Barrier tunneling in the He2 c 3Σ+ g stateDonald C. Lorents, So/ren Keiding, and Nis Bjerre Citation: The Journal of Chemical Physics 90, 3096 (1989); doi: 10.1063/1.455912 View online: http://dx.doi.org/10.1063/1.455912 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/90/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Observation of the spinforbidden O(1 D)+O2(X 3Σ g −) channel in the 317–327 nm photolysis of ozone J. Chem. Phys. 105, 5290 (1996); 10.1063/1.472370 Quantumclassical reaction path study of the reaction O(3 P)+O3(1 A 1)→2O2(X 3Σ− g ) J. Chem. Phys. 104, 9482 (1996); 10.1063/1.471691 Tunnel barrier properties of oxidized bismuth droplets on Al2O3 J. Appl. Phys. 79, 7392 (1996); 10.1063/1.362446 Predissociation dynamics of the O2 B 3Σ− u state: Vibrational state dependence of the product finestructuredistribution J. Chem. Phys. 103, 2495 (1995); 10.1063/1.469671 Energetics and spin selectivity in the infrared multiphoton dissociation HN3(X̃1A’)→N2(X1Σ g+)+NH(X3Σ−,a1Δ) AIP Conf. Proc. 191, 651 (1989); 10.1063/1.38598

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.111.185.72 On: Thu, 18 Dec 2014 14:45:25

Barrier tunneling in the He2 c 3l'tt state Donald C. Lorents,a) Sc6ren Keiding, and Nis Bjerre Institute of Physics. University of Aarhus, DK-8000 Aarhus C, Denmark

(Received 20 October 1988; accepted 1 December 1988)

High resolution fast beam photofragment spectroscopy on the a 3!.: has been used to measure level positions and widths of the c 3!.t in the positive energy region near the top of its barrier. Tunneling through the barrier produces energetic neutral fragments that diverge from the beam and are detected. The information is used to determine the shape and height of the barrier to spectroscopic accuracy.

INTRODUCTION

In the class of rare gas excimer molecules the He2 ex­cimer is exemplary as the simplest and most studied. It has been the subject of a large number of detailed spectroscopic, scattering, and theoretical studies. The bound states of this Rydberg molecule have been spectroscopically character­ized in the well region for many of the lower levels and the Rydberg series has been followed up to n = 17. What makes He2 a particularly interesting molecule is its behavior upon dissociation to the atomic limits. Barriers to dissociation are formed in several states as the molecule changes its character from molecular to atomic. The interactions that produce the barriers were qualitatively suggested by Mulliken I and have their origin in part in the g-u symmetry interaction and in part in the electron exchange interaction (Pauli principle). The structure and barriers in the singlet and triplet Rydberg states have been explored more quantitatively in theoretical studies by Guberman and Goddard2 and by Cohen.3 For example, the He( 1~) + He( 1s18) interaction is repulsive at long range due to the repulsive exchange interaction between the Rydberg orbital and the closed shell core and the result­ing!.: state develops a small barrier before yielding to the attractive well of the a 3!.u+ which is due to the attractive core-core interaction of Het. The repulsive !.t state formed from 1~ + 1s18 rises steeply as R decreases until it interacts with the attractive !.g+ state forming from interac­tion of 1s2 with 1s2p and the resulting barrier is due to the avoided crossing of two electronic states with the same total symmetry. In this case the adiabatic state switches character from predominately 18 at long range to 2p in the well region. The study of these barriers has proved difficult experimen­tally and what is known about them has been mainly derived from theoretical calculations.2

-5 The barrier height of the a

state has been extracted from differential scattering mea­surements of He(2 3S) on He (1 IS) by fitting the param­eters of an analytic potential to the scattering data.6

,7 The barrier in the c state has not been probed experimentally since its height ( - 2500 cm -I) makes it inaccessible to ther­mal scattering experiments and at higher energies the scat­tering is complex and provides little information about the barrier.s

The c state barrier gives rise to a set of quasibound levels

a) Permanent address: Molecular Physical Laboratory, SRI International Menlo Park, CA.

that can dissociate by tunneling to the He(2 3S) + He( liS). In this paper we describe a spectro­copic measurement of these levels and their widths using fast beam laser photofragment spectroscopy. The spectroscopic information is used to determine the shape and height ofthe c state barrier.

EXPERIMENT

The experimental apparatus is shown schematically in Fig. 1. He2+ ions from a hot filament sustained discharge were extracted, accelerated, focused, and mass analyzed and then sent through a charge exchange cell containing Cs va­por. The ion source was operated at reasonably high pressure in order to maximize the He2+ component of the beam. The He! was defined by apertures of 1 mm diameter to an angu­lar divergence of 2 mrad before entering the interaction re­gion. Typically, He2+ ion beam currents of the order of 0.1 to 1 nA could be extracted from the source and 10-20 pA of He! beam could be transmitted through the laser interaction region to the final detector at an energy of 1.7 keY. Low beam energy was necessary to the success of this experiment in order to allow the dissociated atoms sufficient time to separate from the beam and be detected.

The electron capture by the Het in Cs can occur to many levels of the He! but favors the lower electronic levels that are nearly energy resonant. Capture into the singlet manifold leads to rapid radiative decay to the repulsive ground state and is largely lost from the beam before its entry

He -_ .... -...

FIG. 1. Schematic diagram of the apparatus used to observe the predissocia­tion of photoexcited He2 •

3096 J. Chern. Phys. 90 (6). 15 March 1989 0021-9606/89/063096-06$02.10 © 1989 American Institute of Physics

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.111.185.72 On: Thu, 18 Dec 2014 14:45:25

Lorents, Keiding, and Bjerre: Tunneling in He2 c 3 It 3097

to the interaction region. However, capture into the low lev­els of the B I Ug state may radiatively decay slowly to the A state because of its low energy transition. Capture into the triplet manifold can occur into the a 3I.;; and many other levels lying above it such as the b 3Ug and the c 3I.g+ . All of these higher levels are radiatively connected either directly or by cascade to the lowest a state so that most of the capture into the triplet manifold eventually collects in that state. The population of the a 3I.;; can by this means become a sub­stantial fraction of the total electron capture. The vibrational and rotational excitation of these metastables is directly de­pendent on the excitation of the parent Her ion as it is ex­tracted from the ion source. Thus it is to be expected that the a state molecules produced will have considerable vibration­al and rotational excitation.

In the interaction region, molecules in the metastable a 3I.;; state can be excited to the c 3I.g+ state by a laser beam that is superimposed collinearly on the molecular beam. Molecules in the c state can fluoresce back into the a state but for the highest vibrational levels that lie near the top of the barrier (Fig. 2), the decay can also occur by tunneling through the barrier leading to dissociation of the molecule into He ( Is) + He (2s). The excess energy in the dissociation is converted into kinetic energy of the atomic fragments, which therefore scatter out of the main beam.

The photofragments were detected by a channeltron lo­cated 0.9 m downstream from the entrance aperture of the interaction chamber. The channeltron was shielded so that only fragments off axis by 7-15 mm could be detected. Since the energy release in the center of mass of the molecule is as low as 0.2 e V in some cases, it was necessary to operate at low beam energies (1.7 or 1.9 keY) to allow the photofragments to reach the off axis detector. A substantial background of

6000

f' 0 ----­E ~ > C> a: ~-6000 ILl

-12000

-18000

o 0.5 10 15 2.0 2.5 3.0 R(.~)

FIG. 2. Potential energy curves of the He2Q 3I.: and c 3I.g+ states showing photoexcited positive energy levels within the barrier of the c state that can tunnel through the barrier to be detected as photofragments.

dissocation fragments was detected with no laser beam. It results mainly from collisions ofHe2 with the entrance aper­ture and with the background gas in the vacuum chamber. Part of the background may also arise from spontaneous predissociation of molecules in high rotational levels in the a 3I.g+ state or in slowly decaying electronic states such as the B lUg state or high Rydberg states. The signal induced by the laser was separated from the background by using a chopped laser beam and lock-in detection.

The photodissociation of He2 was induced by cw dye lasers with DCM dye. Spectra with a resolution of 1 cm- I

were recorded using a linear laser with a birefringent tuner controlled via a stepper motor. High resolution spectra were recorded using a ring dye laser with 1 MHz linewidth. The wavelengths of the ring laser were measured by means of a wavemeter with a Zeeman stabilized HeNe reference laser calibrated against saturated absorptions in 12,

The wavelengths were monitored with a low resolution spectrometer but the interference fringes from a thin etalon recorded together with the spectra provided a means of accu­rately locating the line positions and measuring their widths. Initially the wavelength calibration was calculated for the 4-o band line positions determined from the constants as mea­sured by Ginter9 on the 4-2 emission band. Later the fringe system was calibrated using the ring dye laser at a specific set of wavelengths measured with the wavemeter. The absolute accuracy of the wave number calibration was better than 0.05 cm -1 and agreed with the Ginter calibration to that accuracy.

The initial dissociation signal was found by tuning the ring laser to transitions to the highest rotational levels of v' = 4 in the c 3I.g+ state that had been observed in the flu­orescence studies by Ginter. Our ability to detect these levels results from the presence oftwo competing decay channels: fluorescence as observed by Ginter and dissociation by tun­neling through the potential barrier as observed here. Once a signal was found it was optimized by adjusting the overlap between the laser and ion beams. Then the laser wavelength was scanned over the appropriate spectral regions at a rate that provided good signal to noise. Since some of these scans were made over a time scale of hours it was necessary to find stable beam conditions for that period of time. Changing conditions of the ion source sometimes required adjustment to keep the beam optimized for the long runs.

The levels of v' = 4 with even rotational quantum num­ber N I = 8 - 18 were observed; the odd rotational levels are absent due to symmetry. The levels N' = 8 and 10 are ob­served with Doppler limited linewidths of about 90 MHz, which allows partial resolution of the spin fine structure as apparent from Fig. 3. The photofragment signals for N I = 8 and 10 are weaker than those of the higher levels, indicating that these levels preferentially decay by fluorescence. The linewidths increase dramatically with N I as a result of the increasing tunneling rate (Fig. 3).

The v' = 5 levels of the c 3I.g+ state dissociate even faster and were therefore not observed in the fluorescence studies. Figure 4 shows a scan with 1 cm -1 resolution of the band­head region of the c ..... a ( 5-1) band. In addition the scan includes the P 17 of the 4-0 band. This scan again illustrates

J. Chern. Phys., Vol. 90, No.6, 15 March 1989

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.111.185.72 On: Thu, 18 Dec 2014 14:45:25

3098 Lorents, Keiding, and Sjerre: Tunneling in He2 c 3 It

...J < z C)

in I­Z UJ ~

~ a: u. o o ::I: a.

o 2 3 5 LASER FREQUENCY (GHz)

FIG. 3. High resolution spectra of the 4-0 band taken with the ring laser. The Iinewidth is limited by the Doppler spread to about 90 MHz. The struc­ture results from transitions between fine structure levels of the C-(J state which disappears at higher N levels due to the increasing tunneling rate.

how the lines broaden with increasing N I. The tunneling life­time, which is longer than the fluorescence lifetime for inter­mediate N I in v' = 4, becomes as short as 0.23 ps for v' = 5, N ' = 10.

In addition to the lines shown in Figs. 3 and 4 we observe a photofragment signal that extends over the whole wave­length range of the OeM dye. This signal has maximum intensity when the polarization of the laser beam is such that the E vector is parallel to the direction between the beam and

(4,0) P17

R7 P5 R9

I

FIG. 4. Scan of the C-(J (5-1) bandhead region of the He2 photofragment spectrum. This scan shows the systematic progression of bandwidths as N' increases. The narrow P 17 line is from the (4-0) band.

TABLE I. Measured energies and widths of the 4-0 and 5-1 bands ofthe a 3I.: + ~ 3I.t transitions in cm -I.

N" Pbranch Width R branch Width

4-0 band 9 15786.11 0.0030" 15982.41 0.0034"

11 15669.24 0.0034" 15903.11 0.0096 13 15531.97 0.0096 15800.52 0.0452 15 15373.86 0.0452 15672.90 0.340 17 15192.25 0.340 15515.93 2.74 19 14981.93 2.74

5-1 band 1 15220.13 1.07 15247.51 2.07 3 15 174.40 2.02 15237.00 2.75 5 15 105.23 2.88 15201.45 5.50 7 15011.51 5.16 15 140.85 9.21 9 14893.42 8.57 15053.75 22.61

"Doppler limited.

the channeltron detector. The signal is absent for the perpen­dicular polarization.

This signal arises from molecules that are excited from the a 3I. u+ state to the continuum of the c 3I.g+ state above the top of the potential barrier. The excited molecules disso­ciate on the time scale of a single vibration, which does not allow time for any significant rotation. Therefore, the photo­fragments are scattered in the direction defined by the mo­lecular axis at the moment of excitation. Since the transition moment for the c .... a transitions lies along the molecular axis, the signal from such transitions should be maximum when the laser is polarized along the direction from the beam to the off axis detector and it should vanish for the perpen­dicular polarization as indeed observed.

DATA ANALYSIS AND c STATE BARRIER POTENTIAL

The detailed spectroscopic measurements of Ginter and colleagues allows the potential of the c state to be well deter­mined in the negative energy range. Recently, these spectro­scopic data were combined with low energy differential scat­tering data and ab initio calculations to derive a potential that describes the well, barrier, and the long range interac­tion regions of the c 3I.t. Using all of the available data including strong guidance from theoretical calculations Jor­dan et al.7 derived an analytic potential extending over the whole range of internuclear distance. This potential was used initially in our experiments to calculate the level posi­tions and widths expected in order to search the appropriate

TABLE II. Rotational constants for the He2 C 3I.t state.

Standard v' B. error D. ( X lif) SEC X lif) H. (X 108

) SEC X 108)

0 6.8526 0.0016 5.5064 0.0042 0.902 0.028 1 6.5544 0.000 31 5.6747 0.0083 - 1.277 0.058 2 6.2229 0.00048 6.013 0.021 - 6.263 0.238 3 5.8341 0.00063 6.685 0.033 - 17.41 0.45 4 5.333 0.0028 7.647 0.206 - 81.5 4 5 4.549 0.022 29.6 5.2 830 31

J. Chern. Phys., Vol. 90, No.6, 15 March 1989

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.111.185.72 On: Thu, 18 Dec 2014 14:45:25

Lorents, Keiding, and Sjerre: Tunneling in He2 c 3 It 3099

TABLE III. Rovibrationallevels of the c 3I.g+ state.

E(cm- I ) E(cm- I )

V' N' exp calc V' N'

0 0 - 4023.82 - 4023.13 2 10 0 2 - 3982.72 - 3982.02 2 12 0 4 - 3886.99 - 3886.22 2 14 0 6 - 3736.98 - 3736.22 2 16 0 8 - 3533.28 - 3532.48 2 18 0 10 - 3276.68 - 3275.85 2 20 0 12 - 2968.18 - 2967.32 3 0 0 14 - 2608.97 - 2608.11 3 2 0 16 -2200.46 - 2199.62 3 4 0 18 - 1744.27 - 1743.44 3 6 0 20 - 1242.19 - 1241.38 3 8 0 22 - 696.21 - 695.41 3 10 0 24 - 108.53 - 107.73 3 12 0 26 518.49 519.29 3 14 0 28 1182.29 1183.06 3 16 0 30 1880.14 1880.75 3 18 1 0 - 2543.80 - 2543.33 3 20 1 2 - 2504.49 - 2503.97 4 0 1 4 - 2412.94 - 2412.28 4 2 1 6 - 2269.52 - 2268.67 4 4 I 8 - 2074.83 - 2073.74 4 6 1 10 -1829.70 - 1828.35 4 8 1 12 - 1535.17 - 1533.55 4 10 1 14 - 1192.52 - 1190.65 4 12 1 16 - 803.24 - 801.14 4 14 1 18 - 369.08 - 366.79 4 16 1 20 108.00 110.44 4 18 2 0 - 1172.08 - 1172.35 5 0 2 2 - 1134.76 - 1135.00 5 2 2 4 -1047.86 - 1048.04 5 4 2 6 -911.78 -911.86 5 6 2 8 -727.17 -727.16 5 8

5 10

_ Doppler limited.

region of energies. Their potential is in fact quite accurate giving the line positions to within a few cm -I and was very useful in locating the predissociation transitions in our ex­periment. As is discussed below we can now improve upon this potential in the well and barrier regions using all of the spectroscopic data which now extends to the top of the bar­rier together with the linewidths which provide information about the shape of the barrier beyond its peal"

The newly measured transitions for v' = 4 and 5 are giv­en in Table I. Our new data combined with the emission data of Ginter were completely analyzed to obtain the new set of constants given in Table II and the set of vN levels for the c 3~g+. In this analysis we used the a state spectroscopic constants of Brown and Ginter lO derived from an accurate analysis of the extensive bands of the e 3IIg- - a 3~: emis­sion system. These constants differ slightly from those de­rived from the earlier c-a spectra which were derived from less extensive data. The set of levels listed in Table III were calculated from the resulting c state constants given in Table II. The absolute position of these levels is based on the To of the a state of 14 913 ± 50 cm- I

. This value is based on the Do(He2+) = 19073 cm- I which may be uncertain by ± 50 cm - I. As a starting point for obtaining an improved poten­tial from these data an RKR analysis valid through v = 4 N = 20 was made. The v = 5 levels were included in the

E(cm- I ) E(cm- I ) Width (cm I) Width (cm I)

exp calc exp calc

-494.92 - 494.83 - 216.18 - 216.03

107.63 107.82 474.81 475.05 883.32 883.68

1330.83 1331.45 75.48 74.83

110.46 109.83 191.89 191.32 319.32 318.80 492.00 491.53 708.91 708.45 968.67 968.20

1269.55 1269.09 1609.40 1609.01 1985.59 1985.41 2394.98 2395.09 1171.32 1171.84 1203.29 1203.85 1277.67 1278.26 1393.90 1394.45 1551.03 1551.41 0.003- 0.000 11 1747.63 1747.65 0.0034- 0.00073 1981.58 1981.19 0.0096 0.0059 2250.00 2249.31 0.0452 0.052 2548.95 2548.14 0.34 0.44 2873.20 2871.87 2.74 3.19 2053.62 2053.77 1.07 1.58 2081.15 2080.80 1.99 1.89 2143.95 2143.39 2.75 2.85 2240.13 2240.16 5.27 5.16 2369.24 2369.02 9.00 10.6 2529.40 2528.00 22.6 22.6

analysis but the potential shape in this region is dominated by the barrier effects and is rapidly changing with R such that the semiclassical analysis does not give reliable inver­sion. The resulting potential was spline fit and smoothly at-

~

'E ~

2500

2000

(ii 1500 a: w z w

1000

1.5 1.8

• Jordan Potential

o Sunil et. aI.

- Spectroscopic Potential

2.1 2.4

R(A)

c3~ POTENTIAL BARRIER

2.7 3.0

FIG. 5. The c state potential (solid line) in the barrier region derived from the spectroscopically determined level positions and widths. The solid dia­monds are from the empirical potential used by Jordan et al., Ref. 7, and the open diamonds are from the potential computed theoretically by Sunil et al., Ref. 4.

J. Chern. Phys., Vol. 90, No.6, 15 March 1989

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.111.185.72 On: Thu, 18 Dec 2014 14:45:25

3100 Lorents, Keiding, and Sjerre: Tunneling in He2 c 3.It

TABLE IV. Tabulated values of the c 3I,g+ potential.

R(A) V(R)(cm I) R(A) V(R)(cm- l )

0.5100 88002 0.9866 - 3642 0.6060 51802 1.0047 -4021 0.6990 26002 1.0299 -4406 0.7498 16002 1.0982 -4798 0.7970 8912 1.1771 -4406 0.8503 3202 1.2141 -4021 0.8933 77 1.2446 - 3642 0.8985 -221 1.2720 - 3269 0.9040 -530 1.2975 -2902 0.9100 - 846 1.3219 - 2542 0.9165 -1170 1.3455 -2188 0.9236 -1502 1.3686 -1841 0.9312 -1841 1.3915 -1502 0.9397 - 2188 1.4142 -1170 0.9491 - 2541 1.4369 - 846 0.9598 -2902 1.4599 - 530 0.9720 - 3269 1.4831 - 221

tached to Jordan's barrier potential to obtain a potential ex­tending over the whole range of R that could be used as a trial potential to calculate level positions and widths. The level positions and widths were calculated for this potential by numerical integration of the Schrodinger equation. Adjust­ments in the repulsive wall and the barrier regions of the potential were made until the energy levels were reproduced to an accuracy of about 1 em - I. The level positions of v' = 4 and 5 determined the shape of the potential in the positive energy region for r<rb where rb is the position of the barrier maximum. For r>rb the potential was adjusted to fit the observed linewidths. All of these adjustments were small but significant changes to the basic Jordan potential and were carried out empirically while preserving the smoothness of the potential by insisting on smooth first and second deriva­tives. As can be seen by comparison of the observed and predicted level positions in Table III, except for the high N levels of v' = 1, the potential is accurate to "'" lcm- I for 0.S<R<2.0 A. In the barrier region the Jordan potential was modified by shifting the peak to smaller r, lowering the height by - 50 cm -I and reducing its width slightly. In the large R region the potential joins smoothly on to that of Jordan as derived from scattering measurements. Figure 5 shows the derived potential in comparison to the Jordan po­tential in the barrier region. These results spectroscopically define a potential valid to the top of the barrier and beyond, a region not probed by any previous measurements. As can be seen from this figure the Jordan potential is slightly higher and peaks at larger R while the theoretical barrier of Sunil et al.4 is higher by about 150 cm- I over the whole range. The tabulated values of the derived potential are given in Table IV.

Although we now have a well defined potential for the well and barrier regions the absolute energies are still uncer­tain relative to the dissociation limit. The 0,0 level of the a 3~: is spectroscopically linked to the 0,0 level of the He/ X 2~u+ through the Rydberg series and this difference is 34 302.2 ± 0.1 cm - I. II However the uncertainty in the Do of the X state of Het is at about ± 50 cm - I. The recom-

R(A) V(R)(cm- l ) R(A) V(R)(cm- l )

1.5065 77 2.1940 2061 1.5309 367 2.2440 1967 1.5564 647 2.2940 1871 1.5832 916 2.3440 1772 1.6115 1173 2.3940 1672 1.6418 1417 2.4440 1573 1.6745 1647 2.4940 1474 1.7111 1852 2.5440 1377 1.7453 2015 2.5940 1282 1.7946 2194 2.6440 1191 1.8336 2294 2.6940 1103 1.8726 2358 2.7440 1020 1.9411 2397 2.7940 941 2.0016 2357 2.8440 866 2.0496 2293 2.8940 798 2.0940 2230 2.9440 734 2.1440 2149 2.9940 676

mended value based on the theoretical lower limit of Liu 12 is 19914 ± 50 cm- I

. A recent experimental value13 of 19 962 ± SO cm -I is consistent with Liu's value but does not reduce the uncertainty limits. Thus the uncertainty in the Do of the c state which is spectroscopically tied to the a state remains at about 50 cm -I.

CONCLUSION

Spectroscopic measurements of the level positions and decay widths in the positive energy region of barrier poten­tials that predissociate are readily obtained with the tech­nique of fast beam photofragment spectroscopy. The infor­mation generated allows the potential of He2 c 3~t to be determined with spectroscopic accuracy to the top of the barrier using the level positions and somewhat beyond using the tunneling widths. This work has confirmed and im­proved the earlier work based on spectroscopic, scattering, and theoretical information on the c state potential. This method can be utilized to measure barrier potentials in high­er states of He2, such as theg 3~t ' that can also be optically pumped for the a 3~u+ state. It can also be applied to other metastable rare gas dimers having metastable states that can be produced in fast beams by the charge transfer method and can be optically excited to dissociating states.

ACKNOWLEDGMENTS

D.C.L. is indebted to the SRI International Fellowship Program for support for three months to carry out this ex­periment at the University of Aarhus and to P. Cosby and H. Helm for many helpful discussions.

IR. S. Mulliken, Phys. Rev. A 136, 962 (1964). 2S. Guberman and W. Goddard, Phys. Rev. A 12,1203 (1975). 3J. S. Cohen, Phys. Rev. A 13, 86 (1976). 4K. K. Sunil, J. Lin, H. Siddiqui, P. E. Siska, K. D. Jordan, and R. Shepard, J. Chern. Phys. 78, 6190 (1983).

J. Chem. Phys., Vol. 90, No.6, 15 March 1989

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.111.185.72 On: Thu, 18 Dec 2014 14:45:25

Lorents, Keiding, and Sjerre: Tunneling in He2 c 3 I;

SD. D. Konowalow and B. H. Lengsfield III, J. Chern. Phys. 87, '4000 (1987).

6B. Brutschy and H. Haberland, Phys. Rev. A 19, 2232 (1979).

9M. L. Ginter, J. Chern. Phys. 42,561 (1965). lOCo M. Brown and M. L. Ginter, J. Mol. Spectrosc. S, 302 (1971). 11M. L. Ginter and D. S. Ginter, J. Chern. Phys. 48, 2284 (1968). 12B. Liu, Phys. Rev. Lett. 27,1251 (1971).

3101

7R. M. Jordan, H. R. Siddiqui, and P. I. Siska, J. Chern. Phys. 84, 6719 (1986). 13J. G. Maas, N. P. F. B. Van Asselt, P. J. C. M. Nowak, J. Los, S. D.

sR. Morgenstern, D. C. Lorents, J. R. Peterson, and R. E. Olson, Phys. Rev. A8, 2372 (1973).

Peyerirnhotr, and R. J. Buenker, Chern. Phys. 17,217 (1976).

J. Chem. Phys., Vol. 90, No.6, 15 March 1989

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.111.185.72 On: Thu, 18 Dec 2014 14:45:25