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Isotope separation involving photoinduced changes in the electric and magnetic properties of molecules and atoms
Volume
16, number
1
OPTIC’S COMMUNICATIONS
ISOTOPE SEPARATION
EVOLVING
PHOTOINRUCED
January
1976
C~NGES
IN THE ELECTRIC AND MAGNETIC PROPERTIES OF MOLECULES AND ATOMS*
P.L. KELLEY Lincoln
Laboratory,
Massachusetts
Institute
of' Technology, Lexington,
Massachusetts
02173,
USA
N.M. KROLL Department
of Physics,
University
ofCalifornia,
San Diego, California
92037,
USA
and
C.K. RHODES* * Lawrence
Livermore
Received
20 October
Laboratory,
Livermore,
Cdifomin
induced changes in the etectro- and magneto-static properties are given of the maximum beam radius and throughput.
Photochemical ([I - -41; for more general discussions of these processes, see [5 1) and photoionization [66X] methods have been used for isotope separation. Photodeflection has also been employed [9-l I] as a means of isotope separation in which only transitions between bound states occur. We discuss here another method of separation in which isotopically selective photoexcitation is used to change the electro- and/or magneto-static properties of bound molecules or atoms. The excitation process can change electric dipole moment, electric polarizability, magnetic dipole moment, and magnetic polarizability. Field gradients then exert different forces on each isotopic species. The forces (and the photoinduced force changes) can be particularly large when one (or both) states involved have a large Zeeman effect, a first order Stark effect or are Stark coupled to near-by levels such that only modest field strengths are required to cause substantial changes in the level splittings. Elecof the results reported here were obtained the 1974 JASON Laser Summer Study supported by the Defense Advanced Research Projects Agency. ** Present address: Stanford Research Institute, Menlo Park, California 94025. during
172
USA
1975
Methods of isotope separation by optically atoms and molecules are examined. Estimates
* A portion
94550,
of neutral
trOniC excitation strongly effects atomic and molecular properties. Large changes in atomic polarizabilities and g-factors are generally associated with the promotion of an electron to an excited shell since large changes in principal and orbital quantum numbers imply large modifications of the spatial and angular rn~~r~~entunl properties of atoms. Similarly substantial alterations commonly occur in molecular systems. particularly in cases involving a change in the bonding character of the orbital thereby lnodifying the electric and magnetic susceptibilities. Long lived isomers would be particularly easy to separate by elcctro- or magnetostatic means. The technique considered here is purely physical, in contrast to methods involving reactive mechanisms, and therefore have general applicability and are free from any adverse chemical reactions. The present process is not unrelated to the ammonia maser [ 121 in which state selection and population inversion is obtained by using the differences in the electro-static properties of two energy states. Note also that isotope shifts and hyperfine structure in the Na D, line have been detected in a very low density polyisot~)pic beam using a laser to state select by optical pumping, a magnetic deflection system for
Volume
16, number
1
state analysis and a mass spectrometer for individually recording the spectra from each isotope [ 131. We will consider the situation in which the electrostatic or magnetostatic forces act perpendicular to an atomic or molecular beam and separation is achieved by the difference in deflections experienced by the excited and unexcited molecules. We evaluate two cases: a) collisionless deflection, b) diffusion limited deflection. Initially the beam is assumed to have transverse coordinate and velocity distributions with rms spatial extent x1 and rms velocity vI. Then the condition that two components (1,2) in the beam, which experience a force difference AF = F, - F2, become separated, is
(AF/4m) t2 > 6:
+ v; t2,
(1)
where ml it: m = m2. In the collisionless case, t is the time spent in the electric or magnetic force field, namely t = l/u,, ,
(2)
where 1 is the distance over which the particles remain in the static force field and v,, is the velocity along the direction of motion of the beam. In this case (1) becomes
(3) Now, AF = n AU/x,, where n is a field index of order unity and AU is the transverse electrostatic or magnetostatic energy difference for the two components. Solving (3) for x1 we find that 212 (nAU/4mvlv,,)2 xf G Jl
t (nAZJ/2mv:)2
(4)
+1 ’
xlmax = Z(nAU/4mvLu,,). For cylindrical symmetry current for isotope 1 = nX:maxUIIPl
we can calculate a beam
= n12(n
AWmqq)2ullfIP,
1976
collisionless we require that
p<.L !!L
(7)
01 Au,,’ where u is the collision cross-section and spread in longitudinal velocity (note that sonic nozzle beam relatively large values AvlI/v,, can be obtained). The maximum becomes
Au,, is the for a superof the ratio current then
2
(8)
fi.
J1max
If a non-fully enriched material is required (as is the case of uranium fuel for light water reactors) of fraction f; then the enriched material current is J1 max multiplied by (1 -fMX
--fl).
(9)
For the diffusion limited case* the differential verse drift velocity II: is given by
trans-
(10) where tc is the collision time and 2, the collision length. We assume here that collisions act only to limit the motion of the molecules and do not cause a loss in selectivity due to excitation transfer. The condition for separation which is analogous to (3) is
(11) repeating the previous arguments we find the maximum diffusion limited current of isotope 1 to be given by 2
In most cases 2n AU < mvf = kT, where T is the tranlation temperature, so that we find a maximum rms transverse spatial distance for complete separation
J lmax
January
OPTICS COMMUNICATIONS
q4 o2
Av2p
fl.
(12)
II
The ratio of the current for the diffusion limited case to that for the collisionless case is given by 1,/l and is constrained to be less than unity. We consider the case of a supersonic nozzle beam ([15-171, for a review see [18]), where the flow is isentropic until the region of the deflection plates is
(6)
where fiis the fraction of the isotope 1 and p is the total number density. In order for the deflection to be
* Radiation pressure isotope regime has been considered
separation in the diffusion limited by Celbwachs and Hartwick [ 141.
173
Volume
16, number
1
OPTICS COMMUNICATIONS
encountered and subsequently free molecular expansion occurs. Then, Au,, = u, and u,, x M& uI, where M is the Mach number and y is the ratio of specific heat at constant pressure to that at constant volume. Also, the relation To/T = I
+3(7--l)M2
(13)
holds, where To is the stagnation temperature. these expressions into (8) WCobtain
Inserting
2 (14) X [, + (22)
M2] 3’21;.
After expansion cooling through a nozzle further lowering of the transverse velocity spread rnay be obtained by collimation (skimmers). Multiple beams, each having a small variation in transverse velocity could be formed from the output of a single nozzle. WC evaluate (14) for an electrostatic case, noting that electric fields typically can exceed lo5 V/cm without breakdown effects occurring in practical systems. Therefore, for molecules without a first order Stark effect, AlJ/Aa 2 3 X 10P8 eV/a3, where Acu is the polarizability in A3. At low temperatures, for molecules with large permanent dipole moments Aa can be of the order of lo3 A3, and hence, AU = 3X 10~5eV.Withn~.2,Tg=300K,I=ltn.u= 7_X lo--l5 cm2, n? = 400 tnE,, y = 1.l and M = 70, we find that J, max = 4 X 1Ol6 .tj /sec. For .fl = 0.01 and f; = 0.05, the current of enriched material is 1016/sec or -25 mg/hr. Considering the small beam diameter (- 0.5 cm) this is a reasonable throughput. If the molecules can be prepared so that they have a significant fraction in an energy state which shows a substantial Zeeman or first-order Stark effect then the value of-AU may be made substantially larger than the above estimate. CO is an example of a molecule in which a large change in electronic configuration and dipole moment can be made by photoexcitation. A weak (spin-forbidden) transition occurs near 2000 .& (Cameron bands) [ 191 from the ground electronic state (’ C) with a dipole moment of 0.1 1 debye [20] to a 3n state with a dipole moment of 1.38 debye [21]. The radiative lifetime [22] of the 37r state is of the order 174
January
1976
of 4 10 msec so that the molecule can pass through an electrostatic deflection apparatus without becoming deexcited. Another example is provided by the molecule NO in a magnetic field. This case illustrates how substantial changes in magnetic properties can be induced by relatively small changes in internal energy. Fig. 1 gives the energy level structure of the 27r1,2 ground electronic state and the nearby (- 121 cm-‘) 2~3,2 state which is split from the 27r1,2 state by spin-orbit coupling [ 191. The g-factors for these two electronic states arc [23] 3 gl? 112(J) = T$Jq)
X-2-(W-1)(2J+3)/3 ~~~~~~~~~_~
1 + ~
(h(X-4)+(2J+1)2]
.__-
1 !15) )
1/Z
wheregyp
andg3/2(J) are respectively the g-factors of the 2~1,2 and 2rr3/2 states, J is the rotational quantum number, and X is the ratio of the spin-orbit constant to the rotational constant which for NO is approximately 73. When h % J then we have (16) and 3
83/2(J) = jcJii_,’
(17)
so that the ratio g1,2(J)/g3,2(J) is less than 2J(J+ 1)/3h. As J increases the spin becomes uncoupled from the orbital motion with the g-factors becoming comparable forNOwhenJ>21/2. If NO is cooled rotationally to 15 K using a supersonic nozzle, only the J = l/2, 3/2, S/2 and 712 states are appreciably occupied (there is no J= l/2 state for the 27r3,2 electronic state). We also assume that the 27r3,2 state becomes unoccupied in the supersonic expansion process. For the ratio of the average g factors of the two electronic states we find Q2lQ2
G ?5.
(18)
This ratio results in a considerably smaller deflection in an inhomogeneous magnetic field for molecules in the 27r1,2 state compared with molecules in the 2,3/Z state. For the J = 3/2, MJ= l/2 state the difference in magnetic energies between the two electronic states for a lo5 gauss field is 2 X lop4 eV which indicates a substantial increase in throughput would be possible
Volume
16, number
J
912 -
1
OPTICS
CQMM~JNI~ATIUNS
2JJ,,,
712 s/2 -
512 3/2 112 -
/
~..~
Fig. 1. Energy level diagram for the ground (u = 0) and first excited (U = I) vibrational states of the ‘mln and 2m312 electronic states.
in c~~mparisolt to the case considered previously. For NO, since the *7r3,* state lies above the 27r4,2 state, the low abundance isotope (es., 15N160, 1 N180) would have to be excited to 2,3,2 states and collected at large deflections in order to obtain a substantiatly enriched sample in a single step. Selective excitation from the 2rr1,2 manifold to the 2,3,2 manifold can be accompIished in NO with laser radiation near 80 i.nm or near 5 pm, as shown in fig. I. We note that CO lasers using various isotopes give a reasonably large number of transitions near 5 km and that d~~~lblil~gand sum frequency generation of CO2 radiation gives even more diverse frequency coverage in this region. The power required to saturate these spinforbidden transitions is in the lo4 -IO5 W/cm* range. In the case ofOH, where the 27r3/2 state lies below the %r1j2 state, the nonabundant isotopic species could be excited to states where relatively small deflection would occur thus somewhat simplifying, in comparison to NO, the single step enrichment of nonabundant isotopes. The general process appears possible in principle for any molec~ar system with nonzero orbital and spin angular momenta in the ground electronic configuration. Independently of the present work, W.F. Krupke of Lawrence Livermore Laboratory has applied for a patent (AEC Case No. IL-59 15) for the case of induced changes in electric pola~zab~li~. A further reference on the same general topic as the present paper has
January
1976
recently come to our attention [24]. These authors consider an example involving molecules that are without a dipole moment in the ground state but which have a constant dipole motnent when vibrationally excited. Studies of this induced dipole in molecules with Td symmetry have been carried out using molecular beam deflection techniques [25]. One of US (P-L-K.) would like to thank H. Kildal and R.&l. Osgood, Jr. for helpful discussions. This work has been supported by the Department of the Air Force, the Defense Advanced Research Projects Agency under Contract No. DAHC 15-75-C0370, and the Energy Research and Development Administration.
References [I] ES. Yeung and C.B. Moore, Appl. Phys. Letters 21 (1972) 109. [2] R.V. Ambartsumian, V.S. Letokhov, G.N. Makarov and I. Puretskii, JETP Letters 17 (1973) 91. [3] S. Rockwood and S.W. Rabideau, Paper Q-l 3, VIII Intern. Quantum Electronics Conf., San Francisco (June, 1974). [4] S.R, Leone and C.B. Moore, Phys. Rev. Letters 33 (1974) 269. [5] V.S. Letokhov, Science 180 (1973)451; C.B. Moore, Act. Chem. Res. 6 (1973) 323. [6] R.II. Levy and G.S. Janes, U.S. Patent +3, 772,519. [‘7] IJ. Brinkmann, W. Hart&, Il. Telle and W. Walther, Paper #Q-l 1, VIII Intern. Quantum Electronics <:onf., San I’rancisco (June, 1974). [8] S.k Tuccio, J.W. Dubrin, O.G. Peterson and B.B. Snavely, Paper Q-14, VIII Intern. Quantum Electronics Conf., San Francisco (June, 1974). [9] A. Ashkin, Phys. Rev. Letters 24 11970) 156. [lo] I. Nebenzahl and A. SzGke, Appl. Phys. Letters 25 (1974) 631. [I 11 A. Bernhard& D. Duerre, J. Simpson and L. Wood, Paper Q-12, VIII Intern. Quantum Electronics Conf., San Francisco (June, 1974). [ 121 J.P. Gordon, II. J. Zeiger and C. II. Townes, Phys. Rev. 95 (1954) 282; J.P. Gordon, H.J. Zeiger and C.H. Townes, Phys. Rev. 99 (1955) 1264. [13] G. Iluber, C.Thibault, R Klapisch, H.T. Duong, J.L. Vialle, J. Pinard, P. Juncar and P. Jacquinot, Phys. Rev. Letters 34 (1975) 1209. [14] J. Gelbwachs and T.S. Hartwick, IEEE J. Quantum EIectron. 11 (1815) 52. fl5j A. Rantrowitz and J. Grey, Rev. Sci. Instrum. 22 (1951) 328.
17s
16, number
1
OPTIC’S COMMUNICATIONS
ISOTOPE SEPARATION
EVOLVING
PHOTOINRUCED
January
1976
C~NGES
IN THE ELECTRIC AND MAGNETIC PROPERTIES OF MOLECULES AND ATOMS*
P.L. KELLEY Lincoln
Laboratory,
Massachusetts
Institute
of' Technology, Lexington,
Massachusetts
02173,
USA
N.M. KROLL Department
of Physics,
University
ofCalifornia,
San Diego, California
92037,
USA
and
C.K. RHODES* * Lawrence
Livermore
Received
20 October
Laboratory,
Livermore,
Cdifomin
induced changes in the etectro- and magneto-static properties are given of the maximum beam radius and throughput.
Photochemical ([I - -41; for more general discussions of these processes, see [5 1) and photoionization [66X] methods have been used for isotope separation. Photodeflection has also been employed [9-l I] as a means of isotope separation in which only transitions between bound states occur. We discuss here another method of separation in which isotopically selective photoexcitation is used to change the electro- and/or magneto-static properties of bound molecules or atoms. The excitation process can change electric dipole moment, electric polarizability, magnetic dipole moment, and magnetic polarizability. Field gradients then exert different forces on each isotopic species. The forces (and the photoinduced force changes) can be particularly large when one (or both) states involved have a large Zeeman effect, a first order Stark effect or are Stark coupled to near-by levels such that only modest field strengths are required to cause substantial changes in the level splittings. Elecof the results reported here were obtained the 1974 JASON Laser Summer Study supported by the Defense Advanced Research Projects Agency. ** Present address: Stanford Research Institute, Menlo Park, California 94025. during
172
USA
1975
Methods of isotope separation by optically atoms and molecules are examined. Estimates
* A portion
94550,
of neutral
trOniC excitation strongly effects atomic and molecular properties. Large changes in atomic polarizabilities and g-factors are generally associated with the promotion of an electron to an excited shell since large changes in principal and orbital quantum numbers imply large modifications of the spatial and angular rn~~r~~entunl properties of atoms. Similarly substantial alterations commonly occur in molecular systems. particularly in cases involving a change in the bonding character of the orbital thereby lnodifying the electric and magnetic susceptibilities. Long lived isomers would be particularly easy to separate by elcctro- or magnetostatic means. The technique considered here is purely physical, in contrast to methods involving reactive mechanisms, and therefore have general applicability and are free from any adverse chemical reactions. The present process is not unrelated to the ammonia maser [ 121 in which state selection and population inversion is obtained by using the differences in the electro-static properties of two energy states. Note also that isotope shifts and hyperfine structure in the Na D, line have been detected in a very low density polyisot~)pic beam using a laser to state select by optical pumping, a magnetic deflection system for
Volume
16, number
1
state analysis and a mass spectrometer for individually recording the spectra from each isotope [ 131. We will consider the situation in which the electrostatic or magnetostatic forces act perpendicular to an atomic or molecular beam and separation is achieved by the difference in deflections experienced by the excited and unexcited molecules. We evaluate two cases: a) collisionless deflection, b) diffusion limited deflection. Initially the beam is assumed to have transverse coordinate and velocity distributions with rms spatial extent x1 and rms velocity vI. Then the condition that two components (1,2) in the beam, which experience a force difference AF = F, - F2, become separated, is
(AF/4m) t2 > 6:
+ v; t2,
(1)
where ml it: m = m2. In the collisionless case, t is the time spent in the electric or magnetic force field, namely t = l/u,, ,
(2)
where 1 is the distance over which the particles remain in the static force field and v,, is the velocity along the direction of motion of the beam. In this case (1) becomes
(3) Now, AF = n AU/x,, where n is a field index of order unity and AU is the transverse electrostatic or magnetostatic energy difference for the two components. Solving (3) for x1 we find that 212 (nAU/4mvlv,,)2 xf G Jl
t (nAZJ/2mv:)2
(4)
+1 ’
xlmax = Z(nAU/4mvLu,,). For cylindrical symmetry current for isotope 1 = nX:maxUIIPl
we can calculate a beam
= n12(n
AWmqq)2ullfIP,
1976
collisionless we require that
p<.L !!L
(7)
01 Au,,’ where u is the collision cross-section and spread in longitudinal velocity (note that sonic nozzle beam relatively large values AvlI/v,, can be obtained). The maximum becomes
Au,, is the for a superof the ratio current then
2
(8)
fi.
J1max
If a non-fully enriched material is required (as is the case of uranium fuel for light water reactors) of fraction f; then the enriched material current is J1 max multiplied by (1 -fMX
--fl).
(9)
For the diffusion limited case* the differential verse drift velocity II: is given by
trans-
(10) where tc is the collision time and 2, the collision length. We assume here that collisions act only to limit the motion of the molecules and do not cause a loss in selectivity due to excitation transfer. The condition for separation which is analogous to (3) is
(11) repeating the previous arguments we find the maximum diffusion limited current of isotope 1 to be given by 2
In most cases 2n AU < mvf = kT, where T is the tranlation temperature, so that we find a maximum rms transverse spatial distance for complete separation
J lmax
January
OPTICS COMMUNICATIONS
q4 o2
Av2p
fl.
(12)
II
The ratio of the current for the diffusion limited case to that for the collisionless case is given by 1,/l and is constrained to be less than unity. We consider the case of a supersonic nozzle beam ([15-171, for a review see [18]), where the flow is isentropic until the region of the deflection plates is
(6)
where fiis the fraction of the isotope 1 and p is the total number density. In order for the deflection to be
* Radiation pressure isotope regime has been considered
separation in the diffusion limited by Celbwachs and Hartwick [ 141.
173
Volume
16, number
1
OPTICS COMMUNICATIONS
encountered and subsequently free molecular expansion occurs. Then, Au,, = u, and u,, x M& uI, where M is the Mach number and y is the ratio of specific heat at constant pressure to that at constant volume. Also, the relation To/T = I
+3(7--l)M2
(13)
holds, where To is the stagnation temperature. these expressions into (8) WCobtain
Inserting
2 (14) X [, + (22)
M2] 3’21;.
After expansion cooling through a nozzle further lowering of the transverse velocity spread rnay be obtained by collimation (skimmers). Multiple beams, each having a small variation in transverse velocity could be formed from the output of a single nozzle. WC evaluate (14) for an electrostatic case, noting that electric fields typically can exceed lo5 V/cm without breakdown effects occurring in practical systems. Therefore, for molecules without a first order Stark effect, AlJ/Aa 2 3 X 10P8 eV/a3, where Acu is the polarizability in A3. At low temperatures, for molecules with large permanent dipole moments Aa can be of the order of lo3 A3, and hence, AU = 3X 10~5eV.Withn~.2,Tg=300K,I=ltn.u= 7_X lo--l5 cm2, n? = 400 tnE,, y = 1.l and M = 70, we find that J, max = 4 X 1Ol6 .tj /sec. For .fl = 0.01 and f; = 0.05, the current of enriched material is 1016/sec or -25 mg/hr. Considering the small beam diameter (- 0.5 cm) this is a reasonable throughput. If the molecules can be prepared so that they have a significant fraction in an energy state which shows a substantial Zeeman or first-order Stark effect then the value of-AU may be made substantially larger than the above estimate. CO is an example of a molecule in which a large change in electronic configuration and dipole moment can be made by photoexcitation. A weak (spin-forbidden) transition occurs near 2000 .& (Cameron bands) [ 191 from the ground electronic state (’ C) with a dipole moment of 0.1 1 debye [20] to a 3n state with a dipole moment of 1.38 debye [21]. The radiative lifetime [22] of the 37r state is of the order 174
January
1976
of 4 10 msec so that the molecule can pass through an electrostatic deflection apparatus without becoming deexcited. Another example is provided by the molecule NO in a magnetic field. This case illustrates how substantial changes in magnetic properties can be induced by relatively small changes in internal energy. Fig. 1 gives the energy level structure of the 27r1,2 ground electronic state and the nearby (- 121 cm-‘) 2~3,2 state which is split from the 27r1,2 state by spin-orbit coupling [ 191. The g-factors for these two electronic states arc [23] 3 gl? 112(J) = T$Jq)
X-2-(W-1)(2J+3)/3 ~~~~~~~~~_~
1 + ~
(h(X-4)+(2J+1)2]
.__-
1 !15) )
1/Z
wheregyp
andg3/2(J) are respectively the g-factors of the 2~1,2 and 2rr3/2 states, J is the rotational quantum number, and X is the ratio of the spin-orbit constant to the rotational constant which for NO is approximately 73. When h % J then we have (16) and 3
83/2(J) = jcJii_,’
(17)
so that the ratio g1,2(J)/g3,2(J) is less than 2J(J+ 1)/3h. As J increases the spin becomes uncoupled from the orbital motion with the g-factors becoming comparable forNOwhenJ>21/2. If NO is cooled rotationally to 15 K using a supersonic nozzle, only the J = l/2, 3/2, S/2 and 712 states are appreciably occupied (there is no J= l/2 state for the 27r3,2 electronic state). We also assume that the 27r3,2 state becomes unoccupied in the supersonic expansion process. For the ratio of the average g factors of the two electronic states we find Q2lQ2
G ?5.
(18)
This ratio results in a considerably smaller deflection in an inhomogeneous magnetic field for molecules in the 27r1,2 state compared with molecules in the 2,3/Z state. For the J = 3/2, MJ= l/2 state the difference in magnetic energies between the two electronic states for a lo5 gauss field is 2 X lop4 eV which indicates a substantial increase in throughput would be possible
Volume
16, number
J
912 -
1
OPTICS
CQMM~JNI~ATIUNS
2JJ,,,
712 s/2 -
512 3/2 112 -
/
~..~
Fig. 1. Energy level diagram for the ground (u = 0) and first excited (U = I) vibrational states of the ‘mln and 2m312 electronic states.
in c~~mparisolt to the case considered previously. For NO, since the *7r3,* state lies above the 27r4,2 state, the low abundance isotope (es., 15N160, 1 N180) would have to be excited to 2,3,2 states and collected at large deflections in order to obtain a substantiatly enriched sample in a single step. Selective excitation from the 2rr1,2 manifold to the 2,3,2 manifold can be accompIished in NO with laser radiation near 80 i.nm or near 5 pm, as shown in fig. I. We note that CO lasers using various isotopes give a reasonably large number of transitions near 5 km and that d~~~lblil~gand sum frequency generation of CO2 radiation gives even more diverse frequency coverage in this region. The power required to saturate these spinforbidden transitions is in the lo4 -IO5 W/cm* range. In the case ofOH, where the 27r3/2 state lies below the %r1j2 state, the nonabundant isotopic species could be excited to states where relatively small deflection would occur thus somewhat simplifying, in comparison to NO, the single step enrichment of nonabundant isotopes. The general process appears possible in principle for any molec~ar system with nonzero orbital and spin angular momenta in the ground electronic configuration. Independently of the present work, W.F. Krupke of Lawrence Livermore Laboratory has applied for a patent (AEC Case No. IL-59 15) for the case of induced changes in electric pola~zab~li~. A further reference on the same general topic as the present paper has
January
1976
recently come to our attention [24]. These authors consider an example involving molecules that are without a dipole moment in the ground state but which have a constant dipole motnent when vibrationally excited. Studies of this induced dipole in molecules with Td symmetry have been carried out using molecular beam deflection techniques [25]. One of US (P-L-K.) would like to thank H. Kildal and R.&l. Osgood, Jr. for helpful discussions. This work has been supported by the Department of the Air Force, the Defense Advanced Research Projects Agency under Contract No. DAHC 15-75-C0370, and the Energy Research and Development Administration.
References [I] ES. Yeung and C.B. Moore, Appl. Phys. Letters 21 (1972) 109. [2] R.V. Ambartsumian, V.S. Letokhov, G.N. Makarov and I. Puretskii, JETP Letters 17 (1973) 91. [3] S. Rockwood and S.W. Rabideau, Paper Q-l 3, VIII Intern. Quantum Electronics Conf., San Francisco (June, 1974). [4] S.R, Leone and C.B. Moore, Phys. Rev. Letters 33 (1974) 269. [5] V.S. Letokhov, Science 180 (1973)451; C.B. Moore, Act. Chem. Res. 6 (1973) 323. [6] R.II. Levy and G.S. Janes, U.S. Patent +3, 772,519. [‘7] IJ. Brinkmann, W. Hart&, Il. Telle and W. Walther, Paper #Q-l 1, VIII Intern. Quantum Electronics <:onf., San I’rancisco (June, 1974). [8] S.k Tuccio, J.W. Dubrin, O.G. Peterson and B.B. Snavely, Paper Q-14, VIII Intern. Quantum Electronics Conf., San Francisco (June, 1974). [9] A. Ashkin, Phys. Rev. Letters 24 11970) 156. [lo] I. Nebenzahl and A. SzGke, Appl. Phys. Letters 25 (1974) 631. [I 11 A. Bernhard& D. Duerre, J. Simpson and L. Wood, Paper Q-12, VIII Intern. Quantum Electronics Conf., San Francisco (June, 1974). [ 121 J.P. Gordon, II. J. Zeiger and C. II. Townes, Phys. Rev. 95 (1954) 282; J.P. Gordon, H.J. Zeiger and C.H. Townes, Phys. Rev. 99 (1955) 1264. [13] G. Iluber, C.Thibault, R Klapisch, H.T. Duong, J.L. Vialle, J. Pinard, P. Juncar and P. Jacquinot, Phys. Rev. Letters 34 (1975) 1209. [14] J. Gelbwachs and T.S. Hartwick, IEEE J. Quantum EIectron. 11 (1815) 52. fl5j A. Rantrowitz and J. Grey, Rev. Sci. Instrum. 22 (1951) 328.
17s