Spectroscopy and dynamics of trapped alkaline earth atoms in superfluid helium

PHYSICS LETTERS A

Physics LettersA 181 (1993) 393—403 North-Holland

Spectroscopy and dynamics of trapped alkaline earth atoms in superfluid helium Jaap H.M. Beijersbergen, Qin Hui and Michio Takami Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 35 1-01, Japan Received 18 August 1993; accepted for publication 31 August 1993 Communicated by B. Fricke

The absorption and emission spectra of two-valence-electron atoms in superfluid helium (He II) are studied systematically usingpulsed dye lasers. Isolated atoms are dispersed in He II by laser ablation. Changes in the bubble size by electronic excitation are determined from the measured spectra. Molecular and cluster lines are identified.

1. Introduction The study of impurities in superfluid helium (He II) has attracted the attention of many scientists for the past several decades because it providespowerful means of elucidating the physical properties of the surrounding superfluid liquid and the impurities in He II as well. Many theoretical and experimental studies have been reported on charged impurities in He II. Low mobility of charged particles in He II led to the prediction that the ions are either surrounded by solid helium [1,2], or trapped in bubble-like cayities due to the repulsive force by electrons [21. A more elaborate examination of the physical properties of impurities in He II has been performed by measuring the optical spectra of the impurities that are highly sensitive to the perturbations from the surrounding liquid. For example, the opticalstudy of an electron in He II revealed that it is trapped in a spherical square-well potential of about 1 eV depth [3]. Recently, the 1p—1 s transition of an electron in this well was observed [41.The emission spectra of neutral species in He II have been known for a long time. However, the results are difficult to interpret since excitation was achieved by the irradiation of high energy particles [5]. Low density of neutral species in He II is another experimental difficulty. The recent development of new experimental techniques to disperse neutral and ionic atoms into

He II made it possible to carry out extensive measurements of the optical spectra of impurities in He II. One such technique is the implantation of atomic ions into He II developed by a group in Heidelberg [6—8].The implanted Ba ions displayed a broad and largely blue-shifted excitation band while the emission line was narrower and slightly blue-shifted. This unusual spectral feature of Ba ions in He II suggested that they were also trapped in the bubbles. Neutralization of implanted positive ions with electrons in the superfluid helium provided recombination emission spectra from high density neutral atoms in He II [8,9]. The recombination lines were close to their free atomic lines but had much larger line widths (about 1 nm). Only the states below the effective ionization limit, which was determined to be 1.8 eV below the value of a free atom, were populated during the recombination process [10]. The study of laser induced fluorescencefrom neutral alkaline earth atoms, in particular the triplet transitions, revealed very broad and largely blue-shifted excitation spectra, which were explained semi-quantitatively by the bubble model [111.Quite recently Yabuzaki and his collaborators reported a new technique to produce neutral atoms in He II by laser ablation of solid samples immersed in the liquid [12,131. They succeeded in observing laser induced fluorescence from Ca, Ba, Rb, and Cs as well as radio frequency transitions among the Zeeman sublevelsof Rb and Cs by

0375-9601/93/S 06.00 © 1993 Elsevier Science Publishers BY. All rights reserved.

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optical pumping [13—15]. The importance of this technique is in its versatility for choosing materials to be suspended in He II. In principle any solid samples can be used to produce atoms, molecules, and clusters in He II and their ionic species as well. In the present paper we report on the optical spectroscopy of alkaline earth atoms in He II produced by the laser ablation method. The primary purpose of this work is to study the physical properties of atoms and molecules in this extraordinary environment. We used pulsed dye lasers for probing these impurities. The advantages of using pulsed dye lasers are an easy access to the UV region, high photon energy to induce dissociation of molecules and clusters, and well-defined time origin to measure ternporal behavior of the impurities. As a first step, we made a systematic study of the two valence electron atoms, Mg, Ca, Sr, Ba, and Yb. Laser induced fluorescence was observed for Ca, Sr, and Ba, adding some new experimental data and confirming the already reported ones [8,11,13]. For the three atoms, semi-empirical potential energy curves for the bubble state were used to determine the change in the bubble size by electronic excitation. The change in bubble size strongly correlates with the change in principal quantum number n. The lowering of ionization energy by 1.8 eV in He II was confirmed also by the absence of laser induced fluorescence from the atomic states above this limit. During this survey, we found new absorption lines which were likely to be the absorption by small van der Waals clusters of Ca and Sr. The emission spectra during the dissociation process of small particles produced by laser ablation were confirmed to be the recombination emission spectra of neutral atoms. The spectra revealed the

25 October 1993

existence of emission bands from atomic ions and molecules.

2. Experimental method The experiment was carried out in a pyrex dewar containing He II at an estimated temperature of 1.5 K. The preparation of isolated atoms in the liquid helium was based on laser ablation of a solid sample immersed in the liquid [13]. The first YAG laser (355 or 532 nm, ~ 80 mJ, 10 Hz) was focused onto the sample through a quartz window on the top flange. The laser ablation produced a large number of small particles of the sample material in He II. The

(a)

*

540

545

550

555

Wavelength [nm] (b)

>~ Ce

2

Ablation YAG

I

I Hell

___

540 _____

~

Dissociation YAG and dye laser

Fig. 1. Experimental setup. The emission light is detected through a monochromator. 394

*

550

560

Wavelength [nmj Fig. 2. The laser 2 ‘S excitation (a) and emission (b) spectra for the 6s6p ‘P?—6s 0 singlet transition of Ba. The signal is not normalized with the laser power. The signal with asterisk (*) is the scattered laser light. The arrows indicate the position of the free atomic line.

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scattered light from the small particles was observed visually along the laser beam. A second YAG laser (532 nm, 50 mJ) dissociated the small particles into atoms and small molecules with a 10 ms delay time. A pulsed dye laser pumped by a XeCl excimer laser excited the isolated atoms after a 8 ~tsdelay time. The emission from the excited atoms was detected with a gated photomultiplier through a monochromator. A boxcar integrator averaged the fluo-

3. Experimental results

rescence signal. Figure 1 presents a schematic diagram of the experimental setup. The measurements were made with several methods. Because the absorption and emission lines of atoms were usually well separated in He II, the excitation spectra were measured by scanning the pulsed dye laser while the monochromator was fixed to the emission lines; the emission spectra were measured by scanning the monochromator while the pulsed dye laser was fixed to the peaks of absorption spectra. After a long ablation time (20 mm, for example), the liquid contained a sufficient amount of small particlesso that the atomic lines were observedwithout ablation. The lines were observed with sufficient intensity even 1 h after the suspension of ablation though the signal intensity decreased to about one half of the original value. This long lifetime of small particles in He II allowed us to use the ablation laser as dissociation laser as well, i.e. to use only one YAG laser and dye laser to measure excitation/emission spectra. The rough performance of the experimental system was examined visually through an optical filter. When the ablation was successful, a clear bright spot was observed on the sample surface, emitting light in the wavelengths longer than that of the YAG laser. Similar emission was also observed along the ablation and dissociation laser beams. This emission was analyzed by synchronizing the gate of the photomultiplier with the ablation or dissociation laser pulse. We define the light detected without pulsed dye laser as direct emission. Wavelengths of the emission lines were calibrated with the reference lines of Ne from a hollow cathode lamp. Accuracy of the wavelengths was about ±0.05 nm which was limited by the resolution of the monochromator.

as an asymmetric broadband with about 6 nm width (FWHM). It was about 4 nm blue-shifted from the free atomic line where the shift was measured from the point of ~ peak intensity on the red side. The emission signal was a symmetric and narrow band with about 1 nm width and slightly blue-shifted. The

3.1. Laser induced fluorescence of the lower atomic transitions The laser induced fluorescence was studied for Ca, Sr, and Ba. Figure 2 shows the excitation and emission signals for the lowest singlet transition of Ba, 6s6p ‘P?—6s2 1S0. The excitation signal was observed

(a)

___________________________________

600

590

610

620

630

Wavelength [nm} (b)

__________________________________ 680

700

690

~

710

1

ave ength [nm]

3S,—5s5p 3P~. Fig. 3. The laser excitation (a) and emission (b) spectra for the 5s6s 2tnplet transition ofSr. The signal is not normalized with the laser power. The signal with asterisk (~)is the scattered laser light. The arrows indicate the position of the free atomic lines.

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fine structurein the excitation spectrum is caused by the convection ofthe liquid in which small particles are distributed inhomogeneously. The singlet transitions of Ca and Sr showed similar spectra, but the emission lines were red-shifted by I nm.

transitions are independent of the excitation wavelength, and in good agreement with the known transition probabilities [161 because the upper state has no fine structure. However, this does not hold for the triplet transition of Ba, 6s6p 3P8_2—6s5d 3D,_3, where

For the triplet transitions the excitation spectra showed large blue shifts. Figure 3 shows the excita3S tion 3P~_ and emission spectra for the 5s6s 1— 5s5p 2triplet transition of Sr. The shift is about 65 nm for Ca and Sr while it is 18 nm for Ba. The emission lines, however, showed only small blue shifts as observed in the singlet transitions. All the observed line positions in both free space and He II are given in table 1. These characteristics of atomic transitions in He II are consistent with those reported previously [8,11,131. For Ca and Sr the relative intensities of the three components of triplet

the upper state has sizable triplet splitting. Some of the triplet transitions of Ba were too weak to be observed [131. It should be noted that the laser excitation is possible only from the lowest component of the triplet state because of fast relaxation among the triplets. 3.2. Direct emission spectra It has been reported that the dissociation of small particles with a YAG laser pulse populates the lowest triplet metastable states and the lowest (ground)

Table 1 The free atomic lines, the measured excitation and emission wavelengths in He II are given. Sand T indicate singlet and triplet transition. The accuracy of the wavelength is ±1 nm for the excitation lines and ±0.1 nm for the emission lines. The relative intensities are taken from ref. [22]. a: Not measured. b: Too close to be resolved. C: Intensity depends on excitation wavelength. d: Not determined due to low photomultiplier sensitivity. e: Measured only as recombination line. Atom

Transition

Type

Free (nm)

Excitation (nm)

Emission (nm)

T

Mg

3S,—C3s3p3P~ 3s4s 3s4s3S,-..3s3p3P~

516.73 517.27 518.36

a a a

b 517.7 518.6

S T

610.27 422.67 612.22 616.22

420 552

S T

679.11 460.73 687.83

457 610

3s4s3S,—.3s3p3P~

Ca

5s5p’P?—Ss2tS 3S,—5s5p3P~ 0 5s6s3S,—5s5p3P~ 5s6s 5s6s3S,—5s5p3P~

Ba

Yb

6s6p ‘P?—6s2 ‘S 3Pl—6s5d3D, 0 Sd6p Sd6p3P?—6sSd3D, 5d6p3P?—6s5d3D 3P~—6s5d3D2 5d6p 3 21S (~,~fl—.6s 0 6s6p ‘P1 3~-.6s2’S _.6s2 ‘So 6s6p3S,-.6s6p3~ 0 6s7s3S 3P? 6s7s

1-÷6s6p 6s7s3S,—.6s6p3~

396

Hell

Reference

gas

0.6

0.2 0.6

1.0

1.0

610.2 423.6 612.0 616.0

0.2 0.6 1.0

0.2 0.6 1.0

11 13

678.7 461.4 687.7

0.3 0.8

0.3 0.9

8,11 8e

706.7

1.0

1.0

4s4p ‘P?—4s2 ‘S 3S,—4s4p3P~ 0 4s5s3S,—4s4p3P? 4s5s 4s5s3S,—4s4p3P~

Sr

Relative intensity

707.01

S T

S T—S T

601.95 553.55 599.71

549 584 584

601.3 553.3 599.1

c

11 11, 13

606.31 611.08

578 578

605.4 610.3

c c

346.44

a

398.80 555.65 648.91

a a

346.2 399 555.7 648.8

1

0.5

679.96 769.95

a a

680.0 769.7

1 d

1 1.1

c

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singlet states of alkaline earth atoms simultaneously [13]. This implies that the laser irradiation produces a plasma-like state in which electronic excitation, ionization, dissociation, and recombination take place. In order to confirm that the direct emission lines originate from the isolated atoms in He II, we measured the direct emission and laser induced fluorescence simultaneously in the following manner. First we merged the ablation and dye laser beam spatially but with 10 us time delay forthe latter. Then the emission along the laser beam was focused into the slit of the monochromator. The two timedelayed emission signals, one from the ablation/ dissociation laser beam and the other from the dye laser beam, were measured simultaneously with two boxcar integrators and displayed on a chart recorder. Figure 4 shows the singlet emission line of Sr measured in this manner. It is clear that the direct emission line is the same as the laser induced fluorescence line within the experimental error. Similar spectral features for the recombination and laser induced fluorescence lines have been reported for the same transition [11]. Therefore we concluded that the direct emission lines were the recombination lines

—

JL

_____________________

455

in He II at least for those atoms for which laser induced fluorescence can be observed. It should be noted that the singlet emission line of Sr in He II is already shifted by 0.7 nm from the free atomic line (see table 1). We made an extensive survey of the direct emission spectra for all the studied atoms. All the lowest singlet and triplet transitions are observed except the singlet transition of magnesium at 285 nm for which our dewar glass was opaque. The measured transitions are also given in table 1. In general the singlet lines show small red shifts while the triplet lines show small blue shifts. All the observed lines have symmetric line shape and about 1 nm width. For Mg, Ca, and Sr, only the lowest singlet and triplet transitions were observed. On the other hand, many emission lines were observed for Ba between 450 and 750 nm. All the lines with wavelength longer than 550 nm were assigned to the atomic transitions among lower singlet and triplet manifolds. Some ofthe weaker lines in the 450—500 nm region were assignable to ionic transitions. Two stronger lines in this region will be discussed in the following section. These observations are consistent with the ionization potential decrease by about 1.8 eV in He II as observed in the recombination lines ofimplanted atomic ions [8,10]. The direction emission spectrum of Yb shows somewhat different features compared with alkaline earth atoms. This spectrum is shown in fig. 5. All the observed lines are relatively weak. The emission from the lowest triplet to the ground singlet state was observed due to large singlet—triplet mixing. Strong

JL

Ce

25 October 1993

460

465

Wavelength [nm] Fig. 4. Comparison of the direct emission (a) and laser induced 2 ‘S fluorescence (b) spectrum observed for the 5s5p ‘P?—5s 0 singlet transition of Sr. The line profile was recorded simultaneously by detecting two emission signals independently. The arrow indicates the position ofthe free atomic line,

identified in most spectra. 3.3. Raman Molecular lines from transitions water or ice in the liquid were As stated above, all the atomic transitions assigned in the direct emission spectrawere those from levels below the reduced ionization limit. Nevertheless, we attempted the search for laser induced fluorescence from the levels above this limit because, with a pulsed dye laser, this energy region is easily accessible by one photon transition from the lowest triplet state. For Ca and Sr no additional emission lines were observed. For Ba, however, new peaks were found. The direct emission spectrum of Ba shows two 397

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PHYSICS LETTERS A

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J~ThI

Yb

350

450

550

650

750

Wavelength [nmj Fig. 5. The direct emission spectrum of Yb. Only the ablation laser was used. The signal with asterisk (*) is the scattered laser light. Unidentified Raman lines are indicated by R(?).

strong peaks at 461.3 and 474.0 nm. The line at 461.3 nm shows a broad and blue-shifted laser excitation spectrum and a narrow emission line similar to iso-

structure. The absence ofvibrational structure in our measurement will be due to a lower vibrational frequency of Ba2.

lated atoms in He II (see table 2). The spectra are shown in fig. 6. If we assume that the excitation is from 3P~—6s5d the lowest3D~at triplet 467 state,nm theinnearest transition is free space. If this 6s7p assignment is correct, the decrease in ionization p0tential in He II is reduced to 1.3 eV. However, this assignment is unlikely because the intensity of the transition in free space is very weak, 1/200 of the singlet transition. Furthermore, the observed blue shift seems to be too small as a triplet transition to a higher excited state. Thus we tentatively assigned this line as a molecular transition, probably a dimer band. The other emission line at 474.0 nm is not well characterized yet. At least the laser induced fluorescence seems to be very weak. Because there is no atomic transition in this vicinity, the line was tentatively assigned as another dimer band. The emission from atomic dimers have been reported for Ag 2 [10] and Na2 [141 with well resolved vibrational

During the survey ofhigher excited states, we found two new absorption lines, one in Ca and one in Sr, which showed dynamics entirely those for isolated atoms in He II. Thesedifferent lines arefrom also listed in table 2. The observed width ofthe excitation spectrum is remarkably narrow, 0.6 nm for Ca and 0.2 nm for Sr. Furthermore, the emission was observed both in the lowest singlet and triplet transitions, but not close to the excitation spectra as observed in isolated atoms. The intensity distribution of the emission lines was the same as the one in the simultaneously measured direct emission spectra. Thus the laser excitation of these absorption lines results in the formation of a plasma-like state. Because these lines are just below their singlet atomic transitions, they were tentatively assigned to the absorption spectra of small van der Waals clusters. These clusters absorb several photons and decompose, thereby releasing atomic ions which emit recombination lines

Table 2 The observed molecular excitation and emission bands. Relative intensities of the singlet and triplet emission lines are given for Ca and Sr. a: We confirmed this is not a Sr singlet line. b: No excitation spectrum observed.

398

Excitation (nm)

Width (nm)

Emission (nm)

Relative intensity S:T

Ba

458 b

6

461.3a 474.0

Ca

428.8

0.6

S+T

1:10

Sr

474.0

0.2

S+T

1:1

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(a)

445

455

465

Wavelength [nm]

(b)

C’S

2

earth atoms. All the studied atoms have two valence electrons. Therefore the ground state is the singlet ns2’S0 state where n increases from 3 for Mg to 6 for Ba and Yb. All 2 ‘S the atoms have strong dipole-allowed nsnp ‘P?—ns 0 singlet transitions. 3P~.The Mg, Ca, Sr, and Yb atoms have the nsnp3S, first2lowest triplet triplet excited metastable the nsnp states. The states lowestand triplet state for Ba is 5d6s 3D 1_3 3P~ and the excited state we studied is 5d6p 2. Therefore, characteristics of the triplet transitions of Ba should be different from those of other alkaline earth atoms. The triplet transitions are about ten times weaker than the singlet transitions for alkaline earth atoms. Ytterbium, which is a member of lanthanide, has a 4f closed shell which is easily excited to form a complicated energy level structure. Furthermore, strong3P?—6s2 singlet—triplet allows the ‘S,,, withmixing intensity roughly transition, 6s6p three times weaker than the triplet—triplet transitions. In fig. 7 the studied levels are given. The observed transitions are indicated by arrows. We also made an attempt to observe laser induced fluorescence for the lowest triplet transitions of Mg and the lowest singlet transition ofYb. However, the observation is not successful so far. For alkali metal atoms, laser induced fluorescence has been observed for Rb and Cs, but not for Li, Na, and K [14]. Our preliminary study of alkali metal atoms suggests that these atoms have two different sites in He II, one in the bubble and the other in a free-atom-like site, where the lighter elements prefer to take the latter. Thus it may be possible that the neutral magnesium atom has electronic properties similar to light alkali

*

450

25 October 1993

460

470

Wavelength [nm] Fig. 6. The laser excitation (a) and emission (b) spectra for the higher excited state of Ba. The transition is tentatively assigned as a molecularband. The signal with asterisk is the scattered laser light.

in the lowest singlet and triplet transitions [171. 4. Discussion Before discussing the experimental results we will first summarize the electronic properties of alkaline

Ot0.

o~I~ff~JJ~

25

Mg

Ca

Sr

Ba

Yb

Fig. 7. The energy level scheme for the free alkaline earth and Yb atoms. The arrows upward indicate that the laser excitation spectrum is measured, and the arrows downward indicate that the emission is measured. The triplet energy level structures are not

indicated. Some of the direct emission lines of Ba are not shown.

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metal atoms, and therefore is difficult to observe by laser induced fluorescence. On the other hand, there is no clear reason why laser induced fluorescence is not observed for Yb, though Yb is not on a mere extension of alkaline earth atoms from Mg to Ba because the 6s orbital shrinks as the number of 4f electrons increases (lanthanide contraction). We need further examination for these atoms. Since the complete experimental data for the excitation/emission spectra have been obtained for the singlet and triplet transitions of Ca, Sr, and Ba, we made an attempt to derive the change in bubble size associated with the electronic excitation. The formation of a bubble introduces complicated dynamics due to the existence of the vibrational motions of the bubble which is coupled to the valence electron ofthe atom. The remarkable difference in energy between the excitation and emission is closely related to the Franck—Condon overlap integral of the lower and upper vibrational states. First we consider a lowest-order energy of an atom trapped in the bubble as a function of the bubble radius R, ‘R’ E(R, = Eatom + E rep ‘R’) + Esorf~.

‘

“~

“

where Eatom is the energy ofthe free atom, Erep is the repulsive energy between the electrons of the helium and the alkaline earth atoms, and ~ is the surface energy of the bubble in the liquid given by 4itR 2a. Here we use the macroscopic surface tension o’= 0.36 erg/cm2 [181 which results in a considerable contribution even at small bubble radii. Two higher-order terms, the pressure—volume work to create the cavity in the liquid and the energy difference due to the radial density change in the surrounding liquid, were neglected because these terms were not important under the present experimental conditions [4,18]. The unusual feature of the absorption and emission spectra is related to the dynamics of the bubble, For an electronic excited state the mean radius of valence electrons usually increases, resulting in a larger bubble radius. In fig. 8 the potential energy curves are given for the ground and the lowest triplet states of Ba. The transition matrix element consists oftwo factors in the lowest-order approximation, the electronic transition matrix element for atomic states which is independent of R, and the Franck—Condon overlap integral of the lower and upper vibrational 400

25 October 1993

2,4

23 22

0,

0.2

0,,

1) 1 0,0

I I

0

5

10

15

20

I

25

Bubble radius [A] Fig. 8. The potential energy curves for the bubble states as a function ofthe bubble radius R. The vibrational relaxation in the excited state is indicatedby an arrow.

wave functions of bubble modes associated with the potential curves in the figure. Thus the width and shift of the transitions are determined by the latter factor. The harmonic vibrational energy at the bottorn of the potential has been calculated to be about 4 cm—’ for the bubble containing neutral Ba in the groundelectronicstate[11]. 1.5 K,therefore, only the ground vibrational state At is populated, indicating that the vibrational wave function is localized around the bottom of the potential. If the upper state has a larger bubble radius as shown in fig. 8, the optical absorption is from the bottom of the potential to the electronic excited state coupled with highly excited bubble modes. Thus, the onset ofabsorption is blueshifted. Furthermore, the overlap integral has a finite value above the excitation threshold until a large number of nodes in the upper vibrational wave function reduces the overlap integral negligibly small. Thus the absorption occurs over a wide energy range. The excited bubble modes rapidly relax to the ground vibrational state by releasing excess energy into He II, and the excited atom fluoresces to the ground electronic state. The fluorescence line is observed with a small shift and narrower width because the transition is between the regions of low curvature. The change in bubble size by the electronic excitation was derived from the experimental data in the following manner. To simplify the calculation, we took the potential energy curves obtained by an ab initio calculation [11,181 which can be approximated quite well by assuming the repulsive part being proportional to R ~,

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PHYSICS LETTERS A 3

E(R)Eatomi+aiR’

+bR2

number in the transition. The small changes in bubble size, about 2.7 A, for the singlet transitions can be understood that the principal quantum number does not change in these transitions. This results in a relatively small change in the mean radius of the valence electron. For the triplet transitions the primcipal quantum number changes, resulting in a larger change in the size of electron orbit which causes a larger change in the bubble size. Indeed changes of about 6.5 A were derived for Ca and Sr. A smaller change in bubble size, 4.0 A, for the triplet transition of Ba will be due to the relatively small change in the size of electron orbit from Sd to 6s despite that the principal quantum number changes in this transition. The above calculations contain two different kinds of uncertainties: the assumption that R0 is 6.5 A for

(2)

.

where i = 0, 1 indicates the lower and upper state, a is the parameter that determines repulsive energy and thus the equilibrium bubble radius, and b is equal to 4xa. Here the interaction is assumed to be spherical symmetric. First we attempted to derive the change in the bubble size by calculating the overlap integral with the vibrational eigenfunctions of the lower and upper bubble state, and then by comparing the calculated intensity profile with the observed one. Unfortunately this procedure was not successful due to the shallowness of our potential curves as also referred to in ref. [111. Thus we employed a much simpler analytical method. The vibrational wave functions relevant to the initial states of absorption and emission are localized around the equilibrium positions with about 0.5 A width. Thus the excitation and emission are assumed to take place from the equilibrium radii as indicated in fig. 8. Then the energy difference, EiE(R), between the excitation and emission spectra is expressed by a function of R0 and R,, the equilibrium radii for the lower and upper state, as 5 —R5)(R3 _R—3) (3) AE(R)— ~b(R I

—

0

0

25 October 1993

.

all the lower states and the errors in zS.E(R). The assumption for R0 = 6.5 A will not be adequate for the ground states of Ca and Sr, and also for all the lowest triplet states. The mean radii of valence electrons have been calculated for the ground state of atoms by a HXR (Hartree plus statistic exchange-relativistic) method. The results show only a 10% decrease in the that sume mean R radius from Ba to Ca [201. Thus we as0 for Ca is also about 10% smaller than that for Ba. For the lowest triplet states, we can use the value of 2.7 A in table 3 as the increase in the bubble size from ns to np. The errors in the changes in bubble size were calculated for the range of R0 —2 to R0 + 3 A where the limits were taken with larger allowance. This results in an error in bubble size of about 15%. It should be noted that AE(R) is independent ofthe absolute value ofR0 if I R0 R1 <
‘

If we assume R0= 6.5 A, we can determine R1 from the observed values of ~.E(R). The value of R0 has been derived from the absorption line of Ba in high pressure He gas [19] and from an ab initio calculation [111. The calculated changes in equilibrium bubble radii for the different elements and transitions are given in table 3. From the table we condude that the change in the bubble size is strongly correlated with the change in the principal quantum

—

Table 3 The change in bubble size for the observed transitions. ±nindicates the change in principal quantum number and b.E is the energy difference between excitation and emission bands. Atom

Transition 2 4s4p—4s 4s5s—4s4p

Sr

5s5p—5s2 5s6s—5s5p

Ba

Ca

Type 5

0

(eV) 0.025

Change in bubble size R,—R0(A) 2.7

T

1

0.21

6.5

S T

0 1

0.026 0.21

2.8 6.4

6s6p—6s2

S

0

0.018

2.3

5d6p—6s5d

T

1

0.053

3.7

LtE

401

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The evaluation of errors in ~.E(R) is not straightforward because the position of vertical resonance from the bottom ofthe ground state to the upper potential curve (upward arrow in fig. 8) cannot be allocated accurately in the excitation spectrum. The change in the bubble size has been calculated by assuming that the vertical resonance is at the point of ~ signal intensity on the red side of the spectrum. The appearance of vertical resonance on the red side is reasonable because the transition to the region above the resonance has still finite intensity in a certain range of energy while the transition below the resonance will be allowed only near the resonance due to the Franck—Condon overlap integral. However, a small error in i~.E(R)may produce a sizable error in R,, especially in the singlet transitions. In fact, if the vertical transition is located 50 cm’’to the blue side ofthe ~ point (about 2 nm at 600 nm), R1 will increase by 0.4 A. For the triplet transitions, the errors will be much smaller, about because the blue shifts are large. Thus once again the errors will be about 15%. Although the observed excitation and emission spectra are complicated compared with the free atomic spectra, the complexity arises solely from the excitation of the bubble modes. When this effect is removed, it seems that the electronic states of atoms are not much affected by the surrounding liquid. For example, the intensity ratio of the three components ofthe triplet emission lines from one common upper level agreed quite well with the theoretical value for a free atom (see table 1). The g-factor of an electron in the bubble [211 determined by ESR agreed with the value in free space within the experimental error. The radio frequency spectroscopy among the Zeeman sublevels of Rb and Cs by optical pumping [15] revealed g-factors almost identical to those in free space. The negligible influence of the liquid on the energy separations in these measurements will be due to the fact that the transitions were within the same electronic configurations and therefore the bubble size did not change. An interesting experiment related to the above discussion is the measurement of electronic transitions in large metal clusters. Because the valence electrons are confined within a spherical square well potential of the cluster, excitation of an electron will little influence the bubble size. As a consequence, an extremely sharp absorption line is ~,

402

25 October 1993

expected in He II. Such a narrowing effect has been partly observed as the sharp absorption lines of small Ca and Sr clusters as discussed [17].

Acknowledgement We would like to thank Professor 1. Yabuzaki of the Kyoto University for the stimulating discussion on this work, and Professor S. Hara ofthe University of Tsukuba for providing computer programs. One of the authors (J.B.) thanks the Science and Techology Agency for the STA fellowship.

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[4] CC. Grimes and G. Adams, Phys. Rev. B 41(1990)41. [5]J. Jortner, L. Meyer, S.A. Rice and E.G. Wilson, Phys. Rev. Lett. 12 (1964) 415.

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