Rydberg States Of Barium Research Articles

Core effect on the diamagnetic spectrum of barium Rydberg states

We study the core effect of nonhydrogenic alkaline-earth-metal barium in its diamagnetic spectrum by one photon transition from the ground state $6{s}^{2}$ ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$ experimentally and theoretically. The non-Coulombic potential of the ion core introduces an extra energy shift compared with hydrogen and a level anticrossing between different $n$ manifolds, characterized by the quantum defect of the concerned angular momentum states. With a complex rotation coordinate technique and a $B$-spline expansion method, we develop a matrix-form Hamiltonian based on an effective potential incorporating the angular-dependent quantum defect into the angular rotation term. The nonhydrogen core effects are investigated by sweeping the quantum defects of different channels in the calculation. Results show that quantum defects of $p$ and $f$ states have a undeniable effect on the intensities and positions of the spectral lines, although barium is closely hydrogenlike in the energy range examined. The anticrossing spectral lines are also identified with the aid of theoretical calculations. The calculations are in good agreement with the experimental observations.

Lifetime Measurement for 6snp Rydberg States of Barium

We present a simple and efficient method for measuring the atomic lifetimes in order of tens of microseconds and demonstrate it in the lifetime determination of barium Rydberg states. This method extracts the lifetime information from the time-of-flight spectrum directly, which is much more efficient than other methods such as the time-delayed field ionization and the traditional laser induced fluorescence. The lifetimes determined with our method for barium Rydberg 6snp (n=37–59) series are well coincident with the values deduced from the absolute oscillator strengths of barium which were given in the literature [J. Phys. B 14 (1981) 4489, 29 (1996) 655] on experiments.

Dipole and quadrupole transition strengths inBa+from measurements ofKsplittings in high-Lbarium Rydberg levels

Measurements of $K$ splittings in high-$L$ Rydberg states of barium are used to deduce electric-dipole and electric-quadrupole matrix elements in ${\text{Ba}}^{+}$. The model used to interpret these splittings is extended here to include the contributions of third- and fourth-order perturbation terms, altering the conclusions of a previous report that omitted those contributions. The analysis leads to improved experimental determinations of dipole $(6s\text{\ensuremath{-}}6p)$ and quadrupole $(6s\text{\ensuremath{-}}5d)$ transition strengths in ${\text{Ba}}^{+}$ that are in good agreement with recent a priori calculations.

Shifts and broadenings of barium Rydberg states perturbed by inert gases

Collisional broadening and shift data for even parity states of neutral barium are presented. A two-photon absorption technique is used to populate Rydberg states of nd 1D2, 3D2 and 1S0 series. High-resolution Ba excitation spectra were measured using a diode detector while scanning the frequency of an excimer pumped dye laser. Inert gases Ar, Kr and Xe were used as perturbers at pressures ranging from 10 mb to 400 mb. Shifts and broadenings of spectral lines were measured as a function of pressure and principal quantum number n. Several perturbations and deviations from expected results are discussed in this paper.

Determination of dipole and quadrupole polarizabilities ofBa+by measurement of the fine structure of high-Ln=9and 10 Rydberg states of barium

The fine structure of high-angular-momentum n=9 and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to (n,n{sup '})=(10,30) (9,17), and (9,20) were induced with a Doppler-tuned CO{sub 2} laser, determining the fine-structure energies corresponding to all n=9 and 10 levels with L{>=}6. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of Ba{sup +} can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of {alpha}{sub 2} due to the lowest excited D state of Ba{sup +}. Our best estimates of these three properties are {alpha}{sub 1}=124.30(16)a{sub 0}{sup 3}, {alpha}{sub 2}=2462(361)a{sub 0}{sup 5}, and {alpha}{sub 2}{sup 0}=1828(88)a{sub 0}{sup 5}.

Experimental investigation of atoms in crossed electric and magnetic fields

We report recent progress in our experimental investigation of high-lying Rydberg states of barium in crossed electric and magnetic fields. Through analysis of the nearest-neighbour level spacing statistics, we investigate the evolution of the electron dynamics as the electric field strength is increased.

Interacting asymmetric double Rydberg series: the Ba 8snl(l = 5) + 5fjn′l′ case

The 8snl double Rydberg states of barium with l = 5 and n = 12–15 are populated by employing an isolated core excitation (ICE) scheme in conjunction with the Stark switching technique. The recorded spectra show strong configuration interaction with three adjacent 5fjn′l′ series. One of the latter series is converging to the 5f5/2 ionization limit and the other two to the higher lying 5f7/2 one. A multichannel quantum defect theory (MQDT) analysis reveals the presence of low-lying members of double Rydberg series converging to higher ionization thresholds and determining the configuration mixing. At least two perturbers, affecting energy level positions, are identified while a comparison between experimental and fitted excitation profiles points towards the presence of a third one. Finally, theoretical calculations of the 8snl(l = 5) series members quantum defects demonstrate the onset of mutual penetration between the two excited electrons. Nevertheless, the most important quantum defect contributions stem from exchange and polarization effects and thus long-range interactions alone are insufficient for a proper description of the double Rydberg states involved.

Indirect spin-orbit interaction in high-LRydberg states with2S1/2cores

In high-L Rydberg states, where exchange interactions are of negligible size, spin-orbit interactions are expected to determine the energy differences between states of different spin orientations. This is well studied in the case of helium, where it results in a fourfold splitting of each high-L term, coming from the two electrons' spin-orbit interactions. A similar structure might be expected in heavier Rydberg states, whose core ion is a {sup 2}S{sub 1/2} state. However, observations in barium Rydberg states and recent observations in Rydberg states of Si{sup 2+} reveal significant deviations from this expectation. Both can be explained as an indirect effect of spin-orbit interactions in virtual excitations of the core ion. A perturbative treatment predicts an indirect spin-orbit interaction for the Rydberg state proportional to the inverse sixth power of the Rydberg electron's radial coordinate. The significance of this term, relative to the direct magnetic interactions, varies by more than six orders of magnitude between the three systems studied, helium, Si{sup 2+}, and barium.

Wave Packets in Perturbed Rydberg Systems

We have excited wave packets in perturbed Rydberg states of barium, an atom with two optically active electrons, and have observed qualitatively different wave packets from those seen in one-electron atoms. In particular, we have found that electron-electron scattering quickly leads to excitation of a doubly excited state and subsequent passage of the population back and forth between different configurations or channels, the quantum analog of two coupled pendula. The experimental results can be successfully described by quantum defect theory. {copyright} {ital 1997} {ital The American Physical Society}

Interference effects in Stark spectra of weakly autoionising 5 dnf states of barium

Weakly autoionising 5d3/2nf Rydberg states of barium around n = 60 have been studied in the presence of a static electric field. The experiment has been carried out in a CW laser-atomic-beam setup. In between the overlapping n = 60 and 61 angular momentum manifolds broad 5d63d resonances interact with the manifold states resulting in pronounced interferences. These interferences (anti-crossings) have been analysed by a direct diagonalisation procedure neglecting interactions with the continuum, and by a Multichannel Quantum Defect Theory (MQDT) analysis including continuum interactions.

Interferometric characterization of Raman redistribution among perturbed Rydberg states of barium.

The evolution of a ``dark'' wave packet in Ba is probed using a bound-state interferometric method. The wave packet is created by photoionizing the 5d7d component of a perturbed Rydberg state having predominantly 6snd character, and thereby redistributing population to neighboring states. Information on which Rydberg-Rydberg Raman transitions dominate the transfer of population to each state is obtained. A closed-form expression for the observed strong-field interferograms is developed for the limit of very short pulses. \textcopyright{} 1996 The American Physical Society.

Short-pulse photoionization of perturbed Rydberg states: Laser-induced autoionization.

Laser-induced autoionization, a form of forced autoionization, is discussed. Highly excited atomic Rydberg states generally have a small cross section for photoionization due to their small overlap with the nucleus. The cross section for photoionization can be strongly enhanced if the Rydberg series is perturbed by an atomic state with a relatively large cross section for photoionization. The photoionization dynamics of such a perturbed Rydberg system shows strong similarities to that of an autoionizing Rydberg series. For intense laser pulses, which strongly couple the perturber to the continuum, the photoionization rate is limited by the coupling between the Rydberg states and the perturber or, in other words, the autoionization rate. The model describing this ionization dynamics is applied to the barium 6 snd(l,3D 2) state, which is perturbed by the 5d7d(l D 2) state. The calculations show good agreement with experimental results of photoionization of barium Rydberg states with subpicosecond laser pulses of light of 620 nm in wavelength.

Line narrowing and reversal in profile symmetry caused by intrachannel mixing of (5dnd)J=0 autoionizing Ba Rydberg series

Using high resolution laser spectroscopy the authors have investigated linewidths and line profiles of (5d32/nd32/)J=0 autoionizing Rydberg states of barium for principle quantum numbers n=14 up to n=99. Configuration interaction with (5d52/n'd52/)J=0 perturbing states (n'=11-14) causes resonant variations in linewidths, inhibition of autoionization (n=26, 60, 61), and a reversal in profile symmetry for Rydberg states (n=66-99) located within the broad contour of the (5d52/14d52/)J=0 perturbing resonance. Linewidths and line profiles were successfully analysed employing a three-channel quantum-defect model.

Inner-electron multiphoton ionization of barium Rydberg states with picosecond pulses.

We have studied multiphoton ionization of Ba 6snl Rydberg states by intenseps pulses and have shown that the duration of the laser pulse compared to the orbit time of the Rydberg electron determines the laser-atom interaction. For high-n states with a long orbit time, the loosely bound Rydberg electron is not affected by the intense laser pulse. Instead the inner electron is ejected by absorption of five photons, leaving the Ba + ion in a Rydberg state. For low-n states the outer electron is ejected and the residual Ba + ion can subsequently be multiphoton ionized to Ba ++

High angular momentum 6pnl and 6dnl doubly excited Rydberg states of barium

6p32/nl (n=11 to 15, l=5 to n-1) and 6d52/nl (n=11 to 14, l=6 to n-1) doubly excited Rydberg states of barium have been studied using a multistep laser excitation technique. The excitation is via the bound 6s12/nl states which are populated using an electric-field switching method which allows the selective population of high-l angular momentum states. The resulting spectra clearly demonstrate the presence of dielectronic correlation. The authors show that this correlation is well described in terms of the (j-l)K coupling scheme, taking into account in a perturbative way the dipole and quadrupole interaction terms.

Field-ionization Stark spectra of Ba Rydberg atoms at high density of states.

Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded at high density of states employing high-resolution laser spectroscopy. The spectra, taken at a binding energy of about \ensuremath{\varepsilon}\ensuremath{\approxeq}-55 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with respect to zero-field threshold and at electric-field strengths F\ensuremath{\approxeq}100 V/cm exhibit dramatic variations in line profiles with increasing external field strength. The WKB quantum-defect theory of the Stark effect of nonhydrogenic atoms was used to analyze the recorded spectra, and excellent agreement between measured and calculated line profiles was achieved. Core-induced coupling of closed and open hydrogenic Stark channels was found to contribute dominantly to the linewidth of the recorded Stark resonances. In addition, a reformulation of this theory by McNicholl, Ivri, and Bergeman (unpublished) in terms of a configuration-interaction model was employed to analyze a particular avoided crossing of several Stark components. In this way recorded line profiles were parametrized within a limited model to obtain resonance energies, linewidths, and Fano q parameters.

Perturbed angular distribution of electrons following photoionization of 6sns 1S0 barium Rydberg states.

Combining high-resolution laser and electron spectroscopy, we have measured angular distributions of electrons emitted from autoionizing Rydberg states close to the 6p $^{2}P_{1/2}$ and 6p $^{2}\mathrm{P}_{3/2}$ ionization limits of barium. Starting from 6sns $^{1}S_{0}$ (12\ensuremath{\le}n\ensuremath{\le}100) Rydberg levels, [6${p}_{1/2}$n's${]}_{J=1}$ (24\ensuremath{\le}n'\ensuremath{\le}50), [6${p}_{1/2}$n'd${]}_{J=1}$ (22\ensuremath{\le}n'\ensuremath{\le}49), and [6${p}_{3/2}$ns${]}_{J=1}$ and [6${p}_{3/2}$n'd${]}_{J=1}$ (11\ensuremath{\le}n'\ensuremath{\le}99) autoionizing Rydberg states were reached by exciting their 6${p}_{3/2}$ns components. Alternatively, by inducing the transition 6s\ensuremath{\rightarrow}6${p}_{1/2}$ of the (${\mathrm{Ba}}^{+}$) ionic core, the [6${p}_{1/2}$24s${]}_{J=1}$ and the neighboring [6${p}_{1/2}$22d${]}_{J=1}$ and [6${p}_{1/2}$23d${]}_{J=1}$ states were excited starting from the 6s24s $^{1}S_{0}$ Rydberg level.We have observed pronounced resonances in the asymmetry parameters \ensuremath{\beta} corresponding to the final ionic states ${\mathrm{Ba}}^{+}$ 6s $^{2}S_{1/2}$, 5d $^{2}D_{3/2}$, and 5d $^{2}D_{5/2}$. These resonances appear in the vicinity of the [6${p}_{1/2}$n's${]}_{J=1}$, [6${p}_{1/2}$n'd${]}_{J=1}$, and [6${p}_{3/2}$n'd${]}_{J=1}$ autoionizing Rydberg states and are caused by configuration interaction with the [6${p}_{3/2}$ns${]}_{J=1}$ Rydberg series. Above the 6p $^{2}\mathrm{P}_{1/2}$ ionization limit the shape of the \ensuremath{\beta} resonances was found to be independent of the principal quantum number. In contrast, the \ensuremath{\beta} resonances associated with [6${p}_{1/2}$n's${]}_{J=1}$ and [6${p}_{1/2}$n'd${]}_{J=1}$ autoionizing Rydberg states change their shapes within the contour of the [6${p}_{3/2}$12s${]}_{J=1}$ perturbing state. In addition to angular distributions we have measured the yield of electrons, leaving the ion in its ground state as well as the total ion yield by scanning the (third) laser across the [6${p}_{3/2}$12s${]}_{J=1}$ perturbing resonance.In addition, kinetic energies of emitted electrons were measured at fixed total excitation energies falling within the contour of the perturbing resonance. Total ion yields, partial ion yields, and electron yields corresponding to the ${\mathrm{Ba}}^{+}$ ground state as well as branching ratios to the $^{2}\mathrm{S}_{1/2}$, $^{2}\mathrm{D}_{3/2}$, and $^{2}\mathrm{D}_{5/2}$ final ionic states exhibit pronounced resonances which have been correlated with the resonances observed in the asymmetry parameters. For each final ionic state a simple multichannel quantum defect model was used to calculate the asymmetry parameter \ensuremath{\beta} as a function of excitation energy. Good agreement with asymmetry parameters derived from experiment was achieved.

Avoided level crossings in bound Rydberg states of barium in an electric field

In a CW laser experiment on bound Rydberg states of barium electric-field-induced level crossings were studied. A regular type of avoided crossing of 6snf3F2 and 6s (n+4)s3S1 levels (n≈60,M=0) was observed under circumstances where the minimum separation was larger than the linewidth involved. This type of crossing could be reproduced using a diagonalisation procedure of the total energy matrix in the presence of the field. However, in the case of avoided crossings of the 6snf3F2 and 6s(n+4)p1P1 sublevels, where the minimum separation was smaller than the linewidth of the3F2 level, an interference-like profile was recorded. An important feature in the explanation of this interference-like profile turned out to be the broadening of the3F2 level by small field inhomogeneities.

Spectroscopy of Rydberg atoms at n

We have observed barium Rydberg states with principal quantum numbers up to $n=520$. Such highly excited states allow quantitative in situ measurements of small electric fields on the order of tens of microvolts per centimeter. Because of the effective suppression of stray electric fields we have observed quasi-Landau resonances in external magnetic fields on the order of tens of gauss. The energy dependence of the spacing between neighboring quasi-Landau resonances was found to be in excellent agreement with calculations involving classical trajectories.

Parametrisation of resonance structures in the multichannel quantum defect theory

The resonance structures corresponding to autoionising states interacting with many continua are parametrised using the multichannel quantum defect theory. All the involved continua are taken into account in an effective way, and collisional parameters which describe the position and width of the resonances are then introduced. The interactions between open and closed channels are parametrised in an original way in terms of vectors whose relative orientation allows stabilisation effects to be described. The introduction of a unitary transformation which rotates the 'degenerate' closed channels greatly simplifies the analysis. This theory is well adapted to the case of core-excited Rydberg states of barium, as is briefly discussed.