- Email: [email protected]
Hyperfine structure of odd-parity levels in 139LaI by laser optogalvanic spectroscopy
Optics Communications 94 (1992) 331-334 North-Holland
OPTICS COMMUNICATIONS
Hyperfine structure of odd-parity levels in 139LaI by laser optogtilvanic spectroscopy Liejuan
Jia, Chunyang
Jing and Fucheng
Lin
Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 800-211. Shanghai 201800, China Received 18 January 1992; revised manuscript received 1 July 1992
The hyperline structure (hfs) of eight odd-parity levels of ‘39LaI has been studied by high-resolution Doppler-limited laser optogalvanic spectroscopy. The magnetic-dipole hfs constants A are obtained by least-squares tits. The A values of five of these levels are reported for the first time to our knowledge. One A value of the three previously reported levels is corrected, and the other two are also given for comparison where the agreements are good.
1. Introduction Because of its complicated atomic-structure, neutral lanthanum, as the first element of the rare-earth series, has a very complicated spectrum. Nevertheless, a great deal of spectroscopic work has been done, and a large number of levels have been identified through systematic study [ 11. Over the years many investigations of hyperline structure (hfs) of ‘39LaI have been carried out. Early studies are concentrated on the even-parity levels. The hfs for the two levels of the ground-state term 5d6s2 2D were measured precisely by Ting [ 21 using atomic-beam magnetic-resonance technique. Afterwards, Childs and Goodman [ 31 used the same technique to determine the hfs constants for all previously unstudied atomic levels below 9200 cm-‘, and analyzed the results in term of a set of eigen-vectors. Recently, Childs and Nielsen [4] measured precisely the hfs constants of most levels below 14000 cm-‘, and compared these results, together with earlier results for lower-lying levels, with multiconfiguration Dirac-Fock (MCDF) ab initio calculations. The odd-parity configurations have also been studied in recent years. In a series of experiments, Hese [ 5 1, and Hese and Btildt [ 6 ] studied the hfs of low-lying levels of the Sd6s6p configuration by levelcrossing techniques. Shortly afterwards, Fischer, Htihnermann and Mandrek [ 71 studied the hfs of 0030-4018/92/$05.00
most states of the 5d6s6p configuration and several states in the 5d26p configuration using a Fabry-Perot interferometer and cold-cathode source. Because the electric-quadrupole hfs constant is so small, the resolution attainable with this technique was unable to obtain any quadrupole hfs information. From 1977, the much higher resolution by Doppler-free laseratomic-beam technique enabled Childs and his coworkers [4,8,9] to study both the magnetic-dipole and electric-quadrupole hfs constants for a number of odd-parity levels. More recently, hfs constants of a great deal of levels have been obtained by several authors with various techniques [ lo- 13 1. Although hfs in ‘39LaI has been investigated extensively, the hfs data are far from complete. The goal of the present work was to extend the earlier studies to several other odd-parity levels. This was achieved by populating the lanthanum atoms in a hollowcathode discharge (HCD) tube, cw dye laser excitation and optogalvanic detecting.
2. Experiment The experimental arrangement is shown in fig. 1. A home-made La-Kr HCD tube was used to obtain lanthanum atomic vapor containing predominantly the ground state and the low-lying metastable states. The tube was filled with about 1 Torr krypton buffer
0 1992 Elsevier Science Publishers B.V. All rights reserved.
331
Volume 94, number
~
5
-
OPTICS
choppx
lens
COMMUNICATIONS
1992
HCD
Fig. 1. Experimental arrangement. HCD, hollow-cathode discharge; FP, Fabry-Perot etalon; PD, photodiode; C, capacitor; R, resistor; PS, power supply.
gas and powered by a voltage-regulated dc supply operating at a current of about 10 mA. An argon laser pumped Spectra-Physics 380D single-frequency tunable dye laser was focused, then incident on the lanthanum hollow-cathode. The laser wavelength was determined to within about f. 0.0 1 8, by a Burleigh 6-digit wavemeter. Some of the laser light was passed through a Fabry-Perot etalon (free-spectra-range 300 MHz) to provide a convenient frequency standard and avoid the uncertainty produced by the nonlinearity of frequency scanning. The optogalvanic signal was amplified by a lock-in amplifier, then recorded by a double-pen X-Y recorder.
3. Results and discussion Figure 2 shows a typical optogalvanic spectrum obtained as the laser was scanned through 5702.72 A. The transition shown is for 9919.82 cm-’ ( 5d26s 2G9,2)+27544.31 cm-’ (4f5d6s ‘Gy,,). In the recorded pattern six hfs components are clearly shown. The noise level is in the order of 1% of the height of a typical component (8+7), and the linewidth for the component is about 600 MHz. Because of the Doppler width, each line may consist of a few hfs components, and the identification above the lines gives only the transition of the predominant component. By means of the frequency markers the separation between the hfs components, together with the nuclear spin I= 7/2 for L39LaI, the known J values of the upper and lower states, and the precisely determined hfs constants for the lower even-parity 332
1 December
,....I,...I....r...*I.~..~I~~~~‘~~~~I~~~~ 0
3
6
9
12
15
LASER FREQUENCY(GHz) Fig. 2. Optogalvanic spectrum recorded as the laser was scanned through the line 5702.72 A. The linewidth is about 600 MHz. Each line may consist of a few hfs components, and the identification above the lines gives the transition of the predominant component.
energies [ 41, the dipole hfs constants A for the upper state then can be obtained to be A = 364 (4) MHz by assuming B=O because of the small electric-quadrupole interaction which can be seen from the previously reported theoretical and experimental results. The uncertainty is calculated only from those transitions from which the A value is obtained. Figure 3 shows the recorded hfs pattern as the laser was scanned through 57 16.11 A. The upper level of the transition is the same as that in fig. 2. Each line may also consist of a few hfs components, and the identification above the lines gives the transition of the predominant component. The A value calculated is 369 (5) MHz and agrees well with 364( 4) MHz obtained from different lower level. The energy-level diagram corresponding to the transitions in fig. 2 and fig. 3 is shown in fig. 4. The hfs separations of the level 27455.31 cm-’ (J=7/2) and two other lower levels are drawn according to our results and ref. [4], respectively. Only the transitions corresponding to the identification above the lines in the two figures are given. The energy spacings between the fine structures are not drawn to scale, and the hfs separations of the level 9919.82 cm-’ ( 5d26s *G9,*) are drawn to scale which is twice the scale of two other levels. The recorded hfs pattern for the transition 9960.90 cm-’ (5d26p, J= cm-’ (5d26s 2G,,2) +27393.04
1 December 1992
OPTICS COMMUNICATIONS
Volume 94, number 5
* : F-F-l *I: P-P *‘I: p-p+1
1111111111,111,
0
3
6
1
9
12
15
18
21
,
24
LASER FREQUENCY(GHz) Fig. 3. Optogalvanic spectrum recorded as the laser was scanned through the line 5716.11 A. The upper level of the transition is the same as that in fig. 2. Each line may consist of a few hfs components, and the identification above the lines gives the transition of the predominant component.
P’
I
4fM6s(J=7/2)
I 3
I
I 6
I
I 9
I
I 12
I
I 15
1
I 18
1
1 21
LASER FREQUENCY(GW Fig. 5. Optogalvanic spectrum recorded as the laser was scanned through the line 5736.58 A. Each line may consist of a few hfs components, and the identification above the lines gives the transition of the predominant component. The relative position of all the hfs components calculated from the A value in present work and the calculated relative intensity are given below the hfs pattern, and the relative position of a part of hfs components calculated from the A value in ref. [ 111 is also given in short bars at the middle of the pattern. The same letter corresponds to the same transition.
2 5 6 7
5d26s 2c,/2 Fig. 4. The energy-level diagram corresponding to the transitions in fig. 2 and fig. 3. Only the transitions corresponding to the identification above the lines in the two figures are given. The hfs separations of the level 99 19.82 cm-’ ( 5d26s ZG9,2) are drawn to scale which is twice the scale of two other levels.
5 /2 ) is shown in fig. 5. The A value of the upper level is corrected to be A= 144(4) MHz. The relative position of all the hfs components calculated from the A value in the present work and the calculated rel-
ative intensity are given below the hfs pattern, and the relative position of a part of hfs components calculated from the A value in ref. [ 111 is also given in short bars at the middle of the pattern. The same letter corresponds to the same transition. It can be seen that our result agrees well with the experiment. Table 1 summarizes the atomic lines [ 1 ] used in the present study. The laser wavelength (in vacuum) is given in the first column, and the identifying data for the lower (E,) and upper (E2) states are listed in the next six columns. Table 2 lists the magnetic-dipole constants A determined for 139LaI by laser optogalvanic spectroscopy. The first column gives the excitation energy, 333
Volume 94, number
5
OPTICS
COMMUNICATIONS
1 December
Table 1 Lines used in the present study of ‘%a1 . The first column gives the laser wavelength fying data for the lower (E,) and upper (E,) states for the transition.
(in vacuum),
the next six columns
1992
list the identi-
1 (A)
Configuration
E, (cm-‘)
SLJ
Configuration
E2 (cm-‘)
J
5853.89 5746.00 5905.93 5814.98 5829.16 5712.39 5702.72 5736.53 5716.11
5d26s 5d26s 5d26s 5d26s 5d26s 5d26s 5d26s 5d26s 5d26s
7679.94 7679.94 8052.16 8446.04 9183.80 9719.44 9919.82 9960.90 9960.90
4P 512 4P s/2
5d26p? 5d26p 5d26p? 5d26p 5d26p 5d26p 4f5d6s 5d26p 4f5d6s
24762.60 25083.36 24984.29 25643.00 26338.93 27225.26 27455.31 27393.04 27455.31
312
2F,,z ‘D,,z ‘D~,z 2P 3/2 2%2 ‘G/z ‘G/z
Table 2 Magnetic-dipole hfs constants A determined for ‘39LaI by laser optogalvanic spectroscopy. The A values of the same upper level 27455.31 cm-’ excited from different lower levels 9919.82 cm-’ and 9960.90 cm-’ are 364(4) MHz and 369(5) MHz, respectively. The mean value 367 (5) MHz is given in the table. E2 (cm-‘)
A (MHz) present work
24762.60 24984.29 25083.36 25643.00 26338.93 27225.26 27393.04 27455.31
previous
work
524(28) 294( 10) 65(2) 146(34) ill(6) -11(17) 144(4) 367(5)
77(4)
other previously studied levels are also given comparison, and the agreements are good.
for
Acknowledgments The work is supported by the National Natural Science Foundation of China. The authors wish to acknowledge professor Zhiyao Zhou for helpful discussions and Mrs. Shijie Jiang for her technical assistance.
Ill1
100.7 [4] -153(5)[11]
the A values of the present and previous work are given in the next two columns. Five of the A constants of eight odd-parity levels are reported for the first time to our knowledge. From the table it can be seen that two of the three A values in the present work agree well with that in previous work, another one has been corrected by us. The A values of the same upper level excited from different lower levels 9919.82 cm-’ and 9960.90 cm-’ are 364(4) MHz and 369 (5) MHz, respectively, and agree well each other. The mean value 367 ( 5) MHz is given in table 2. In conclusion, we have extended the studies of the hfs of 139LaI odd-parity levels to five previously unstudied levels by laser optogalvanic spectroscopy, and make a correction to the A value of the previously studied level at 27393.04 cm-‘. The A values of two 334
712 512 312 512 312 712 512 712
References [ 1] W.C. Martin, R. Zalubas and L. Hagan, Atomic energy levels -The Rare Earth Elements, Natl. Bur. Stand. Ref. Data Ser., Natl. Bur. Stand. (U. S.) Circ. No 60 (U. S. GPO, Washington, D.C., 1978). [2] Y. Ting, Phys. Rev. 108 (1957) 295. [3] W.J. Childs and L.S. Goodman, Phys. Rev. A 3 (1971) 25. [4] W.J. Childs andN. Nielsen, Phys. Rev. A 37 (1988) 6. [ 51 A. Hese, Ann. Phys. (Germany) 25 (1970) 299; 2. Phys. 236 (1970) 42. [ 61 A. Hese and G. Buldt, Z. Naturforsch. A 25 ( 1970) 1537. [ 71 W. Fischer, H. Huhnermann and K. Mandrek, Z. Phys. 248 (1971) 53. [S] W.J. Chi1dsandL.S. Goodman, J.Opt. Soc.Am. 67 (1977) 1230. [9] W.J. Childsand L.S. Goodman, J. Opt. Sot. Am. 68 (1978) 1348. [lo] H.-O. Behrens and G.H. Guthohrlein, J. Phys. Colloq. (France) 44 (1983) C7-149. [ 111 J. Govindarajan and T. Pramila, J. Opt. Sot. Am. B 6 ( 1989) 1275. [ 121 R.W. Shaw, J.P. Young, D.H. Smith, A.S. Bonanno and J.M. Dale, Phys. Rev. A 41 (1990) 2566. [ 131 Luo Caiyan, Qu Jianan, Zhu Lizhou and Lin Fucheng, .I. Phys. D 23 (1990) 1327.
OPTICS COMMUNICATIONS
Hyperfine structure of odd-parity levels in 139LaI by laser optogtilvanic spectroscopy Liejuan
Jia, Chunyang
Jing and Fucheng
Lin
Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 800-211. Shanghai 201800, China Received 18 January 1992; revised manuscript received 1 July 1992
The hyperline structure (hfs) of eight odd-parity levels of ‘39LaI has been studied by high-resolution Doppler-limited laser optogalvanic spectroscopy. The magnetic-dipole hfs constants A are obtained by least-squares tits. The A values of five of these levels are reported for the first time to our knowledge. One A value of the three previously reported levels is corrected, and the other two are also given for comparison where the agreements are good.
1. Introduction Because of its complicated atomic-structure, neutral lanthanum, as the first element of the rare-earth series, has a very complicated spectrum. Nevertheless, a great deal of spectroscopic work has been done, and a large number of levels have been identified through systematic study [ 11. Over the years many investigations of hyperline structure (hfs) of ‘39LaI have been carried out. Early studies are concentrated on the even-parity levels. The hfs for the two levels of the ground-state term 5d6s2 2D were measured precisely by Ting [ 21 using atomic-beam magnetic-resonance technique. Afterwards, Childs and Goodman [ 31 used the same technique to determine the hfs constants for all previously unstudied atomic levels below 9200 cm-‘, and analyzed the results in term of a set of eigen-vectors. Recently, Childs and Nielsen [4] measured precisely the hfs constants of most levels below 14000 cm-‘, and compared these results, together with earlier results for lower-lying levels, with multiconfiguration Dirac-Fock (MCDF) ab initio calculations. The odd-parity configurations have also been studied in recent years. In a series of experiments, Hese [ 5 1, and Hese and Btildt [ 6 ] studied the hfs of low-lying levels of the Sd6s6p configuration by levelcrossing techniques. Shortly afterwards, Fischer, Htihnermann and Mandrek [ 71 studied the hfs of 0030-4018/92/$05.00
most states of the 5d6s6p configuration and several states in the 5d26p configuration using a Fabry-Perot interferometer and cold-cathode source. Because the electric-quadrupole hfs constant is so small, the resolution attainable with this technique was unable to obtain any quadrupole hfs information. From 1977, the much higher resolution by Doppler-free laseratomic-beam technique enabled Childs and his coworkers [4,8,9] to study both the magnetic-dipole and electric-quadrupole hfs constants for a number of odd-parity levels. More recently, hfs constants of a great deal of levels have been obtained by several authors with various techniques [ lo- 13 1. Although hfs in ‘39LaI has been investigated extensively, the hfs data are far from complete. The goal of the present work was to extend the earlier studies to several other odd-parity levels. This was achieved by populating the lanthanum atoms in a hollowcathode discharge (HCD) tube, cw dye laser excitation and optogalvanic detecting.
2. Experiment The experimental arrangement is shown in fig. 1. A home-made La-Kr HCD tube was used to obtain lanthanum atomic vapor containing predominantly the ground state and the low-lying metastable states. The tube was filled with about 1 Torr krypton buffer
0 1992 Elsevier Science Publishers B.V. All rights reserved.
331
Volume 94, number
~
5
-
OPTICS
choppx
lens
COMMUNICATIONS
1992
HCD
Fig. 1. Experimental arrangement. HCD, hollow-cathode discharge; FP, Fabry-Perot etalon; PD, photodiode; C, capacitor; R, resistor; PS, power supply.
gas and powered by a voltage-regulated dc supply operating at a current of about 10 mA. An argon laser pumped Spectra-Physics 380D single-frequency tunable dye laser was focused, then incident on the lanthanum hollow-cathode. The laser wavelength was determined to within about f. 0.0 1 8, by a Burleigh 6-digit wavemeter. Some of the laser light was passed through a Fabry-Perot etalon (free-spectra-range 300 MHz) to provide a convenient frequency standard and avoid the uncertainty produced by the nonlinearity of frequency scanning. The optogalvanic signal was amplified by a lock-in amplifier, then recorded by a double-pen X-Y recorder.
3. Results and discussion Figure 2 shows a typical optogalvanic spectrum obtained as the laser was scanned through 5702.72 A. The transition shown is for 9919.82 cm-’ ( 5d26s 2G9,2)+27544.31 cm-’ (4f5d6s ‘Gy,,). In the recorded pattern six hfs components are clearly shown. The noise level is in the order of 1% of the height of a typical component (8+7), and the linewidth for the component is about 600 MHz. Because of the Doppler width, each line may consist of a few hfs components, and the identification above the lines gives only the transition of the predominant component. By means of the frequency markers the separation between the hfs components, together with the nuclear spin I= 7/2 for L39LaI, the known J values of the upper and lower states, and the precisely determined hfs constants for the lower even-parity 332
1 December
,....I,...I....r...*I.~..~I~~~~‘~~~~I~~~~ 0
3
6
9
12
15
LASER FREQUENCY(GHz) Fig. 2. Optogalvanic spectrum recorded as the laser was scanned through the line 5702.72 A. The linewidth is about 600 MHz. Each line may consist of a few hfs components, and the identification above the lines gives the transition of the predominant component.
energies [ 41, the dipole hfs constants A for the upper state then can be obtained to be A = 364 (4) MHz by assuming B=O because of the small electric-quadrupole interaction which can be seen from the previously reported theoretical and experimental results. The uncertainty is calculated only from those transitions from which the A value is obtained. Figure 3 shows the recorded hfs pattern as the laser was scanned through 57 16.11 A. The upper level of the transition is the same as that in fig. 2. Each line may also consist of a few hfs components, and the identification above the lines gives the transition of the predominant component. The A value calculated is 369 (5) MHz and agrees well with 364( 4) MHz obtained from different lower level. The energy-level diagram corresponding to the transitions in fig. 2 and fig. 3 is shown in fig. 4. The hfs separations of the level 27455.31 cm-’ (J=7/2) and two other lower levels are drawn according to our results and ref. [4], respectively. Only the transitions corresponding to the identification above the lines in the two figures are given. The energy spacings between the fine structures are not drawn to scale, and the hfs separations of the level 9919.82 cm-’ ( 5d26s *G9,*) are drawn to scale which is twice the scale of two other levels. The recorded hfs pattern for the transition 9960.90 cm-’ (5d26p, J= cm-’ (5d26s 2G,,2) +27393.04
1 December 1992
OPTICS COMMUNICATIONS
Volume 94, number 5
* : F-F-l *I: P-P *‘I: p-p+1
1111111111,111,
0
3
6
1
9
12
15
18
21
,
24
LASER FREQUENCY(GHz) Fig. 3. Optogalvanic spectrum recorded as the laser was scanned through the line 5716.11 A. The upper level of the transition is the same as that in fig. 2. Each line may consist of a few hfs components, and the identification above the lines gives the transition of the predominant component.
P’
I
4fM6s(J=7/2)
I 3
I
I 6
I
I 9
I
I 12
I
I 15
1
I 18
1
1 21
LASER FREQUENCY(GW Fig. 5. Optogalvanic spectrum recorded as the laser was scanned through the line 5736.58 A. Each line may consist of a few hfs components, and the identification above the lines gives the transition of the predominant component. The relative position of all the hfs components calculated from the A value in present work and the calculated relative intensity are given below the hfs pattern, and the relative position of a part of hfs components calculated from the A value in ref. [ 111 is also given in short bars at the middle of the pattern. The same letter corresponds to the same transition.
2 5 6 7
5d26s 2c,/2 Fig. 4. The energy-level diagram corresponding to the transitions in fig. 2 and fig. 3. Only the transitions corresponding to the identification above the lines in the two figures are given. The hfs separations of the level 99 19.82 cm-’ ( 5d26s ZG9,2) are drawn to scale which is twice the scale of two other levels.
5 /2 ) is shown in fig. 5. The A value of the upper level is corrected to be A= 144(4) MHz. The relative position of all the hfs components calculated from the A value in the present work and the calculated rel-
ative intensity are given below the hfs pattern, and the relative position of a part of hfs components calculated from the A value in ref. [ 111 is also given in short bars at the middle of the pattern. The same letter corresponds to the same transition. It can be seen that our result agrees well with the experiment. Table 1 summarizes the atomic lines [ 1 ] used in the present study. The laser wavelength (in vacuum) is given in the first column, and the identifying data for the lower (E,) and upper (E2) states are listed in the next six columns. Table 2 lists the magnetic-dipole constants A determined for 139LaI by laser optogalvanic spectroscopy. The first column gives the excitation energy, 333
Volume 94, number
5
OPTICS
COMMUNICATIONS
1 December
Table 1 Lines used in the present study of ‘%a1 . The first column gives the laser wavelength fying data for the lower (E,) and upper (E,) states for the transition.
(in vacuum),
the next six columns
1992
list the identi-
1 (A)
Configuration
E, (cm-‘)
SLJ
Configuration
E2 (cm-‘)
J
5853.89 5746.00 5905.93 5814.98 5829.16 5712.39 5702.72 5736.53 5716.11
5d26s 5d26s 5d26s 5d26s 5d26s 5d26s 5d26s 5d26s 5d26s
7679.94 7679.94 8052.16 8446.04 9183.80 9719.44 9919.82 9960.90 9960.90
4P 512 4P s/2
5d26p? 5d26p 5d26p? 5d26p 5d26p 5d26p 4f5d6s 5d26p 4f5d6s
24762.60 25083.36 24984.29 25643.00 26338.93 27225.26 27455.31 27393.04 27455.31
312
2F,,z ‘D,,z ‘D~,z 2P 3/2 2%2 ‘G/z ‘G/z
Table 2 Magnetic-dipole hfs constants A determined for ‘39LaI by laser optogalvanic spectroscopy. The A values of the same upper level 27455.31 cm-’ excited from different lower levels 9919.82 cm-’ and 9960.90 cm-’ are 364(4) MHz and 369(5) MHz, respectively. The mean value 367 (5) MHz is given in the table. E2 (cm-‘)
A (MHz) present work
24762.60 24984.29 25083.36 25643.00 26338.93 27225.26 27393.04 27455.31
previous
work
524(28) 294( 10) 65(2) 146(34) ill(6) -11(17) 144(4) 367(5)
77(4)
other previously studied levels are also given comparison, and the agreements are good.
for
Acknowledgments The work is supported by the National Natural Science Foundation of China. The authors wish to acknowledge professor Zhiyao Zhou for helpful discussions and Mrs. Shijie Jiang for her technical assistance.
Ill1
100.7 [4] -153(5)[11]
the A values of the present and previous work are given in the next two columns. Five of the A constants of eight odd-parity levels are reported for the first time to our knowledge. From the table it can be seen that two of the three A values in the present work agree well with that in previous work, another one has been corrected by us. The A values of the same upper level excited from different lower levels 9919.82 cm-’ and 9960.90 cm-’ are 364(4) MHz and 369 (5) MHz, respectively, and agree well each other. The mean value 367 ( 5) MHz is given in table 2. In conclusion, we have extended the studies of the hfs of 139LaI odd-parity levels to five previously unstudied levels by laser optogalvanic spectroscopy, and make a correction to the A value of the previously studied level at 27393.04 cm-‘. The A values of two 334
712 512 312 512 312 712 512 712
References [ 1] W.C. Martin, R. Zalubas and L. Hagan, Atomic energy levels -The Rare Earth Elements, Natl. Bur. Stand. Ref. Data Ser., Natl. Bur. Stand. (U. S.) Circ. No 60 (U. S. GPO, Washington, D.C., 1978). [2] Y. Ting, Phys. Rev. 108 (1957) 295. [3] W.J. Childs and L.S. Goodman, Phys. Rev. A 3 (1971) 25. [4] W.J. Childs andN. Nielsen, Phys. Rev. A 37 (1988) 6. [ 51 A. Hese, Ann. Phys. (Germany) 25 (1970) 299; 2. Phys. 236 (1970) 42. [ 61 A. Hese and G. Buldt, Z. Naturforsch. A 25 ( 1970) 1537. [ 71 W. Fischer, H. Huhnermann and K. Mandrek, Z. Phys. 248 (1971) 53. [S] W.J. Chi1dsandL.S. Goodman, J.Opt. Soc.Am. 67 (1977) 1230. [9] W.J. Childsand L.S. Goodman, J. Opt. Sot. Am. 68 (1978) 1348. [lo] H.-O. Behrens and G.H. Guthohrlein, J. Phys. Colloq. (France) 44 (1983) C7-149. [ 111 J. Govindarajan and T. Pramila, J. Opt. Sot. Am. B 6 ( 1989) 1275. [ 121 R.W. Shaw, J.P. Young, D.H. Smith, A.S. Bonanno and J.M. Dale, Phys. Rev. A 41 (1990) 2566. [ 131 Luo Caiyan, Qu Jianan, Zhu Lizhou and Lin Fucheng, .I. Phys. D 23 (1990) 1327.