Z. Phys. D 38, 201—209 (1996) CW laser spectroscopy of autoionising 6p 3/2 nl states of Barium G.J. Kuik, W. Vassen, W. Hogervorst Laser Centre Vrije Universiteit, Department of Physics and Astronomy, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands Received: 21 June 1996 Abstract. 6pnl states of Ba with l55, excited with two narrowband, tunable CW lasers have been studied. In the first excitation step 6snl states were populated from metastable states of the 5d2 configuration: to 6s40h (l"5) states in the absence, and to parabolic 6pnk (n"30, 35, 40) states in the presence of an electric field. The atomic motion was used to adiabatically reduce this field to zero before applying the second excitation step to high-l 6p nl 3@2 states (Stark-switching). A slow decrease in the autoionisation rate for increasing value of l and, in case of 6pnh, a dependence on the fine-structure state was measured. The narrowest autoionisation linewidth observed is 113(11) MHz, relatively close to the 20 MHz linewidth corresponding to the radiative lifetime of the 6p state of the Ba`-ion. PACS: 32.80.Dz; 32.70.Jz; 31.50.#w 1 Introduction Doubly-excited Rydberg states of two-electron atoms have been the subject of investigation by several theoretical and experimental groups. The studies on doubly-excited Rydberg states of alkaline-earth atoms partly focus on the understanding of autoionisation processes [1—6] and partly on effects of correlated electron motion [7—11]. High angular momentum Rydberg states received special attention as in this case the Rydberg electron does not penetrate the orbit of the inner (excited) electron, thus reducing autoionisation rates. To populate high angular momentum l-states from a low-l ground state in a onephoton excitation step a Stark switching technique can be applied. In pulsed laser excitation Stark switching is performed by excitation of a first electron in the presence of a strong electric field, followed by adiabatical reduction of the field to zero. A Rydberg electron excited in the presence of a sufficiently strong electric field is hydrogenic and may be characterized with a parabolic wavefunction (with parabolic quantum number k). It can be expressed as a sum of spherical harmonic functions with l"0 to l"n!1. The relative contributions of the spherical harmonics depend on the electric field strength. In the presence of an electric field in principle each parabolic quantum state k may be excited provided that the angular momentum l that can be reached in the one-photon transition is sufficiently strongly mixed into the k parabolic wave function. When the electric field is reduced to zero the composition of the k parabolic wave function changes to a pure single spherical harmonic function with l equal to k!1. In the present experiment, we use a Stark switching technique in an excitation process with CW lasers which does not allow to use the technique of simply changing a voltage over a set of two capacitor plates in time. The technique we applied is described in paragraph 2 of this paper. The application of CW lasers to populate doublyexcited Rydberg states is not obvious. In general, to reach doubly-excited states, powerful pulsed lasers are required which have a relatively broad bandwidth. Usually this is not a problem as fast autoionisation often results in broad resonances as well. However, in the case of doubly-excited high angular momentum Rydberg states the autoionisation rates may be strongly reduced and the high spectral resolution of a CW laser experiment becomes attractive. To demonstrate the use of CW lasers in the study of doubly-excited high angular momentum states we investigated 6p nl states with l55. These states, if sufficiently 3@2 narrow, may then be used for further excitation to e.g. 7dn@l@. The high resolution may provide new insights in a regime where spectra become extremely complicated [8]. 2 Experiment The experimental setup is an extension of the setup used in earlier studies of the properties of 6snh Rydberg states of Barium [12—14] and is shown schematically in Fig. 1. In the experiment we use a well-collimated atomic beam, in which metastable states of the 5d2 configuration are populated by running a DC discharge between the bariumfilled tantalum oven and a heating wire. A fraction of 202 Fig. 1. Experimental setup (E.M., electron multiplier; P.D., photo diode; W.P., Wollaston prism). E.M. 1 is used to detect the autoionising states whereas E.M. 2 is used to lock the first step about 10~4 of the atoms is transferred to the metastable 5d2 1G state at 24696.278 cm~1. The atomic beam is 4 perpendicularly intersected by narrow band (\1 MHz) laser light to eliminate Doppler effects to a large extent (\10 MHz). Due to configuration interaction this 5d2 1G 4 state has some 6s5g character, allowing for the direct excitation of 6snh Rydberg levels using a single Rhodamine 6G laser around 580 nm (ionization limit at 42034.902 cm~1). We used a CW frequency stabilized ring dye laser (Spectra Physics 380D) with an output power of typically 500 mW for good signal strength. In zero electric field both the 6snf and 6snh states are excited; however, excitation of 6snf states is an order of magnitude weaker. In the presence of a sufficiently strong electric field (perpendicular to the laser polarisation) all components of an angular momentum manifold originating from the 6snh state can be resolved and individually excited. The high J-value of the metastable state prevents selection of a single M-value. In two-step excitation experiments to 6pnl states the first laser was frequency locked on the transition to 6snh (field-free excitation) or to a selected angular momentum manifold component (excitation in an electric field). For this purpose we used a system with three well-shielded and separated interaction regions (see Fig. 2). In the first region a capacitor plate was mounted to generate a homogeneous electric field for the excitation of manifold peaks. The excited, long-lived Rydberg atoms leave the field adiabatically because of their relative slow motion in the gradually decreasing static electric field. This ensures that the atoms remain in the same state when the field decreases to zero. Downstream, in a second, well-shielded field-free interaction region the inner 6s electron is excited to 6p with a Stilbene 3 ring dye laser operating at 3@2 a wavelength of 450 nm (also Spectra Physics 380D). The excited nl electron is a spectator in this isolated-core excitation process. The zero-field excitation of the 6p 40h-multiplet was performed using only the second 3@2 and third chamber, with both lasers spatially overlapping. Electrons released by autoionisation decay of 6pnl states will diffuse through a grounded wire mesh and are counted with an electron multiplier. In a third interaction Fig. 2. Interaction Region: [1] First excitation in a homogeneous electric field; [2] Field-free inner-core excitation after Stark switching; [3] Field-ionisation of singly-excited atoms for locking the first laser to the atomic transition. (E.M."electron multiplier) 203 Fig. 3. Calculated energies as a function of the electric field strength for the n"40, DMD"4 manifold. The arrow at 1.5 V/cm shows the fixed laser frequency to excite the k"21 state. When the electric field is reduced to zero the character of the k-wavefunction changes until in zero field the l"k!1 state results. This is schematically depicted by the arrows pointing towards zero field along the k"21 electric field line Fig. 4. Calculated 6s40k Stark manifold at 1.5 V/cm. The individual lines are convoluted with a Gauss function (50 MHz FWHM) region the atoms left in the 6snl Rydberg state are field ionised and counted with a second electron multiplier. This signal is used to lock the laser for the first excitation step on the transition. For this purpose the laser frequency is modulated at 10 Hz and the ionisation signal demodulated using a computer controlled lock-in technique. The first laser may be frequency-locked to any component of the angular momentum manifold originating from the 6snh configuration in the presence of the electric field (linear Stark effect). The excited atoms leave the diverging field adiabatically over a distance of 12 mm, corresponding to a time of \30 lsec (atomic velocity \450 m/sec). A manifold state in the field, labelled with the parabolic quantum number k, obtains a pure l-character (with l"k!1) when the electric field gradually reduces to zero. This is illustrated in Fig. 3, where for n"40 a calculated 6snk manifold as a function of the electric field F is shown for M"4 only. In zero electric field (F"0 V/cm) the experimental spectrum consists of pure 6snl states (l"0 to 39 for M"0 and l"4 to 39 for M"4), separated in energy E by the quantum defect d : E"I!R/(40!d )2 l l (I"42034.902 cm~1 and R"109736.88 cm~1). Only the singlet fraction of Rydberg states is excited from the 5d2 1G state. As barium has a large core with s-, p- and 4 d-electrons the quantum defects of the 1S, 1P and 1D series are large, respectively 4.210, 4.033 and 2.699. Due to mixing with levels of 5dn@l@ series many perturbations occur, leading to singlet-triplet mixing and a strong variation of the quantum defect over the Rydberg series. However, we studied only a small energy range (n"30—40) where the quantum defects are constant. For increasing l the Rydberg states change their coupling from ¸S (for l43) to jj (for l'3). This e.g. leads to the excitation of both 6snh (weak) and 6snh (strongest) states 9@2 11@2 from the 5d2 1G state. Other relevant quantum defects 4 are 0.0368 for the perturbed 6snf 1F series (value for 3 n"40), 0.0522 and 0.0560 for 6sng and 6sng respec9@2 7@2 tively, and 0.0179 and 0.0187 for 6snh for 6snh 11@2 9@2 respectively. For even larger l the quantum defect reduces to zero with a l~5 dependence. For non-zero electric field the energy positions are calculated by diagonalisation of the Stark Hamiltonian in a jj-coupled basis. 6snl states with l-values lower than 5 do not mix strongly into the 6snk states at the relatively weak electric fields applied in our experiments. Fig. 3 shows the calculated manifold energy levels as a function of the electric field strength. At field strengths below 1 V/cm low-l values are not yet mixed into the manifold. At a field of 1.5 V/cm all levels with l54 are strongly mixed into the manifold. In the excitation from 5d2 1G at zero field 4 6s40f 1F and 6s40h are primarily populated. There3 11@2 fore inside the manifold the f- and h-fractions in the different k-levels determine the oscillator strength distribution. In Fig. 4 a calculated manifold (folded with a 50 MHz line width profile) is shown, assuming that the M"0!5 components are excited equally strong. For the electric field used, i.e. 1.5 V/cm, the M'2 spectra are almost hydrogenic, whereas the M42 spectra are influenced by 6snl (l42) levels not yet mixed into the manifold. Therefore at the low-frequency side of the spectrum different M-values for one k-value are non-degenerate and vary considerably in intensity. In the middle of the manifold the small field dependence results in near degeneracy. At the high-frequency side of the manifold the larger field dependence results again in an M-splitting. With an experimental resolution of about 10 MHz it 204 3 Results and discussion 3.1 6p3 2 40h states @ Fig. 5. The 6s40k manifold recorded as a function of frequency for F"1.5 V/cm follows from Fig. 4 that a field of less than a few V/cm is already sufficiently strong to resolve most k-components. This is shown in Fig. 5, where the experimental 6s40k manifold, recorded in the same field of 1.5 V/cm, is reproduced. In the spectrum six different M-values are excited. For k around 20 even the small M-dependence of manifold peak positions is still visible. The good agreement between experiment (Fig. 5) and calculation (Fig. 4) shows that the spectra are well understood. It is obvious that any k-value '7 may be selected for Stark switching. In the second excitation region the blue ring dye laser is scanned over the 6s!6p ionic transition for each 3@2 setting of the first laser. The resulting autoionisation signal and the signal of a calibrated Fabry-Perot interferometer are recorded and stored on a computer which also controls the scanning of the laser. We recorded 6p 40h spectra in two-step excitation from 3@2 the metastable 5d2 1G state via the 6s 40h J"5 4 1@2 11@2 bound Rydberg states in a field-free configuration (in Sect. 2 of the excitation chamber shown in Fig. 2). In Fig. 6 a spectrum of the 6p 40h multiplet is shown as 3@2 a function of the frequency of the second, blue laser. The three multiplet components with K"13/2 (strongest), 11/2 and 9/2 (weakest), difficult to separate in a pulsed laser experiment, are well resolved. We use a ( jl) K-coupling scheme to assign the resonances. From these spectra intensities, quantum defects, multiplet splitting and autoionisation widths of part of the 6p 40h configura3@2 tion could be determined accurately. The experimental data are collected in Table 1. The absolute quantum defect of the 6p 40h [K"13/2] state was determined from 3@2 absolute frequency measurements using the 6p ionisa3@2 tion limit (at 63987.324 cm~1) and the 5d2 1G level 4 (at 24696.278 cm~1). The 6p nl-multiplet splitting follows from the elec3@2 trostatic repulsion between the two valence electrons. It can be calculated from [2]: ¼ "S6p nlKJD»D6p nlKJT. (1) K 3@2 3@2 To evaluate the matrix elements of (1) the Coulomb repul1 1 sion term of the operator »" ! is expanded in r r 12 1 multipoles: = rk (2) " + : C(k) C(k). rk`1 1 2 12 k/0 ; Here C(k) and C(k) are spherical harmonic operators, and 2 1 r (r ) is the larger (smaller) of the radial positions of both ; : electrons (r , r ). The zero-order terms cancels the 1/r 1 2 1 term in ». The first non-trivial term (k"1) gives the screening effect of the 6p electron and is not relevant for 1 r Fig. 6. Experimental spectrum of the 6s40hP6p 40h transition 3@2 205 Table 1. Experimental quantum defects d with respect to the 6p ionisation l 3@2 limit, experimental and theoretical position DE (in GHz) and intensity I relative to the K"13/2 component, and autoionisation line width C in (GHz) for the 6p 40h configuration 3@2 Label 6p 40h 3@2 6p 40h 3@2 6p 40h 3@2 6p 40h 3@2 6p 40h 3@2 d DE %91 DE 5) 0.027 (1) 0.0 0.0 2.93!, 3.09!, 4.11!, 4.33!, l K"13/2, J"6 K"9/2, J"4 K"9/2, J"5 K"11/2, J"5 K"11/2, J"6 H 0.051 (1) H 0.065 (1) 2.4 (2) 3.9 (2) 2.63" 2.76" 3.68" 3.88" I %91 I 5) C %91 C 5) 1.0 1.0 0.3 0.5 0.3 0.6 1.10 (5) 0.65 0.50 0.50 0.42 0.42 0.2 0.6 0.67 (2) 0.80 (2) !Calculated with the bound-bound matrix element S6pDr2D6pT of Pruvost et al. [4] "Idem with value of Jaffe et al. [16] Table 2. Bound-bound matrix elements Sn l DrkDn l T 00 22 n l 00 k n l 22 Value (au) Ref. 5d 5d 6s 6p 6p 1 3 1 2 2 6p 6p 6p 6p 6p 2.522 81.43 3.781 33.95 30.44 [3] [3] [3] [4] [16] the multiplet splitting. The second term leads to the quadrupole splitting: ¼ "S6pDr2D6pTSnlDr~3DnlT Q ]Sp lKJDCM (2) ·CM (2) Dp lKJT. (3) 3@2 1 2 3@2 The matrix element S6pDr2D6pT has been calculated by Jaffe et al. [16] and Pruvost et al. [4] and is given in Table 2. The hydrogenic value of SnlDr~3DnlT equals (n3(l#1) (l#1/2) l)~1 [15]. The angular part can be calculated using standard techniques [15]. In Table 1 the multiplet splitting, calculated with the quadrupole term, is given relative to the K"13/2 energy. Using the data on singlet—triplet mixing in the 6s40h state [14] 11@2 the transition probabilities to the different 6p 40h 3@2 K-components were obtained. These values are, together with the observed values, included in Table 1 as well. From the oscillator strength distribution it is clear that the 6p 40h K"13/2, J"6, 6p 40h K"9/2, J"5, 3@2 3@2 and 6p 40h K"11/2, J"6 components are excited pre3@2 ferably, and, although weaker, 6p 40h K"9/2, J"4 3@2 and 6p 40h K"11/2, J"5. It should be noted that the 3@2 calculated oscillator strength distributions do not directly correspond to the measured peak heights due to the different autoionisation rates for the different K-components. The calculated relative energies and intensities of the observed K-components compare well with the low-n (n"7—13) members of the 6p nh states investigated by 3@2 Bente and Hogervorst [2] and Pruvost et al. [4]. The quantum defects of the 6p 40h K-states are slightly lar3@2 ger than the quantum defects for the low-n states close to the 6p -limit observed by Bente and Hogervorst [2]. 1@2 Their quantum defects for the low-n members differ significantly from the quantum defects for the same states calculated by Pruvost et al. [4]. It has to be noted that these calculated quantum defects were derived with a model potential to determine the Ba` matrix element S6pDr2D6pT. Its value differs from the one reported by Jaffe et al. [16]. For comparison both calculated values for the matrix elements are listed in Table 2. As shown in Table 1 the calculated multiplet splitting with the matrix element of Jaffe et al. [16] compares best with the experimental values. Pruvost et al. [4] did not report accurate experimental data to compare energies of resonances. The calculated positions and intensities of the K-components are in good agreement with the experimental data, confirming our assignment. The J-splitting of each K-doublet due to the spin-orbit interaction of the Rydberg electron could not be resolved. The observed autoionisation linewidths differ for the various K-components. The autoionisation rate into the n l el continuum can be expressed as [6]: 00 C "2nDSn l elKJD»Dn l n l KJTD2. (4) K 00 22 11 For the 6p nh state (n "6, l "1, n "n, l "5) as well 3@2 2 2 1 1 as for the continuum states the inner electron at r is 2 assumed always to be closer to the core than the outer electron at r . Furthermore, ignoring configuration inter1 action, single configuration wave functions can be used. The exchange contributions to the matrix elements are neglected as the outer electron is in a high-l state and the overlap with the inner electron will be small. With these assumptions the autoionisation rate for an atom in a ( jl ) K-coupled doubly-excited n l n l 22 11 state ionising into a n l el continuum may be expressed 00 as [3]: C "2n[l , l , l , l, j , j ] K 2 1 0 0 2 ] + Sn l DrkDn l T2SelDr~k~1Dn l T2 00 22 11 k51 l k l 2 l k l 2 2 1 ] 0 0 0 0 0 0 0 A G BA HG B H l s j 2 j l K 2 0 0 · (5) ] 0 j k l l j k 2 2 1 2 Here [l , l , 2 ] stands for (2l #1) (2l #1) etcetera. 2 1 2 1 The autoionisation rate is independent of J for a given Kvalue. The bound-bound matrix elements for the barium ion have been calculated by Poirier [3] and by Pruvost et al. [4] by numerical integration of the one-electron Schro~ dinger equation taking core-polarization effects into account. These values are included in Table 2. The boundfree matrix elements can be calculated by numerical integration as well [3]. The outer Rydberg electron is 206 represented by a hydrogenic wave function and the continuum wave function of the ejected electron by a regular Coulomb wave function. Three different K-components of the 6p 40h mul3@2 tiplet were observed. The K"13/2-component may autoionise into the 5d eg, 5d ei, 5d ek, 5d ei, 5@2 5@2 5@2 3@2 5d ek, 6p ej and 6s ei continua, the K"11/2-com3@2 1@2 1@2 ponent into 5d eg, 5d ei, 5d ek, 5d eg, 5d ei, 5@2 5@2 5@2 3@2 3@2 6p eh and 6s ei and the K"9/2-component through 1@2 1@2 dipolar coupling into 5d ed, 5d eg, 5d ei, 5d eg, 5@2 5@2 5@2 3@2 6p eh and 6s eg. 1@2 1@2 In Table 3 the calculated bound-free matrix elements are given. In Table 1 the calculated autoionisation rates are included, whereas in Table 4 branching ratios to the different continua are given. The scaled linewidths (C]n*3) (FWHM, n* is the effective quantum number) of the different K-components for n"40 are of the same order of magnitude as those deduced from the line widths observed by Bente and Hogervorst [2], for low n. A detailed comparison is not possible due to the large scatter in these scaled linewidths data. Comparison of the experimental autoionisation widths with the theoretical calculations shows agreement within a factor of 2. We conclude that the model explains the dominant autoionisation mechanism but calculations in all cases underestimate the measured widths. The neglect of the exchange interaction and the use of hydrogenic wavefunctions cannot account for the extra broadening. However, two effects may have an influence on the observed linewidths: — a small admixture of e.g. 7sNl or 6dNl character into the 6p 40h wavefunction. 7s and 6d are highly3@2 excited states in Ba`, so admixture of states with a low N-value is possible. The polarisation of the 6p electron by the Rydberg electron through dipole coupling allows for such small admixtures despite the fact that these states lie far away in energy. This effect becomes of interest when the total ionisation rate significantly depends on a quadrupole coupling between the bound and continuum state. The contribution of quadrupole coupling to the autoionisation decay rate can be of the same order as two dipole—dipole couplings. In the case of 6p 40h a large fraction (up to 40%) 3@2 autoionises into 6p el continua through quadrupole 1@2 coupling. A similar effect was observed by Luc-Koenig et al. [17] for the 5d5g states of barium. As the rk matrix elements (see 5) scale as 1/N3 small admixtures may have a large effect on the autoionisation width of 6p 40l. The influence of this effect is extremely difficult to 3@2 assess. — a small admixture of 6p 40g and/or 6p 40f. As 3@2 3@2 these low-l states have much larger autoionising linewidths (see Table 5) a small admixture may induce considerable broadening. We calculated the effect of a stray electric field of 10 mV/cm on the 6s40h level 11@2 and conclude that this will result in an admixture of 0.02% 6s40g (and 0.2% 6s40i) character into the 6s40h wavefunction at the intermediate level. This induces a negligible broadening of the 6p 40h states. However, the 3@2 weak stray electric field may mix the 6p 40h with 3@2 6p 40g (and 6p 40f ) directly. Several K- components of 3@2 3@2 6p 40h, 6p 40g and 6p 40f resonances partly overlap 3@2 3@2 3@2 at their high frequency sides, but the amount of mixing Table 3. Bound-free matrix elements SelDr~k~1D40hT Continuum e (au) l k K Value (au) 6p ej 1@2 5d eg 5@2 5d eg 5@2 5d ei 5@2 5d ei 5@2 5d ek 5@2 5d ei 3@2 5d ei 3@2 5d eg 3@2 6s ei 1@2 6p eh 1@2 5d ed 5@2 5d eg 5@2 5d eg 5@2 5d ei 5@2 5d ei 5@2 5d eg 3@2 5d eg 3@2 5d ei 3@2 5d ei 3@2 6s eg 1@2 6p eh 1@2 5d eg 5@2 5d eg 5@2 5d ei 5@2 5d ei 5@2 5d ek 5@2 5d eg 3@2 5d eg 3@2 5d ei 3@2 5d ei 3@2 6s ei 1@2 0.1216 0.3843 0.3843 0.3843 0.3843 0.3843 0.3937 0.3937 0.3937 0.4466 0.1216 0.3843 0.3843 0.3843 0.3843 0.3843 0.3937 0.3937 0.3937 0.3937 0.4466 0.1216 0.3843 0.3843 0.3843 0.3843 0.3843 0.3937 0.3937 0.3937 0.3937 0.4466 7 4 4 6 6 8 6 6 8 6 5 2 4 4 6 6 4 4 6 6 4 5 4 4 6 6 8 4 4 6 6 6 2 1 3 1 3 3 1 3 3 1 2 3 1 3 1 3 1 3 1 3 1 2 1 3 1 3 3 1 3 1 3 1 13/2 13/2 13/2 13/2 13/2 13/2 13/2 13/2 13/2 13/2 9/2 9/2 9/2 9/2 9/2 9/2 9/2 9/2 9/2 9/2 9/2 11/2 11/2 11/2 11/2 11/2 11/2 11/2 11/2 11/2 11/2 11/2 7.873]10~6 1.867]10~5 4.695]10~7 8.034]10~5 7.290]10~7 6.637]10~7 7.686]10~5 7.111]10~7 6.666]10~7 6.468]10~5 1.260]10~5 1.286]10~8 1.867]10~5 6.637]10~7 8.034]10~5 7.290]10~7 2.771]10~5 6.666]10~7 7.686]10~5 7.111]10~7 1.275]10~5 1.260]10~5 1.867]10~5 4.695]10~7 8.034]10~5 7.290]10~7 6.637]10~7 2.771]10~5 4.561]10~7 7.686]10~5 7.111]10~7 6.468]10~5 Table 4. Branching ratios of 6p 40h states calculated for autoionisation into the 6p el, 5d el,3@25d el, and 6s el continua 1@2 5@2 3@2 1@2 State K"13/2 K"9/2 K"11/2 6p continuum 5d1@2 continuum 5d5@2 continuum 6s 3@2 continuum 1@2 25.2% 11.8% 4.6% 58.5% 40.7% 53.1% 4.8% 1.4% 28.0% 38.7% 7.9% 25.4% Table 5. Autoionisation widths (in GHz) for 6p 40l states. Data for 3@2 lO5 were deduced using a l~5 scaling of the 6p 40h K"13/2 3@2 autoionisation width, except for l"3 6p 40l 3@2 l"3! l"4 l"5 l"6 l"7 l"8 l"9 l"10 Width 33 3.5 1.1 0.44 0.2 0.1 0.06 0.03 ! Ref. [20] cannot be determined directly. A very small field-induced admixture of 6p 40g (and 6p 40f ) character could ex3@2 3@2 plain the observed widths (see also Sect. 3.2). 207 nl states 3@2 3.2 6p Using the Stark-switching technique discussed in Sect. 2 we studied the 6p nl configuration for n"30, 35 and 3@2 40 for various values of l (or k, see Fig. 5). We investigated for a given n the l-dependence of the autoionising linewidth. For these high-l states the wave function of the Rydberg electron is localized in a region well outside the classical turning point of the 6p electron at 4a (a " 0 0 0.53 As ) [2]. For this reason it is expected that the autoionisation decay will be completely suppressed for high-l states. In that case the decay is dominated by the radiative transitions 6p!5d and 6p!6s in the Ba`-ion, corresponding to a linewidth of 20MHz. From a simple polarisation model, incorporating non-penetrating Rydberg electrons, a l~5 dependence for the autoionisation linewidth is expected for a given n-value. In Table 5 measured and extrapolated autoionisation widths for 6p 40l 3@2 are given for l"3 to 10. For l'10 the autoionisation decay rate is expected to be lower than the radiative decay rate of the 6p electron, resulting in an expected decrease in signal strength at constant linewidth. Poirier [3] calculated autoionisation rates for barium 6p 24l states 3@2 with l"2, 4, 6, 8. His data show that for l58 the autoionisation linewidth becomes comparable to the radiative linewidth. Jones et al. [1] report autoionisation rates for 6p nl states (n"11—13, l"4—11) using a satu1@2 ration broadening technique which confirms that the autoionisation rate drops below the radiative decay rate for lK8. In Fig.7 one measurement using the Stark-switching technique is presented. In this case 6s40k"21 is excited in the first step (connected to l"20 in zero field). We observe indeed a significant decrease in autoionisation width compared to the l"5 case (Fig. 6). Only a single peak is observed as the K-splitting is expected to decrease rapidly with l, see (3), while the coupling changes from jK to jj. This was also observed by Pruvost et al. [4]. We, however, do not observe the expected radiative linewidth. We find a more or less constant linewidth independent of the k-value (for k'10). For n"30, 35 and 40 autoionisation widths vary slightly: the average linewidths were 250, 160 and 160 MHz for n"30, 35 and 40 respectively (averaged for k'10). The smallest width we observed was 113 (11) MHz exciting 6s35k"20. We investigated several processes to understand the observed autoionisation linewidths. — Firstly, the influence of black body radiation during the Stark switching process was considered. The rate of absorption of black body radiation is determined as the inverse of the black body lifetime qB by [18]: n 1 4a3k ¹ ¹ B "6.79]104· " s~1, (6) qB 3n*2 n*2 n where a is the fine structure constant, k Boltzmann’s B constant, ¹ the temperature and n*"n!d the effective quantum number. At a temperature of 300 K for n"30, 35, 40 the black body radiative lifetimes are approximately 45 lsec, 60 lsec, and 80 lsec respectively. During the Stark switching time (30 lsec) some excitations/de-excitations may take place due to black body Fig. 7. Autoionisation spectrum recorded in a two-step experiment with the first laser locked to the 6s40k"21 component shown in the Stark-manifold of Fig. 5 radiation. However, this will be at a limited scale, and moreover, most probably to other high-l Rydberg states. Therefore this process can not be responsible for the observed autoionisation widths. — Secondly, admixture of low-l character into the wave function of the 6snl Rydberg state may occur when the electric field is not zero after the Stark switching at the time of the inner-core 6s!6p excitation. This is likely to be the case in our experiment. Although the excitation chambers have been carefully designed and every percaution was taken to limit stray electric fields, the residual electric field in the second excitation chamber used for the inner-core 6s!6p excitation is estimated to be 5 to 10 mV/cm. As the high-n, high-l Rydberg states are extremely sensitive to electric fields even residual electric fields of this order of magnitude induce lower- and higher-l character to be mixed into their wave functions. This has been confirmed through calculations of wave function compositions of high-l Rydberg states in electric fields of the order of 5 to 10 mV/cm using a direct diagonalization procedure. For l"20 at 10 mV/cm all higher-l values mix into the wavefunction, but admixtures of l-character with l(10 are extremely small. The effect on the calculated autoionisation linewidth, using the data provided in Table 5, is such that at most 1 MHz would be added to the radiative decay rate. Lower-l 6snl Rydberg states, obtained after Stark switching using low k-manifold components show a similar behaviour. For example, for l"9 the total width is calculated to be 36 MHz and for l"6 the calculated width is 261 MHz, in both cases the extra broadening is 1 MHz only. — Thirdly, the adiabaticity of the Stark switching process may be questioned. The adiabaticity condition for 208 ture of about 0.3% suffices to understand the '100 MHz width of the observed states. 4 Conclusions Fig. 8. Schematic drawing of overlapping 6p 40l resonances (l"3, 3@2 4 and 5) with autoionisation line widths of 45, 5 and 0.7 GHz respectively. (For clarity the oscillator strength of the 6p 40h 3@2 state is taken as one fifth of the oscillator strengths of the other two states Stark switching, i.e. the reduction of the electric field to zero on a time scale such that the character of the k-wavefunction gradually changes to a well defined l-wavefunction in zero field without ‘hopping’ to another k field line (see Fig. 3), is determined by the relation (in a.u.) [4]: A B dF 2 (7) ; n~8(d !d )2 l l`1 dt F/0 3 where d and d are the quantum defects of 6snl and l l`1 6sn(l#1) states respectively. (dF/dt)"1.4 · 10~30 a.u. for a field of 1.5 V/cm reducing to zero in 27 lsec. Using the l~5 scaling law of Freeman and Kleppner [19] to determine the quantum defects for high-l values, the right-hand side of (7) becomes 2.8 · 10~24 a.u. for n"40 and l"20. So the adiabaticity condition is easily met. — Finally, assuming that the Stark switching is correct and that for k"20 indeed primarily l'10 6s40l states are excited, a 10 mV/cm stray electric field may induce mixing of 6p 40l with 6p 40f (and 6p 40g) states. The 3@2 3@2 3@2 6p 40f autoionising states of barium are extremely broad 3@2 (33 to 45 GHz) [20]. The quantum defects of the 6p 40f 3@2 states vary from 0.15 to 0.30. The 6p 40g (quantum 3@2 defects between 0.07 and !0.01 and autoionising widths between 3.5 to 5 GHz) [16] and 6p 40h resonances (this 3@2 work) both lie on the high frequency wing of 6p 40f (see 3@2 Fig. 8). As 6p 40l states with l'5 have small quantum 3@2 defects and are nearly degenerate with 6p 40h states it is 3@2 probable that 6p 40l states with l'3 do acquire an 3@2 admixture of 6p 40f in a small electric field. An admix3@2 We have measured in high resolution a spectrum of the 6p 40h state with a well resolved fine structure splitting. 3@2 The autoionisation widths for the different fine structure components compare reasonably well with calculations assuming a ( jl) K-coupling scheme. The Rydberg electron may be described with a hydrogenic wave function. Only the direct integrals have to be taken into account. The fine structure splitting within the multiplet is understood calculating the electrostatic quadrupole energies in a ( jl) K-coupling scheme as well. We have demonstrated the Stark switching technique in a static electric field and have studied 6p nl Rydberg 3@2 states with high-l values which still show autoionisation. The residual stray electric fields in the interaction region where the core electron is excited are of the order of 5 to 10 mV/cm. These residual fields may induce a coupling with the very broad 6p nf states. A small admixture of 3@2 this configuration is the most probable explanation for the observed autoionisation of the high-l 6p nl Rydberg 3@2 states. Although the linewidth could not be reduced down to 20 MHz (corresponding to the radiative decay rate of the Ba`6p state), the observed resonances are sufficiently narrow and 6p nl states may be used as intermediates for 3@2 further CW excitation to states just below the Ba2`-limit. This was one of the reasons to investigate the 6p nl 3@2 states at high resolution. 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