σi L0 ≥ 1) there is significant absorption of laser radiation and the medium is known to be optically thick for the radiation. On the other hand, the medium is optically thin to the incident radiation when the product is less than unity (i.e. N0 σi L0  1). Since the bound to bound level transition is more likely than the bound to continuum transition, the excitation cross section σ1 (∼3 × 10−16 m2 ) is much larger than the ionization cross section σ2 (∼2 × 10−21 m2 ). For a typical atom density N0 ∼ 5 × 1016 m−3 there is absorption of the excitation radiation i.e. N0 σ1 L0 > 1 and negligible absorption of the ionizing radiation i.e. N0 σ2 L0  1. Under this condition the kinetics of the photoionization processes are described by the following rate equations [19]:   g0 ∂n0 + K1 n1 , = −σ1 J1 n0 − n1 (1a) ∂t g1   ∂n1 g0 = σ 1 J1 n0 − n1 − K1 n1 − K2 n1 − σ2 J2 n1 , (1b) ∂t g1 ∂ni = σ 2 J2 n1 , (1c) ∂t   g0 ∂J1 1 ∂J1 . (1d) + = −σ1 J1 N0 n0 − n1 ∂z c ∂t g1 The quantities n(t) represent the time-dependent normalized populations in the ground state (n0 ), intermediate excited state (n1 ) and the ionized state (ni ). J1 and J2 are the laser photon fluxes (photons cm−2 s−1 ) for the excitation and the ionization step respectively. K1 and K2 are the spontaneous transition probabilities from the excited state to the ground state and to metastable state, respectively. It is assumed that the initial atom density (N0 ) in the ground state is uniform throughout the interaction volume. The above three equations (1a, b, c) describe the population dynamics of different levels at a particular distance, z along the interaction length. Equation (1d) represents the variation of laser photon flux of excitation radiation, as the atomic medium is optically

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thick to the excitation radiation. These equations are also the same for an optically thin layer. A new local time variable τ = (t − z/c) is introduced [39] in place of global time t for simplicity in the calculation. The above equations are thus transformed in the following forms using local variables:   g0 ∂n0 + K1 n1 , = −σ1 J1 n0 − n1 (2a) ∂τ g1   ∂n1 g0 = σ 1 J1 n0 − n1 − K1 n1 − K2 n1 − σ2 J2 n1 , ∂τ g1 (2b) ∂ni = σ 2 J2 n1 , ∂τ   g0 ∂J1 . = −σ1 J1 N0 n0 − n1 ∂z g1

(2c) (2d)

The temporal variation of photon flux J (z, τ ) at a given z is discussed below. 4.2 Numerical simulation In our case the temporal profile of the laser pulse is not rectangular but nearly Gaussian in shape as shown in Fig. 3. The temporal variation of energy density Ei (z, τ ) of the Gaussian pulses [40] can be written as     Ei (z, τ ) = Eip (z) exp − (τ − τpi )2 /Ti2 4 ln 2 where Eip is the maximum energy densities at a particular z and at time τpi . Ti is the pulse duration (FWHM) of the laser pulse. The values of i = 1 for excitation pulse and i = 2 for ionizing pulse are chosen. It is not possible to solve the coupled equations analytically for the time-varying laser pulses. It is also difficult to achieve a perfectly synchronized laser pulses from two different lasers in experiment. So the above coupled differential equations (2a, b, c) are numerically solved using a fourth-order Runge–Kutta technique [41]. The time-dependent population of different levels and the ionization yield of the process at a particular z value are calculated. As the atomic medium is optically thick for the excitation radiation, its energy density variation along the propagation direction is given by (3), which is obtained from the solution of (2d), E1 (z) = E10 (z = 0) exp(−N0 σ1 z)

(3)

where E10 is the initial energy density of the excitation pulse incident on the medium at z = 0. A numerical program is written in FORTRAN language. The thick medium of thickness L0 is divided into many layers of thickness z such that N0 σ1 z  1. The layer of thickness z is considered to be thin medium and the energy density remains unchanged throughout the length of z. At each layer the peak value of the energy density for

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Fig. 5 (a) Variation of excitation energy density and (b) the corresponding change in ionization yield along length of thick medium, N0 σ1 L0 ∼ 1 for Np ∼ 1

excitation pulse is calculated from (3). At each layer the ionization yield is calculated from the simulation. To get a stable solution instead of unstable/periodic solution, the time step should follow the criterion t < (max [σ1 J1 ])−1 . In the simulation the following quantities are chosen: z = 1 × 10−3 m and t = 1 × 10−12 sec. It is assumed that the laser beams are co-propagating and remain parallel throughout the interaction length.

5 Results and discussion 5.1 Features of optically thin/thick medium The medium is defined as optically thin/thick to the incident radiation depending on the absorption of light intensity within the medium. The medium is optically thick when a significant part of the incident radiation is absorbed within the medium; otherwise it is known as optically thin for negligible absorption of the light. The absorbance of light in the medium depends on the value of N0 σi L0 , which physically represents the effective number of atoms for the interaction with incident radiation within σi cross section area. The criterion for optically thin medium is N0 σi L0  1, whereas N0 σi L0 ≥ 1 for the thick medium. In our case the medium has been experimentally varied from optically thin to thick for the excitation radiation by increasing N0 in the interaction region. In thick medium the energy required to saturate the excitation transition throughout the medium and the ionization yield both depend on the incident number of photons per atom (Np ). The number Np is defined as the number of photons in an individual laser pulse divided by the number of atoms seen by the pulse [37] and it is given by Np = hνNW0 L0 S . Here W is the incident pulse energy, hν is the photon energy and S is the cross section area of laser

beam. In thin medium, the pulse energy does not change significantly along the interaction length and as a result the ionization yield remains the same over the length. But in thick medium, the energy in the excitation pulse decreases along the length due to its absorption. For the optical thick medium of N0 σ1 L0 ∼ 1 and the incident excitation pulse of Np = 1 at z = 0, the change in energy density of excitation pulse is shown in Fig. 5 (curve a). Figure 5 (curve b) shows the change in ionization yield along the interaction length due to variation of the energy density of the excitation pulse. We have defined an average ionization yield in thick medium which is obtained from the ratio of total ions produced by laser radiation and the total neutral atoms in the interaction volume. The ionization yield is directly related to the incident photon flux of the excitation radiation, which can be increased by increasing the value of Np . The variation of average ionization yield with Np is shown in Fig. 6 for the medium with N0 σ1 L0 ∼ 1. When Np is sufficiently large, the laser radiation strongly bleaches the working excitation transition in every layer along the length and the population in excited state gets saturated throughout the length. As a result the ionization yield remains constant over the length. In view of the ionization yield calculation, the corresponding thick layer can be treated as a thin layer with constant ionization yield along the length. From Fig. 6 it is seen that the required number of photons per atom is nearly 15 to completely bleach the transition in the optical medium with N0 σ1 L0 ∼ 1. It is observed from the simulation that the ionization yield will be maximum when both excitation and ionization transitions are simultaneously saturated by their corresponding laser radiations. 5.2 Effect of time delay between pulses The ionization rate from the excited state depends on ionization probability and the number density in the excited state

Ionization yield of two-step photoionization process in an optically thick atomic medium of barium

Fig. 6 Variation of average photoionization yield with incident number of photons per atom for optically thick medium, N0 σ1 L0 ∼ 1

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Fig. 8 Time-dependent variation of normalized populations density in ground state (n0 ), excited state (n1 ) and ionized state (ni ) with the measured values of different experimental parameters

ization yield will be optimum when there is a good temporal overlap and a small delay in time between the laser pulses. 5.3 Population dynamics of Ba atoms

Fig. 7 Variation of ionization yield with time delay between two laser beams

simultaneously. It is seen from Fig. 3 that the temporal profile of the laser pulse is nearly Gaussian in shape. Therefore it takes time to get sufficient population in the excited level by the initial rising part of the exciting pulse. The excited atoms are ionized with greater ionization rate by the second laser pulse which comes with a time delay relative to first one. Figure 7 shows the variation of the ionization yield with time delay between exciting and ionizing pulses. It is observed that the ionization yield increases, reaches a maxima and decreases with delay time. Initially the yield increases with delay time due to the greater ionization rate. The decrease in ionization yield is due to (1) the less temporal overlap between the pulses and (2) deexcitation of excited atoms by a spontaneous emission process before arival of the ionizing pulse. Therefore it is observed that the ion-

Figure 8 shows the variation of normalized population densities with time in ground state (n0 ), intermediate excited state (n1 ) and ionized state (ni ) for initial atom density N0 = 5 × 1016 m−3 . For the Gaussian pulse, all the photons are distributed within a time which is nearly three times of its pulse duration (FWHM). In the experiment, the time spans of excitation and ionization pulses are ∼21 ns and ∼27 ns, respectively, and the ionizing pulse comes after 4 ns with respect to the excitation pulse. The total time span is divided into four regions. In region I (0–4 ns), only the initial rising part of the excitation pulse is present. In our case, the energy density of the excitation pulse is too large (Np ∼ 1100) with respect to the required energy density to saturate the corresponding transition. As a result it completely bleaches the transition throughout the medium and the population in the excited state gets saturated immediately with the initial rising part of the exitation pulse. Almost 75% of the atoms are populated in the excited state. More than 50% population is observed in the excited state because it has a higher degeneracy factor than that of the ground state. In region II (4–21 ns), both the excitation and ionization pulses are present. Because of the ionization process, the population decreases in the excited state and increases in the ionized state. In region III (21–27 ns), there is only ionizing pulse. The available energy density of the ionizing pulse is much less than that required to saturate the transition. As a result a small fraction of atoms (∼10%) are ionized. Since the atoms in the excited state has a finite life time (∼8.37 ns)

848 Table 1 Comparisons between experimentally measured and numerically estimated ionization yield of two-step photoionization process

B. Jana et al. Experimentally measured

Ionization yield

Estimated from

experiment

numerical simulation (%)

Atom density N0 (/m3 )

Ion density Ni (/m3 )

(4.0 ± 0.4) × 1015

(3.8 ± 0.4) × 1014

9.5 ± 1.9

10.95

(5.0 ± 0.5) × 1016

(5.0 ± 0.5) × 1015

10.0 ± 2.0

10.82

(6.0 ± 0.6) × 1017

(4.0 ± 0.4) × 1016

6.7 ± 1.3

4.20

the remaining excited atoms relax through largely populating the ground state. This process is continued till region IV (>27 ns) where no laser pulses are present. 5.4 Comparison with experiment In the experiment, the total ions produced by the ionization method and the total neutral atoms have been measured within the interaction volume. They are measured with nearly 10% error and their ratio gives the measured ionization yield. Using the experimental values of various parameters the ionization yield is calculated from numerical simulation. Both the experimental and numerical results are compared in Table 1. The numerical values comply with the experiment within the error.

6 Conclusion The rate equations of two-step photoionization for optically thick atomic medium of Ba have been formulated. The absorption of exciting radiation (553.5 nm) along its propagation direction has been considered. However, for ionizing radiation (355 nm) the medium is assumed to be optically thin. Experiments have been performed to photoionize all the isotopes in two-step method using pulse lasers. The ionization yield has been measured. The rate equations are solved numerically to estimate the ionization yield for timevarying Gaussian shaped laser pulses. The experimental and simulated values are in good agreement (within 10%). It has been observed that when the number of photons per atom for excitation is large, the corresponding transition is completely saturated and the ionization yield remains constant throughout the medium. By introducing a small optical delay between the pulses, the ionization yield is maximized. Acknowledgements The authors thank to Dr. L.M. Gantayet, Director of Beam Technology Development Group, B.A.R.C., for his encouragement to pursue this work. They also thank to Dr. G.P. Gupta for helpful discussions.

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