- Email: [email protected]
Rainbow scattering of K(4 2P32 ) from Hg at hyperthermal energies
Volume 88, number 2
RAINBOW
CHLMICAL
SCATTERING
U LACKSCHEWITZ, nler-PlatrcR.htstrtrrl
PIIYSICS LClTCRS
30 Aprd 1982
OF K(4 ‘)P,,?) FROM Hg AT HYPERTHERMAL
J. MAIER
ENERGIES
and H. PAULY
pir Stratrurrrgsforscitttttg,
DWOO
Ci)tttttgerc.
Federal
Republic
oJ Gcrmmy
Rccclved 2 hlmch 1982
TOM dlfkrcntnl cross scctlons for the scdtlcrmg of lascr-cuxted #(4 *P) dams by Hg 31 colhwn cncgw bctwcrn 0 5 and 4 cV arc rcportcd. A prchminxy cvaluat~on of lhc obscrvcd rambow slructurcs usmg the clashc approvimalon y~rldc model polentitlls for both the B 2~ and the A211 branch of the CWtcd-rtdtc polcnrnl
Continuing
previous scattermg elpenmcnts
with
laser-ehclted atoms [I ,3_1we measured total diffcrential cross sections for colhslons of K(4 2P) atoms with ground-state
tlg atoms JL center-of-mass energres bc-
state scattermg is proportional da*/dw
a rl f rr*I-
where A =I+ - I-
,
The apparatus IS essentially the same as that de-
[I ,7-J
scribed by Htiwel and co-workers
A seeded po-
(1)
is the dlffcrcncc
tector and II* IS the fraction
tween 0.5 and 4 eV.
to
signal at the de-
of potass~urn atoms
lhe ekcltcd stale. Fg. I shows an e.\pcrrment,d
m
result. Here the dif-
tassmm atom beam (carrier gases HZ, He or mixtures of both gases) from a two-chamber
nozzle source
(nozzle diameters between 0 I and 0 2 mm) IS crossed, after velocity
selcctlon (Flzeau-type
selector, Au/u =
3.5%), by a Hg beam from an effusive source with a thin-walled
onkc
(diameter
0.5 mm) which can be
opened and closed by an electromagnetically opernted Internal shutter [3]. The scattered potassium 31orns arc detcctcd
by surface uxxzntion
in NI “out-
second detector momtors the incoming K beam mtenslty. Excltatlon of Ihe K
of-plane”
arrangement.
atoms is performed
A
by a laser beam (Coherent
Radla-
tion model CR 599-2 I with oxazm dye) whrch passes through the target at rlght angles to both atomtc beams. The plane of polarization
of the Imcarly polar-
ized laser light can be rotated by a polarlzatlon tor. Control
rota.
of the measurements and data acquIsI-
bon is performed and a CAMAC
by a mmicomputer
(NOVA
11-00)
system as Interface between apparatus
and computer. In order to obtam the dlfferentlal scattered intensity
cross section the
for a given collision energy IS
measured with laser “on” (I+) and “off” the total differential cross section do*/do
0 009-2614/82/0000-0000/S
(I-) Thus for cxcited-
02.75 0 1982 North-Holland
rig. I. Dlffcrcnlldl sralrermg cross sccI#on, trcghtcd w~rh 0 sin 0 3s J fUnCtlOfl of the laboratory rngk 0 for a CCnlCf4m&s cncrgy of I.56 eV. The c\ckulon of IIIC li atoms ISperformed wllh lmcarly pokzcd hgbt The squzcs stand for ZI mcJsurcmcnt wab the clcccnc licld vcclor E parallel !o lhc
rdatwcvcloc~lyg, IIIC clrclcs arc obtamcd WII~ & pcrpcndlcuIX log. The sohd Imcs are wlculakd m the cldslrc approumalion. usmg two Lcnnard-Jones (8.6) potenMs paramctcrs gven m table I.
ullh 11:~
733
Volume 88. number 7,
CHEMICAL
LtlTCRS
PHYSICS
feren!la:scatteringcrosssectloll (werghted with 0 sine) is plotted against the angle of deflection for a colhsion energy of I .56 eV (center-of-mass system) for two dlf’fercnt polarizations of the exciting light (electric field vector E parallel to the relative velocity g and perpendicular tog). Slmdar lo the Na(‘P)-Hg system [I ,2] the dlfferentlal cross section shows two separate rainbow structures, whrch strongly depend on the polarkation of the laser light and which can be nttributed
to
B
-I
30 April 1982
I
the 2P and 211 potentials of the excited
collision pair. In J prehminary evalualron of the data WC compared [he measured cross sections with calculations m the elssilc dpproxrmation [4-61, whrch was shown to be valid in the case of Na(?P)-Hg [2]. For these calculations we assumed LennardJones (8.6) potentials for both the Z and ll branch. In table I the resulting potential parameters are summarized. The calculated cross sections for the two polarlzatlons of the light arc shown m fig. I as full curves. The agreement with the measurements IS good II one takes mto account f.ha~ the model potentials may not have the correct shape. At higher energies, we observe an additional hump in the differential scattering cross section at large angles (on the shadow side of the II rainbow). This can be seen from fig. 2, which shows the large-angle part of the weighled differential cross sectlon ’ I*(B)0 sin0 for a center-of-mass colhsion energy of 3 5 eV and for the two different polarizations of the escltmg laser light described before. The amplitude of this hump shows the same dependence on polanza[Ion as the amphtude of the C rainbow (opposite to the ll rainbow shown UI fig. 3). It may, therefore, be
caused by a shoulder or a hump in the repulsive ‘fable
rc
1. Differcnttal scattering cross sectton, weighted with function of the laboratory angle 0 for a ccntcr-ofmass energy 3.5 cV. On the dark side of’ the fl rambow, an addulonal hump IS observed, which shows the same dcpcndcncc on the polzinzation of the Iascr hght as the S rainbow (squares belong to Ellg, circles to ELg)
0 sm 0. ns a
of the L: potential, which has also been found in the K(‘P)-Ar
and K(2P)-Kr
case [7] _ The full curves
shown in fig. 2 have been’calculated m the elastic approximation using a modified Lennard-Jones ‘8,6) model for the X potential: V = ~(31-8
- 4+)
- e.
exp [-7(x-
A-~)~],
part
I
Results oF3 preliminary
analysts of the e\perimcntal cross secttons in the c&tic appro\lmation (panmclers of LcnnardJoncs (8,6) potentials, modlficd cccordmg to cq (2) m the wsc of the ?: potential)
e WI ‘rn (A) EO WO
r0 (19 ‘y
234
S potcnltrd
fl polcntral
0.14 4.40
061 3.53
0 056 3 1-8 650
-
Fig.3.ExperimenIallydetermined model potcntials(LenntudJones (8,6), with Gauss modification in the X case) for the K*-Hg mteracuon. .
(2)
Volume 88, number 2
CHEMICALPHYSICS
with x = r/r,,, and x0 = ro/r,,, , which allows us to produce a hump of given shape, Hrldthand positron m the repulsive part of the LennardJones (8,6) potential. The parameters eo, 7, and rO necessary to lit the experimental data are also listed III table I. Fig. 3 shows the excited-state potentials determined from our measurements. Similarly to the Na-Hg case, the II-state potential is seen to be deeper by a factor
of 4 than
the one for the X state.
In addition,
the shoulder In the Z-state potentral is clearly visible. The comparison with availablecalculated potentials [s] shows considerable discrepancies. As recent calculatrons for alkali-inert-gas systems have shown [9], these discrepancres must be attributed to the model potential used in the calculations for K*-Hg. We wash to thank R. Dgren for many valuable discussions. For the computer time we are obliged to the
LETTERS
30 Aprd 1982
Gesellschaft fUr wissenschaftlichc Datenver.rrbcrtung, Gbttingcn.
References [I]
L Hllwcl, J Maw,
R K.B Hclbing and H Pnuly, Chcm.
Phys. Letters 74 (1980) 459. [2] L. Hliwcl. J. hfaler and H. Pwly. J Chem. Phys.. IO be published. [3] R DIlrcn and H 0. Hoppc. J. Phys. BIL (1978)
2143.
[4] S Wofsy.R.H C Reid and A. Dalgamo.Astrophys. J. 168 (1971) 161. [Sj R H C. Rcld. J. Phys. 86 (1973)
2018.
[S] R H.C. Reid, J Phys 88 (1973)
L492.
[7]
R Dllrcn. E. Hasselbrink, S. hll1osevif.G. Prchlcr and II. Tlscher,Chem. Phys. Letters, to be published
[6]
R. DIlren, J. Phys. BlO(l977)
3467; Report lZ.BIax-
Planck-lnstrtut mr Stramungsforschung (1977). [9] R. Dllren, E. Hassclbrmk and C hlorllz. 2. Physlk. to bc publahcd.
235
RAINBOW
CHLMICAL
SCATTERING
U LACKSCHEWITZ, nler-PlatrcR.htstrtrrl
PIIYSICS LClTCRS
30 Aprd 1982
OF K(4 ‘)P,,?) FROM Hg AT HYPERTHERMAL
J. MAIER
ENERGIES
and H. PAULY
pir Stratrurrrgsforscitttttg,
DWOO
Ci)tttttgerc.
Federal
Republic
oJ Gcrmmy
Rccclved 2 hlmch 1982
TOM dlfkrcntnl cross scctlons for the scdtlcrmg of lascr-cuxted #(4 *P) dams by Hg 31 colhwn cncgw bctwcrn 0 5 and 4 cV arc rcportcd. A prchminxy cvaluat~on of lhc obscrvcd rambow slructurcs usmg the clashc approvimalon y~rldc model polentitlls for both the B 2~ and the A211 branch of the CWtcd-rtdtc polcnrnl
Continuing
previous scattermg elpenmcnts
with
laser-ehclted atoms [I ,3_1we measured total diffcrential cross sections for colhslons of K(4 2P) atoms with ground-state
tlg atoms JL center-of-mass energres bc-
state scattermg is proportional da*/dw
a rl f rr*I-
where A =I+ - I-
,
The apparatus IS essentially the same as that de-
[I ,7-J
scribed by Htiwel and co-workers
A seeded po-
(1)
is the dlffcrcncc
tector and II* IS the fraction
tween 0.5 and 4 eV.
to
signal at the de-
of potass~urn atoms
lhe ekcltcd stale. Fg. I shows an e.\pcrrment,d
m
result. Here the dif-
tassmm atom beam (carrier gases HZ, He or mixtures of both gases) from a two-chamber
nozzle source
(nozzle diameters between 0 I and 0 2 mm) IS crossed, after velocity
selcctlon (Flzeau-type
selector, Au/u =
3.5%), by a Hg beam from an effusive source with a thin-walled
onkc
(diameter
0.5 mm) which can be
opened and closed by an electromagnetically opernted Internal shutter [3]. The scattered potassium 31orns arc detcctcd
by surface uxxzntion
in NI “out-
second detector momtors the incoming K beam mtenslty. Excltatlon of Ihe K
of-plane”
arrangement.
atoms is performed
A
by a laser beam (Coherent
Radla-
tion model CR 599-2 I with oxazm dye) whrch passes through the target at rlght angles to both atomtc beams. The plane of polarization
of the Imcarly polar-
ized laser light can be rotated by a polarlzatlon tor. Control
rota.
of the measurements and data acquIsI-
bon is performed and a CAMAC
by a mmicomputer
(NOVA
11-00)
system as Interface between apparatus
and computer. In order to obtam the dlfferentlal scattered intensity
cross section the
for a given collision energy IS
measured with laser “on” (I+) and “off” the total differential cross section do*/do
0 009-2614/82/0000-0000/S
(I-) Thus for cxcited-
02.75 0 1982 North-Holland
rig. I. Dlffcrcnlldl sralrermg cross sccI#on, trcghtcd w~rh 0 sin 0 3s J fUnCtlOfl of the laboratory rngk 0 for a CCnlCf4m&s cncrgy of I.56 eV. The c\ckulon of IIIC li atoms ISperformed wllh lmcarly pokzcd hgbt The squzcs stand for ZI mcJsurcmcnt wab the clcccnc licld vcclor E parallel !o lhc
rdatwcvcloc~lyg, IIIC clrclcs arc obtamcd WII~ & pcrpcndlcuIX log. The sohd Imcs are wlculakd m the cldslrc approumalion. usmg two Lcnnard-Jones (8.6) potenMs paramctcrs gven m table I.
ullh 11:~
733
Volume 88. number 7,
CHEMICAL
LtlTCRS
PHYSICS
feren!la:scatteringcrosssectloll (werghted with 0 sine) is plotted against the angle of deflection for a colhsion energy of I .56 eV (center-of-mass system) for two dlf’fercnt polarizations of the exciting light (electric field vector E parallel to the relative velocity g and perpendicular tog). Slmdar lo the Na(‘P)-Hg system [I ,2] the dlfferentlal cross section shows two separate rainbow structures, whrch strongly depend on the polarkation of the laser light and which can be nttributed
to
B
-I
30 April 1982
I
the 2P and 211 potentials of the excited
collision pair. In J prehminary evalualron of the data WC compared [he measured cross sections with calculations m the elssilc dpproxrmation [4-61, whrch was shown to be valid in the case of Na(?P)-Hg [2]. For these calculations we assumed LennardJones (8.6) potentials for both the Z and ll branch. In table I the resulting potential parameters are summarized. The calculated cross sections for the two polarlzatlons of the light arc shown m fig. I as full curves. The agreement with the measurements IS good II one takes mto account f.ha~ the model potentials may not have the correct shape. At higher energies, we observe an additional hump in the differential scattering cross section at large angles (on the shadow side of the II rainbow). This can be seen from fig. 2, which shows the large-angle part of the weighled differential cross sectlon ’ I*(B)0 sin0 for a center-of-mass colhsion energy of 3 5 eV and for the two different polarizations of the escltmg laser light described before. The amplitude of this hump shows the same dependence on polanza[Ion as the amphtude of the C rainbow (opposite to the ll rainbow shown UI fig. 3). It may, therefore, be
caused by a shoulder or a hump in the repulsive ‘fable
rc
1. Differcnttal scattering cross sectton, weighted with function of the laboratory angle 0 for a ccntcr-ofmass energy 3.5 cV. On the dark side of’ the fl rambow, an addulonal hump IS observed, which shows the same dcpcndcncc on the polzinzation of the Iascr hght as the S rainbow (squares belong to Ellg, circles to ELg)
0 sm 0. ns a
of the L: potential, which has also been found in the K(‘P)-Ar
and K(2P)-Kr
case [7] _ The full curves
shown in fig. 2 have been’calculated m the elastic approximation using a modified Lennard-Jones ‘8,6) model for the X potential: V = ~(31-8
- 4+)
- e.
exp [-7(x-
A-~)~],
part
I
Results oF3 preliminary
analysts of the e\perimcntal cross secttons in the c&tic appro\lmation (panmclers of LcnnardJoncs (8,6) potentials, modlficd cccordmg to cq (2) m the wsc of the ?: potential)
e WI ‘rn (A) EO WO
r0 (19 ‘y
234
S potcnltrd
fl polcntral
0.14 4.40
061 3.53
0 056 3 1-8 650
-
Fig.3.ExperimenIallydetermined model potcntials(LenntudJones (8,6), with Gauss modification in the X case) for the K*-Hg mteracuon. .
(2)
Volume 88, number 2
CHEMICALPHYSICS
with x = r/r,,, and x0 = ro/r,,, , which allows us to produce a hump of given shape, Hrldthand positron m the repulsive part of the LennardJones (8,6) potential. The parameters eo, 7, and rO necessary to lit the experimental data are also listed III table I. Fig. 3 shows the excited-state potentials determined from our measurements. Similarly to the Na-Hg case, the II-state potential is seen to be deeper by a factor
of 4 than
the one for the X state.
In addition,
the shoulder In the Z-state potentral is clearly visible. The comparison with availablecalculated potentials [s] shows considerable discrepancies. As recent calculatrons for alkali-inert-gas systems have shown [9], these discrepancres must be attributed to the model potential used in the calculations for K*-Hg. We wash to thank R. Dgren for many valuable discussions. For the computer time we are obliged to the
LETTERS
30 Aprd 1982
Gesellschaft fUr wissenschaftlichc Datenver.rrbcrtung, Gbttingcn.
References [I]
L Hllwcl, J Maw,
R K.B Hclbing and H Pnuly, Chcm.
Phys. Letters 74 (1980) 459. [2] L. Hliwcl. J. hfaler and H. Pwly. J Chem. Phys.. IO be published. [3] R DIlrcn and H 0. Hoppc. J. Phys. BIL (1978)
2143.
[4] S Wofsy.R.H C Reid and A. Dalgamo.Astrophys. J. 168 (1971) 161. [Sj R H C. Rcld. J. Phys. 86 (1973)
2018.
[S] R H.C. Reid, J Phys 88 (1973)
L492.
[7]
R Dllrcn. E. Hasselbrink, S. hll1osevif.G. Prchlcr and II. Tlscher,Chem. Phys. Letters, to be published
[6]
R. DIlren, J. Phys. BlO(l977)
3467; Report lZ.BIax-
Planck-lnstrtut mr Stramungsforschung (1977). [9] R. Dllren, E. Hassclbrmk and C hlorllz. 2. Physlk. to bc publahcd.
235