- Email: [email protected]
Multichannel Raman spectroscopy of molecules on evaporated metal films
CHEBlIC4L
\\:hik 1nuc11 Cal’the inlet-es1 in surtice-enhanced kutlall (Sl:R) scattering stems from its potential as 3 t~wl 1;)1 io situ surl‘acc and interface characterizatiou. tltt 131-gccottttibutiou to SIIH scattering by the whanccd clrcrromagnctic liclds associated with contlucti~ui ckcrrw rr’sonanccs has restricted its applicalion p~iniarily to noble tnctals (for recent reviews. see 11211[ 1 1). llsing c’onvcntiorial photon counting, it :rpIxxrs Sli# scrrttcring can only be conveniently ~pplictl
10 the noble
liwitilq
c’omttht.
and alk;lli metals. an estremcl> Ilec~‘ntl~, Campion ct al. [Z] dem-
~)1istt;itr~l 11131~nulticli~rincl
oplical detectors
now
LYIIII~~WCIW~IIIL’I~~~~IICC‘L~ km1311 scattering from ad5011UtT?;iI1 ultra-ltigli vacuum (1IlIV). III [his IXIIWI. UY present results obtained using a I!ipk llli)li~1~l1ro1li;~t~~~1<9iiim system with a multiL-l~a~t~~clcq~lic~l dc1skzto1-. Thcsc include Raman spectra I‘I~uI~~~-a~llill~~l~L’rl~.c)i~ acid (PAM) and p-nitrobenzoic :i ( II3‘S) junztiuns [_;I laid down on smooth
~ul)Stl;llcS. WC sllo\\~ lhat the multichannel detection lcthat considered theoretically I,>, .4ravind ct al. I-11 _ The 1kmx1n spectra were obtained using 3 subtrac-
172
14 January
PHYSICS LEl-TERS
tive dispersion
double mouochromator
1983
in series with
a 0.3 or 0.5 m spectrograph. The spectral bandpass was 1000 cm-1 with a resolution of -30 cm-‘_ The detector was an SIT vidicon cooled to between -30
and -40°C. The spectra were excited in air at 5145 or 4SS0 a with between 5 and 50 mW of power and integrated between 600 and 3600 s. 1ETS spectra characterizing the junctious were obtained at 4.2 K [;I_ The metal films were laid down in an evaporator at IOe7 Torr and doped from 5 to 0.05 mg/ml soluof I’ABA or I’NBA in ethanol with the excess washed off with tetrahydrofuran. Fig. la is the Raman spectrum between 1100 and 1700 cm-l of a 3 mglml PNBA solutiou in ethanol with the ethanol contribution to the spectrum subtracted out. The dominant lines are the 1599 cm-‘,
lions
spun and/or
v8 ring mode and the 1354 cm-’ mode of NO,. Fig. 1 b is the Raman spectrum of a submonolayer of
PNBA adsorbed on a smooth, 1000 A thick, Al surface from a 0.05 mplml solution [ 5] _A weak line can be clearly seen near 1600 cm-l with the suses[ion of additional structure between 1350 and 1500 Gill -I _ A considerably stronger spectrum is shown in fig. Ic. This was obtained from a PNBA monolayer on an Al film laid down
on an SO00 a periodicity grating [3]. The Raman intensity in fig. lc is enhanced by the coupling of the optical fields to the Al surface plasmon polariton field. The presence of a chemisorbed layer on the AlO_, surface is inferred from the new structure near 1400 cm-1 due to the symmetric vibration of the carboxylate group on alumina [S].
0 009-26 14/83/0000-0000/S
03.00 0 1983 North-Holland
CHEhfICAL PHYSICS
Volume 94. nunlber 2
x104
6.0
PNBA in Ag junction
e) PABA in Ag junctiin
g) IETS-PNBA
frequency
doped
Pb junction
shift (cm’1
Fig_ 1. (0) The Ramltn spectrum ofp-nitrobenzoic
acid O’NBA)
in solution. (b) The Rnman spectrum of a submondayer of PNBA on 1000 A of smooth AL (c) The Raman spectrum of PNBA ou a 1000 A thick Al fiim on an 8000 A periodicity Si grating. (d) The Raman spectrum of a microscopically smooth. PNBA doped Ag-AlOx-AI tunnel junction. (c)The
Kanlsn spectrum of a microscopically smooth, PABA doped Ag-AlO_,-Al tunnel junction. (f) The Raman spectrum of PARA in a SniAlO_,/Al tunnel junction. &) The IETS spectrum of PNBA iu a Pb/AIOx/Al junction at 4.2 E.
The scattering at 1460 cm-’ is similar to the forbidden structure observed by Domhaus et al. [6] for pyrazine on Ag and also suggests a significant interaction between the PNBA and the adsorbing AlO_, surface. Fig. 1d shows the Raman spectrum of unroughened Al doped with PNBA and covered with 300 A of Ag. This spectrum is similar to those observed in SER studies of deliberately roughened PNBA doped Ag tunnel junctions [3] _ It shows that the changes previously observed between the spectrum of the doping solution and the SER spectrum of the completed
junction are due to the formation of the junction and not the deliberately introduced roughness. The changes in the spectra on adsorbtion on AIO,
LETTERS
14 Jnnuiuy 1953
and after completion of the junction complicate any direct comparison of the adsorbate and solution Raman intensities. Taking however the two strongest lines in fig. la, the spectrum in fig. lb is 4-10X stronger than the spectrum in fig. la when normalized against the scattering volume in the solution. This is close to, but larger than the calculated enhancement for a molecule on a reflector [7]. The spectrum in fig. lc is x30X stronger than that in fig. 1b. The maximum enhancement of the Raman intensity due to the optical excitation of the Al surface plasmon polariton is ~30 [S]. Fig. 1 d is >lOOX stronger than fig. lb when the attenuation due to the Ag is considered. This enlmcement is comparable to the estra enhancement previously reported in deliberately roughened Ag tunnel junctions [3] and the enhancement observed for pyridine adsorbed on unroughened Ag surfaces in vacuum [l]_ The extra enhancement has been attributed either to a short-range interaction between the molecule and the adsorbing surface of the presence of local, submicroscopic, roughness introduced by the sample prep aration [I]_ Fig. le is the Raman spectrum of a PABA doped Al-AlO_,-Agjunction with a smooth continuous Ag counterelectrode. The spectrum is remarkably similar to the PNBA spectrum with a similar erkmcement of the Kaman intensity [Y]. This similarity has also been observed in the IETS spectra
of PNBA and PABA doped Pb tunnel junctions
where no trace of the PNBA NO1 vibrations is observed and both show structure at the energy of the PABA NH2 vibration [9] _ Fig. 1f shows the Raman spectrum of an Al/AlO_,/Sn junction laid down on smooth glass and doped with PABA. The Sn is 300 i$ thick and is discontinuous as seen in both electron micrographs and its resistivity. The evaporation of the Sn layer on the adsorbed PABA produces at least an order-ofmagnitude enhancement of the Raman intensity over that observed for the molecule before the Sn evaporation_ Since the optical transmission of the Sn film is almost 0.1, this suggests that the actual enhancement of the Raman intensity will be between 100 and 1000. The Raman intensity grows rapidly with increasing thickness before saturating and decreasing for thickness above 300 a. This enhancement was not observed’ when the PABA was laid down on a smooth microscope slide and the Sn layer evaporated on it_ Fig. 1g shows the 1ETS spectrum of a PNBA doped Al/AlO_J Pb tunnel junction_ The strong similarities between junction spectra d-g confirm that we observe Raman 173
CHEMICAL PHYSICS LETTERS
\‘~~111!11l!94. nu1nbcr 1
from the adsorbed molecular layer. Our resulrs clearly show the power of the cooled rnul~ichannel detector combined with the triple monochroma~or. The detector allows us to observe Raman ssaircring tionl monolayers at solid-solid and solidair i~r~crfacrs ii1 the absence of any giant enhancescattering
IIWII~Sami using modest power levels which do not dcsrro~ tile sainple. The triple monochromator aT_
imdsussulilcienr
rejecrion lo observe Raman scatraring from die adsorbed species in the presence of srroric ciask scat Wring from the rough Sn surface_ We have been able to observe the evolution of the IC~iiiaii spectra oi doped runnel junctions from the initial doping IO the conlpletion of the junction. This S!IOWSci~a~qcs in the molecular Raman spectrum both OII adsorption IO tlw aside surface and after the evaporalion of rlw countcrelecrrode. Our results on Al are consisten with electromagnetic theory while the Xg results slow the presence of an additional en!ILIIICCI~CIIICWII in the absense of deliberately
intro-
duced rou$~ ncss on microscopic scale [ 1.3 1. Our results suggest 11131the enhancements in the doped Sn iunctions are associated with tile metaii~~~ui~~or~-n~~talsnndwi~icil structure and the disconrinUIUS nature of rhc Sn counterelectrode. The rough
contcrclrclrodc cxmo~. by itself. produce a substanti~l field (>5X) enhancen~cn~ of the Raman inIcrisity hccausc 0f the optical constants of Sn [IO] which hcavii~ chip the conduction-electron resoKII~CCS.I lowve~-. Uir inreraction of the localized p\~lxk:nicln (kids of the Sn strucmrcs with the Al substrate cm produrc a substantial enhancement of
Raman scattering
14 January 1983.
will be a powerful
probe of impuri-
ties in composite materials. In conclusion, using optical multichannel detection of the Raman signa: and a triple monochromator system, we have obtained Raman scattering at the solidsolid and solid-gas interfaces from molecular monolayers laid down on evaporated, non-noble-metal films.
This has been done in the absence of the conditions previously required for the observation of surfaceenhanced Raman scattering. In doing so, we have demonstrated a new geometry for field-enhanced Raman scattering in the absence of optically active conduction-electron resonances. It is clear that the use of multichannel Raman spectroscopy greatly expands the scope and applicability of Raman spectroscopy on virtually alI metallic and non-metallic substrates in solids and gases as well as vacuum. We thank A.M. Torresson, Y.J. Thefaine and M-T. l’rikas for technical assistance and Dr. J.E. Demuth, Professor A. Campion and Professor H. Metiu for helpful discussions.
References
SII
fhc krpticai Ikids in tile junctiou
region. Such a gxmrtn for the enhancement of the local ticlds has ~WCI~considered by Aravind et al. [4,1 l] W!IUcrticul~~rcd 911 enhancanent of 100 for the Raman
scartcring
I‘rum a molrcuie
under a 200 1%Sn sphere
energies uscti by us. The total enha~icen~en~ will include many c,t!lr’r ixrors WI&AI cm borh increase and decrease the 10wi crhnccnwit. it is clear however that the SII s1rucIure induced coupling of the optical fields to rlw iullction rrsion is responsible for a substantial
_TO ..\ 3hw2
3 flat
XI surface 31 the escitation
pxt crl‘111~cnhncernent which we observe. This eniixiscuicnt nirclianisni is 3 general result of the interaction
bctwwn poixizablr bodies and will be obs+Nable CVCIIwhen 1i01lcof rhe resonances of the polarizallie hL)dics arc king excited. When combined with our ciii~~ncc‘dsensirivity, it su,nflesrs that multichannel
174
RX C-hang and TX. Iktak. edr, Surface-enhanced Ranian scatrering (Plenum Press. NCWYork, 1962). I21 -4. Campion, J.E. Brown and V-M. Grizzle. Surface Sci. 115 (1982) L153. 131 J.C. Tsmg. J.R. Kirtley, T-N. Theis and S.S. Jha. Phys. Rrw. 825 (1982) 5074. l4l P-K. Arsvind. R.N. Rendell nnd H. hlotiu, Chem. Phys. Letters SS (1982) 396. 151 J-D. Lan:gm and P-K. Hansnx~. Surface Sci. 52 (1975) 211. 161 R. Dornhaus, XI-B. Long. RX. Bcnner and R-K. Chang, Surface Sci 93 (1980) 240. 171 R.G. Grcenlcr and l-L. Slager, Spectrochim. Acta 29A (1973) 193; Y.J. Chcn. W.P. Chrn and E. Burstein, Phys. Rev. Letters
ill
19 (1976)Sll. 151 \?‘.lI.Wcber and G.W. Ford, Opt. Letters 6 (1981) 123; P-K. -4ravind. E. Hood and Ii. hletiu. Surface Sci. 109 (1981) 95; S.S. Jha, J.R. Kirtlcy and J.C. Tsan_e. Phys. Rev. B22 (1980) 3973. 191 J.C. Tsang. Ph. Avouris and J.R. Kirtley. Proceedings of the 3rd International Conference on Vibrations at Surfaces, Asilomu. California. Scptenlber l-4, 1982.
to be published.
IlO1 R.A. MacCrae, E.T.
Arakawa and M.W. \Viiihns. Phps. Rev. 162 (1967) 615. 1111 P-K. Aravind. private communication.
\\:hik 1nuc11 Cal’the inlet-es1 in surtice-enhanced kutlall (Sl:R) scattering stems from its potential as 3 t~wl 1;)1 io situ surl‘acc and interface characterizatiou. tltt 131-gccottttibutiou to SIIH scattering by the whanccd clrcrromagnctic liclds associated with contlucti~ui ckcrrw rr’sonanccs has restricted its applicalion p~iniarily to noble tnctals (for recent reviews. see 11211[ 1 1). llsing c’onvcntiorial photon counting, it :rpIxxrs Sli# scrrttcring can only be conveniently ~pplictl
10 the noble
liwitilq
c’omttht.
and alk;lli metals. an estremcl> Ilec~‘ntl~, Campion ct al. [Z] dem-
~)1istt;itr~l 11131~nulticli~rincl
oplical detectors
now
LYIIII~~WCIW~IIIL’I~~~~IICC‘L~ km1311 scattering from ad5011UtT?;iI1 ultra-ltigli vacuum (1IlIV). III [his IXIIWI. UY present results obtained using a I!ipk llli)li~1~l1ro1li;~t~~~1<9iiim system with a multiL-l~a~t~~clcq~lic~l dc1skzto1-. Thcsc include Raman spectra I‘I~uI~~~-a~llill~~l~L’rl~.c)i~ acid (PAM) and p-nitrobenzoic :i
~ul)Stl;llcS. WC sllo\\~ lhat the multichannel detection lc
172
14 January
PHYSICS LEl-TERS
tive dispersion
double mouochromator
1983
in series with
a 0.3 or 0.5 m spectrograph. The spectral bandpass was 1000 cm-1 with a resolution of -30 cm-‘_ The detector was an SIT vidicon cooled to between -30
and -40°C. The spectra were excited in air at 5145 or 4SS0 a with between 5 and 50 mW of power and integrated between 600 and 3600 s. 1ETS spectra characterizing the junctious were obtained at 4.2 K [;I_ The metal films were laid down in an evaporator at IOe7 Torr and doped from 5 to 0.05 mg/ml soluof I’ABA or I’NBA in ethanol with the excess washed off with tetrahydrofuran. Fig. la is the Raman spectrum between 1100 and 1700 cm-l of a 3 mglml PNBA solutiou in ethanol with the ethanol contribution to the spectrum subtracted out. The dominant lines are the 1599 cm-‘,
lions
spun and/or
v8 ring mode and the 1354 cm-’ mode of NO,. Fig. 1 b is the Raman spectrum of a submonolayer of
PNBA adsorbed on a smooth, 1000 A thick, Al surface from a 0.05 mplml solution [ 5] _A weak line can be clearly seen near 1600 cm-l with the suses[ion of additional structure between 1350 and 1500 Gill -I _ A considerably stronger spectrum is shown in fig. Ic. This was obtained from a PNBA monolayer on an Al film laid down
on an SO00 a periodicity grating [3]. The Raman intensity in fig. lc is enhanced by the coupling of the optical fields to the Al surface plasmon polariton field. The presence of a chemisorbed layer on the AlO_, surface is inferred from the new structure near 1400 cm-1 due to the symmetric vibration of the carboxylate group on alumina [S].
0 009-26 14/83/0000-0000/S
03.00 0 1983 North-Holland
CHEhfICAL PHYSICS
Volume 94. nunlber 2
x104
6.0
PNBA in Ag junction
e) PABA in Ag junctiin
g) IETS-PNBA
frequency
doped
Pb junction
shift (cm’1
Fig_ 1. (0) The Ramltn spectrum ofp-nitrobenzoic
acid O’NBA)
in solution. (b) The Rnman spectrum of a submondayer of PNBA on 1000 A of smooth AL (c) The Raman spectrum of PNBA ou a 1000 A thick Al fiim on an 8000 A periodicity Si grating. (d) The Raman spectrum of a microscopically smooth. PNBA doped Ag-AlOx-AI tunnel junction. (c)The
Kanlsn spectrum of a microscopically smooth, PABA doped Ag-AlO_,-Al tunnel junction. (f) The Raman spectrum of PARA in a SniAlO_,/Al tunnel junction. &) The IETS spectrum of PNBA iu a Pb/AIOx/Al junction at 4.2 E.
The scattering at 1460 cm-’ is similar to the forbidden structure observed by Domhaus et al. [6] for pyrazine on Ag and also suggests a significant interaction between the PNBA and the adsorbing AlO_, surface. Fig. 1d shows the Raman spectrum of unroughened Al doped with PNBA and covered with 300 A of Ag. This spectrum is similar to those observed in SER studies of deliberately roughened PNBA doped Ag tunnel junctions [3] _ It shows that the changes previously observed between the spectrum of the doping solution and the SER spectrum of the completed
junction are due to the formation of the junction and not the deliberately introduced roughness. The changes in the spectra on adsorbtion on AIO,
LETTERS
14 Jnnuiuy 1953
and after completion of the junction complicate any direct comparison of the adsorbate and solution Raman intensities. Taking however the two strongest lines in fig. la, the spectrum in fig. lb is 4-10X stronger than the spectrum in fig. la when normalized against the scattering volume in the solution. This is close to, but larger than the calculated enhancement for a molecule on a reflector [7]. The spectrum in fig. lc is x30X stronger than that in fig. 1b. The maximum enhancement of the Raman intensity due to the optical excitation of the Al surface plasmon polariton is ~30 [S]. Fig. 1 d is >lOOX stronger than fig. lb when the attenuation due to the Ag is considered. This enlmcement is comparable to the estra enhancement previously reported in deliberately roughened Ag tunnel junctions [3] and the enhancement observed for pyridine adsorbed on unroughened Ag surfaces in vacuum [l]_ The extra enhancement has been attributed either to a short-range interaction between the molecule and the adsorbing surface of the presence of local, submicroscopic, roughness introduced by the sample prep aration [I]_ Fig. le is the Raman spectrum of a PABA doped Al-AlO_,-Agjunction with a smooth continuous Ag counterelectrode. The spectrum is remarkably similar to the PNBA spectrum with a similar erkmcement of the Kaman intensity [Y]. This similarity has also been observed in the IETS spectra
of PNBA and PABA doped Pb tunnel junctions
where no trace of the PNBA NO1 vibrations is observed and both show structure at the energy of the PABA NH2 vibration [9] _ Fig. 1f shows the Raman spectrum of an Al/AlO_,/Sn junction laid down on smooth glass and doped with PABA. The Sn is 300 i$ thick and is discontinuous as seen in both electron micrographs and its resistivity. The evaporation of the Sn layer on the adsorbed PABA produces at least an order-ofmagnitude enhancement of the Raman intensity over that observed for the molecule before the Sn evaporation_ Since the optical transmission of the Sn film is almost 0.1, this suggests that the actual enhancement of the Raman intensity will be between 100 and 1000. The Raman intensity grows rapidly with increasing thickness before saturating and decreasing for thickness above 300 a. This enhancement was not observed’ when the PABA was laid down on a smooth microscope slide and the Sn layer evaporated on it_ Fig. 1g shows the 1ETS spectrum of a PNBA doped Al/AlO_J Pb tunnel junction_ The strong similarities between junction spectra d-g confirm that we observe Raman 173
CHEMICAL PHYSICS LETTERS
\‘~~111!11l!94. nu1nbcr 1
from the adsorbed molecular layer. Our resulrs clearly show the power of the cooled rnul~ichannel detector combined with the triple monochroma~or. The detector allows us to observe Raman ssaircring tionl monolayers at solid-solid and solidair i~r~crfacrs ii1 the absence of any giant enhancescattering
IIWII~Sami using modest power levels which do not dcsrro~ tile sainple. The triple monochromator aT_
imdsussulilcienr
rejecrion lo observe Raman scatraring from die adsorbed species in the presence of srroric ciask scat Wring from the rough Sn surface_ We have been able to observe the evolution of the IC~iiiaii spectra oi doped runnel junctions from the initial doping IO the conlpletion of the junction. This S!IOWSci~a~qcs in the molecular Raman spectrum both OII adsorption IO tlw aside surface and after the evaporalion of rlw countcrelecrrode. Our results on Al are consisten with electromagnetic theory while the Xg results slow the presence of an additional en!ILIIICCI~CIIICWII in the absense of deliberately
intro-
duced rou$~ ncss on microscopic scale [ 1.3 1. Our results suggest 11131the enhancements in the doped Sn iunctions are associated with tile metaii~~~ui~~or~-n~~talsnndwi~icil structure and the disconrinUIUS nature of rhc Sn counterelectrode. The rough
contcrclrclrodc cxmo~. by itself. produce a substanti~l field (>5X) enhancen~cn~ of the Raman inIcrisity hccausc 0f the optical constants of Sn [IO] which hcavii~ chip the conduction-electron resoKII~CCS.I lowve~-. Uir inreraction of the localized p\~lxk:nicln (kids of the Sn strucmrcs with the Al substrate cm produrc a substantial enhancement of
Raman scattering
14 January 1983.
will be a powerful
probe of impuri-
ties in composite materials. In conclusion, using optical multichannel detection of the Raman signa: and a triple monochromator system, we have obtained Raman scattering at the solidsolid and solid-gas interfaces from molecular monolayers laid down on evaporated, non-noble-metal films.
This has been done in the absence of the conditions previously required for the observation of surfaceenhanced Raman scattering. In doing so, we have demonstrated a new geometry for field-enhanced Raman scattering in the absence of optically active conduction-electron resonances. It is clear that the use of multichannel Raman spectroscopy greatly expands the scope and applicability of Raman spectroscopy on virtually alI metallic and non-metallic substrates in solids and gases as well as vacuum. We thank A.M. Torresson, Y.J. Thefaine and M-T. l’rikas for technical assistance and Dr. J.E. Demuth, Professor A. Campion and Professor H. Metiu for helpful discussions.
References
SII
fhc krpticai Ikids in tile junctiou
region. Such a gxmrtn for the enhancement of the local ticlds has ~WCI~considered by Aravind et al. [4,1 l] W!IUcrticul~~rcd 911 enhancanent of 100 for the Raman
scartcring
I‘rum a molrcuie
under a 200 1%Sn sphere
energies uscti by us. The total enha~icen~en~ will include many c,t!lr’r ixrors WI&AI cm borh increase and decrease the 10wi crhnccnwit. it is clear however that the SII s1rucIure induced coupling of the optical fields to rlw iullction rrsion is responsible for a substantial
_TO ..\ 3hw2
3 flat
XI surface 31 the escitation
pxt crl‘111~cnhncernent which we observe. This eniixiscuicnt nirclianisni is 3 general result of the interaction
bctwwn poixizablr bodies and will be obs+Nable CVCIIwhen 1i01lcof rhe resonances of the polarizallie hL)dics arc king excited. When combined with our ciii~~ncc‘dsensirivity, it su,nflesrs that multichannel
174
RX C-hang and TX. Iktak. edr, Surface-enhanced Ranian scatrering (Plenum Press. NCWYork, 1962). I21 -4. Campion, J.E. Brown and V-M. Grizzle. Surface Sci. 115 (1982) L153. 131 J.C. Tsmg. J.R. Kirtley, T-N. Theis and S.S. Jha. Phys. Rrw. 825 (1982) 5074. l4l P-K. Arsvind. R.N. Rendell nnd H. hlotiu, Chem. Phys. Letters SS (1982) 396. 151 J-D. Lan:gm and P-K. Hansnx~. Surface Sci. 52 (1975) 211. 161 R. Dornhaus, XI-B. Long. RX. Bcnner and R-K. Chang, Surface Sci 93 (1980) 240. 171 R.G. Grcenlcr and l-L. Slager, Spectrochim. Acta 29A (1973) 193; Y.J. Chcn. W.P. Chrn and E. Burstein, Phys. Rev. Letters
ill
19 (1976)Sll. 151 \?‘.lI.Wcber and G.W. Ford, Opt. Letters 6 (1981) 123; P-K. -4ravind. E. Hood and Ii. hletiu. Surface Sci. 109 (1981) 95; S.S. Jha, J.R. Kirtlcy and J.C. Tsan_e. Phys. Rev. B22 (1980) 3973. 191 J.C. Tsang. Ph. Avouris and J.R. Kirtley. Proceedings of the 3rd International Conference on Vibrations at Surfaces, Asilomu. California. Scptenlber l-4, 1982.
to be published.
IlO1 R.A. MacCrae, E.T.
Arakawa and M.W. \Viiihns. Phps. Rev. 162 (1967) 615. 1111 P-K. Aravind. private communication.