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Differential cross sections for fine-structure inelastic collisions of K(42P) with Ar, Kr and N2
Volume 112, number-5
DIFFERENTIAL
CHEMCAL
CROSS SECTIONS FOR FINE-STRUCTURE
OF K(4 2P) WITH Ar;fi
and G. HILLRICHS
fiir S~r~t~lu~lssfor~c~~~~tlg. 03400
Rcccived 26 September
INELASTIC COLLISIONS
AND N,
R. DijREN, E. HASSELBRINK hlax-Plarlck-ItlstitId
21 December 1984
PHYSICS LETTERS
Giittiugen.
Federal
Republic
of Germany
1984
WC report measurements of differential cross sections for tine-structure inelastic collisions of potassium (4 ‘P,b -4 ‘P,/?) with Ar, Kr and Nz_ The experiment uses crossed molecular beams and a method to detect scattering angles by the analysis of Doppler shifts in laser induced fluorescence. The espcrimental results for I(-Ar arc compared with calculations.
fixed from other measurements, level-resolved data will make it possible to adjust the B ‘Z potential. Work is in progress to evaluate the data presented here in this way.
1. Introduction The interaction of excited alkali atones with rare targets has been the subject of many investigations within the last ten years [ I] _ Parameters of the A 2 II potential well have been worked out for many systems using several experimental methods: far-wing broadcning [I], spectroscopy ofvan dcr Waals molecules [I+], and scattering of atomic beam [4]. The energy dcpcndencc of the irztegral fine-structure transition cross section has been dctcmincd using cell [5-S] and crossed-beam techniques [9]. These cxpcrimcnts test primarily the coupling iii the long-range p3rts of the interatomic potentials_ Differential cross sections of fine-structure inelastic collisions have only been reported for Na-Ar [IO] introducing a new experimental method which uses two dye lasers, one to excite rhe atomic species and a second to detect electronic trausitiou and scattering angle by the Doppler shift of the laser induced fluorescence. This argument settles Ihe problems arising from thk small energy transfer aud the short lifetime of the excited atomic state. Potential curves aild scattering theory of such collisions are well established [-I 1,12]_ From this it is known t!lat the fine-structure resolved differential cross
gas
section
exhibits
Stiickelbergtype
oScillations
2. Experimental The cspcriment uses a crossed-molecular-beam apparatus which has been described in most aspecrs before [ 131. T11c potassium beam is produced in a nozzle oven, velocity selected (U== 1050 m/s, 4u/u =Z3%) and collimated, resulting in a divergence of 5-7 ulin before crossing the target beam. The secondary beam is produced with a multichannel source which cau be cooled down to liquid nitrogen temperature (U-k = 218 Ill/S, av/iI-= SO%, 40 = 30”). Excitation oithe potassium bcarn is performed with a single-frequency dye laser using oxaziue I. The laser is dircctcd into the scattering volume perpendicular to both atomic beamsand tuned tP the4 “Sliz(F=2)4 zP3,2(F= 3) transition. Because of the near ncighborhood of the upper F = 2 state, which is only 2 1 Mi-fz apart, circularly polarized light isused to reduce optical pumping. Compared with linearly polarized light, this rcsuits in a gain of escitatioii efficiency of approsirnately
at large
s&ond singl&node dye k&r roguing with rhodamine GG intersects the.coliision region along
are due to interference involving the A ?ll and the B ‘Z potential. Because the A"IIcurve is .
0 009-2614/84/S 03.00 0 Elsevier Scikce Publishers (North-Holland Physics Publishing Division)
75%.
The
anSlcswhich
B.V.
441
Volume 112, number 5
the relative velocity axis. Tuned to the4 ‘P,,2-S 2D,,, (5812.2 a) transition it excites those K atoms that have undergone the 4 2Pj,z--4 zP,,, fine-structure transition. The population of the 4 2P,,2 level is monitored by observing the fluorescence at 3447 and 4044A (fig. I). A slightly cooled photomultiplier (RCA SSSO) views the sc~ttcringvolunle
througha
lensand
aperture
system. Cutoff filters in front of the photomultiplier and light baffles in the laser input and output ports reduce the background signal. Typical numbers for rhe background and the peak from scattered atoms arc 100 and 4000 counts/s, respectively. To measure the differential cross section, the analysis laser is tuned over the Doppler profile of the second excitation sIep_ The Doppler shift for an atom scattered into the center-of-mass an& 0 is AY’U’Ix(I whcren’
- COSO),
is the final center-of-niass
speed of the inelastic
scattered
particle, h the transition wavelength and the frcqucncy offset 4v = 0 is defined to correspond to O” deflection. Because this arrangement has a roughly constant resolution in av, the fluorescence signal is &zctly
prol>ortional
21 December
CHEMICAL PHYSICS LETTERS
to the differential
scatrcringcross
7s 6s -
5s -
1984
section per unit solid angle dS2, i.e. I(ne)
a du(B)/dSl_
This so-called ang&r djstribution from Doppler shift (ADDS) [ 1] technique has the advantage of providing level specificity and the ability to detect all atoms scattered by 19into-different azimutal angles Q within the short lifetime of nn excited atomic state. On the other hand, the resolution at 0” and 18Oo is poor. Power broadening and the hypcrfine structure of the states involved in the second excitation step (42P1,2: 57.7 MHz, 5 3D,,z: 0.4-l .3 MHz) [ 141 alsb degrade the resolution somewhat. A Nova 4 minicomputer which is interfaced to the experiment using Camac modules scans the analysis laser in 256 steps with 100 ms sample time through the Doppler profile and stores the number of counted photons. These scans are repeated and accumulated for sonle hours. During this time both lasers arc frequency
stabilised
by the colnputer
system
to avoid
thermal
long-time drifts referencing the atomic fluorCSCCIICCfor the first one and an additional FabryPerot interferometer (Burleigh CFT-500, drift < 5 MHz/h) for the second one. The stabilisation of the analysis laser can be controlled regarding the position of the forward peak in the observed spectra which is clsarly visible after a few minutes, and thcsc have been found to differ only by one channel (==I3 MHz) over a period of several hours_ The analysis laser was operated with an output power of 40 mW focused into a spot of 3 mm diameter at the scattering region. This llas btcn found to be sufficient to saturllte the transition. The choice of the 4 zP1,7--5 ?D3j7 transition has the disadvantage that sign&are by a &or of 2 smaller than those with the4 *P 1j2-7 zS1,2 transition -which is possible too - whereas the last one seems to lead to a worse resolution. because of the larger hyperfincstructure splitting of the 7 ‘S level (2 1 MHz). We found no significant effects caused by different polarisations of the analysis laser.
3. Results and discussion
I;@. 1. l’ottissium obsrrvcd
(aary)
cncrgy
lcvcls
transitions
with escirxtion
S~IOWIL
(strong) and
Fig. 2 presents the recorded spectra for K-Ar at a collision energy of 1 12 meV. The signal observed at angles outside the range of O”-180” comes from the
Volume 112, number 5 Scattering 030
60
CHEhliCAL
kgle
PHYSICS
cm (deg) 120 .
90 L
180 I>
K* - Ar
I\ i
21 December 1984
LE-I-l-ERS
used for the scattering calculation_ We think that the remaining uncertainties in the A ‘-II potential determined in a previousscattering experiment are too small to account for that discrepancy. Therefore it is evident that the shape of the B ‘C potential has to be corrected to come into agreement with the measured pattern. This will give new information on the potential not accessible with other esperiments. The data for K-Kr (fig. 3) shows two inflection points at 40° and 62O. The first one can be attributed to the 1~rainbow, the second one is due to 3 shoulder or hump in the repulsive part of the B ‘IZ potential. This is in agreement with older total differential cross section [4] and satellite measurements. The strong decrease in the cross section can be understood in terms of hard-sphere scattering. The shoulder in the repulsive B 2X potential gives rise to a strong increase of the
Scattering
0 30 1
0.5
0.0
-0.5
-1.5
-1.0
Freq. - offset
-2.0
60
Angle
cm (deg)
90
120
.
180 I
.
K* - Kr
-2.5
[GHz]
Fig. 2. Experimental (points) and calculated I(-Ar fiie-structure transition cross section for a collision energy of 112 meV. The tbcoretical curve uses the potential from ref. [S]_ Oscillations at large angles are clearly visible due to interference betiveen trajectories involving the n and X potential.
imperfect
ztngular
resolution
of tile apparJtUS.
Tile
crosssection is strongly peaked in the forward direction. The slight shoulder at 220 MHz offset (-lo) is due to the rainbow of the rr scat tering [4] _The oscillations at large an8les are clearly visible even though the modulation at the high end is only less pronounced. This reflects the poor resolution at extreme an8les. Also in fig. 2 we give the result of a close-coupling calculation of the differential cross section based on the model potentials calculated in a previous work [ Ill. The result has been roughly averaged to match the experimental resohrtion. The coarse structure of the theoretical curve is in fair agreement with the experimental observation_ It is obvious, however, that quantitatively the spacing and the phase of the oscillations tire not reproduced by the calculation. This difference must be attributed to inaccuracies in the potentials
- _
0.0
-0.5
-1.0
Freq.
-1.5
- offset
-2.0
-2.5
[GHz]
I-ig. 3. Measured tine-structure transitions cross section for I<-Kr at a collision energp of 164 meV. The fist shoulder in the cross section can be attributed to the B rainbow second one to a shoulder in the B *2 potential.
and the
443
Volume
112, number
CHEMICAL
5
Scattering 030 60 .I
Angle
PHYSICS
cm (deg)
90
120
LETTERS
21 Deccmbcr
1984
Acknowledgement
180
.
WC arc indebted to H. Pauly for continuoussupport of this work. In addition we thank P. Andrcsen and W. Rappe for help in constructing the photon detector. For the computer time we are grateful to the Cesellschaft fiir wissenschaftIichc Datenverarbeitung in Giit
tinge11 _
References [I] R. Dilren,
Advan. At. hfol. Phys. 16 (1980) 55. [Z] A. Gnlla$cr, in: Atomic physics, Vol. 4, cds. C. zu Putlitz, E.W. Webcr and A. Winnacker (Plenum Press. New York, 1975) pp 559-579. [3] J. Teltinghuisen. A. Ragone, SK. blying. D.A. Auerbach. R.E. Smalley, L. Warton and D.H. Levy, J. Chem.
.
*
.
-%
_g,
[4]
-y-y--y_
0.5
-0.5
0.0
Freq.
chssical
turning
point
angles)
“~02“
-1.0
-1.5
-2.0
[Gllzj
over 3 range of few nngilhr InOangular nwnient:l (ix. snmllcr 13rgct than largcl-angular sIxitlc~-
I~CIII;~. Consec~~icntly
Ixrgcr
- offset
3
(i.e. smaller angles). Outside this feature no oscillariom iIrC ObsCrvCd. As an cs:mplc foi- ~111 atom-nlolcculc system K-N-, wis stutlicd (fig. 4). Iii Illis cast the tcnipcrxt~~rc of tlw SOLIKC W;IS I I5 K. The data show no struchm. 11 111lfg bc suptwscd 111311l1ese ill’c waslltd by tltc dcpc~dmcc ol‘tl~c polcntial OII the orientation and the relational sI;itc of the molcculc. 1iiu1Iicm13
444
Phys. 71 (1979) 1283. K. Diircn, E. Hxselbrink
nnd 11. Tiscbcr, J. Chem. Phys. 77 (19S2) 3186. [S] P.L. Lijnsc, J. Quant. Spcctry. Ilad. Transfer 14 (1974) 1195_ [6] G.D. Chapman and L. Kmusc. tin. J. Phys. 44 (1966) 753. [7] D.A. hlcCillisand C. Krause, J. Res. NBS 7% (1968) 553. [S] P.L. Lijnsc wd J.C. llarnlun, J. Quan~ Spcctry. Rad. Trnnsfcr 14 (1974) 1074. 19 1 J.hl. Xtestdagb, J. Cuwllier. J. Bcrlande, A. Binct and P. dc Pujo, J. Phys. 813 (1980) 4589. [IO] W.D. Phillips, J.A. Serri. D.J. Ely. D.E. I’ritchard. K.R. Wuv nnd J.L. Knscy, Pbys. Rev. Lctwrs 41 (1978) 937. [ 11) R. Diircn, E. Hasselbrink and G. hloritz, Z. Physik A307 (1987) I. 1121 R.H.G. Reid. J. Phys. B6 (1973) 201s. [ 131 II. Diiren, W. Gr+x. E. I&xxzlbrink and R. Licdtke, J. Cbcm. Phye. 74 (1961) 6806. [ 141 E. Arimondo. hl. Infusio and I’. Violino, Rev. Mod. Phys. 49 (1977) 31.
DIFFERENTIAL
CHEMCAL
CROSS SECTIONS FOR FINE-STRUCTURE
OF K(4 2P) WITH Ar;fi
and G. HILLRICHS
fiir S~r~t~lu~lssfor~c~~~~tlg. 03400
Rcccived 26 September
INELASTIC COLLISIONS
AND N,
R. DijREN, E. HASSELBRINK hlax-Plarlck-ItlstitId
21 December 1984
PHYSICS LETTERS
Giittiugen.
Federal
Republic
of Germany
1984
WC report measurements of differential cross sections for tine-structure inelastic collisions of potassium (4 ‘P,b -4 ‘P,/?) with Ar, Kr and Nz_ The experiment uses crossed molecular beams and a method to detect scattering angles by the analysis of Doppler shifts in laser induced fluorescence. The espcrimental results for I(-Ar arc compared with calculations.
fixed from other measurements, level-resolved data will make it possible to adjust the B ‘Z potential. Work is in progress to evaluate the data presented here in this way.
1. Introduction The interaction of excited alkali atones with rare targets has been the subject of many investigations within the last ten years [ I] _ Parameters of the A 2 II potential well have been worked out for many systems using several experimental methods: far-wing broadcning [I], spectroscopy ofvan dcr Waals molecules [I+], and scattering of atomic beam [4]. The energy dcpcndencc of the irztegral fine-structure transition cross section has been dctcmincd using cell [5-S] and crossed-beam techniques [9]. These cxpcrimcnts test primarily the coupling iii the long-range p3rts of the interatomic potentials_ Differential cross sections of fine-structure inelastic collisions have only been reported for Na-Ar [IO] introducing a new experimental method which uses two dye lasers, one to excite rhe atomic species and a second to detect electronic trausitiou and scattering angle by the Doppler shift of the laser induced fluorescence. This argument settles Ihe problems arising from thk small energy transfer aud the short lifetime of the excited atomic state. Potential curves aild scattering theory of such collisions are well established [-I 1,12]_ From this it is known t!lat the fine-structure resolved differential cross
gas
section
exhibits
Stiickelbergtype
oScillations
2. Experimental The cspcriment uses a crossed-molecular-beam apparatus which has been described in most aspecrs before [ 131. T11c potassium beam is produced in a nozzle oven, velocity selected (U== 1050 m/s, 4u/u =Z3%) and collimated, resulting in a divergence of 5-7 ulin before crossing the target beam. The secondary beam is produced with a multichannel source which cau be cooled down to liquid nitrogen temperature (U-k = 218 Ill/S, av/iI-= SO%, 40 = 30”). Excitation oithe potassium bcarn is performed with a single-frequency dye laser using oxaziue I. The laser is dircctcd into the scattering volume perpendicular to both atomic beamsand tuned tP the4 “Sliz(F=2)4 zP3,2(F= 3) transition. Because of the near ncighborhood of the upper F = 2 state, which is only 2 1 Mi-fz apart, circularly polarized light isused to reduce optical pumping. Compared with linearly polarized light, this rcsuits in a gain of escitatioii efficiency of approsirnately
at large
s&ond singl&node dye k&r roguing with rhodamine GG intersects the.coliision region along
are due to interference involving the A ?ll and the B ‘Z potential. Because the A"IIcurve is .
0 009-2614/84/S 03.00 0 Elsevier Scikce Publishers (North-Holland Physics Publishing Division)
75%.
The
anSlcswhich
B.V.
441
Volume 112, number 5
the relative velocity axis. Tuned to the4 ‘P,,2-S 2D,,, (5812.2 a) transition it excites those K atoms that have undergone the 4 2Pj,z--4 zP,,, fine-structure transition. The population of the 4 2P,,2 level is monitored by observing the fluorescence at 3447 and 4044A (fig. I). A slightly cooled photomultiplier (RCA SSSO) views the sc~ttcringvolunle
througha
lensand
aperture
system. Cutoff filters in front of the photomultiplier and light baffles in the laser input and output ports reduce the background signal. Typical numbers for rhe background and the peak from scattered atoms arc 100 and 4000 counts/s, respectively. To measure the differential cross section, the analysis laser is tuned over the Doppler profile of the second excitation sIep_ The Doppler shift for an atom scattered into the center-of-mass an& 0 is AY’U’Ix(I whcren’
- COSO),
is the final center-of-niass
speed of the inelastic
scattered
particle, h the transition wavelength and the frcqucncy offset 4v = 0 is defined to correspond to O” deflection. Because this arrangement has a roughly constant resolution in av, the fluorescence signal is &zctly
prol>ortional
21 December
CHEMICAL PHYSICS LETTERS
to the differential
scatrcringcross
7s 6s -
5s -
1984
section per unit solid angle dS2, i.e. I(ne)
a du(B)/dSl_
This so-called ang&r djstribution from Doppler shift (ADDS) [ 1] technique has the advantage of providing level specificity and the ability to detect all atoms scattered by 19into-different azimutal angles Q within the short lifetime of nn excited atomic state. On the other hand, the resolution at 0” and 18Oo is poor. Power broadening and the hypcrfine structure of the states involved in the second excitation step (42P1,2: 57.7 MHz, 5 3D,,z: 0.4-l .3 MHz) [ 141 alsb degrade the resolution somewhat. A Nova 4 minicomputer which is interfaced to the experiment using Camac modules scans the analysis laser in 256 steps with 100 ms sample time through the Doppler profile and stores the number of counted photons. These scans are repeated and accumulated for sonle hours. During this time both lasers arc frequency
stabilised
by the colnputer
system
to avoid
thermal
long-time drifts referencing the atomic fluorCSCCIICCfor the first one and an additional FabryPerot interferometer (Burleigh CFT-500, drift < 5 MHz/h) for the second one. The stabilisation of the analysis laser can be controlled regarding the position of the forward peak in the observed spectra which is clsarly visible after a few minutes, and thcsc have been found to differ only by one channel (==I3 MHz) over a period of several hours_ The analysis laser was operated with an output power of 40 mW focused into a spot of 3 mm diameter at the scattering region. This llas btcn found to be sufficient to saturllte the transition. The choice of the 4 zP1,7--5 ?D3j7 transition has the disadvantage that sign&are by a &or of 2 smaller than those with the4 *P 1j2-7 zS1,2 transition -which is possible too - whereas the last one seems to lead to a worse resolution. because of the larger hyperfincstructure splitting of the 7 ‘S level (2 1 MHz). We found no significant effects caused by different polarisations of the analysis laser.
3. Results and discussion
I;@. 1. l’ottissium obsrrvcd
(aary)
cncrgy
lcvcls
transitions
with escirxtion
S~IOWIL
(strong) and
Fig. 2 presents the recorded spectra for K-Ar at a collision energy of 1 12 meV. The signal observed at angles outside the range of O”-180” comes from the
Volume 112, number 5 Scattering 030
60
CHEhliCAL
kgle
PHYSICS
cm (deg) 120 .
90 L
180 I>
K* - Ar
I\ i
21 December 1984
LE-I-l-ERS
used for the scattering calculation_ We think that the remaining uncertainties in the A ‘-II potential determined in a previousscattering experiment are too small to account for that discrepancy. Therefore it is evident that the shape of the B ‘C potential has to be corrected to come into agreement with the measured pattern. This will give new information on the potential not accessible with other esperiments. The data for K-Kr (fig. 3) shows two inflection points at 40° and 62O. The first one can be attributed to the 1~rainbow, the second one is due to 3 shoulder or hump in the repulsive part of the B ‘IZ potential. This is in agreement with older total differential cross section [4] and satellite measurements. The strong decrease in the cross section can be understood in terms of hard-sphere scattering. The shoulder in the repulsive B 2X potential gives rise to a strong increase of the
Scattering
0 30 1
0.5
0.0
-0.5
-1.5
-1.0
Freq. - offset
-2.0
60
Angle
cm (deg)
90
120
.
180 I
.
K* - Kr
-2.5
[GHz]
Fig. 2. Experimental (points) and calculated I(-Ar fiie-structure transition cross section for a collision energy of 112 meV. The tbcoretical curve uses the potential from ref. [S]_ Oscillations at large angles are clearly visible due to interference betiveen trajectories involving the n and X potential.
imperfect
ztngular
resolution
of tile apparJtUS.
Tile
crosssection is strongly peaked in the forward direction. The slight shoulder at 220 MHz offset (-lo) is due to the rainbow of the rr scat tering [4] _The oscillations at large an8les are clearly visible even though the modulation at the high end is only less pronounced. This reflects the poor resolution at extreme an8les. Also in fig. 2 we give the result of a close-coupling calculation of the differential cross section based on the model potentials calculated in a previous work [ Ill. The result has been roughly averaged to match the experimental resohrtion. The coarse structure of the theoretical curve is in fair agreement with the experimental observation_ It is obvious, however, that quantitatively the spacing and the phase of the oscillations tire not reproduced by the calculation. This difference must be attributed to inaccuracies in the potentials
- _
0.0
-0.5
-1.0
Freq.
-1.5
- offset
-2.0
-2.5
[GHz]
I-ig. 3. Measured tine-structure transitions cross section for I<-Kr at a collision energp of 164 meV. The fist shoulder in the cross section can be attributed to the B rainbow second one to a shoulder in the B *2 potential.
and the
443
Volume
112, number
CHEMICAL
5
Scattering 030 60 .I
Angle
PHYSICS
cm (deg)
90
120
LETTERS
21 Deccmbcr
1984
Acknowledgement
180
.
WC arc indebted to H. Pauly for continuoussupport of this work. In addition we thank P. Andrcsen and W. Rappe for help in constructing the photon detector. For the computer time we are grateful to the Cesellschaft fiir wissenschaftIichc Datenverarbeitung in Giit
tinge11 _
References [I] R. Dilren,
Advan. At. hfol. Phys. 16 (1980) 55. [Z] A. Gnlla$cr, in: Atomic physics, Vol. 4, cds. C. zu Putlitz, E.W. Webcr and A. Winnacker (Plenum Press. New York, 1975) pp 559-579. [3] J. Teltinghuisen. A. Ragone, SK. blying. D.A. Auerbach. R.E. Smalley, L. Warton and D.H. Levy, J. Chem.
.
*
.
-%
_g,
[4]
-y-y--y_
0.5
-0.5
0.0
Freq.
chssical
turning
point
angles)
“~02“
-1.0
-1.5
-2.0
[Gllzj
over 3 range of few nngilhr InOangular nwnient:l (ix. snmllcr 13rgct than largcl-angular sIxitlc~-
I~CIII;~. Consec~~icntly
Ixrgcr
- offset
3
(i.e. smaller angles). Outside this feature no oscillariom iIrC ObsCrvCd. As an cs:mplc foi- ~111 atom-nlolcculc system K-N-, wis stutlicd (fig. 4). Iii Illis cast the tcnipcrxt~~rc of tlw SOLIKC W;IS I I5 K. The data show no struchm. 11 111lfg bc suptwscd 111311l1ese ill’c waslltd by tltc dcpc~dmcc ol‘tl~c polcntial OII the orientation and the relational sI;itc of the molcculc. 1iiu1Iicm13
444
Phys. 71 (1979) 1283. K. Diircn, E. Hxselbrink
nnd 11. Tiscbcr, J. Chem. Phys. 77 (19S2) 3186. [S] P.L. Lijnsc, J. Quant. Spcctry. Ilad. Transfer 14 (1974) 1195_ [6] G.D. Chapman and L. Kmusc. tin. J. Phys. 44 (1966) 753. [7] D.A. hlcCillisand C. Krause, J. Res. NBS 7% (1968) 553. [S] P.L. Lijnsc wd J.C. llarnlun, J. Quan~ Spcctry. Rad. Trnnsfcr 14 (1974) 1074. 19 1 J.hl. Xtestdagb, J. Cuwllier. J. Bcrlande, A. Binct and P. dc Pujo, J. Phys. 813 (1980) 4589. [IO] W.D. Phillips, J.A. Serri. D.J. Ely. D.E. I’ritchard. K.R. Wuv nnd J.L. Knscy, Pbys. Rev. Lctwrs 41 (1978) 937. [ 11) R. Diircn, E. Hasselbrink and G. hloritz, Z. Physik A307 (1987) I. 1121 R.H.G. Reid. J. Phys. B6 (1973) 201s. [ 131 II. Diiren, W. Gr+x. E. I&xxzlbrink and R. Licdtke, J. Cbcm. Phye. 74 (1961) 6806. [ 141 E. Arimondo. hl. Infusio and I’. Violino, Rev. Mod. Phys. 49 (1977) 31.