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Laser spectroscopy of alkaline earth atoms in He II
Volume 146, number 3
PHYSICS LETTERS A
14 May 1990
LASER SPECTROSCOPY OF ALKALINE EARTH ATOMS IN He II H. BAUER, M. BEAU, B. FRIEDL, C. MARCHAND, K. MILTNER Physikalisches Instit Ut der Universität Heidelberg, Philosophenweg 12, D-6900 Heidelberg, FRG
and H.J. REYHER Fachbereich Physik der Universjtaj Osnabruck, Barbarastrasse 7, D-4500 OsnabrOck. FRG Received 23 February 1990; accepted for publication 19 March 1990 Communicated by J.I. Budnick
The absorption and emission bands from calcium, strontium and barium atoms produced in superfluid helium have been observed. A model calculation on the basis of the bubble model is reported, which can describe the main observed features such as line shifts and broadenings. From a comparison with the experiment we conclude that the investigated atoms form a bubble state in the liquid similar to the system of barium ions and excess electrons.
I. Introduction The optical properties of defects in condensed matter open interesting insights into the nature of these imperfections. Quite generally, the interaction with the host matrix will disturb the electronic structure, especially the structure of the valence electrons of the defect particles. Consequently their optical properties will differ from those of the free ions or atoms, and line shifts and broadenings are observed in absorption and emission spectra. The interpretation of these observables, or in general, of the line shapes, lead to a first understanding of how the species are imbedded in the solid. More elaborated methods like, e.g. magneto-optical experiments, may then be used to give more detailed information. In the case of liquid helium, studies of this kind have been carried out for electrons [1—3], metastable helium atoms [4,5] and more recently, for foreign ions [6,7] and atoms [81. The results of laserexcitation spectroscopy of Ba~in liquid helium have been interpreted qualitatively in terms of a bubble state for the Ba~ion [7]. A general method for the production of atoms in liquid helium via ion—electron recombination and first observations related to 134
the recombination process has been published in ref. [8]. The subject of this paper will be the presentation of the excitation spectra of Ca, Sr and Ba in Iiquid helium and a comparison of these data with the corresponding ones of Ba~ [7] using the results of bubble-model calculations for these impurities.
2. Experimental setup and detection method Only a brief description of the apparatus and the experimental procedure will be given here because experimental details have been publishedin refs. [6— 8]. A chamber filled with liquid helium (usually at 1.5 K) is mounted in a bath cryostat. The optical access is provided by windows standing at right angles. Fig. 1 shows the components installed in the chamber. A special ion source is located closely above the probe volume in the helium vapour. The ions are implanted into the liquid by means of a downward gas flow. Once immersed in the superfluid the ions enter a drift cell, which allows the modulation of the ionic current and can be used to measure the mobility of the ions. The optional metal tip at the bottom serves as an electron emitter in the liquid [9]. In the elec-
0375-9601/90/$ 03.50 © Elsevier Science Publishers By. (North-Holland)
Volume 146, number 3
PHYSICS LETTERS A
I
I ~
14 May 1990
50000
ION
__
600 ~
40000
lasertluor
______
FLOWING
AFTERGLOW
20000
as
HELIUM LEVEL
—
~
100
0~
FRISCH GRID
0
0
________
100
time
VOLUME ~
~DIAPHRA~PHRAG\IS~
L
d
10000
E~ROR ~ ~
200
0
:
______
:
~
30000
SOURCE
.. C. GRIDS
500 400
ELECTROMETER AMPLIFIER
‘~
200
300
(msec)
Fig. 2. Photon mte independence oftimeafter gate-pulse for laserexcited (excitation 455 nm, emission 461 nm) and recombination induced emission (emission 461 nm) ofstrontium. The width ofthe gate pulses was 20 nm.
\EXTERIMENTAL CELL —
Fig. I. Probe chamber in the cryostat with ion source and drift cell. The lower gate-grid is pulsed, in order to prevent modulation of the stray light from the afterglow. The direction of observation is perpendicular to the laser beam.
10000
—
3.5kV
1 2.5 kV --l5kV .~
0
tric field of the drift cell and the tip, directed downwards, the electrons and the ions move together and recombine for distances at which the Coulomb field exceeds the external field [8]. The recombination light can be observed from the optical volume whenever the positive ions are gated, typically for about 20 ms, into the drift cell. The atoms produced in this, volume can be excited by laser light. The modulation of the ion current and the correlated atom production allows measurements “with” and “without” atoms to discriminate against stray light from the ion source and the laser beam.
3. Results Because the produced atoms are swapped out of the optical volume within a few 100 ms (see below) a time dependent signal of the laser-excited fluorescence is observed. Fig. 2 shows the photon rate for the Sr singlet line (460.73 nm) for both the recombination signal and the laser-excited fluorescence signal as a function of the time after the gate-pulse. The intensity of the recombination signal is propor-
0
0
200
time
400
(msec)
600
Fig. 3. The photon rate ofthe laser-excited fluorescence signal as a function of the time after the gate-pulse for different emitter voltages.
tional to the production rate ofatoms. Therefore the laser-excited signal, which in turn is proportional to the number of produced atoms, shows the integral form of the recombination signal during the production ofatoms. Afterwards this recombination signal decays within some hundreds of ms depending on the emitter voltage applied. The electron producing microscopic gas discharge at the end of the tip causes a heat flow, rinsing out the atoms of the optical volume. Fig. 3 shows the laser-excited signal for different emitter voltages, 1.5, 2.5 and 3.5 kV, indicating that both signal strength and decay time are voltage dependent. The knowledge of this time dependence is important for the setting of time windows during the absorption and emission measurements to eliminate the stray light from the laser beam 135
Volume 146, number 3
PHYSICS LETTERS A
and the ion source. A typical excitation spectrum is shown in fig. 4 for the 460.73 nm line of strontium. Each channel of this spectrum contains the fluorescence light ofa time interval with atoms present minus that of the same period without atoms. The excitation bands (shift, FWHM) of the investigated atoms are listed in table 1. These bands are blue-shifted with respect to the free atomic lines by typically 3—5 nm, broadened and
1,0
‘~
05
0,0
__________________________________
4 4 0
45
0
14 May 1990
asymmetric while the emission lines are less in width and without shift within the experimental resolution. The observed emission spectra are presented in table 2. Fig. 5 shows the recombination spectrum and the laser-excited fluorescence spectrum for the 460.73
4 6 0
wavelength (nm) Fig. 4. Excitation band of the 460.7 nm line of Sr in liquid hehum. The curve is corrected for constant laser power. Stilbene 3 was used as a dye.
Table I Data of the singlet excitation bands of the alkali atoms observed in liquid helium and the corresponding transitions of the free atoms. The data of the D, transition of Ba’~were taken from ref. [7] for the comparison ofthe theoretical results listedin the last four columns. Method 1 and 2 see text. Free atom [101 atom
Atom in liquid He (this work)
transition
A (nm)
experimental shift ~ (nm)
Ca 4s ‘S—.4p ‘P Sr 5s ‘S—.Sp ‘P Ba 6s ‘S—.6p ‘P 2S—~6p2P Ba~ 6s ~ 50% rise to maximum in the
422.67 460.73 553.55 493.4
theoretical FWHM (nm)
—2.65±0.5 —3.3 ±0.5 —4.3 ±0.5 —11.4 ±0.5
method I
4.75±0.5 5.95±0.5 8.5 4.4 ±0.5 ±0.5
method 2
shift~ (nm)
FWHM (nm)
—21.5 —25.0 —33.5 —6.8
5.6 6.3 7.6 2.7
shift’~ (nm) — —
—37 —6.8
FWHM (nm) — —
II4
case ofthe atoms.
Table 2 Data ofthe singlet emission bands ofthe alkali atoms observed in liquid helium and the corresponding transitions of the free atoms. Ba~ data from ref. [7]. Free atom [10]
Atom in liquid He (this work)
atom
recombination fluorescence
laser-excited fluorescence
A (nm)
shift (nm)
FWHM (nm)
shift (nm)
FWHM (nm)
422.67 460.73 553.55 493.4
0.63±1 0.64±1 —0.43 ±0.5
1.3±0.5 1.2±0.5 3.8±0.5
0.96±1 0.96±1 —0.65±1 —2.4 ±0.5
1.0 ±0.5 0.93±0.5 2.5 ±0.5 —2.0 ±0.5
Ca Sr Ba Ba’~
136
transition
‘ip ‘P—.4s ‘S 5p ‘P—~5s‘S 6p ‘P—.6s ‘S 6p2P—.6s2S
—
—
Volume 146, number 3
PHYSICS LETTERS A
recombinatiofl signal—
—,
Iaserexc.tluoresc. signal
I ,~
apparative resolution
II
I 450
14 May 1990
cause other processes like convection are limiting the time during which the atoms are present in the optical volume. The following section gives a description of the model calculations leading to the configuration-coordinate diagrams of the involved atomic states and consequently to a prediction of line shifts and line shapes of the optical transitions.
470
wavelength (nm)
4. Model calculations Fig. 5. The photon rate of laser-excited and recombination signal ofthe singlet line of Sr (emission 461 nm, apparative resolution I nm).
nm line of strontium. Within the experimental resolution of the monochromator (1 nm) no difference between both signals could be detected. The linewidths are small compared to the excitation bandwidth and to the monochromator apparitive width too. Also some triplet lines of barium have been investigated by laser excitation. The results are listed in table 3 indicating that higher states suffer a slightly stronger distortion by the liquid than the fundamental ones. The fact that these triplet states can be excited by laser light, producing relative strong fluorescence signals, indicates that they must be metastable in liquid helium for at least many milhseconds. Lifetime measurements are in progress in ourlaboratory to gain additional information on this question. 3P A preliminary result for the lifetime of the 5d6p 0 state of barium in liquid helium is ‘r> 55 ms. This value for r has been worked out by optical mobility measurements and is only a lower limit be-
As proposed in the literature [7,111 the barium ion resides within a bubble, and very likely the barium atom and other alkaline earth atoms also form bubble states. This has to be concluded from the fact that, for atoms, the absence ofthe strong monopole— dipole interaction leads rather to a weaker bond of the defect atom to its environment and therefore to an enlargement ofthe cavities ofthe defects in liquid helium. These ideas have been confirmed by the results of model calculations starting with a bubble structure for the foreign atoms. Such calculations have already been carried out for metastable helium atoms [5] and electrons [12] in LHe II. The density distribution around the defect [12] was taken as p(r, r0, a)=,oo{l— [l+a(r—r0)]
=
Xexp[—a(r—ro)]},
forr~r0,
0,
for r~r0,
(1)
where r0 and a may be considered as fit parameters to be determined by minimizing the total energy of the defect,
Table 3 Data of the triplet excitation bands of the alkali atoms observed in liquid helium and the corresponding transitions of the free atoms. The prime at ni refers to states with one electron in the (n—I )d-state. Free atom [101 transition 3P 3D 6p’ 3P0—r6s’ 3D1 6p’ 3P1—.6s’ 3D1 6p’ 1—.6s’ 2
Atom in liquid He (this work) A (nm)
601.95 599.71 606.31
excitation
emission
shift (nm)
FWHM (nm)
shift (nm)
FWHM (nm)
13.5±1 —13.5±1 —20.5±1
7.5±1 7.5±1 7 ±1
—0.71 ±1 —0.95±1 —1.2 ±1
3.5±1 1.7±0.5 2.8±0.5
—
137
Volume 146, number 3
E,
0,
Eatom +Ebubble
PHYSICS LETTERS A
(2)
.
The energyfor contains volume terms.bubble Expressions these terms haveand beensurface taken from ref. [11], except for the surface energy, which has been approximated by the classical expression, as shown in ref. [2]. The first term of (2) accounts for the interactions of the valence electrons with both the ion core and the surrounding helium atoms. Hence this term contains the atomic energy terms, which are taken to be those of the free atoms or ions, and the attractive and repulsive parts of the interaction with the liquid. The attractive terms are approximated by a van der Waals potential and the monopole—dipole interaction [13], if the defect is charged. The repulsive energy terms are due to Pauli forces and are therefore evaluated by the pseudopotential (PSP) formalism [14]. If the Hamiltonian HHe describes the interaction of an extra electron with core and electrons of a single helium atom, the PSP formalism leads to the following approximate expression for the energy [14],
(r) =
~
I
HHe Oval>
(3) Here Oval is the wave function of the valence electron of the foreign particle which is Schmidt-orthogonalized to the wave function of the helium atom OHe~ In the numerical evaluation of the two center integrals in V~we used free atom wave functions from a Hartree—Fock program [15]. The same wave functions have been used to compute the van der Waals constants for the system metal—He by means of an obvious extension of the formulas in ref. [16]. Since relatively large terms exist with different sign and nearly equal magnitude (cancellation theorem), a very exact and, hence, time consuming integration —
.
traction would beof necessary. large terms We therefore an analytical performed way, the subarriving at thein small difference which now cananbeexpression computedfor rather quickly. The total energy (2), i.e. the integration over all the atoms of the liquid, has to be written as a functional of the helium density distribution PHe ( r, r 0, a). The energy-shiji EsE of the system “defect with hehum” relative to the free atom is now 138
14 May 1990
AE(r, r0, a) =E,0,
=J[
~Eçree
3r V~5~(r) + Va,Ir(r)]pHe(r, r0, a) d
+ Ebubble, (4) where r is the distance from the defect atom. For small r, the energy-shift ~.E is dominated by the strong repulsive short range pseudopotential ~ (Pauli principle) and for large r by the long-range van der Waals interaction (plus the monopole—dipole term in the case of charged defects) and the bubble terms. As a result of these calculations the configuration-coordinate diagrams for the electronic ground 6s2 and excited 6s6p states of the barium atom are shown in fig. 6. The ordinate is the energy-shift relative to the free atomic states as a function of the bubble radius. These configuration-coordinate diagrams have been calculated for calcium, strontium and barium atoms and for the barium ion. The corresponding energy shifts relative to the free atomic states and the line widths are listed in the columns 6 and 7 of table 1. These values are a first estimate for the expected line shifts, because here we simply calculated the difference between the total energies of the ground and excited states, weighted by the squares of the corresponding ground state functions IX,~=oI2 (method 1). This procedure is the well known approximation to replace the anharmonic oscillator functions of the excited p-state by ö-functions. In order to come to a 150
6p
\
6s
0
\\~_
____________ _________________
____________ _________________
____________ _________________
0 Radius (atomic units)
20
Fig. 6. Configuration-coordinate diagrams for the Ba ground (6s) and excited states (6p) in liquid helium. The y-axis is the energy shift relative to the free atomic states.
Volume
146, number 3
PHYSICS LETTERS A
more quantitative prediction of the line shifts and line shapes, the Franck—Condon factors (FCF), i.e. I2, have been calculated (method 2). Here
x0 and x~are the anharmonic oscillator functions for the vibronic states of the electronic ground and excited state. To determine these wave functions we fittedthe potential curves from the configuration-coordinate diagrams with Morse potentials [17] in the case of the barium ions and with Kratzer potentials [18] in the case ofthe barium atoms. Both types have been chosen because the Schrödinger equation allows in both cases a full analyticalsolution [181. The used effective masses have been estimated as in ref. [2]. Since the vibronic energy steps (6 K) of the elecironic ground state are large compared to the thermal energy at T= 1.5 K, the excitation starts mainly from the state with v= 0. This reduces the problem to calculating the overlap integrals between the vibronic ground state of the electronic s-type ground state and the excited vibronic states of the excited electronic p-type state. The final states of excitation are those of very high vibronic quantum numbers v’ because the excited configuration-coordinate curve is shifted against the ground state one. Consequently the computation of the vibronic wave functions x~ contains terms which may take very high numerical values. In order to avoid numerical instabilities considerable care has to be taken during the evaluation of these integrals. The results for the shifts and widths of the calculated lineshape functions of the barium atom and ion in liquid helium are presented in table 1 in the last two columns. Comparing columns 8 and 9 with columns 6 and 7 we find no significant improvement for the theoretical prediction with respect to the experimental values, therefore we condude that this discrepancy results from the used pairpotentials as discussed below,
5. Conclusion We have observed the laser excitation and emission bands of calcium, strontium and barium atoms in liquid helium. Since the fluorescent light is only slightly shifted with respect to the free particle lines, an unambiguous attribution to the atomic transitions is possible. To come to the density distribution
14 May 1990
around the immersed particles, i.e. the defect structure, calculations based on the bubble model have been worked out which describe the most important features of our measurements in a qualitative way, namely line shifts and broadenings. As can be seen from table 1, the results ofthe model calculations give a prediction of the line shifts and shapes of defect atoms and ions in liquid helium in a qualitatively acceptable way. We further conclude that the ansatz described above is not the adequate way to come to a satisfactory quantitative description of the problem. Especially, the method ofcalculating the metal— He pair potentials seems to be in doubt: Comparing the Na—He pair potentials calculated by our method with those deduced from molecular calculations [9], we find an almost exact agreement for s-states of Na. For the p-state, instead, our pair potential is much too repulsive, particularly for small values of r, the distance between Na and He. As described in ref. [20] for Cs—Xe, this trend is due to the neglect of the covalent admixture of unoccupied higher metal atom states. Since the vertical optical transitions to the p-state in absorption (see fig. 6) are located in that “critical” range ofr, our calculations result in an overestimation of the blue shift. On the other hand we may emphasize that our model calculations describe the small experimental shifts and broadenings in the case of emission quite well, especially the striking difference of the line shifts and shapes in absorption and emission. All investigated transitions in emission of Ca, Sr and Ba starting from the p-state equilibrium radii end on the less sloped s-state configuration-coordinate curves (see fig. 6 for Ba) explainingthe small experimental linewidths. The much weaker curvature of the configuration-coordinate diagrams for final s-states relative to that encountered in absorption (final p-states) results in almost symmetrical bands in emission. In this range of the interaction potential, the bubble and long range metal—He terms are dominant. Therefore, these terms seem to be understood quite well. As the theoretical parameters in absorption are very sensitive to the pseudo-potentials of the p-state, the best improvement of the bubble model should be in replacing the pseudopotentials used here by pair potentials from molecular calculations [19]. Yet the most promising way is to work out ab initio calculations for excited states as has been done 139
Volume 146, number 3
PHYSICS LETTERS A
for the ground state of cesium atoms in liquid hehum [211). Our model calculationsyield for a Cs bubble a repulsive energy of about 290 K and an equilibrium radius of about 6.5 A to be compared with about 260 K and 6 A for the onset ofthe radial distribution function of the Cs—He pair (see fig. 3 in ref. [21]). This very satisfactory agreement, at least for the s-states, indicates that the bubble model can be improved for p-states, to give better quantitative results for the line shifts and shapes.
Acknowledgement We thank Professor G. zu Putlitz for continuous support and encouragement.
14 May 1990
[6] H. Bauer, M. Hausmann, R. Mayer, H.J. Reyher, E. Weber and A. Winnacker, Phys. Lett. A 110 (1985) 279. [7] Hi. Reyher, H. Bauer, C. Huber, R. Mayer, A. Schafer and A. Bauer, Winnacker, Phys. A 115 B. (1986) 238. [8] H. M. Beau, A.Lett. Bemhardt, Friedel and H.J. Reyher, Phys. Lett. A 137 (1989) 217. [9] P.V.E. McClintock, J. Low Temp. Phys. 11(1973) 15. [10] W.L. Wiese and G.A. Martin, in: CRC handbook of chemistry and physics, 62nd Ed. (CRC Press, Boca Raton, 1981) p. E-335; J. Reader and C.H. Corliss, in: CRC handbook ofchemistry and physics, 62nd Ed. (CRC Press, Boca Raton, 1981) p. E-205. [11] M.W. Cole and R.A. Bachman, Phys. Rev. B 15 (1977) 1388. [12] K. Hiroike, N.R. Kestner, S.A. Rice and J. Jortner, J. Chem. Phys. 43 (1965) 2625. [13] K.R. Atkins, Phys. Rev. 116 (1953) 1339. [14]J. Jortner, N.R. Kestner, S.A. Rice and M.H. Cohen, J. Chem.Phys.43 (1965) 2614.
References [1] J.A. Northby and T.M. Sanders, Phys. Rev. Lett. 18 (1967) 1184.
[15] C. Froese Fischer, Comput. Phys. Commun. 14 (1978) 145. [16] J. Callaway and E. Bauer, Phys. Rev. 140 (1965) A1072. [17] P.M. Morse, Phys. Rev. 34 (1929) 57. [181 5. Flugge, Practical quantum mechanicsI (Springer, Berlin,
[2] W.B. Fowlerand D.L. Dexter, Phys. Rev. 176 (1968) 337 [3] B. DuVall and V. Celli, Phys. Rev. 180 (1969) 276. [4] W.A. Fitzsimmons, in: Atomic physics, Vol. 3, eds. Ci. Smith and G.K. Walters (Plenum, New York, 1973) p. 477. [5] A.P. Hickman, W. Steels and N.F. Lane, Phys. Rev. B 12 (1975) 3705.
1971). [19] J. Hanssen, R. McCarroll and P. Valirion, J. Phys. B 12 (1979) 899. [20] J. Pascale and J. Vandeplanque, J. Chem. Phys. 60 (1974) 2278. [21] K.E. Kurten and M.L. Ristig, Phys. Rev. B 27 (1983) 5479.
140
PHYSICS LETTERS A
14 May 1990
LASER SPECTROSCOPY OF ALKALINE EARTH ATOMS IN He II H. BAUER, M. BEAU, B. FRIEDL, C. MARCHAND, K. MILTNER Physikalisches Instit Ut der Universität Heidelberg, Philosophenweg 12, D-6900 Heidelberg, FRG
and H.J. REYHER Fachbereich Physik der Universjtaj Osnabruck, Barbarastrasse 7, D-4500 OsnabrOck. FRG Received 23 February 1990; accepted for publication 19 March 1990 Communicated by J.I. Budnick
The absorption and emission bands from calcium, strontium and barium atoms produced in superfluid helium have been observed. A model calculation on the basis of the bubble model is reported, which can describe the main observed features such as line shifts and broadenings. From a comparison with the experiment we conclude that the investigated atoms form a bubble state in the liquid similar to the system of barium ions and excess electrons.
I. Introduction The optical properties of defects in condensed matter open interesting insights into the nature of these imperfections. Quite generally, the interaction with the host matrix will disturb the electronic structure, especially the structure of the valence electrons of the defect particles. Consequently their optical properties will differ from those of the free ions or atoms, and line shifts and broadenings are observed in absorption and emission spectra. The interpretation of these observables, or in general, of the line shapes, lead to a first understanding of how the species are imbedded in the solid. More elaborated methods like, e.g. magneto-optical experiments, may then be used to give more detailed information. In the case of liquid helium, studies of this kind have been carried out for electrons [1—3], metastable helium atoms [4,5] and more recently, for foreign ions [6,7] and atoms [81. The results of laserexcitation spectroscopy of Ba~in liquid helium have been interpreted qualitatively in terms of a bubble state for the Ba~ion [7]. A general method for the production of atoms in liquid helium via ion—electron recombination and first observations related to 134
the recombination process has been published in ref. [8]. The subject of this paper will be the presentation of the excitation spectra of Ca, Sr and Ba in Iiquid helium and a comparison of these data with the corresponding ones of Ba~ [7] using the results of bubble-model calculations for these impurities.
2. Experimental setup and detection method Only a brief description of the apparatus and the experimental procedure will be given here because experimental details have been publishedin refs. [6— 8]. A chamber filled with liquid helium (usually at 1.5 K) is mounted in a bath cryostat. The optical access is provided by windows standing at right angles. Fig. 1 shows the components installed in the chamber. A special ion source is located closely above the probe volume in the helium vapour. The ions are implanted into the liquid by means of a downward gas flow. Once immersed in the superfluid the ions enter a drift cell, which allows the modulation of the ionic current and can be used to measure the mobility of the ions. The optional metal tip at the bottom serves as an electron emitter in the liquid [9]. In the elec-
0375-9601/90/$ 03.50 © Elsevier Science Publishers By. (North-Holland)
Volume 146, number 3
PHYSICS LETTERS A
I
I ~
14 May 1990
50000
ION
__
600 ~
40000
lasertluor
______
FLOWING
AFTERGLOW
20000
as
HELIUM LEVEL
—
~
100
0~
FRISCH GRID
0
0
________
100
time
VOLUME ~
~DIAPHRA~PHRAG\IS~
L
d
10000
E~ROR ~ ~
200
0
:
______
:
~
30000
SOURCE
.. C. GRIDS
500 400
ELECTROMETER AMPLIFIER
‘~
200
300
(msec)
Fig. 2. Photon mte independence oftimeafter gate-pulse for laserexcited (excitation 455 nm, emission 461 nm) and recombination induced emission (emission 461 nm) ofstrontium. The width ofthe gate pulses was 20 nm.
\EXTERIMENTAL CELL —
Fig. I. Probe chamber in the cryostat with ion source and drift cell. The lower gate-grid is pulsed, in order to prevent modulation of the stray light from the afterglow. The direction of observation is perpendicular to the laser beam.
10000
—
3.5kV
1 2.5 kV --l5kV .~
0
tric field of the drift cell and the tip, directed downwards, the electrons and the ions move together and recombine for distances at which the Coulomb field exceeds the external field [8]. The recombination light can be observed from the optical volume whenever the positive ions are gated, typically for about 20 ms, into the drift cell. The atoms produced in this, volume can be excited by laser light. The modulation of the ion current and the correlated atom production allows measurements “with” and “without” atoms to discriminate against stray light from the ion source and the laser beam.
3. Results Because the produced atoms are swapped out of the optical volume within a few 100 ms (see below) a time dependent signal of the laser-excited fluorescence is observed. Fig. 2 shows the photon rate for the Sr singlet line (460.73 nm) for both the recombination signal and the laser-excited fluorescence signal as a function of the time after the gate-pulse. The intensity of the recombination signal is propor-
0
0
200
time
400
(msec)
600
Fig. 3. The photon rate ofthe laser-excited fluorescence signal as a function of the time after the gate-pulse for different emitter voltages.
tional to the production rate ofatoms. Therefore the laser-excited signal, which in turn is proportional to the number of produced atoms, shows the integral form of the recombination signal during the production ofatoms. Afterwards this recombination signal decays within some hundreds of ms depending on the emitter voltage applied. The electron producing microscopic gas discharge at the end of the tip causes a heat flow, rinsing out the atoms of the optical volume. Fig. 3 shows the laser-excited signal for different emitter voltages, 1.5, 2.5 and 3.5 kV, indicating that both signal strength and decay time are voltage dependent. The knowledge of this time dependence is important for the setting of time windows during the absorption and emission measurements to eliminate the stray light from the laser beam 135
Volume 146, number 3
PHYSICS LETTERS A
and the ion source. A typical excitation spectrum is shown in fig. 4 for the 460.73 nm line of strontium. Each channel of this spectrum contains the fluorescence light ofa time interval with atoms present minus that of the same period without atoms. The excitation bands (shift, FWHM) of the investigated atoms are listed in table 1. These bands are blue-shifted with respect to the free atomic lines by typically 3—5 nm, broadened and
1,0
‘~
05
0,0
__________________________________
4 4 0
45
0
14 May 1990
asymmetric while the emission lines are less in width and without shift within the experimental resolution. The observed emission spectra are presented in table 2. Fig. 5 shows the recombination spectrum and the laser-excited fluorescence spectrum for the 460.73
4 6 0
wavelength (nm) Fig. 4. Excitation band of the 460.7 nm line of Sr in liquid hehum. The curve is corrected for constant laser power. Stilbene 3 was used as a dye.
Table I Data of the singlet excitation bands of the alkali atoms observed in liquid helium and the corresponding transitions of the free atoms. The data of the D, transition of Ba’~were taken from ref. [7] for the comparison ofthe theoretical results listedin the last four columns. Method 1 and 2 see text. Free atom [101 atom
Atom in liquid He (this work)
transition
A (nm)
experimental shift ~ (nm)
Ca 4s ‘S—.4p ‘P Sr 5s ‘S—.Sp ‘P Ba 6s ‘S—.6p ‘P 2S—~6p2P Ba~ 6s ~ 50% rise to maximum in the
422.67 460.73 553.55 493.4
theoretical FWHM (nm)
—2.65±0.5 —3.3 ±0.5 —4.3 ±0.5 —11.4 ±0.5
method I
4.75±0.5 5.95±0.5 8.5 4.4 ±0.5 ±0.5
method 2
shift~ (nm)
FWHM (nm)
—21.5 —25.0 —33.5 —6.8
5.6 6.3 7.6 2.7
shift’~ (nm) — —
—37 —6.8
FWHM (nm) — —
II4
case ofthe atoms.
Table 2 Data ofthe singlet emission bands ofthe alkali atoms observed in liquid helium and the corresponding transitions of the free atoms. Ba~ data from ref. [7]. Free atom [10]
Atom in liquid He (this work)
atom
recombination fluorescence
laser-excited fluorescence
A (nm)
shift (nm)
FWHM (nm)
shift (nm)
FWHM (nm)
422.67 460.73 553.55 493.4
0.63±1 0.64±1 —0.43 ±0.5
1.3±0.5 1.2±0.5 3.8±0.5
0.96±1 0.96±1 —0.65±1 —2.4 ±0.5
1.0 ±0.5 0.93±0.5 2.5 ±0.5 —2.0 ±0.5
Ca Sr Ba Ba’~
136
transition
‘ip ‘P—.4s ‘S 5p ‘P—~5s‘S 6p ‘P—.6s ‘S 6p2P—.6s2S
—
—
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PHYSICS LETTERS A
recombinatiofl signal—
—,
Iaserexc.tluoresc. signal
I ,~
apparative resolution
II
I 450
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cause other processes like convection are limiting the time during which the atoms are present in the optical volume. The following section gives a description of the model calculations leading to the configuration-coordinate diagrams of the involved atomic states and consequently to a prediction of line shifts and line shapes of the optical transitions.
470
wavelength (nm)
4. Model calculations Fig. 5. The photon rate of laser-excited and recombination signal ofthe singlet line of Sr (emission 461 nm, apparative resolution I nm).
nm line of strontium. Within the experimental resolution of the monochromator (1 nm) no difference between both signals could be detected. The linewidths are small compared to the excitation bandwidth and to the monochromator apparitive width too. Also some triplet lines of barium have been investigated by laser excitation. The results are listed in table 3 indicating that higher states suffer a slightly stronger distortion by the liquid than the fundamental ones. The fact that these triplet states can be excited by laser light, producing relative strong fluorescence signals, indicates that they must be metastable in liquid helium for at least many milhseconds. Lifetime measurements are in progress in ourlaboratory to gain additional information on this question. 3P A preliminary result for the lifetime of the 5d6p 0 state of barium in liquid helium is ‘r> 55 ms. This value for r has been worked out by optical mobility measurements and is only a lower limit be-
As proposed in the literature [7,111 the barium ion resides within a bubble, and very likely the barium atom and other alkaline earth atoms also form bubble states. This has to be concluded from the fact that, for atoms, the absence ofthe strong monopole— dipole interaction leads rather to a weaker bond of the defect atom to its environment and therefore to an enlargement ofthe cavities ofthe defects in liquid helium. These ideas have been confirmed by the results of model calculations starting with a bubble structure for the foreign atoms. Such calculations have already been carried out for metastable helium atoms [5] and electrons [12] in LHe II. The density distribution around the defect [12] was taken as p(r, r0, a)=,oo{l— [l+a(r—r0)]
=
Xexp[—a(r—ro)]},
forr~r0,
0,
for r~r0,
(1)
where r0 and a may be considered as fit parameters to be determined by minimizing the total energy of the defect,
Table 3 Data of the triplet excitation bands of the alkali atoms observed in liquid helium and the corresponding transitions of the free atoms. The prime at ni refers to states with one electron in the (n—I )d-state. Free atom [101 transition 3P 3D 6p’ 3P0—r6s’ 3D1 6p’ 3P1—.6s’ 3D1 6p’ 1—.6s’ 2
Atom in liquid He (this work) A (nm)
601.95 599.71 606.31
excitation
emission
shift (nm)
FWHM (nm)
shift (nm)
FWHM (nm)
13.5±1 —13.5±1 —20.5±1
7.5±1 7.5±1 7 ±1
—0.71 ±1 —0.95±1 —1.2 ±1
3.5±1 1.7±0.5 2.8±0.5
—
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Volume 146, number 3
E,
0,
Eatom +Ebubble
PHYSICS LETTERS A
(2)
.
The energyfor contains volume terms.bubble Expressions these terms haveand beensurface taken from ref. [11], except for the surface energy, which has been approximated by the classical expression, as shown in ref. [2]. The first term of (2) accounts for the interactions of the valence electrons with both the ion core and the surrounding helium atoms. Hence this term contains the atomic energy terms, which are taken to be those of the free atoms or ions, and the attractive and repulsive parts of the interaction with the liquid. The attractive terms are approximated by a van der Waals potential and the monopole—dipole interaction [13], if the defect is charged. The repulsive energy terms are due to Pauli forces and are therefore evaluated by the pseudopotential (PSP) formalism [14]. If the Hamiltonian HHe describes the interaction of an extra electron with core and electrons of a single helium atom, the PSP formalism leads to the following approximate expression for the energy [14],
(r) =
~
I
HHe Oval>
.
traction would beof necessary. large terms We therefore an analytical performed way, the subarriving at thein small difference which now cananbeexpression computedfor rather quickly. The total energy (2), i.e. the integration over all the atoms of the liquid, has to be written as a functional of the helium density distribution PHe ( r, r 0, a). The energy-shiji EsE of the system “defect with hehum” relative to the free atom is now 138
14 May 1990
AE(r, r0, a) =E,0,
=J[
~Eçree
3r V~5~(r) + Va,Ir(r)]pHe(r, r0, a) d
+ Ebubble, (4) where r is the distance from the defect atom. For small r, the energy-shift ~.E is dominated by the strong repulsive short range pseudopotential ~ (Pauli principle) and for large r by the long-range van der Waals interaction (plus the monopole—dipole term in the case of charged defects) and the bubble terms. As a result of these calculations the configuration-coordinate diagrams for the electronic ground 6s2 and excited 6s6p states of the barium atom are shown in fig. 6. The ordinate is the energy-shift relative to the free atomic states as a function of the bubble radius. These configuration-coordinate diagrams have been calculated for calcium, strontium and barium atoms and for the barium ion. The corresponding energy shifts relative to the free atomic states and the line widths are listed in the columns 6 and 7 of table 1. These values are a first estimate for the expected line shifts, because here we simply calculated the difference between the total energies of the ground and excited states, weighted by the squares of the corresponding ground state functions IX,~=oI2 (method 1). This procedure is the well known approximation to replace the anharmonic oscillator functions of the excited p-state by ö-functions. In order to come to a 150
6p
\
6s
0
\\~_
____________ _________________
____________ _________________
____________ _________________
0 Radius (atomic units)
20
Fig. 6. Configuration-coordinate diagrams for the Ba ground (6s) and excited states (6p) in liquid helium. The y-axis is the energy shift relative to the free atomic states.
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more quantitative prediction of the line shifts and line shapes, the Franck—Condon factors (FCF), i.e. I
x0 and x~are the anharmonic oscillator functions for the vibronic states of the electronic ground and excited state. To determine these wave functions we fittedthe potential curves from the configuration-coordinate diagrams with Morse potentials [17] in the case of the barium ions and with Kratzer potentials [18] in the case ofthe barium atoms. Both types have been chosen because the Schrödinger equation allows in both cases a full analyticalsolution [181. The used effective masses have been estimated as in ref. [2]. Since the vibronic energy steps (6 K) of the elecironic ground state are large compared to the thermal energy at T= 1.5 K, the excitation starts mainly from the state with v= 0. This reduces the problem to calculating the overlap integrals between the vibronic ground state of the electronic s-type ground state and the excited vibronic states of the excited electronic p-type state. The final states of excitation are those of very high vibronic quantum numbers v’ because the excited configuration-coordinate curve is shifted against the ground state one. Consequently the computation of the vibronic wave functions x~ contains terms which may take very high numerical values. In order to avoid numerical instabilities considerable care has to be taken during the evaluation of these integrals. The results for the shifts and widths of the calculated lineshape functions of the barium atom and ion in liquid helium are presented in table 1 in the last two columns. Comparing columns 8 and 9 with columns 6 and 7 we find no significant improvement for the theoretical prediction with respect to the experimental values, therefore we condude that this discrepancy results from the used pairpotentials as discussed below,
5. Conclusion We have observed the laser excitation and emission bands of calcium, strontium and barium atoms in liquid helium. Since the fluorescent light is only slightly shifted with respect to the free particle lines, an unambiguous attribution to the atomic transitions is possible. To come to the density distribution
14 May 1990
around the immersed particles, i.e. the defect structure, calculations based on the bubble model have been worked out which describe the most important features of our measurements in a qualitative way, namely line shifts and broadenings. As can be seen from table 1, the results ofthe model calculations give a prediction of the line shifts and shapes of defect atoms and ions in liquid helium in a qualitatively acceptable way. We further conclude that the ansatz described above is not the adequate way to come to a satisfactory quantitative description of the problem. Especially, the method ofcalculating the metal— He pair potentials seems to be in doubt: Comparing the Na—He pair potentials calculated by our method with those deduced from molecular calculations [9], we find an almost exact agreement for s-states of Na. For the p-state, instead, our pair potential is much too repulsive, particularly for small values of r, the distance between Na and He. As described in ref. [20] for Cs—Xe, this trend is due to the neglect of the covalent admixture of unoccupied higher metal atom states. Since the vertical optical transitions to the p-state in absorption (see fig. 6) are located in that “critical” range ofr, our calculations result in an overestimation of the blue shift. On the other hand we may emphasize that our model calculations describe the small experimental shifts and broadenings in the case of emission quite well, especially the striking difference of the line shifts and shapes in absorption and emission. All investigated transitions in emission of Ca, Sr and Ba starting from the p-state equilibrium radii end on the less sloped s-state configuration-coordinate curves (see fig. 6 for Ba) explainingthe small experimental linewidths. The much weaker curvature of the configuration-coordinate diagrams for final s-states relative to that encountered in absorption (final p-states) results in almost symmetrical bands in emission. In this range of the interaction potential, the bubble and long range metal—He terms are dominant. Therefore, these terms seem to be understood quite well. As the theoretical parameters in absorption are very sensitive to the pseudo-potentials of the p-state, the best improvement of the bubble model should be in replacing the pseudopotentials used here by pair potentials from molecular calculations [19]. Yet the most promising way is to work out ab initio calculations for excited states as has been done 139
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for the ground state of cesium atoms in liquid hehum [211). Our model calculationsyield for a Cs bubble a repulsive energy of about 290 K and an equilibrium radius of about 6.5 A to be compared with about 260 K and 6 A for the onset ofthe radial distribution function of the Cs—He pair (see fig. 3 in ref. [21]). This very satisfactory agreement, at least for the s-states, indicates that the bubble model can be improved for p-states, to give better quantitative results for the line shifts and shapes.
Acknowledgement We thank Professor G. zu Putlitz for continuous support and encouragement.
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[6] H. Bauer, M. Hausmann, R. Mayer, H.J. Reyher, E. Weber and A. Winnacker, Phys. Lett. A 110 (1985) 279. [7] Hi. Reyher, H. Bauer, C. Huber, R. Mayer, A. Schafer and A. Bauer, Winnacker, Phys. A 115 B. (1986) 238. [8] H. M. Beau, A.Lett. Bemhardt, Friedel and H.J. Reyher, Phys. Lett. A 137 (1989) 217. [9] P.V.E. McClintock, J. Low Temp. Phys. 11(1973) 15. [10] W.L. Wiese and G.A. Martin, in: CRC handbook of chemistry and physics, 62nd Ed. (CRC Press, Boca Raton, 1981) p. E-335; J. Reader and C.H. Corliss, in: CRC handbook ofchemistry and physics, 62nd Ed. (CRC Press, Boca Raton, 1981) p. E-205. [11] M.W. Cole and R.A. Bachman, Phys. Rev. B 15 (1977) 1388. [12] K. Hiroike, N.R. Kestner, S.A. Rice and J. Jortner, J. Chem. Phys. 43 (1965) 2625. [13] K.R. Atkins, Phys. Rev. 116 (1953) 1339. [14]J. Jortner, N.R. Kestner, S.A. Rice and M.H. Cohen, J. Chem.Phys.43 (1965) 2614.
References [1] J.A. Northby and T.M. Sanders, Phys. Rev. Lett. 18 (1967) 1184.
[15] C. Froese Fischer, Comput. Phys. Commun. 14 (1978) 145. [16] J. Callaway and E. Bauer, Phys. Rev. 140 (1965) A1072. [17] P.M. Morse, Phys. Rev. 34 (1929) 57. [181 5. Flugge, Practical quantum mechanicsI (Springer, Berlin,
[2] W.B. Fowlerand D.L. Dexter, Phys. Rev. 176 (1968) 337 [3] B. DuVall and V. Celli, Phys. Rev. 180 (1969) 276. [4] W.A. Fitzsimmons, in: Atomic physics, Vol. 3, eds. Ci. Smith and G.K. Walters (Plenum, New York, 1973) p. 477. [5] A.P. Hickman, W. Steels and N.F. Lane, Phys. Rev. B 12 (1975) 3705.
1971). [19] J. Hanssen, R. McCarroll and P. Valirion, J. Phys. B 12 (1979) 899. [20] J. Pascale and J. Vandeplanque, J. Chem. Phys. 60 (1974) 2278. [21] K.E. Kurten and M.L. Ristig, Phys. Rev. B 27 (1983) 5479.
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