The in-gas-jet laser ion source: resonance ionization spectroscopy of radioactive atoms in supersonic gas jets
Yu. Kudryavtsev, R. Ferrer, M. Huyse, P. Van den Bergh, P. Van Duppen
TThe in-gas-jet laser ion source: resonance ionization spectroscopy ofradioactive atoms in supersonic gas jets
Yu. Kudryavtsev ∗ , R. Ferrer, M. Huyse, P. Van den Bergh, and P. Van Duppen Instituut voor Kern- en Stralingsfysica, KU Leuven,Celestijnenlaan 200D, B-3001 Leuven, Belgium
Abstract
New approaches to perform efficient and selective step-wise Resonance Ionization Spectroscopy(RIS) of radioactive atoms in different types of supersonic gas jets are proposed. This novelapplication results in a major expansion of the In-Gas Laser Ionization and Spectroscopy (IGLIS)method developed at KU Leuven. Implementation of resonance ionization in the supersonic gasjet allows to increase the spectral resolution by one order of magnitude in comparison with thecurrently performed in-gas-cell ionization spectroscopy. Properties of supersonic beams, obtainedfrom the de Laval-, the spike-, and the free jet nozzles that are important for the reduction ofthe spectral line broadening mechanisms in cold and low density environments are discussed.Requirements for the laser radiation and for the vacuum pumping system are also examined.Finally, first results of high-resolution spectroscopy in the supersonic free jet are presented forthe 327.4 nm 3d S / → P / transition in the stable Cu isotope using an amplifiedsingle mode laser radiation.
Keywords: resonance ionization spectroscopy, laser ion source, gas jet, de Laval nozzle, spikenozzle
1. Introduction
The method of laser Resonance Ionization Spectroscopy (RIS) [1, 2] was developed at theend of the last century. Nowadays resonance photoionization with pulsed lasers is widely used orplanned, in particular, for the production of pure beams of short-lived isotopes at several on-lineRadioactive Ion Beam (RIB) facilities [3–18]. In addition to the production of element-pure or ∗ Corresponding author
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[email protected], Tel.:+32 16327271, Fax:+32 16327985 (Yu.Kudryavtsev )
Preprint submitted to Nuclear Instruments and Methos B October 31, 2018 a r X i v : . [ phy s i c s . a t o m - ph ] N ov utoionizing state Metastable state Ground state λ λ IP Continuum a) b)
Fig.1 P T ρ RF ion guide laser beams λ , λ gas cell accelerator beam target ions to mass separator gas Figure 1: a) Layout of the in-gas-cell laser ion source for the production of radioactive ion beams, b) two steplaser resonance ionization scheme. P , T , and ρ represent the stagnation conditions of pressure, temperature,and density in the gas cell, respectively. isomeric-pure beams, RIS can be used to obtain nuclear-model independent information on theproperties of nuclear ground and long-living excited states such as nuclear spins, nuclear mag-netic dipole moments, quadrupole moments, and changes in the mean-square charge radii fromatomic spectra [19–25]. Numerous two- and three-step ionization schemes have been proposed toproduce and investigate radioactive nuclei using resonance ionization techniques [26]. Since theradioactive isotopes of interest are created in nuclear reactions in very small quantities, togetherwith a huge background of contaminating nuclei, the RIB production and detection methodshave to be sensitive, efficient, selective, and fast. Currently, collinear Resonance Ionization Spec-troscopy (CRIS) in an accelerated atomic beam ( >
10 keV) [27–31] is one of the most sensitivedetection methods. Owing to the reduction of the Doppler width by the electrostatic accelera-tion [32], a high spectral resolution and a high selectivity can be provided for the detection ofshort-lived- and low-abundant long-lived radioactive isotopes [33–35].Another sensitive atomic spectroscopy and selective production method is in-source laser res-onance ionization spectroscopy. This method has been implemented in two distinctly different2ays at Isotope Separator On Line (ISOL) systems to produce RIBs and to perform laser spec-troscopy measurements. The two approaches are based on resonance ionization either in a hotcavity [36–38] or in a buffer gas cell [5–7, 39]. The spectral resolution in a hot cavity is limitedby Doppler broadening as the temperature has to be above 2000 K in order to keep the reactionproducts volatile and in their atomic form. In a gas cell, additionally to the room temperatureDoppler broadening, the spectral resolution is limited by collision broadening with the buffer gasatoms. In spite of the limited spectral resolution in comparison with the collinear photo ion-ization spectroscopy, the in-source technique is very sensitive; results have been obtained withbeams of less than 1 atom per second [40, 41], and it can be applied for the study of isotopeswith a large hyperfine splitting [42–44].The In-Gas Laser Ionization and Spectroscopy (IGLIS) technique, developed at KU Leuvensince the late 1980s [5, 6, 45, 46], is used at the Leuven Isotope Separator On Line (LISOL) facility[47] to produce short-lived radioactive beams in different regions of the chart of nuclides usinglight and heavy-ion induced fusion or fission reactions. The basic principle of the IGLIS methodcan be summarized as follows. Nuclear-reaction products are thermalized and neutralized inthe high-pressure noble gas in their ground- and possibly in low-lying metastable atomic states(see Fig. 1a). They are subsequently transported by the gas flow towards the exit orifice.Shortly before leaving the gas cell, the atoms undergo element-selective two-step resonance laserionization (Fig. 1b). Outside the gas cell the laser-produced ions are captured by the RadioFrequency (RF) field of a SextuPole Ion Guide (SPIG) for further transport towards the massseparator [48]. The use of a repelling voltage to suppress unwanted ions and laser ionize thenuclei of interest in an RF trap, the so-called Laser Ion Source Trap (LIST) technique, was firstproposed for the hot cavity approach [49] and recently successfully applied in on-line conditions[50]. The coupling of the LIST method to the gas cell approach was suggested at Jyv¨askyl¨a [51].In order to improve the spectral resolution and the selectivity, the possibility of laser ionization inthe free gas jet has been investigated at LISOL with 200 Hz [52] and 10 kHz [53] pulse repetitionrate lasers. In these experiments, the ionizing laser beams passed through the gas cell and theexit orifice to reach the expanding free gas jet. By applying a positive potential to the SPIGrods relative to the gas cell the ions created in the gas jet could be separated from those createdin the gas cell. Compared to in-gas cell ionization an improved spectral resolution down to2.6 GHz was achieved for in-gas jet ionization owing to the low pressure and low temperatureenvironment of the supersonic gas jet, however, major developments were required in order toimprove the efficiency, selectivity, and spectral resolution to be able to perform spectroscopic3 de Laval nozzle jet gas jet laser beam expander accelerator beam target
Spike nozzle jet P T ρ gas jet accelerator beam target a) b) Free jet
Fig.2 c) gas gas P T ρ P T ρ λ accelerator beam target gas λ λ gas jet λ λ λ Figure 2: Proposed setup layouts for the production and spectroscopy of radioactive isotopes in a) a free jet, andin jets produced by b) a de Laval nozzle and c) a spike nozzle. The production target is here located in the gascell and the primary beam from the accelerator is therefore entering the cell. studies of the nuclei. The supersonic gas jet can be a natural part of the target-ion-sourcesystem for on-line mass separators. In this paper we propose new approaches for high-resolution,efficient, and selective step-wise laser resonance ionization of radioactive atoms using differenttypes of supersonic jets. The spectral resolution that can be reached in the supersonic gas jet iscalculated and found to be far superior to that in the gas cell. The requirements for the laserradiation and for the vacuum pumping system are also discussed. Finally, first off-line results oftwo-step high resolution laser resonance ionization spectroscopy in the supersonic free jet thatshow the feasibility of this method are presented.4 . Brief introduction to the different jet-formation schemes
Three different approaches for gas-jet formation suitable for resonance ionization are consid-ered in this article and can be found schematically illustrated in Fig. 2. • The supersonic free-jet expansion technique, Fig. 2a, proposed in [54] is used nowadays indifferent fields of research involving cold atoms and molecules. Effective translation, rota-tion, and vibration cooling of the molecules seeded into the jet allow to perform fluorescencespectroscopy of complex molecules with very high resolution [55, 56]. Sub-Doppler resolu-tion was achieved with very well collimated beams, where owing to the strong collimationonly a small part of all atoms coming out the gas cell were used. The most importantadvantage of this low-temperature molecular spectroscopy consists in the simplification ofthe spectra due to the compression of the population distribution in low-lying vibrationand rotational levels. The collimated supersonic free-jet beams in a crossed-beam geometryprepared in well-defined states are used to study chemical reaction dynamics [57]. Studiesof gas-jet formation have been performed in preparation of the gas cell-based LIST project[58, 59]. • Unlike the free-jet nozzle, the de Laval nozzle, Fig. 2b, has been used to produce a homo-geneous flow of cold molecules to investigate ion-molecular and neutral-neutral reactions atvery low temperatures [60–64]. Continuous-flow and pulsed-supersonic-expansion appara-tus have been developed. Carefully designed nozzles allow to obtain a homogenous flow anda low temperature zone of up to 30 cm in length [65]. A pulsed de Laval nozzle has beenused to study neutral-neutral reactions initiated by laser photolysis and consecutive laserphotoionization of the product species inside a time-of-flight mass spectrometer [64]. Theuniform, supersonic, and axisymmetric beams have been combined with a high-resolutionFourier transform spectrometer to perform infra-red molecular absorption spectroscopy[66]. The properties of high-Mach-number jets have been studied to better understand thebehavior of astrophysical jets simulated in an Earth Laboratory [67]. • The third type of nozzle that will be considered in this article is an axisymmetric spikenozzle, Fig. 2c. This nozzle also allows to produce a quasi-parallel supersonic atomic beamwith high Mach numbers. Applications of this type of nozzle though is currently mainlylimited to the rocket design [68, 69]. 5 as cell chamber Diff. pumping chamber Extraction chamber S-shaped RFQ de Laval nozzle Gas Cell
Thin entrance window Position of the stopped nuclei
Gas jet < 1 · -5 mbar · -3 - 2·10 -5 mbar 2 -1 · -2 mbar Extraction electrode
Extraction RFQ λ λ In-gas-cell ionization In-gas-jet ionization λ λ Ion collector
Towards mass separator
Fig.3 from in-flight separator gas
Figure 3: Generic layout of an In Gas Laser Ionization and Spectroscopy (IGLIS) setup coupled on-line to anin-flight mass separator.
3. In-gas-jet laser ion source. Principle of operation
Gas catchers are used in radioactive ion beam research as an alternative to solid or liquidcatchers owing to the physicochemical limitations of the latter. Nuclear reaction products re-coiling out of a target located in the gas cell or coming from an in-flight mass separator caneffectively be stopped in a high pressure noble gas. The buffer gas pressure needed to stop thenuclear reaction products is defined by the energy of the ions and their atomic mass number.Argon at a pressure of 100-500 mbar is the most suitable gas because of its large stopping power.Helium can also be used for nuclear reactions with small recoil energy. Two possibilities can beconsidered: one can optimize the choice of the gas and the design of the gas cell to thermalize thenuclei in their 1 + (possibly 2 + ) charge-state and evacuate them as such [70–74] or, alternatively,all parameters can be optimized in order to have the nuclei neutralized in their atomic groundstate. Figure 3 shows the generic layout of an In Gas Laser Ionization and Spectroscopy (IGLIS)setup coupled on-line with an in-flight mass separator. Energetic ions from the separator arestopped and neutralized in a well-defined volume inside the gas cell. Argon as a buffer gas isalso a better choice for neutralization as its recombination coefficient is one order of magnitudelarger than that for helium [75, 76]. Neutralized radioactive species are transported along withthe buffer gas towards the nozzle. In order to have only laser-ionized nuclei injected in the mass6eparator unwanted ions can be removed from the gas flow with the aid of electric fields appliedto collecting electrodes located inside the cell upstream of the nozzle. Since the primary beamand the reaction products create a high plasma density inside the cell, the collection of remainingions with electrical fields is not a trivial task [77]. To overcome this problem a dual chambergas cell [78] has to be used with the stopping volume out of the direct view of a second adjacentvolume, where the remaining ions can be collected safely with electrical fields and subsequentlaser ionization can be performed either within the gas cell or in the gas jet. In the setup depictedin Fig. 3, the dual chamber effect is accomplished by the displacement of the laser ionizationvolume relative to the axis of the incoming ion beam.In Fig. 3, a de Laval nozzle type is used to create an axisymmetric supersonic gas jet. Thisgas jet is characterized by a low atom density and a low temperature, which result in a strongreduction of the collision- and Doppler broadening mechanisms in comparison with those existingin the gas cell. Since the gas-flow velocity inside the gas cell is low, laser ionization in this regionshould be avoided, otherwise all atoms would get ionized and collected before they reach thejet. One should thus prevent the two laser beams from reaching inside the gas cell. To achievesuch conditions and at the same time provide high-resolution excitation and efficient ionizationin the two-step laser ionization process, a special geometry of the laser beams must be arranged.This can be realized in a crossed-laser-beam configuration with any of the nozzles consideredhere, or in the case of the spike-nozzle, even using a parallel beam geometry configuration. Theformer can be realized if the ionization volume in the supersonic atomic beam is defined by thecrossing of the first- and second step laser beams. Usually the first excitation step is employedfor the laser spectroscopy measurement. In this case the first-step laser beam is directed axiallycounterpropagating with the supersonic atomic beam. The second step circularly-shaped laserbeam is converted by a one-dimensional telescope in a planar beam and is directed perpendicularto the supersonic beam, only in the region where a uniform and cold gas flow is formed, to ionizethe excited atoms. Notice that under these temperature conditions the population of those atomswith low-lying metastable states will be kept in the atomic ground state. Throughout this articleonly two-step ionization is considered but the same could also be applied to three-step laserionization schemes. In such a case, the third step laser beam can be directed perpendicular oralong the jet axis. The laser-produced ions are then moved by the gas flow in the directionof the S-shaped Radio Frequency Quadrupole (RFQ) ion guide, where they are confined andtransported through the gas cell chamber. Segmentation of the RFQ rods allows to use a dcdragging field to improve the transport efficiency. Additionally, a weak electrical field can be7pplied between the nozzle and the first segment of the RFQ ion guide to attract the laser ionsinto the RFQ structure. The bending of the RFQ structure allows to send the full beam of thefirst-step laser between the rods. In Fig. 3 an S-shaped RFQ is shown but a 90 ◦ bent RFQ canalso be used. The laser-produced ions are subsequently transferred to a linear RFQ, acting as adifferential pumping region, that guides the ions towards the acceleration region preceding themass separator. To assure that all atoms get ionized, the laser pulse repetition rate has to behigh enough to irradiate all radioactive atoms in the fast supersonic jet. The following conditionneeds to be fulfilled to ensure that all radioactive atoms interact with the laser light at least oncein their transit through the ionization region f laser ≥ / ( L/u ) , (1)where L is the length of the ionization zone and u is the jet velocity. For atoms moving in asupersonic argon jet with u = 550 m/s the length of the ionization zone has to be 5.5 cm for alaser pulse repetition rate of 10 kHz. To provide two-step ionization the first-step laser frequency ν has to be red-shifted owing to the Doppler shift undergone by the moving atoms, while thefrequency of the second step ν remains unshifted. We find then ν = ν · (1 − u/c ) and (2) ν = ν , (3)where ν and ν are the atomic transition frequencies of the first and second steps, respectively,and c is the speed of light. The spectral resolution that can be achieved is defined by thetemperature and the atom density in the jet.
4. Characterization of the supersonic jet produced by a de Laval nozzle
The de Laval nozzle is the most popular type of convergent-divergent nozzle that allows togenerate an axisymmetric supersonic flow of approximately constant temperature and density.Here we discuss only the properties of the gas jet that are important for selective, efficient, andhigh-resolution laser ionization spectroscopy of radioactive atoms. These atoms can be consideredas seeded into the buffer gas and as such they do not have any influence on the properties of thesupersonic gas flow. Indeed, for a total fusion cross section ∼ and a projectile beam current of 1 p µ A the total production rate amounts to about 10 nuclei/s,8
100 200 300 400 500 600 0 5 10 15 20 S t r e a m v e l o c i t y u ( m / s ) Mach Number
Argon
Fig.4
Figure 4: The argon stream velocity u at the exit of the de Laval nozzle as a function of the Mach number startingwith a stagnation temperature T = 300 K. which is much smaller than the typical buffer-gas flow of 10 atoms/s. The gas moving from thecell through the converging part of nozzle with a subsonic velocity becomes sonic at the nozzlethroat where the cross-sectional area (S ∗ ) is the smallest. Downstream in the divergent part,the gas expands and the stream velocity becomes progressively more supersonic. Provided thatduring the isentropic and adiabatic gas expansion the sum of the specific enthalpy and the kineticenergy remains constant, a very low gas temperature can be reached. The expansion is axiallysymmetric. The shape of the divergent part has to be designed to avoid reflection of secondaryexpansion waves [63]. The flow at the exit of the nozzle is uniform with parallel streamlines andit is characterized by the final Mach number ( M ), which is defined as the ratio of the streamvelocity u to the local speed of sound a , i.e. M = u/a . The speed of sound and the streamvelocity are expressed as a = (cid:114) γ k Tm and (4) u = (cid:115) γ k T M m (1 + [( γ − / M ) , (5)where k is the Boltzmann constant, m is the mass of the buffer gas atom, T and T are the gastemperatures in the jet and in the gas cell, respectively, and γ = C p /C v is the ratio of specificheat capacities, which for monatomic gases like argon and helium equals to 5 /
3. The streamvelocity for argon as a function of Mach number is shown in Fig. 4 for a stagnation gas-celltemperature T = 300 K. The stream velocity at M = 12 reaches 99% of its maximum valueof 558 m/s. The temperature T , the density ρ , and the pressure P in the supersonic flow arerelated to the corresponding values T , ρ and, P in the stagnation region of the gas cell via the9 .1 1 10 100 1000 0 5 10 15 20 25 30 T e m p e r a t u r e ( K ) Mach number T =300 K γ =
0 5 10 15 20 25 30 D e n s i t y , P r ess u r e Mach number
Density Pressure a) b) γ =
Fig.5
Figure 5: a) Temperature in the supersonic jet as a function of the Mach number for a monoatomic gas ( γ =5/3) at the stagnation temperature T = 300 K. b) Density and pressure reduction in the supersonic jet for amonoatomic gas relative to those in the stagnation region as a function of the Mach number. Mach number as TT = [1 + (cid:18) γ − (cid:19) M ] − (6) ρρ = [1 + (cid:18) γ − (cid:19) M ] − γ − (7) PP = [1 + (cid:18) γ − (cid:19) M ] − γγ − . (8)During expansion, the thermal energy of the atoms in the cell is converted into kinetic flowenergy. Figures 5a,b show the dependence of the temperature, the relative density, and the10elative pressure as a function of the Mach number for argon with the stagnation temperature T = 300 K. The gas temperature, density, and pressure drop very fast with increasing Machnumber.The radioactive atoms in the cell are in thermal equilibrium with the buffer gas atoms andthus they move with the same flow velocity and have the same temperature. For laser excitationnot the average velocity of the atoms but the velocity distribution components v i ( i = x, y, z )are important because they determine the width of the resonance lines. In the gas cell, the onedimensional Maxwell-Boltzmann velocity distribution of atoms F th ( v i ) is given by F th ( v i ) = (cid:114) m π k T · exp − (cid:18) m v i k T (cid:19) , (9)with m representing now the mass of the radioactive atom. The three directions x , y , and z areequivalent. The velocity distribution of the supersonic atomic beam in the direction of the flow( i = z ) is expressed by the shifted Maxwell-Boltzmann velocity distribution F ss F ss ( v z ) = (cid:114) m π k T · exp − (cid:18) m ( v z − u ) k T (cid:19) , (10)where u is the stream velocity defined by Eqn. (5). The other two components v x and v y ofthe supersonic velocity distribution are similar to Eqn. (9) with the temperature T defined byEqn. (6). The one-dimensional velocity distributions F ss ( v z ) in the supersonic beam for differentMach numbers and for the thermal motion in the gas cell F th ( v i ) at T = 300 K are shown inFig. 6. The full width at half maximum (FWHM) of these distributions for atoms with mass m depends only on the temperature and can be written as∆( F ) = 2 √ ln 2 · (cid:114) k Tm . (11)The mass flow through the de Laval nozzle is defined by the throat area S ∗ . The flowstreamlines are all parallel to the nozzle axis and the specified Mach number defines the shapeof the nozzle and its exit area S . The nozzle can be designed only for the preliminary definedexit temperature T , the mass flow and, the type of gas. The relationship between the exit andthe throat diameters can be calculated using the exit to throat areas ratio SS ∗ = 1 M (cid:20)(cid:18) γ + 1 (cid:19) (cid:18) γ − M (cid:19)(cid:21) γ +12 ( γ − . (12)The nozzle exit diameter for a noble gas and for a throat of 1 mm in diameter results in 4.88mm and 10.51 mm for Mach numbers 7 and 12, respectively.11 .000 0.005 0.010 0.015 0.020 0.025 0.030 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 800 I n t e n s i t y ( a r b . u . ) Velocity (m/s)
M=25
M=7
M=1 F ss (v z ) F th (v i ) T=300K Cu Fig.6
Figure 6: One-dimensional velocity distribution of Cu atoms in the gas cell (F th (v i )) and in the supersonicargon beam (F ss (v z )) for different Mach numbers and a stagnation temperature T = 300 K. In practice, viscous and heat transfer effects from the wall of the nozzle to the gas jet haveto be considered, particularly for small-size nozzles. This effects are usually taken into accountby splitting the flow into central isentropic core and boundary layer near the wall [63]. The flowuniformity outside the nozzle is strongly influenced by the background pressure in the gas cellchamber. Ideally the background pressure has to be equal to the static flow pressure defined byEqn. (8). The matching has to be done very accurately since it will define the beam divergencethat is crucial for the spectral resolution and for an efficient overlap between the laser beamsand the gas jet, as is discussed in the following paragraph.
5. Laser spectroscopy in a supersonic jet and in a gas cell
In this section we shall perform a comparison between laser ionization spectroscopy in agas cell and in a supersonic gas jet in view of the resulting resonance linewidth. The shapeof the spectral line is mainly determined by two broadening mechanisms: Doppler broadeningand collision broadening. The former is defined by the velocity distribution of atoms and has aGaussian shape, while the latter follows a Lorentzian distribution. The resulting shape of thespectral line will therefore be a convolution of Lorentzian and Gaussian functions which is knownas a Voigt profile or Doppler-broadened Lorentzian.12
200 400 600 800 1000 1200 1400 1600 0 2 4 6 8 10 12 14 16 18 20 D opp l e r F W H M ( M H z ) Mach number o o Fig.7
Figure 7: Doppler broadening (FWHM) of the 327.4 nm 4s S / - 4p P / transition in copper as a function ofthe Mach number (solid line). The pointed- and dashed lines show the increase of the linewidth for transverseexcitation caused by the jet angular divergence of 2 and 5 degrees, respectively. The Gaussian contribution to the line shape associated with the Doppler effect on theMaxwell-Boltzmann velocity distribution of atoms as expressed in Eqn. (9) is given by G ( ν ) = G · exp (cid:34) − c ( ν − ν ) ν
201 2 kTm (cid:35) . (13)The full width at half maximum of this distribution is∆ ν Doppler = 2 √ ln 2 ν c (cid:114) k Tm (14)and can be rewritten in the following way∆ ν Doppler = 7 . · − ν (cid:112) T /A , (15)where ν is the atomic transition frequency in cm − , T is the absolute temperature in K, and A is the atomic mass number. For example, for the 327.4 nm 4s S / → P / atomic transitionin copper ( ν = 30535.3 cm − ), the Doppler FWHM at T = 300 K amounts to 0.048 cm − or 1.43 GHz. In the supersonic beam the Doppler width is diminished owing to the reducedtemperature, as given by Eqn. (6). The dependence of the Doppler FWHM as a function of theMach number is illustrated in Fig. 7 by the solid line. It drops down to 200 MHz for the Machnumber M =12, which corresponds to a temperature of the atomic beam of 6 K. The effect of the13eam divergence is very important for the high Mach number atomic beams in case of transversedirection of the laser beam used for excitation. If the atomic beam is not parallel but has anangle θ between the stream velocity vector and the beam axis, then an additional broadening∆ ν tr = ν u sin θ/c (16)has to be added to the Doppler linewidth given by Eqn. (14) owing to the presence of theadditional velocity component u · sin θ in the direction defined by the laser used for excitation.This effect is also shown in Fig. 6 for the angles θ =2 ◦ and 5 ◦ . The Doppler width is increasedfrom 200 MHz up to 260 MHz or 350 MHz for a beam with Mach number M = 12 with divergenceof 2 ◦ or 5 ◦ , respectively. The influence of the beam divergence on the total Doppler width ismuch smaller if the laser light is directed axially with the atomic beam. In this case only thevelocity components along the jet axis u · cos θ contribute to the additional broadening. Thiscontribution can be written as ∆ ν ax = ν u (1 − cos θ ) /c , (17)which for an atomic beam divergence of 5 ◦ results in only 6.4 MHz. Non-resonant collisions of the atoms of interest with the buffer gas atoms cause a shift anda broadening of the spectral lines. The natural broadening associated with spontaneous decayof excited atoms, and the collision-induced shift and broadening are described by a shiftedLorentzian function L ( ν − ν ) = 12 π Γ( ν − ν + Γ sh ) + (Γ / , (18)where Γ = Γ nat + Γ coll represents the FWHM, and with Γ sh and Γ coll being the line shift- andbroadening rates, respectively. The natural linewidth Γ nat depends on the atomic transitionprobability A between the ground and the excited levels and can be written asΓ nat = A / π . (19)The shift Γ sh and collision Γ coll rate parameters are proportional to the density ρ of the buffergas in the following way Γ coll = γ coll · ρ and (20)Γ sh = γ sh · ρ , (21)14
0 50 100 150 200 250 300 γ c o ll c o e ff i c i e n t T (K) n=0.3 n =0.41 Fig.8 Figure 8: Normalized collision-broadening coefficient (at T=300K) as a function of the temperature for twotemperature dependence indexes of 0.3 and 0.41. where the lower case γ coll and γ sh represent the collision and shift broadening rate coefficients,respectively. They are usually expressed in units of 10 − cm − /cm − , which approximatelyamounts to 8 MHz/mbar at room temperature. For most resonant atomic transitions γ sh hasa negative sign for argon and a positive sign for helium [79]. This means that the resonanceis shifted to a smaller frequency (red shift) if argon is used as a buffer gas. For example, the4s S / → P / transition at 327.4 nm in copper has a natural linewidth Γ nat = 22 MHz(A = 1.36 · s − ). The collision broadening rate coefficient γ coll in argon for this transitionhas not been measured but a close look at the literature values for similar transitions seems toindicate a value of about 1.5 · − cm − /cm − . The Lorentzian contribution to the spectrallinewidth Γ in the gas cell is mainly defined by the collision broadening and results in 1090 MHzand 5450 MHz for the gas pressure of 100 mbar and 500 mbar, respectively.In the supersonic jet with Mach number M = 12, the buffer gas density drops down to0.003 of the stagnation value ρ (see Fig. 5b) and the collision broadening Γ coll for a stagnationgas pressure P = 500 mbar equals to 16 MHz. This value is smaller than the natural linewidthΓ nat = 22 MHz, however, estimating the collision effect we assumed that the collision broadeningrate coefficient γ coll is the same as at T=300 K. In reality, γ coll has a power-law dependence onthe temperature of the form γ coll ≈ T n with (22) n = p − p − , (23)15here p characterizes the type of interaction of the lower and the upper atomic levels with thenoble gas [80, 81]. For the long-range attractive van der Waals potential ( p = 6) the temperaturedependence of the pressure broadening coefficient has the form of γ coll ≈ T . . In some casesthe repulsive part (C R − ) of the Lennard-Jons potential ( p = 12) correctly describes thetemperature dependence of the collision-broadening coefficient as γ coll ≈ T . . This dependenceis a more realistic power law for the broadening by light perturbers such as helium, while the T . relation is more suitable for heavier perturbers like argon. Experimental values of thetemperature dependence index n vary between 0.2 and 0.5 for different spectral lines and canbe used as a very crude approximation for the extrapolation of the measured coefficient towardslower temperatures [82]. Figure 8 shows the T n dependence of the collision broadening coefficientfor n = 0.3 and n = 0.41. One can safely conclude that by reducing the gas temperature thecollision-induced broadening coefficient can only be smaller than that at T= 300 K. The half width of the Voigt profile, which is the convolution of Gaussian and Lorentzianfunctions, cannot be expressed by an analytical formula. The FWHM of the convoluted shapecan be estimated using the following expression [83]∆
V oigt ≈ . (cid:113) . + ∆ ν Doppler . (24)For the 327.4 nm transition in copper the Voigt FWHM in the gas cell at T = 300 K results in∆ V oigt = 2110 MHz and 5830 MHz for 100 mbar and 500 mbar, respectively. In the supersonicgas jet ( M = 12) the Voigt FWHM results in 220 MHz and consists mainly of the Dopplercontribution. The different components that contribute to a single spectral line are shown inFigs. 9a,b for the gas cell at two different buffer gas pressures and in Fig. 9c for the supersonicgas jet with a Mach number M = 12. The spectral linewidth of the laser is also displayed in allfigures.For laser spectroscopy with pulsed laser beams a well suitable way to produce a narrow laserlinewidth is by amplification of the light from a continuous wave (CW) single mode laser in apulsed amplifier. For a Gaussian time profile of the pump laser pulse with a length of τ pulse ,the spectral line profile is the Fourier transform and has also a Gaussian shape with a spectralFWHM δ laser that can be calculated as δ laser = 441 /τ pulse , (25)16
500 -400 -300 -200 -100 0 100 200 300 400 500
Frequency (MHz) -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000
Gaussian Doppler Lorentzian collision Laser T =300 K P =500 mbar T =100 mbar Jet M=12 T =6 K ρ=0.003ρ Doppler Laser a) b) c)
Lorentzian
Fig.9
Figure 9: Gaussian, Lorentzian, and laser contributions to the shape of a spectral line in a) the gas cell P = 500mbar, T = 300 K, b) in the gas cell P = 100 mbar, T = 300 K , and c) in a supersonic gas jet of Mach numberM=12, T=6 K, and ρ = 0.003 ρ . a (atoms/cm ) 2 . · . · . · Collision broadening FWHM (MHz) 1086 15 3.3Natural Broadening (MHz) 21.7 21.7 21.7Lorentzian FWHM (MHz) 1108 37 25Voight FWHM (MHz) 2110 364 214 a Corresponding with a stagnation pressure P =100 mbarTable 1: P-T parameters and contribution of different broadening mechanisms to the 327.4 nm single spectralline in copper for the gas cell and for the supersonic gas jet. with τ pulse given in ns and δ laser in MHz. A laser pulse of 5 ns length has therefore a spectralbandwidth of 88 MHz, which is smaller than the Doppler width of the M = 12 supersonic beam(Fig. 9c). This spectral bandwidth can, however, still provide excitation of the essential part ofthe atoms in the beam resulting in a high ionization efficiency at resonance. In our example ofthe excitation of copper atoms the laser pulse length is shorter than the lifetime of the upperlevel (7.4 ns), and in a first approximation the saturation of the atomic transition is definedby the photon fluence (photons/cm ) and can be calculated as Φ sat = 1 / (2 σ ), where σ is theatomic transition cross section. However, to ensure the excitation of all atoms in the beam,power broadening has to be involved and the transition has to be oversaturated by a factor of4.3 [1] to excite all atoms in the inhomogeneous-broadened Doppler line profile. This will causeLoreantzian tails but the resolution will still be defined by the Doppler width (see Sec. 8 for moredetails). The contribution of different broadening mechanisms to the spectral line broadening inthe gas cell and in the supersonic gas jet with Mach numbers 7 and 12 are summarized in Tab.1. During the gas expansion of heavy atoms along with the lighter noble gas atoms the trans-lational energy of the first exceeds by tenfold their thermal energy in the gas cell. For example,atoms with atomic mass number A = 100 expanding in a helium jet have an energy of 1.64 eV.Although in collinear photonization spectroscopy much higher energies are used, this acceler-ation would already affect the line shape [32, 84, 85] and would cause an additional artificial18 .01 0.1 1 10 100 1000 0 100 200 300 400 500 H a g e n a p a r a m e t e r G * P (mbar) He Ar
Fig.10
Figure 10: Hangena parameter G ∗ as a function of the gas-cell pressure P for helium and argon at a stagnationtemperature T = 300 K and a throat diameter of 0.5 mm and 1 mm. The dashed line at G ∗ = 300 indicates thebeginning of fast growth of clusters. isotope shift [27] that has to be taken into consideration while measuring the chain of radioac-tive isotopes. In contrast to standard collinear spectroscopy where the energy of all isotopesremains constant, in the case of supersonic expansion the velocity of all isotopes is constant.This monokinetization during the gas expansion assures that no additional kinematic isotopeshift is produced. A difference between the velocity of the particles under investigation and thebuffer-gas velocity, the so-called ”velocity slip” effect, has been observed in the supersonic freejet expansion for heavy particles with a big mass difference and seems to be not important forheavy isotopes of the same element [86]. The expansion of the buffer gas through the nozzle results in a substantial cooling and con-sequently in small relative atom velocities, hence the interaction between atoms in the beam cancause formation of dimers, trimers, and even clusters. The dimer formation requires three-bodycollisions in which the third particle removes the excess of energy of the collision complex. Thedimers serve as condensation centers for further growth of clusters. This can happen only inthe beginning of the expansion part of the nozzle close to the throat, where the three-body col-lision probability is high enough. In principle, formation of multimers consisting only of noble19as atoms does not play an essential role for the laser excitation. However, this process can beimportant if the concentration of clusters is increased so much that it changes the properties ofthe gas jet. This nucleation process is related with the van der Waals interaction. The noblegas cluster formation has been studied extensively in many laboratories [87–91]. The clusteringeffect is determined by the temperature T and the pressure P in the gas cell, the shape andthe size of the nozzle [92], and the strength of the interatomic bonds. The onset of clusteringand the size of created clusters in a free jet can be described by an empirical scaling parameter G ∗ known as the Hagena parameter G ∗ = η d . T . P , (26)where d is the nozzle diameter in µ m, T is in Kelvin, P in mbar, and η represents the condensa-tion parameter related to the bond formation that results in 3.85 and 1650 for helium and argon,respectively. The dependence of the Hagena parameter as a function of the gas pressure is shownin Fig. 10 for argon and helium and for a throat diameter of 0.5 mm and 1 mm. The clusteringstarts when the Hagena parameter G ∗ >
300 [93], in such case the average number of atoms percluster N c is increased very fast from several atoms at G ∗ = 300 up to 1000 atoms per clusterat G ∗ = 2000. Only for large values of the nozzle diameter a high pressure can cause clusteringduring the jet formation. The number of atoms per cluster N c scales as N c ∼ G ∗ . − . and isextremely sensitive to the gas temperature in the cell N c ∼ T − . Consequently, a small increaseof the gas temperature in the case of argon can prevent the formation of big clusters withoutessentially influencing the Doppler resonance width.Formation of van der Waals molecules between the atoms of interest and the noble gas atomscauses a reduction of the efficiency. This molecular formation can only happen in the beginningof the expansion, where the three-body collision frequency is high enough. The amount ofmolecules formed depends on the condensation parameter η related to the interatomic bondformation. The formation of weakly-bound complexes of laser-produced radioactive ions withnoble gas- or impurity atoms plays a very important role in the case of laser ionization in thegas cell. Gas purity at the ppb (part per billion) level is required to minimize the reactionrate of the investigated species in ionic form with the impurity molecules [94]. In most casesthe weakly-bound complexes can be decomposed by an electrical field applied between the gascell and the RF structure. For in-gas-jet ionization, however, only the loss of the investigatedspecies in atomic form is important. Since the chemical reaction rate for atoms with the impuritymolecules is much smaller than that for ions, the requirements on the gas purity can be relaxed.20 .0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03
0 5 10 15 20 P ( m b a r ) Mach number
P = 500 mbar P = 100 mbar
0 5 10 15 20 W ( l / s ) Mach number d = 1 mm d = 0.5 mm a) b)
Fig.11
Figure 11: The required a) pressure P in the gas-cell chamber as a function of the Mach number M for a gas cell P = 100 mbar and P = 500 mbar at T = 300 K and b) pumping speed W as a function of the Mach number M for a nozzle throat diameter of 0.5 mm and 1 mm. Furthermore, the loss of laser-produced ions due to molecular formation in the jet is smaller thanthat in the gas cell owing to the low gas density and the short interaction times.
To ensure a homogeneous flow of the supersonic gas jet, the pumping system has to be ableto provide the required background pressure in the gas cell chamber. The pressure in the gascell is defined by the amount of gas needed to stop the energetic reaction products. The gasthroughput of the nozzle will then define the transit time of the radioactive atoms in the gas celland could lead to decay losses for short-lived nuclei. The amount of gas that has to be pumped21ut depends on the throat area, the pressure, the temperature in the gas cell, and the typeof noble gas. As mentioned before, the larger the Mach number one aims for, the smaller thebackground pressure should be. The volume flow rate of the buffer gas Q (in l/s) with atomicmass number A and stagnation temperature in the gas cell T (in K) is given by Q = 0 . d (cid:114) T A , (27)with the throat diameter d given in mm. The background pressure in the gas cell chamber P asa function of the required Mach number is obtained using Eqn. (8), and is shown in Fig. 11a foran stagnation argon pressure P = 100 mbar and 500 mbar. To provide this required pressure,the pumping speed of the vacuum system W (in l/s) should fulfill that W = Q P P . (28)The dependence of the pumping speed as a function of the Mach number is shown in Fig. 11bfor a throat diameter of 0.5 mm and 1 mm. Supersonic beams with a Mach number in the range5 to 15 require a gas cell chamber background pressure in the range between 2 and 0.001 mbarfor a gas cell pressure of 500 mbar, (see Fig. 11a). The combination of roots- and big turbomolecular pumps can provide the required pressure range.To avoid decay losses of the radioactive nuclei, the transit time in the gas cell should besmaller than their half-life. For example, isotopes of
Sn produced in the reaction Ni + Ti → Sn + 4n and separated by an in-flight mass separator enter the gas cell with an energy of88 MeV. They can be stopped in 500 mbar Ar gas at a distance of 12.3 mm relative to a 4 µ m Moentrance window with a longitudinal straggling range of 2.8 mm, see Fig. 3. The cross sectionof the Sn beam is about 3 by 4 cm . The volume of the stopping compartment of the dualchamber gas cell, downstream from the position of the stopped nuclei, together with the laserionization volume V cell is about 60 cm . In this case the transit time T tr of nuclei through thecell can be estimated as T tr = V cell / Q , where Q is the volume flow rate defined by Eqn. (27).For an exit orifice diameter of 1 mm, T tr amounts to 0.42 s, which is smaller than the half-lifeof Sn (T / = 0.94 s).
6. Laser ionization in the jet produced by an axisymmetric spike nozzle
The other type of jet that can be used for laser resonance ionization spectroscopy is theone provided by an axisymmetric spike (or plug) nozzle. The geometry of the spike nozzle isshown in Fig. 12a. As mentioned earlier usage of this type of nozzle, other than in the field22
10 20 30 40 50 60 70 80 90 0 5 10 15 20 A ng l e ( d e g . ) Mach number a) b) γ = λ λ S e / S t Mach number c) γ = λ λ ( ) M ϑ r e r t Cowl lip
Spike P o T o ρ o Gas jet
Figure 12: a) Shape of the spike nozzle and a possible laser beam arrangement for laser ionization and spectroscopy,b) the Prandtl-Meyer expansion fan angle as a function of the Mach number, and c) the exit- to the throat arearatio as a function of the Mach number for monoatomic gases ( γ = 5/3).
23f rocket design, can not be found in the literature. The reason for this might well be in themanufacturing difficulties to provide the tolerances required in smaller scale nozzles to thoseemployed in propulsion engine applications. As an example, the width of the ring slit in a nozzleof 8 mm in diameter giving a throughput equivalent to the 1 mm converging-diverging nozzlewould be only 31 µ m. Unlike the de Laval nozzle, the configuration of the spike nozzle allowsdirecting both laser beams for the two-step ionization along the nozzle axis as the laser beamscannot penetrate inside the gas cell. This fact enables excitation and ionization of atoms outsidethe cell only, where the gas flow is supersonic. Furthermore, in this beam configuration oneavoids the use of the laser beam expander, which reduces the laser energy density. This can beimportant if the second step transition is weak and is difficult to saturate with the available laserpower. However, to get a high spectral resolution the ionization should be performed only in theregion where a low gas temperature is reached. It should be noted here that this fact could favorthe use of a crossed laser beam geometry as well for this kind of nozzles.In the spike nozzle the gas from the stagnation region is accelerated to sonic speed whilemoving between two opposite walls, which are coming closer to each other. At the point whereone wall ends and the gas expands around its edge, the other wall forms the spike contour. Thedesign approach for the contour of the spike nozzle is based on a Prandtl-Meyer expansion fanaround a cowl lip. The optimal contouring of nozzles has been studied by several groups [95–99].In order to get the gas flow with the Mach number M to be parallel to the nozzle axis at its exit,the thruster angle θ ( M ) has to fulfill that θ ( M ) = (cid:114) γ + 1 γ − (cid:114) γ − γ + 1 ( M − − arctan (cid:112) M − . (29)This Prandtl-Meyer function is shown in Fig. 12b for the ratio of specific heat capacities γ =5/3. Similarly as for the de Laval nozzle, the exit- to the throat areas ratio S e /S t for the desiredMach number M should be fulfilled (see Eqn. (12)). The required ratio of areas as a function ofMach number is shown in Fig. 12c for γ = 5/3. The throat and the exit areas are defined as A t = π ( r e − r t ) cos θ and (30) A e = π r e , (31)with r t and r e representing the radii of the throat and the cowl lip, respectively. Since the Prandtl-Meyer equation is valid only for a planar plug nozzle configuration with a one-dimensional inflow,the method of characteristics is applied for the plug contour definition of the axisymmetric nozzle[100, 101]. Despite of the technical limitation found presently to construct a spike nozzle with24he suitable dimensions to be used in conventional laser laboratories the authors look forwardto the future technological progress that will allow the use of such nozzles in laser spectroscopyexperiments.
7. Laser ionization in a free jet
A supersonic free jet can be obtained in the expansion of gas through a round orifice from ahigh-pressure gas cell into a low-pressure gas cell chamber. The term ”free” refers to the absenceof external surfaces that restrict the gas expansion, as e.g. in the de Laval or spike nozzles. Theproperties of free jets have been investigated in detail [102–104]. During the gas expansion twotypes of shock zones are developed, see Fig. 13a. A barrel shock is formed around the center lineof expansion starting from the exit orifice. This expansion terminates at the second shock zone,referred to as the Mach disk, which is perpendicular to the centerline of the beam. Currently thereexist many techniques based on electron beam-induced fluorescence [105, 106] and light-inducedscattering- and fluorescence [107–109] techniques that allow visualization of the free-jet shockstructures. Figure 13b illustrates the visualization of an argon jet in a helium background witha pressure ratio of P /P bg = 1600 and a terminal Mach number M = 32. The analysis of imagesobtained through electron beam-induced fluorescence permits accurate density measurementsthat are important for detailed studies of the barrel shock and Mach disk morphology [110]. Thelocation of the Mach disk depends only on the ratio between the stagnation gas cell pressure P and the background pressure P bg in the gas cell chamber. The Mach disk distance expressedrelative to the orifice diameter d can be written as Z M d = 0 . (cid:115) P P bg . (32)Notice that Z M is not sensitive to the ratio of specific heats γ . The thickness of the Mach disk isof the order of the local mean free path and depends on the background pressure. The diameterof the Mach disk is more difficult to correlate since it depends on both P /P bg and γ . For anargon jet it is of the order of 0.45 Z M [111]. The position of the Mach disk for an orifice diameterof 0.5 mm and a stagnation temperature T = 300 K is shown in Fig. 13c as a function of theargon stagnation pressure P for the background pressure 0.05 mbar and 0.1 mbar. The core ofthe expansion, limited by the barrel- and the Mach disk shocks, is isentropic and its propertiesdo not depend on P bg . The expanding gas can be considered as ideal and heat conduction andviscous effects can be neglected. In the beginning of the expansion, where the flow is continuous,25 bg =0.1 mbar P bg =0.05 mbar
30 35 0 100 200 300 400 500 Z M , Z t ( mm ) P (mbar) Zt Z M d=0.5 mm T =300K Z M - Z t Mach disk jet boundary zone of silence P T ρ barrel shock λ Z t Z M λ a) b) c) Mach disk
Figure 13: a) Supersonic free jet expansion in vacuum and a possible arrangement of the laser beams. b)Visualization of an argon jet by the electron beam-induced fluorescence method [106] using helium as backgroundgas at the pressure ratio of P /P bg = 1600 (courtesy of the Department of Aerospace Engineering of the Politecnicodi Milano). c) Mach disk position Z M for a background pressure in the gas cell chamber of 0.1 mbar and 0.05mbar, and the location Z t of the terminal Mach number as a function of the argon stagnation pressure in the gascell for an orifice diameter d = 0.5 mm and T = 300 K. M ac h nu m b e r Distance (z/d)
Fig.14
Figure 14: Mach number in the free-jet expansion for a monoatomic gas ( γ = 5/3) as a function of the distancefrom the exit orifice measured in units of the exit orifice diameter. the gas temperature, pressure, and density are described by the same equations (Eqns. (6-8))as for the Laval nozzle. The gas undergoes isentropic wall-free expansion and the collision rate,responsible for the cooling, falls rapidly with increasing distance from the jet orifice. At somepoint in the expansion the collision rate is too low to provide continuum flow and the transitionto a free-molecular expansion begins. At this point the axial velocity distribution and the Machnumber is getting frozen. This terminal Mach number M t is defined by the total number ofcollisions that atoms undergo during the continuum expansion and can be calculated for argonas [112, 113] M t = 3 .
32 ( P d ) . , (33)where P is the stagnation gas cell pressure in mbar and d is the orifice diameter in mm. Thedistance in the orifice diameters at which this terminal Mach number is reached can be calculatedin first approximation as Z t d = (cid:18) M t . (cid:19) . . (34)This distance is also shown in Fig. 13c as a function of the argon pressure P for d = 0.5 mm and T = 300 K. Since the distance Z t does not depend on the background pressure it is possible toincrease the difference Z M − Z t to allow laser ionization in the so-called ’zone of silence’ [104]. Inthis case a minimum in the Doppler broadening can be obtained. In the example of Fig. 13c theterminal Mach number M t amounts to 21 at the stagnation pressure of 200 mbar and Z M − Z t =13 mm. The temperature corresponding to M = 21 is equal to 2 K and the Doppler broadeningat this temperature is much smaller than that associated with the divergence of the supersonicbeam. To estimate the influence of the divergence on the spectral linewidth one should know the27 Z /d B C C C C D E
Table 2: Parameters employed in the calculations of the centerline Mach number for the axisymmetric free jetflow in Eqns. (35) through (37) flow-field properties of the free jet.The variation of the centerline Mach number M as a function of the distance from the exitorifice z/d for z/d > M = B (cid:18) z − z d (cid:19) γ − − (cid:16) γ +1 γ − (cid:17) B (cid:0) z − z d (cid:1) γ − . (35)This equation describes the expansion as spherical with streamlines starting as a point sourcelocated at z /d . A better fit of the central line Mach number at smaller distances can beperformed using the following formulas [104, 115] M = (cid:16) zd (cid:17) γ − (cid:20) C + C ( zd ) + C ( zd ) + C ( zd ) (cid:21) for zd > . M = 1 . D (cid:16) zd (cid:17) − + E (cid:16) zd (cid:17) for 0 < zd < . . (37)Figure 14 shows the dependence of the central line Mach number as a function of the distancefrom the exit orifice as given by Eqns. (36) and (37). Already at the distance of 6 exit orificediameters a Mach number greater than 10 is reached. The parameters used in Eqns. (35-37) aregiven in Tab. 2.The atom density distribution for directions perpendicular to the jet axis is given by ρ ( y, z ) ρ (0 , z ) = cos θ · cos (cid:18) π θ φ (cid:19) and ρ ( R, θ ) ρ ( R,
0) = cos (cid:18) π θ φ (cid:19) , (38)where tan θ = y z and R = z + y . The dependence of the centerline atom density as a functionof the distance from the exit orifice is shown in Fig. 15a and the off-axis atom density distributionat different distances from the orifice in Fig. 15b. The off-axis distance is also defined in units ofthe orifice diameter. The inset in Fig. 15b displays the full width at half maximum of the atomdensity distribution as a function of the distance from the orifice. From this linear dependenceone can determine the angle of the jet relative to the central beam axis to be equal to 30.5 ◦ .This angle is obviously much larger than that obtained using the de Laval nozzle. Nevertheless,28 .0001 0.001 0.01 0.1 1
0 1 2 3 4 5 6 7 8 9 10 R e l a t i ve a t o m d e n s i t y ρ / ρ o Distance from jet axis (x /d) (y/d) z/d=1 z/d=3 z/d=10
0 2 4 6 8 10 F W H M x / d , y / d Distance from exit orifice (z/d) 0.0001 0.001 0.01 0.1 1 0 5 10 15 20 R e l a t i ve a t o m d e n s i t y ρ / ρ o Distance (z/d) a) b)
Fig.15
Figure 15: a) The centerline atom density in the supersonic free jet normalized to the density in the stagnationregion is shown as a function of the distance from the exit orifice. b) Atom density in the direction perpendicularto the jet axis normalized to the density in the stagnation region as a function of the distance from the jet axis,the inset shows the FWHM of the atom-density distribution as a function of the distance from the exit orifice.All distances are give relative to the exit orifice diameter and the value of the parameter φ in Eqn. (38) amountsto 1.365 for γ = 5/3.
200 400 600
0 5 10 15 20 D opp l e r b r o a d e n i ng ( M H z ) Mach number
From jet divergence
Total broadening
Fig.16
Figure 16: Total Doppler broadening in the supersonic free jet of the 327.4 nm 4s S / → P / transition incopper. The contribution to the total broadening caused by the divergence of the jet is also shown. by using the axial direction for the first step laser beam one can obtain a reasonable spectralresolution as given by Eqn. (17). In Fig. 16 the contributions of the jet divergence ( θ = 30.5 ◦ )to the resonance width and of the total Doppler broadening for the 327.4 nm line in copper areshown as a function of the Mach number. For M = 11 the contribution due to the divergenceresults in about 225 MHz, while the total Doppler broadening amounts to 440 MHz.
8. Requirements for the laser system
To ensure an efficient excitation and subsequent efficient ionization of radioactive atoms thelaser system should provide temporal and spatial overlap of the pulsed laser beams with theradioactive atoms in the supersonic jet and, in addition, the laser energy density should be highenough to saturate both transitions. These conditions can be fulfilled more easily for the de Lavaland the spike nozzles because they can produce long and well-collimated jets. A full temporaloverlap is guaranteed if the laser pulse repetition rate is high enough to irradiate all atoms inthe continuous atomic jet; for this to happen the condition given by Eqn. (1) should be fulfilled.For the spatial overlap the dimensions of the laser beams should not be smaller than the sizeof the gas jet. For two-step ionization processes via a short-lived auotioinizig state or throughthe continuum, the duration of the laser pulses of both steps and the time delay between themshould be shorter than the relaxation time of the population of the intermediate level. At thesame time, to get ionized the maximum fraction of atoms, the energy fluence (photons/cm ) ofthe pulse Φ , Φ must satisfy respectively the conditions30 ≥ Φ sat = (2 σ exc ) − and (39)Φ ≥ Φ sat = σ − ion , (40)with Φ sat , σ exc and Φ sat , σ ion representing the saturation energy fluence and cross sectionsfor the excitation and ionization steps, respectively [1]. The saturation energy fluence for theresonant transition is very low and can be easily obtained. For the excitation cross section in therange of 10 − -10 − cm − it is found to be between 3-300 nJ/cm ( λ = 330 nm). Equation (39)is valid for a laser bandwidth δ laser of the first step smaller than the homogeneous-broadenedspectral line Γ nat (Eqn. (19)). If the laser bandwidth given by Eqn. 25 is bigger than Γ nat ,the saturation energy fluence should be increased by a factor δ laser / Γ nat . The width of theresonance in a supersonic jet is mainly determined by the Doppler broadening (Eqns. (14,15)).The ideal condition for the first excitation step would be the equality of the laser and the Dopplerwidth. For the Doppler linewidth shown in Fig. 9c this condition can only be satisfied for Machnumbers greater than 20, see Fig. 7. The only way to excite all atoms in an inhomogeneous-broadened Doppler line for smaller Mach numbers is to oversaturate the transition by increasingthe energy fluence. The disadvantage of this is the presence of Lorentzian tails in a power-broadened spectral line. The energy fluence condition for the second step (Eqn. 39) is moreeasily fulfilled for the ionization via an autoionization level owing to the higher cross sectionin comparison to non-resonant ionization into the continuum. The laser bandwidth should besmaller than the linewidth of the autoionizing transition, which is usually bigger than 1 cm − .For a second-step transition cross section of 1 · − cm − , the saturation energy fluence resultsin 0.4 mJ/cm ( λ = 500 nm).
9. Experimental proof-of-principle of laser spectroscopy in a free jet.
The proof-of-principle for the in-gas-jet laser ion source using a free jet has been demonstratedat the Leuven Isotope Separator On-Line (LISOL) in a series of off-line experiments. In order toperform these tests, the front end of the mass separator had to be modified with the incorporationof a 90 ◦ bent RFQ to allow for the possibility of using a cross laser beam geometry with oneof the laser beams counterpropagating to the atomic jet, see Fig. 17a. In previous experiments[52, 53] either the laser beams passed first through the gas cell or were both sent transversallyto the jet, thus limiting the performance of the technique.31 ) L2 L1
Gas cell 90 o bent RFQ Towards extraction RFQ Shaped rod segments
Fig.17 b) L2 Gas cell Free jet expansion L1 90 o bent RFQ L1 P =200 mbar Extraction RFQ Extraction electrode
Towards mass separator -4 mbar 0.1 mbar Ar Cu filament
Gas cell chamber Extraction chamber
Figure 17: a) 3D view of the laser beams defining the ionization region and of the 90 ◦ bent RFQ ion guide. b) Lay-out of the experimental setup employed at LISOL for the high-resolution laser resonance ionization spectroscopymeasurements performed in the supersonic free jet with a crossed laser beam (L1 and L2) geometry. In these tests the standard LISOL gas cell for fusion-evaporation reactions [39] was placedin the gas cell chamber, see layout in Fig. 17b. Argon as buffer gas was supplied into the cellafter additional purification to sub-ppb level in a getter-based purifier. Copper atoms from aresistively-heated filament were seeded into the argon gas. Argon expanded from the gas cellinto the gas-cell chamber through the nozzle, which consisted of a sharp-edged orifice of 1 mmin diameter with a flat surface at the outer side of the nozzle flange and a spherical surface ofradius r = 5 mm at the gas cell side.The segmented 90 ◦ bent RFQ ion guide has an entrance- and exit linear parts, and a curvedpart with a central radius of 60 mm and an inter-rod spacing (inscribed diameter) of 12 mm. Therod segments are 9 mm long, 12 mm in diameter and are separated by 1 mm gaps in the axialdirection. The distance between the exit orifice and the first segment of the entrance part of theRFQ is 8 mm. The design of the RFQ ion guide allows to send the first step laser beam betweenthe rods counterpropagating with the supersonic gas jet. Four of the segments in the curved part32re especially shaped to let the full laser beam interact with the jet. A laser beam diameter ofup to 8 mm can be inserted through these segments towards the ionization region, see Fig. 17a.The second step laser beam was sent perpendicular to the jet axis. The crossing of the two laserbeams and the gas jet defined the zone of selective laser ionization. After the 90 ◦ bending theions were transferred into a smaller RFQ structure (inter-rod spacing of 4 mm, length of 4 mm,and diameter of the segments of 4 mm) acting as a pumping barrier that transported the ions intothe extraction chamber Fig. 17b. The combination of the LISOL pumping system [47] with thedifferential pumping element provided by the extraction RFQ resulted in a pressure suppressionfactor between the gas cell chamber and the extraction chamber of three orders of magnitude.Finally, the extracted ions were accelerated to an energy of 40 keV and transported to a dipolemagnet, where those ions with an A/Q= 63 were mass selected and subsequently detected by aFaraday cup or by a Secondary Electron Multiplier (SEM). The background pressure in the gascell chamber, which defines the size of the jet, could be precisely adjusted to a value of 0.1 mbarby changing the pumping capacity of the roots pump system by means of a movable shutter.The copper atoms in the supersonic free gas jet were ionized in a two-step process accordingto Fig. 18a. The ground state 3d S / atoms, excited by the 327.4 nm first step laser beamto the intermediate 3d P / level, were further excited by the 287.9 nm second step laserbeam to the 3d D / autoionizing state leading to ionization. The laser setup employedis similar to that described in [6] with the only exception that for these tests a narrow- bandlaser was used for the first excitation step. To accomplish this, a single mode tunable laser beamof 654.8 nm delivered by a continuous wave (CW) diode laser (Ta-pro, Toptica Photonics) wasamplified in a two-stage pulsed dye amplifier. To get the required radiation at 327.4 nm, theamplified light was frequency-doubled in a second-harmonic generation unit. The pulse lengthof the 327.4 nm radiation was 5 ns, which resulted in a spectral bandwidth of 88 MHz (Eqn.(25)). The first-step laser beam directed to the jet was additionally attenuated to avoid powerbroadening of the atomic transition. The second-step laser light at 287.9 nm was produced byfrequency doubling of the 575.8 nm (0.15 cm − bandwidth) radiation from a dye laser (Scanmate,Lambda Physik). The amplifier and the dye laser were pumped by two time-synchronized XeClexcimer lasers (LPX 240i, Lambda Physik) with a pulse repetition rate of 50 Hz. Both laserbeams were transported a distance of 15 m to the front end of the mass separator. The first-and second-step laser beams had a diameter of about 3 mm in the jet region and the center ofthe second step beam crossed the gas jet 6.5 mm away from the exit orifice, thus copper atomsin the region between 5 and 8 mm were ionized. The jet at this distance was about 7.5 mm in33iameter (see inset in Fig. 15b).In the reference cell, located in the laser hut, a collimated atomic beam of copper atoms witha natural abundance ( Cu= 69%, Cu= 31%) was produced by resistive heating of a graphitecrucible at a temperature of 1250 K. The residual pressure in the reference cell was 1 · − mbar.Atoms from the crucible entered the laser ionization zone through a collimating orifice of 3 mmin diameter. The collimation ratio of the atomic beam in the setup amounts to 1/12. About5% of the laser power was directed towards the reference cell. The first and the second steplaser beams were parallel to each other and crossed the atomic beam at 90 ◦ . The laser-producedions were pushed out the ionization zone by an electrical field and detected by a SEM. No massseparation was available in the reference cell. The ion signals from the gas jet and from thereference cell were recorded simultaneously as a function of the first-step laser wavelength. Thewavelength was measured by a lambda meter LM 007 (ATOS). The results presented here were taken at a stagnation pressure P = 200 mbar (pressure inthe gas cell) and background pressure P bg = 0.1 mbar (pressure in the gas cell chamber), henceresulting in a pressure ratio of 2000. The stagnation temperature was estimated to be T =300 K. The measured ion signal as a function of the frequency of the first step laser, given inwavenumbers, for the Cu isotopes in the gas jet and for the natural copper in the referencecell are shown in Fig. 18. The displayed frequency range covers two resonances correspondingto transitions from the ground state, with a total angular momentum F=1, to the first excitedstate, with F’=1 and F’=2, denoted in Fig. 18 by a and b , respectively. In the reference cell, the b line of Cu is mixed with a small contribution from the a line of the lower-abundant copper Cu isotope, illustrated by a dashed line. The centroid of line a of Cu is 60 MHz away fromthe center of line b of Cu towards higher wavenumbers and the contribution of this line to thewidth and the position of the Cu b line is not more than 10 MHz.The measured hyperfine splitting (the distance between the lines a and b ) of 995(30) MHzboth in the gas jet and in the reference cell is in agreement with the literature values of 1013.2(20)MHz [116] and 960(30) MHz [117]. The resonances in the jet are shifted to lower wave numbersrelative to those in the reference cell owing to the counterpropagating direction of the first steplaser with respect to the atomic beam. This Doppler shift amounts to 1830(30) MHz and results,using Eqn. (2), in a stream velocity in the ionization region of u = 599(10) m/s. Applying Eqn.(33), the terminal Mach number M t is found to be 28. However, this value is only reached at34 utoionizing state Ground state λ = 327.395 nm λ = 287.9 nm IP S P -1 D -1 Cu I a b cm -1 F’=2
F=2
F=1
995 MHz a) I on s i gna l ( a r b . u . ) Wavenumber ( cm -1 ) b) a a b b
450 MHz
300 MHz Cu Ref. Cell Cu Gas Jet Cu a Fig.18
F’=1
Figure 18: a) The two-step ionization scheme of copper atoms (not to scale) used in these experiments, b) ionsignal from Cu in the gas jet (purple) and from the copper sample of natural abundance in the reference cell(black). Points represent experimental values, while the solid lines are the best Gaussian fits to the experimentaldata in order to determine the total FWHM (see table 3). The dashed line is the contribution of the line a of Cu to the line b of Cu in the reference cell.
35 distance of 25 mm from the orifice. At the position of the second-step laser beam of 6.5 mm,the Mach number is equal to 11, see Fig. 14. At this Mach number, the stream velocity reachesalmost the maximum value (see Fig. 4) and it can be used to estimate the gas temperature inthe cell (see Eqn.(5)). If the temperature in the cell is 300 K, the stream velocity should be552 m/s, which should correspond to a Doppler shift of ∆ ν Doppler = 1683 MHz. The measuredshift points to higher gas cell temperature of 355 K and can be explained by the additionalheating of the gas caused by the glowing filament. Collisions in the free jet shift the spectralline position to smaller wave numbers. The shift-rate coefficient γ sh is usually smaller than thecollision-broadening coefficient γ coll [79]. The shift rate Γ sh (Eqn. (21)) is estimated to be notmore than 8 MHz, which gives the maximum error on the jet velocity of 2.6 m/s and on the gascell temperature of about 3 K.A key point in these studies was to find the answer to the question of what spectral resolutioncan be obtained by using a combination of axial excitation and transverse ionization in thesupersonic free jet. The measured width (FWHM) of the resonance was found to be 450 MHz forboth lines. Calculated contributions of different broadening mechanisms to the 327.4 nm spectrallines (F=1, F’=1,2) in copper in the ionization region of the supersonic free gas jet and in thereference cell are given in Tab. 3. In the jet ionization region, the main contribution to the totalVoigt line profile with a FWHM of 420 MHz is due to the Gaussian contribution with FWHM of402 MHz. The Gaussian width is defined by the residual Doppler broadening with FWHM of 242MHz at the jet temperature of 8.6 K, the additional broadening due to the divergence of the jet isestimated to be 150 MHz, and the laser bandwidth amounts to 88 MHz (5 ns laser pulse length).A Lorentzian FWHM of 30 MHz is mainly given by the natural linewidth of 22 MHz, resulting ina much smaller contribution due to the collision broadening. The experimentally found FWHM(450 MHz) is very close to that estimated (420 MHz). A smaller Doppler width can be obtainedin the case of performing the ionization farther from the exit orifice, where larger Mach numberscan be reached. The essential contribution to the linewidth comes from the jet divergence. Thiscontribution was reduced in the experiments to 150 MHz by restricting the ionization volume. Ifall atoms in the jet would undergo laser ionization the additional broadening would be 225 MHzand the total FWHM close to 500 MHz. Hence the gas jet divergence is the limiting factor forhigh-resolution spectroscopy in the free jet.In the reference cell the Doppler FWHM of the spectral line ∆ ν ∗ Doppler was found to be 249MHz. It was calculated using the expression ∆ ν ∗ Doppler = ∆ ν Doppler · sin (cid:15) , where ∆ ν Doppler isthe Doppler FWHM at the crucible temperature of 1250 K (15) and sin (cid:15) is the collimation ratio36ree Jet Reference CellStagnation temperature T (K) 355Stagnation pressure P (mbar) 200Mach number M 11Jet temperature T (K) 8.6Stream velocity (m/s) 599Doppler FWHM (MHz) 242Divergence broadening (MHz) 150Laser bandwidth (MHz) 88Gaussian FWHM (MHz) 402Atom density (cm − ) 1.8 · Collision broadening FWHM (MHz) 8Natural broadening FWHM (MHz) 22Lorentzian FWHM (MHz) 30Voigt FWHM (MHz) 420Experimental FWHM (MHz) 450Temperature of the crucible (K) 1250Doppler FWHM a (MHz) 2920Collimation ratio 1 / a For a temperature T= 1250 KTable 3: Conditions in the stagnation region (gas cell) and contributions of different broadening mechanisms tothe 327.4 nm spectral lines in copper (3d S / → P / ) in the ionization region of the supersonicfree gas jet and in the reference cell.
10. Conclusions and outlook
Different approaches for selective two-step laser resonance ionization that can be used forhigh-resolution spectroscopy of radioactive isotopes produced in nuclear reactions have beenconsidered in various types of supersonic gas jets. Although the efficiency of the total ionizationprocess was not determined in this study, it will be low due to the low repetition rate of thelasers (50 Hz) and to the limited overlap of the laser beams with the gas jet. An improvementof the spatial overlap will be possible when the de Laval or spike nozzles are used. A bettercollimation of the gas jet by these two types of nozzle will allows to obtain a much more efficientoverlap with the laser beams over a much longer distance. The cylindrical shape of such jets canbe made easier to match with the shape of the laser beams. Since the radial size of the de Lavaland the spike nozzle beams can be kept smaller than the radial size of the free-jet beam, a higherlaser-energy density will be available to saturate the atomic transitions. In addition, optimumtemporal overlap will be provided by high-repetition rate pulsed lasers of typically 10 kHz, thatwill enable irradiation of all isotopes in the well collimated fast-moving gas jet.The crossed first- and second-step laser beams interacting with the supersonic jet are criticalto select the ionization region with cold atoms when a high spectral resolution is needed. Here, ithas been shown experimentally that a spectral resolution δν/ν = 4.9 · − can be obtained usinglaser ionization in a supersonic free-gas jet. In this jet the resolution is limited by the intrinsicdivergence of the atomic beam. The spectral resolution can be further improved up to 2.3 · − by using better collimated supersonic jets produced by the de Laval- or by the spike nozzles.The IGLIS technique combining laser ionization in a gas cell or in a gas jet, is especiallyadapted for production and spectroscopy of rare radioactive isotopes (see Fig. 3). Broad res-onance structures can be first investigated using in-gas cell laser ionization and the obtainedZ-selective beams can be mass separated and sent to the typical experimental setups developedat ISOL facilities. When maximum selectivity and resolution is needed, repelling fields can beused to eliminate all contaminating ions and laser ionization might be performed in the gas jet.This will allow high-resolution and high-sensitivity laser spectroscopy studies in different exoticregions of the nuclear chart and also the production of purified-isomeric beams.The gas-jet properties that are important to achieve an optimum spectral resolution weredescribed without taking into account the influence of mechanical structures (such as the RFQ)38n the gas flow field. For the final design of the set-up, 3D fluid dynamics flow calculations willbe needed. Efforts in this direction are underway and prototypes will be validated. Moreover,optimal conditions to perform high-resolution spectroscopy with collimated supersonic beamsand with high repetition rate lasers will be investigated in a new off-line laboratory that is beingcommissioned at KU Leuven. As a next step for the on-line studies, high-resolution spectroscopyof Cu will be performed at LISOL.An optimized IGLIS setup to perform laser ionization spectroscopy in the gas cell and in thegas jet, including high repetition lasers, will be installed at the Super Separator Spectrometer(S3), which will be coupled to the superconducting linear accelerator of the SPIRAL2 facility atGANIL [119].
Acknowledgments
This work was supported by FWO-Vlaanderen (Belgium), by GOA/2010/010 (BOF KULeuven), by the IAP Belgian Science Policy (BriX network P6/23), by the European Commis-sion within the Seventh Framework Programme through I3-ENSAR (contract No. RII3-CT-2010-262010), and by a Grant from the European Research Council (ERC-2011-AdG-291561-HELIOS). We are grateful to E. Mogilevskiy for fruitful discussions during the preparation ofthe manuscript.
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