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Hyperfine structure in laser-induced shifts in electron spin resonance spectra of sodium atoms
9 April 1999
Chemical Physics Letters 303 Ž1999. 427–434
Hyperfine structure in laser-induced shifts in electron spin resonance spectra of sodium atoms Li Li, Dongming Chen, Tianjing He, Xiuyan Wang, Fan-Chen Liu
)
Department of Chemical Physics, UniÕersity of Science and Technology of China, Hefei, Anhui 230026, China Received 17 December 1998; in final form 16 February 1999
Abstract The influence of the hyperfine interaction on laser-induced shifts in electron spin resonance spectra is investigated and calculated, taking the sodium atom as an example. As the incident laser frequency is near-resonant, the different hyperfine lines may produce distinguishable shifts which may be important for the application of the effect to practical analysis. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Observable shifts in electron spin resonance ŽESR. spectra are predicted to occur as a result of the application of linearly or circularly polarized light at a frequency near optical absorption, which are physically based on the quadratic Stark effect of optical fields and are proportional to the laser intensity and the polarizabilities w1,2x. The general formulas for the laser-induced ESR shifts were deduced w1x and their order of magnitude evaluated for a sodium atom as an example w1–3x. These theories and calculations w1–3x did not take account of the hyperfine structure Žhfs. and considered only the ESR shift as a translation of the whole hfs spectrum under the action of the optical field, which is applicable if the hfs is indistinguishable in ESR spectra like that in liquid sodium w4x or if the incident frequency is not ) Corresponding author. Fax: q86 551 363 1760; e-mail: [email protected]
near the optical absorptions. Nevertheless, ESR spectra of most paramagnetic systems contain important information about the hfs w5x. For example, in the ESR spectra of sodium atoms trapped in an argon matrix at 4 K four hyperfine lines were observed and each included six components due to matrix effects w6x. Also for Na atomic beams one expects to observe the hfs in ESR spectra since their optical spectra clearly show hyperfine lines with a half-width of 0.003 cmy1 w7x. As resonance is approached, it is necessary to consider the influence of the hfs on the light shifts and discuss the respective shifts of these hyperfine lines. This Letter attempts to explore the influence of the hfs on the laser-induced ESR shift by using a semiclassical dispersion theory w1,8x for a sodium atom in an atomic beam or trapped in a matrix as an example. The results indicate that for a circularly polarized laser beam at a frequency not near optical absorption, the light shifts of the four hyperfine lines are nearly equal and the ESR shifts can be consid-
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 2 3 9 - 0
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
428
ered approximately as a whole translation of the ESR spectrum. In fact, in this case, the influence of the hyperfine interaction can be neglected and the behaviour of the shifts are as in the previous theory w1–3x. However, as resonance is approached the hfs becomes important and the influence of the hyperfine interaction complicates the laser-induced ESR shifts. The different hyperfine lines show distinguishable shifts under the action of the optical field. Thus the hyperfine interaction can be important for the application of the laser-induced ESR shifts in practical analysis of most paramagnetic systems. This effect may be capable of providing a new fingerprint of a sample in the study of a color center in a crystal or ion trapped in a matrix because it may enable one to identify the nuclear species and matrix effects that give rise to the hyperfine splitting w11,16x.
2. Energy level shift in an optical field
ground state < n:, G is the radiative width of the excited state < j :. m ˆ "s "2y1 r2 Ž mˆ x . i mˆ y . is the dipole moment operator and m ˆ )" is its complex conjugate. a " is the induced polarizability for a right Žq. or left Žy. circularly polarized laser beam, which includes the contribution of symmetric and antisymmetric polarizabilities. Eq. Ž1. is equivalent to that of Buckingham and Parlett’s perturbation theory w1x on the light-induced energy change of a polarizable atom or molecule w10x. Buckingham and Parlett emphasized correctly the contribution of antisymmetric polarizabilities. Taking the transition between electron spin magnetic energy levels < m z s " 12 : as an example, based on Eq. Ž1., the laser-induced ESR shift is D n "s
DW "Ž1r2.y DW "Žy1r2.
sy
h
Ž E Ž0. .
2
2h It is known w8x that the oscillating electric field of a light wave can cause Stark shifts of the energy levels of an atom or molecule. In a circularly polarized optical field, the interaction of the polarizability tensors with the electric field of a right or left circularly polarized laser beam will alter the electron spin energy levels and give rise to a shift in the ESR spectral lines proportional to the intensity of the laser w1x. According to the semiclassical dispersion theory w8x, in a right Žq. or left Žy. circularly polarized laser beam propagating in the z-direction, parallel to the external magnetic field B, it is found that as a result of virtual transitions to the excited-state sublevel < j : the ground-state sublevel < n: will be shifted by an amount w9,10x DW "Ž n.s y
Ž E Ž0. .
2
Ý
2h
j
Ž E Ž0. . 2
Ž 2.
where a " Ž 12 . and a " Žy 12 . are the polarizabilities of the < m s s 21 : and < m s s y 21 : states, respectively. In addition, in a linearly polarized optical field, in terms of its circularly polarized components, the laser-induced ESR shift is w2,3x Dn s
D nyq D nq 2
.
Ž 3.
The above equations are the fundamental formulas of the laser-induced ESR shifts, which had been applied to a sodium atom to evaluate the order of magnitude of the shifts without considering the influence of the hyperfine interaction upon the ESR shifts w1–3x.
n jn y n 3. hfs Light shift of a sodium atom
2 Ž n jn y n . q G 2r4
=Re Ž ² n < m ˆ )" < j :² j < mˆ " < n: . sy
a " Ž 12 . y a " Ž y 12 . ,
2
a" ,
Ž 1.
where hn jn s W Ž j. y W Ž n. is the energy difference between the unperturbed excited state < j : and the
The hyperfine interaction is seen in ESR to be equivalent to the addition of an extra magnetic field proportional to the z-component of the nuclear spin. Since the nucleus can take up only quantized orientation, the electron spin resonance is split into 2 I q 1 Žequally spaced. lines w11x. For a sodium atom with a nucleus of spin 3r2, one expects to observe four
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
hyperfine lines with equal spacing. Under the action of a circularly polarized optical field, each hyperfine line should have its own shift. First we discuss the hfs of a sodium atom in a uniform external magnetic field B.
g XI s g I m N rm B is a small number of order m erM Žwhere m e and M are the mass of an electron and proton, respectively., and the Lande´ g-value g J is gJs
J Ž J q 1. q L Ž L q 1. y S Ž S . 1. 2 J Ž J q 1.
3.1. hfs Energy leÕels The energy of an atom with finite nuclear spin in a magnetic field is determined by the zeroth-order Hamiltonian which includes the central field and all electrostatic and magnetic interactions internal to the electron system H0 and the hfs Hamiltonian H w12x H s A J I P J q g J m B Jz B y g XI m B I z B ,
Ž 4.
where A J is the magnetic hfs constant to be determined from experiments, m B the Bohr magneton,
429
q gs
J Ž J q 1. y L Ž L q 1. q S Ž S q 1. 2 J Ž J q 1.
.
Ž 5.
Here we omit the nuclear electric quadruple interaction since this term is too small to be considered for the sodium atoms. ESR experiments are usually done at either 9.5 or 35 GHz corresponding to magnetic fields of 0.34 or 1.25 T. Comparing with the ground-state hfs con-
Fig. 1. Zeeman splitting of hyperfine structure of the D1 and D 2 lines of sodium atoms in an external magnetic field of 1.25 T. The absorption transitions of the m I s 3r2 hyperfine line are grouped by the polarization, indicated by solid arrows pointing up, and labeled simply as numbers from 1 to 6. The diagram is not to scale but the relative magnitudes of the splitting due to the magnetic field are indicated; the D1 and D 2 frequencies is 16956.18 and 16973.38 cmy1 , respectively.
430
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
stant of sodium atoms 885.82 MHz w13x, g J m B B 4 A J , it is the case of a strong field. The complete hyperfine Hamiltonian is evaluated in the uncoupled representation < g JIm J m I : and the energy obtained using first-order perturbation theory is given by D Em J m I s g J m B Bm J y g XI m B Bm I q A J m J m I .
Ž 6.
The electric dipole selection rules of the transitions between hyperfine levels are D m I s 0; D m J s 0," 1 .
Ž 7.
These rules are related to the polarization of the electric vector: D m J s 0 corresponds to an electric dipole oscillating in the z-direction Ž p polarization., and D m J s "1 correspond to oscillation in the x–y plane Ž s polarization.. In terms of the above discussion, we can draw the hyperfine splitting diagram of the D 1 and D 2 transitions for a sodium atom in a magnetic field, which is shown in Fig. 1. As an example, Fig. 1 shows the transitions occurring with the selection rules ŽEq. Ž7.. from the < m J s " 12 , m I s 32 : s < n " : states of the 3 2 S 1r2 level to the 3 2 P1r2 and 3 2 P3r2 levels, which are grouped according to the polarization, sq and sy, indicated by solid arrows pointing up and labeled simply as numbers from 1 to 6.
ized light, based on Eqs. Ž1. and Ž2., the laser-induced ESR shift of the hyperfine line m I s 32 is D nqs y
2h
2
2
n1 yn 2 Ž n 1 y n . q G 2r4
1 1 1 )<1 < ˆ q < nq :. =Re Ž² nq < m ˆq 2 ,y 2 :² 2 ,y 2 m n2yn q 2 Ž n 2 y n . q G 2r4 1 3 1 )<3 < ˆ q < nq :. =Re Ž² nq < m ˆq 2 ,y 2 :² 2 ,y 2 m n3yn y 2 Ž n 3 y n . q G 2r4 3 3 3 )<3 < ˆ q < ny :. =Re Ž² ny < m ˆq 2 ,y 2 :² 2 ,y 2 m
sy =
q
y
Ž E Ž0. .
2
<²3s < m z <3 pz :< 2
6 h2
2Ž n 1 y n . 2 Ž n 1 y n . q G 2r4
n2yn 2 Ž n 2 y n . q G 2r4
3Ž n 3 y n . 2 Ž n 3 y n . q G 2r4
.
Ž 8.
Similarly, for left circularly polarized light, the expression of the shift reduces to
3.2. Laser-induced ESR shift
Dnys y As the incident frequency approaches the 3 2 S 1r2 ™ 3 2 P1r2 ,3 2 P3r2 resonances, considering the influence of the hfs, we discuss the respective ESR shifts of the four hyperfine lines. For convenience, we label the four hyperfine lines by their respective nuclear spin magnetic quantum number m I . First taking the transition of the hyperfine levels of the ground state 3 2 S 1r2 , < m J ,m I : s < y 12 , 32 : ™ < 12 , 3 : 2 , as an example, we calculate the shift of this hyperfine line under the action of the optical field. Since the electric dipole transition moment is independent of the nuclear magnetic moment ŽEq. Ž7.., we abbreviate the wavefunction < g JIm J m I : of the hfs sublevels to < J,m J :. For right circularly polar-
Ž E Ž0. .
=
y
y
Ž E Ž0. . 6h
2
2
<²3s < m z <3 pz :< 2
3 Ž n4 y n . 2 Ž n4 y n . q G 2r4
n5 y n 2 Ž n 5 y n . q G 2r4
2Ž n6 y n . 2 Ž n 6 y n . q G 2r4
.
Ž 9.
Proceeding as above, similar formulas on the shifts for the other three hyperfine lines can be obtained. The above discussion indicates that each hyperfine line should show its own shift under the action of the optical field since the different hyperfine
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
levels correspond to the different polarizability tensors due to the different frequencies of the relative virtual transitions.
4. Results and discussion By using Eqs. Ž8. and Ž9. and the similar formulas for the other hyperfine lines, we have calculated the respective light shifts of the four hyperfine lines of a sodium atom in an external magnetic field of 1.25 T. The frequencies of the D 1 and D 2 lines are 16956.18
431
cmy1 Ž5.083336 = 10 14 Hz. and 16973.38 cmy1 Ž5.088492 = 10 14 Hz. w13x. The frequencies of the virtual absorption transitions corresponding to the hfs can be obtained in terms of Eq. Ž6. and Fig. 1, where the hfs constants A J are 885.82 Ž3 2 S 1r2 ., 94.3 Ž3 2 P1r2 . and 18.65 MHz Ž3 2 P3r2 . which are derived from resonance fluorescence techniques w13x. For example, for the m I s 32 hyperfine line, the six frequencies are n 1 s 5.083095 = 10 14 , n 2 s 5.088193 = 10 14 , n 3 s 5.088322 = 10 14 , n 4 s 5.088660 = 10 14 , n 5 s 5.083576 = 10 14 , and n 6 s 5.088789 = 10 14 Hz. The matrix element
Table 1 The ESR shifts Ž D nyy D nq . on modulating from left to right circularly polarized and D n in linearly polarized light related to the different hyperfine lines for a sodium atom at a frequency near D1 line in an external magnetic field of 1.25 T
n Ž10 14 Hz.
5.075000 5.082800 5.082950 5.083000 5.083037 5.083050 5.083094 5.083096 5.083098 5.083100 5.083101 5.08104 5.083106 5.083109 5.083111 5.083120 5.083138 5.083250 5.083500 5.083517 5.083561 5.083562 5.083566 5.083567 5.083571 5.083572 5.083576 5.083577 5.083600 5.083618 5.083650 5.083800 5.084500
Ž D nyy D nq . ŽMHz.
D n ŽMHz.
m I s 3r2
1r2
y1r2
y3r2
3r2
1r2
y1r2
y3r2
0.023 1.09 2.04 2.99 4.71 5.94 201.0 y200.2 y80.7 y52.6 y43.4 y28.3 y22.9 y17.8 y15.5 y9.68 y5.38 y0.95 2.58 3.54 15.6 16.8 23.5 26.1 45.9 56.3 232.4 y241.9 y11.2 y6.63 y3.97 y1.59 y0.58
0.023 1.08 1.99 2.86 4.37 5.39 41.8 62.0 118.2 233.4 y240.8 y66.5 y43.4 y28.3 y22.9 y12.2 y6.15 y0.99 2.81 3.93 23.5 26.1 45.8 56.3 232.3 y241.9 y53.6 y44.4 y9.33 y5.99 y3.75 y1.57 y0.57
0.023 1.06 1.94 2.75 4.10 4.97 23.8 29.2 37.8 50.0 62.0 201.0 y200.2 y61.1 y40.9 y16.2 y7.08 y1.03 3.05 4.36 43.1 52.3 240.6 y233.6 y57.6 y47.1 y27.3 y24.8 y8.11 y5.50 y3.58 y1.55 y0.57
0.023 1.05 1.89 2.64 3.84 4.59 16.4 18.7 21.8 25.4 28.2 41.8 62.0 201.0 y200.1 y24.5 y8.43 y1.08 3.35 4.92 240.6 y233.6 y57.6 y47.1 y27.4 y24.8 y18.1 y16.9 y7.14 y5.06 y3.41 y1.53 y0.57
y0.00072 y0.26 y0.66 y1.10 y1.93 y2.54 y100.0 100.6 40.8 26.8 22.2 14.6 12.0 9.41 8.24 5.34 3.22 1.20 1.96 2.42 8.42 8.98 12.3 13.6 23.5 28.7 116.8 y120.3 y5.03 y2.78 y1.48 y0.38 y0.044
y0.00070 y0.26 y0.63 y1.03 y1.76 y2.26 y20.4 y30.5 y58.6 y116.2 120.9 33.8 22.2 14.6 12.0 6.63 3.61 1.23 2.08 2.62 12.3 13.6 23.5 28.8 116.7 y120.3 y26.2 y21.6 y4.11 y2.45 y1.37 y0.37 y0.043
y0.00067 y0.25 y0.61 y0.98 y1.62 y2.04 y11.4 y14.1 y18.4 y24.5 y30.5 y100.0 100.6 31.1 21.0 8.61 4.08 1.27 2.21 2.84 22.2 26.8 120.9 y116.2 y28.2 y22.9 y13.1 y11.8 y3.50 y2.21 y1.27 y0.36 y0.042
y 0.00064 y0.24 y0.58 y0.92 y1.49 y1.85 y7.70 y8.87 y10.4 y12.2 y13.6 y20.4 y30.5 y100.0 100.6 12.8 4.76 1.30 2.37 3.13 120.9 y116.2 y28.2 y23.0 y13.1 y11.8 y8.44 y7.88 y3.00 y1.98 y1.19 y0.34 y0.041
The laser intensity is 10 W cmy2 and G s 1 = 10 8 Hz. The four hyperfine lines are labeled by their respective nuclear spin magnetic quantum number m I .
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
432
²3s < m z <3 pz : is taken to be 2.1026 = 10y2 9 C m w14x. Laser intensity 10 W cmy2 , i.e. E Ž0. s 86.6 V cmy1 w1x. All the linewidths were assumed to have the same magnitude of G s 1 = 10 8 Hz Žfor the atomic beam, giving a half-width of 0.003 cmy1 w7x., and for comparative purposes G s 3 = 10 9 Hz w14x. Here we did not take account of the influence of line shape of the incident light since the laser linewidth can be ; 1 MHz w15x. The calculated results are in Tables 1 and 2 and Figs. 2 and 3. To obtain a detailed look at the light shifts of the different hyperfine lines as resonance is approached,
we consider only the frequency range near the D 1 line. For the frequency range near the D 2 line similar conclusions can be deduced. Tables 1 and 2 show the values of the modulated circularly polarized shift Ž D nyy D nq . and the linearly polarized shift D n near the D 1 frequency for the different linewidths G s 1 = 10 8 and 3 = 10 9 Hz, where the four hyperfine lines are represented by their respective nuclear spin magnetic quantum number m I . Also the behavior of the modulated shift Ž D nyy D nq . of the four hyperfine lines at resonance is plotted in Figs. 2 and 3 focusing on the frequency range 5.08304 = 10 14 to
Table 2 The ESR shifts Ž D nyy D nq . and D n related to the different hyperfine lines for a sodium atom at a frequency near D1 line in an external magnetic field of 1.25 T
n Ž10 14 Hz.
5.075000 5.082800 5.082950 5.083000 5.083037 5.083050 5.083095 5.083096 5.083100 5.083101 5.083105 5.083106 5.083110 5.083111 5.083120 5.083138 5.083250 5.083500 5.083517 5.083561 5.083562 5.083566 5.083567 5.083570 5.083571 5.083575 5.083577 5.083581 5.083600 5.083618 5.083650 5.083800 5.084500
Ž D nyy D nq . ŽMHz.
D n ŽMHz.
m I s 3r2
1r2
y1r2
y3r2
3r2
1r2
y1r2
y3r2
0.023 1.08 2.02 2.92 4.42 5.39 0.43 y0.69 y4.35 y5.14 y7.22 y7.50 y7.95 y7.93 y6.97 y4.78 y0.94 2.45 3.27 7.75 7.74 7.22 6.92 5.41 4.69 0.86 y1.37 y5.94 y8.21 y5.97 y3.85 y1.58 y0.58
0.023 1.07 1.97 2.80 4.14 4.98 5.50 4.64 0.81 y0.31 y4.34 y5.13 y7.21 y7.49 y7.62 y5.29 y0.98 2.64 3.58 7.21 6.90 4.68 3.86 0.85 y0.26 y4.53 y6.21 y8.48 y7.52 y5.51 y3.66 y1.56 y0.58
0.023 1.06 1.93 2.70 3.91 4.65 8.10 7.74 5.51 4.65 0.45 y0.67 y4.60 y5.36 y7.92 y5.84 y1.02 2.85 3.91 4.92 4.13 0.10 y1.02 y4.22 y5.14 y7.79 y8.49 y9.02 y6.91 y5.14 y3.49 y1.54 y0.58
0.023 1.05 1.88 2.60 3.69 4.34 8.83 8.81 8.22 7.88 5.52 4.66 0.46 y0.66 y7.29 y6.51 y1.07 3.10 4.32 0.090 y1.03 y5.15 y5.98 y7.80 y8.20 y8.98 y9.03 y8.67 y6.32 y4.79 y3.34 y1.52 y0.58
y0.00072 y0.26 y0.66 y1.07 y1.79 y2.26 0.26 0.82 2.66 3.05 4.10 4.24 4.47 4.46 3.99 2.92 1.19 1.89 2.28 4.46 4.46 4.20 4.04 3.29 2.93 1.01 y0.11 y2.40 y3.56 y2.45 y1.42 y0.38 y0.045
y0.00070 y0.25 y0.63 y1.00 y1.64 y2.05 y2.27 y1.84 0.080 0.64 2.66 3.06 4.11 4.25 4.32 3.18 1.22 2.00 2.44 4.20 4.05 2.93 2.52 1.01 0.46 y1.68 y2.52 y3.67 y3.20 y2.22 y1.32 y0.37 y0.044
y0.00067 y0.25 y0.60 y0.95 y1.52 y1.88 y3.56 y3.38 y2.26 y1.83 0.27 0.83 2.81 3.18 4.48 3.46 1.26 2.11 2.62 3.06 2.67 0.65 0.086 y1.52 y1.98 y3.31 y3.66 y3.93 y2.89 y2.04 y1.23 y0.36 y0.043
y0.00064 y0.24 y0.57 y0.89 y1.41 y1.72 y3.92 y3.91 y3.61 y3.44 y2.25 y1.82 0.28 0.84 4.17 3.80 1.29 2.25 2.83 0.65 0.092 y1.97 y2.39 y3.30 y3.50 y3.90 y3.92 y3.75 y2.59 y1.85 y1.55 y0.34 y0.042
The laser intensity is 10 W cmy2 and G s 3 = 10 9 Hz. The four hyperfine lines are labeled by their respective nuclear spin magnetic quantum number m I .
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
433
Fig. 2. The ESR shift Ž D nyy D nq . of the different hyperfine lines for a sodium atom on modulating from left to right circularly polarized light at a frequency range 5.08304 = 10 14 to 5.08316 = 10 14 Hz in an external magnetic field of 1.25 T. The laser intensity is 10 W cmy2 and G s 1 = 10 8 Hz. The curves a, b, c and d present the behavior of the shifts for the four hyperfine lines m I s 3r2, 1r2, y1r2 and y3r2, respectively.
5.08316 = 10 14 Hz for the different linewidths G s 1 = 10 8 and 3 = 10 9 Hz, respectively.
From Tables 1 and 2, we can deduce that in non-resonant regions the light shifts of the four
Fig. 3. The ESR shift Ž D nyy D nq . of the different hyperfine lines for a sodium atom on modulating from left to right circularly polarized light at a frequency range 5.08304 = 10 14 to 5.08316 = 10 14 Hz in an external magnetic field of 1.25 T. The laser intensity is 10 W cmy2 and G s 3 = 10 9 Hz. The curves a, b, c and d present the behavior of the shifts for the four hyperfine lines m I s 3r2, 1r2, y1r2 and y3r2, respectively.
434
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
hyperfine lines are nearly equal and the ESR shifts can be considered as a translation of the whole hfs spectrum under the action of the optical field. In fact, in this case the influence of the hyperfine interaction can be neglected and the behaviour of the shifts are as in the previous theory w1–3x, which is in agreement with the qualitative discussion for the complex ion wIrBr6 x 2y in Ref. w17x. However, as resonance is approached the influence of the hyperfine interaction complicates the ESR shifts. As shown in Figs. 2 and 3, the four hyperfine lines are produced distinguishable different shifts under the action of the optical field. Acknowledgements This work was supported by the National Science Foundation of China. References w1x A.D. Buckingham, L.C. Parlett, Chem. Phys. Lett. 243 Ž1995. 15.
w2x L. Li, T. He, X. Wang, F.C. Liu, Chem. Phys. Lett. 268 Ž1997. 549. w3x L.C. Parlett, Chem. Phys. Lett. 296 Ž1998. 571. w4x N.S. Garif’ianov, Soviet Phys. JETP 5 Ž1957. 111. w5x A. Carrington, A.D. McLachlan, Introduction to Magnetic Resonance, Wiley, New York, 1979. w6x W. Weltner Jr., Magnetic Atoms and Molecules, Van Nostrand Reinhold, New York, 1983, p. 19. w7x D.A. Jackson, H. Kuhn, Proc. Roy. Soc. A 167 Ž1938. 205. w8x S. Pancharatnam, J. Opt. Soc. Am. 56 Ž1966. 1636. w9x W. Happer, Progress in Quantum Electronics, vol. 1, Pergamon Press, Oxford, 1971, p. 51. w10x L. Li, T. He, D. Chen, X. Wang, F.C. Liu, J. Phys. Chem. A 102 Ž1998. 10385. w11x C.P. Slichter, Principle of Magnetic Resonance, Chap. 11, Springer, 1990. w12x G.K. Woodgate, Elementary Atomic Structure, Clarendon Press, Oxford, 1980. w13x A. Corney, Atomic and Laser Spectroscopy, Clarendon Press, Oxford, 1977. w14x M.P. Bogaard, A.D. Buckingham, B.J. Orr, Mol. Phys. 13 Ž1967. 533. w15x H.-O. Hamaguchi, A.D. Buckingham, M. Kakimoto, Opt. Lett. 5 Ž1980. 114. w16x W. Weltner Jr., R.J. Van Zee, S. Li, J. Phys. Chem. 99 Ž1995. 6277. w17x L. Li, T. He, D. Chen, X. Wang, F.C. Liu, Chem. Phys. Lett. 291 Ž1998. 179.
Chemical Physics Letters 303 Ž1999. 427–434
Hyperfine structure in laser-induced shifts in electron spin resonance spectra of sodium atoms Li Li, Dongming Chen, Tianjing He, Xiuyan Wang, Fan-Chen Liu
)
Department of Chemical Physics, UniÕersity of Science and Technology of China, Hefei, Anhui 230026, China Received 17 December 1998; in final form 16 February 1999
Abstract The influence of the hyperfine interaction on laser-induced shifts in electron spin resonance spectra is investigated and calculated, taking the sodium atom as an example. As the incident laser frequency is near-resonant, the different hyperfine lines may produce distinguishable shifts which may be important for the application of the effect to practical analysis. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Observable shifts in electron spin resonance ŽESR. spectra are predicted to occur as a result of the application of linearly or circularly polarized light at a frequency near optical absorption, which are physically based on the quadratic Stark effect of optical fields and are proportional to the laser intensity and the polarizabilities w1,2x. The general formulas for the laser-induced ESR shifts were deduced w1x and their order of magnitude evaluated for a sodium atom as an example w1–3x. These theories and calculations w1–3x did not take account of the hyperfine structure Žhfs. and considered only the ESR shift as a translation of the whole hfs spectrum under the action of the optical field, which is applicable if the hfs is indistinguishable in ESR spectra like that in liquid sodium w4x or if the incident frequency is not ) Corresponding author. Fax: q86 551 363 1760; e-mail: [email protected]
near the optical absorptions. Nevertheless, ESR spectra of most paramagnetic systems contain important information about the hfs w5x. For example, in the ESR spectra of sodium atoms trapped in an argon matrix at 4 K four hyperfine lines were observed and each included six components due to matrix effects w6x. Also for Na atomic beams one expects to observe the hfs in ESR spectra since their optical spectra clearly show hyperfine lines with a half-width of 0.003 cmy1 w7x. As resonance is approached, it is necessary to consider the influence of the hfs on the light shifts and discuss the respective shifts of these hyperfine lines. This Letter attempts to explore the influence of the hfs on the laser-induced ESR shift by using a semiclassical dispersion theory w1,8x for a sodium atom in an atomic beam or trapped in a matrix as an example. The results indicate that for a circularly polarized laser beam at a frequency not near optical absorption, the light shifts of the four hyperfine lines are nearly equal and the ESR shifts can be consid-
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 2 3 9 - 0
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
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ered approximately as a whole translation of the ESR spectrum. In fact, in this case, the influence of the hyperfine interaction can be neglected and the behaviour of the shifts are as in the previous theory w1–3x. However, as resonance is approached the hfs becomes important and the influence of the hyperfine interaction complicates the laser-induced ESR shifts. The different hyperfine lines show distinguishable shifts under the action of the optical field. Thus the hyperfine interaction can be important for the application of the laser-induced ESR shifts in practical analysis of most paramagnetic systems. This effect may be capable of providing a new fingerprint of a sample in the study of a color center in a crystal or ion trapped in a matrix because it may enable one to identify the nuclear species and matrix effects that give rise to the hyperfine splitting w11,16x.
2. Energy level shift in an optical field
ground state < n:, G is the radiative width of the excited state < j :. m ˆ "s "2y1 r2 Ž mˆ x . i mˆ y . is the dipole moment operator and m ˆ )" is its complex conjugate. a " is the induced polarizability for a right Žq. or left Žy. circularly polarized laser beam, which includes the contribution of symmetric and antisymmetric polarizabilities. Eq. Ž1. is equivalent to that of Buckingham and Parlett’s perturbation theory w1x on the light-induced energy change of a polarizable atom or molecule w10x. Buckingham and Parlett emphasized correctly the contribution of antisymmetric polarizabilities. Taking the transition between electron spin magnetic energy levels < m z s " 12 : as an example, based on Eq. Ž1., the laser-induced ESR shift is D n "s
DW "Ž1r2.y DW "Žy1r2.
sy
h
Ž E Ž0. .
2
2h It is known w8x that the oscillating electric field of a light wave can cause Stark shifts of the energy levels of an atom or molecule. In a circularly polarized optical field, the interaction of the polarizability tensors with the electric field of a right or left circularly polarized laser beam will alter the electron spin energy levels and give rise to a shift in the ESR spectral lines proportional to the intensity of the laser w1x. According to the semiclassical dispersion theory w8x, in a right Žq. or left Žy. circularly polarized laser beam propagating in the z-direction, parallel to the external magnetic field B, it is found that as a result of virtual transitions to the excited-state sublevel < j : the ground-state sublevel < n: will be shifted by an amount w9,10x DW "Ž n.s y
Ž E Ž0. .
2
Ý
2h
j
Ž E Ž0. . 2
Ž 2.
where a " Ž 12 . and a " Žy 12 . are the polarizabilities of the < m s s 21 : and < m s s y 21 : states, respectively. In addition, in a linearly polarized optical field, in terms of its circularly polarized components, the laser-induced ESR shift is w2,3x Dn s
D nyq D nq 2
.
Ž 3.
The above equations are the fundamental formulas of the laser-induced ESR shifts, which had been applied to a sodium atom to evaluate the order of magnitude of the shifts without considering the influence of the hyperfine interaction upon the ESR shifts w1–3x.
n jn y n 3. hfs Light shift of a sodium atom
2 Ž n jn y n . q G 2r4
=Re Ž ² n < m ˆ )" < j :² j < mˆ " < n: . sy
a " Ž 12 . y a " Ž y 12 . ,
2
a" ,
Ž 1.
where hn jn s W Ž j. y W Ž n. is the energy difference between the unperturbed excited state < j : and the
The hyperfine interaction is seen in ESR to be equivalent to the addition of an extra magnetic field proportional to the z-component of the nuclear spin. Since the nucleus can take up only quantized orientation, the electron spin resonance is split into 2 I q 1 Žequally spaced. lines w11x. For a sodium atom with a nucleus of spin 3r2, one expects to observe four
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
hyperfine lines with equal spacing. Under the action of a circularly polarized optical field, each hyperfine line should have its own shift. First we discuss the hfs of a sodium atom in a uniform external magnetic field B.
g XI s g I m N rm B is a small number of order m erM Žwhere m e and M are the mass of an electron and proton, respectively., and the Lande´ g-value g J is gJs
J Ž J q 1. q L Ž L q 1. y S Ž S . 1. 2 J Ž J q 1.
3.1. hfs Energy leÕels The energy of an atom with finite nuclear spin in a magnetic field is determined by the zeroth-order Hamiltonian which includes the central field and all electrostatic and magnetic interactions internal to the electron system H0 and the hfs Hamiltonian H w12x H s A J I P J q g J m B Jz B y g XI m B I z B ,
Ž 4.
where A J is the magnetic hfs constant to be determined from experiments, m B the Bohr magneton,
429
q gs
J Ž J q 1. y L Ž L q 1. q S Ž S q 1. 2 J Ž J q 1.
.
Ž 5.
Here we omit the nuclear electric quadruple interaction since this term is too small to be considered for the sodium atoms. ESR experiments are usually done at either 9.5 or 35 GHz corresponding to magnetic fields of 0.34 or 1.25 T. Comparing with the ground-state hfs con-
Fig. 1. Zeeman splitting of hyperfine structure of the D1 and D 2 lines of sodium atoms in an external magnetic field of 1.25 T. The absorption transitions of the m I s 3r2 hyperfine line are grouped by the polarization, indicated by solid arrows pointing up, and labeled simply as numbers from 1 to 6. The diagram is not to scale but the relative magnitudes of the splitting due to the magnetic field are indicated; the D1 and D 2 frequencies is 16956.18 and 16973.38 cmy1 , respectively.
430
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
stant of sodium atoms 885.82 MHz w13x, g J m B B 4 A J , it is the case of a strong field. The complete hyperfine Hamiltonian is evaluated in the uncoupled representation < g JIm J m I : and the energy obtained using first-order perturbation theory is given by D Em J m I s g J m B Bm J y g XI m B Bm I q A J m J m I .
Ž 6.
The electric dipole selection rules of the transitions between hyperfine levels are D m I s 0; D m J s 0," 1 .
Ž 7.
These rules are related to the polarization of the electric vector: D m J s 0 corresponds to an electric dipole oscillating in the z-direction Ž p polarization., and D m J s "1 correspond to oscillation in the x–y plane Ž s polarization.. In terms of the above discussion, we can draw the hyperfine splitting diagram of the D 1 and D 2 transitions for a sodium atom in a magnetic field, which is shown in Fig. 1. As an example, Fig. 1 shows the transitions occurring with the selection rules ŽEq. Ž7.. from the < m J s " 12 , m I s 32 : s < n " : states of the 3 2 S 1r2 level to the 3 2 P1r2 and 3 2 P3r2 levels, which are grouped according to the polarization, sq and sy, indicated by solid arrows pointing up and labeled simply as numbers from 1 to 6.
ized light, based on Eqs. Ž1. and Ž2., the laser-induced ESR shift of the hyperfine line m I s 32 is D nqs y
2h
2
2
n1 yn 2 Ž n 1 y n . q G 2r4
1 1 1 )<1 < ˆ q < nq :. =Re Ž² nq < m ˆq 2 ,y 2 :² 2 ,y 2 m n2yn q 2 Ž n 2 y n . q G 2r4 1 3 1 )<3 < ˆ q < nq :. =Re Ž² nq < m ˆq 2 ,y 2 :² 2 ,y 2 m n3yn y 2 Ž n 3 y n . q G 2r4 3 3 3 )<3 < ˆ q < ny :. =Re Ž² ny < m ˆq 2 ,y 2 :² 2 ,y 2 m
sy =
q
y
Ž E Ž0. .
2
<²3s < m z <3 pz :< 2
6 h2
2Ž n 1 y n . 2 Ž n 1 y n . q G 2r4
n2yn 2 Ž n 2 y n . q G 2r4
3Ž n 3 y n . 2 Ž n 3 y n . q G 2r4
.
Ž 8.
Similarly, for left circularly polarized light, the expression of the shift reduces to
3.2. Laser-induced ESR shift
Dnys y As the incident frequency approaches the 3 2 S 1r2 ™ 3 2 P1r2 ,3 2 P3r2 resonances, considering the influence of the hfs, we discuss the respective ESR shifts of the four hyperfine lines. For convenience, we label the four hyperfine lines by their respective nuclear spin magnetic quantum number m I . First taking the transition of the hyperfine levels of the ground state 3 2 S 1r2 , < m J ,m I : s < y 12 , 32 : ™ < 12 , 3 : 2 , as an example, we calculate the shift of this hyperfine line under the action of the optical field. Since the electric dipole transition moment is independent of the nuclear magnetic moment ŽEq. Ž7.., we abbreviate the wavefunction < g JIm J m I : of the hfs sublevels to < J,m J :. For right circularly polar-
Ž E Ž0. .
=
y
y
Ž E Ž0. . 6h
2
2
<²3s < m z <3 pz :< 2
3 Ž n4 y n . 2 Ž n4 y n . q G 2r4
n5 y n 2 Ž n 5 y n . q G 2r4
2Ž n6 y n . 2 Ž n 6 y n . q G 2r4
.
Ž 9.
Proceeding as above, similar formulas on the shifts for the other three hyperfine lines can be obtained. The above discussion indicates that each hyperfine line should show its own shift under the action of the optical field since the different hyperfine
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
levels correspond to the different polarizability tensors due to the different frequencies of the relative virtual transitions.
4. Results and discussion By using Eqs. Ž8. and Ž9. and the similar formulas for the other hyperfine lines, we have calculated the respective light shifts of the four hyperfine lines of a sodium atom in an external magnetic field of 1.25 T. The frequencies of the D 1 and D 2 lines are 16956.18
431
cmy1 Ž5.083336 = 10 14 Hz. and 16973.38 cmy1 Ž5.088492 = 10 14 Hz. w13x. The frequencies of the virtual absorption transitions corresponding to the hfs can be obtained in terms of Eq. Ž6. and Fig. 1, where the hfs constants A J are 885.82 Ž3 2 S 1r2 ., 94.3 Ž3 2 P1r2 . and 18.65 MHz Ž3 2 P3r2 . which are derived from resonance fluorescence techniques w13x. For example, for the m I s 32 hyperfine line, the six frequencies are n 1 s 5.083095 = 10 14 , n 2 s 5.088193 = 10 14 , n 3 s 5.088322 = 10 14 , n 4 s 5.088660 = 10 14 , n 5 s 5.083576 = 10 14 , and n 6 s 5.088789 = 10 14 Hz. The matrix element
Table 1 The ESR shifts Ž D nyy D nq . on modulating from left to right circularly polarized and D n in linearly polarized light related to the different hyperfine lines for a sodium atom at a frequency near D1 line in an external magnetic field of 1.25 T
n Ž10 14 Hz.
5.075000 5.082800 5.082950 5.083000 5.083037 5.083050 5.083094 5.083096 5.083098 5.083100 5.083101 5.08104 5.083106 5.083109 5.083111 5.083120 5.083138 5.083250 5.083500 5.083517 5.083561 5.083562 5.083566 5.083567 5.083571 5.083572 5.083576 5.083577 5.083600 5.083618 5.083650 5.083800 5.084500
Ž D nyy D nq . ŽMHz.
D n ŽMHz.
m I s 3r2
1r2
y1r2
y3r2
3r2
1r2
y1r2
y3r2
0.023 1.09 2.04 2.99 4.71 5.94 201.0 y200.2 y80.7 y52.6 y43.4 y28.3 y22.9 y17.8 y15.5 y9.68 y5.38 y0.95 2.58 3.54 15.6 16.8 23.5 26.1 45.9 56.3 232.4 y241.9 y11.2 y6.63 y3.97 y1.59 y0.58
0.023 1.08 1.99 2.86 4.37 5.39 41.8 62.0 118.2 233.4 y240.8 y66.5 y43.4 y28.3 y22.9 y12.2 y6.15 y0.99 2.81 3.93 23.5 26.1 45.8 56.3 232.3 y241.9 y53.6 y44.4 y9.33 y5.99 y3.75 y1.57 y0.57
0.023 1.06 1.94 2.75 4.10 4.97 23.8 29.2 37.8 50.0 62.0 201.0 y200.2 y61.1 y40.9 y16.2 y7.08 y1.03 3.05 4.36 43.1 52.3 240.6 y233.6 y57.6 y47.1 y27.3 y24.8 y8.11 y5.50 y3.58 y1.55 y0.57
0.023 1.05 1.89 2.64 3.84 4.59 16.4 18.7 21.8 25.4 28.2 41.8 62.0 201.0 y200.1 y24.5 y8.43 y1.08 3.35 4.92 240.6 y233.6 y57.6 y47.1 y27.4 y24.8 y18.1 y16.9 y7.14 y5.06 y3.41 y1.53 y0.57
y0.00072 y0.26 y0.66 y1.10 y1.93 y2.54 y100.0 100.6 40.8 26.8 22.2 14.6 12.0 9.41 8.24 5.34 3.22 1.20 1.96 2.42 8.42 8.98 12.3 13.6 23.5 28.7 116.8 y120.3 y5.03 y2.78 y1.48 y0.38 y0.044
y0.00070 y0.26 y0.63 y1.03 y1.76 y2.26 y20.4 y30.5 y58.6 y116.2 120.9 33.8 22.2 14.6 12.0 6.63 3.61 1.23 2.08 2.62 12.3 13.6 23.5 28.8 116.7 y120.3 y26.2 y21.6 y4.11 y2.45 y1.37 y0.37 y0.043
y0.00067 y0.25 y0.61 y0.98 y1.62 y2.04 y11.4 y14.1 y18.4 y24.5 y30.5 y100.0 100.6 31.1 21.0 8.61 4.08 1.27 2.21 2.84 22.2 26.8 120.9 y116.2 y28.2 y22.9 y13.1 y11.8 y3.50 y2.21 y1.27 y0.36 y0.042
y 0.00064 y0.24 y0.58 y0.92 y1.49 y1.85 y7.70 y8.87 y10.4 y12.2 y13.6 y20.4 y30.5 y100.0 100.6 12.8 4.76 1.30 2.37 3.13 120.9 y116.2 y28.2 y23.0 y13.1 y11.8 y8.44 y7.88 y3.00 y1.98 y1.19 y0.34 y0.041
The laser intensity is 10 W cmy2 and G s 1 = 10 8 Hz. The four hyperfine lines are labeled by their respective nuclear spin magnetic quantum number m I .
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
432
²3s < m z <3 pz : is taken to be 2.1026 = 10y2 9 C m w14x. Laser intensity 10 W cmy2 , i.e. E Ž0. s 86.6 V cmy1 w1x. All the linewidths were assumed to have the same magnitude of G s 1 = 10 8 Hz Žfor the atomic beam, giving a half-width of 0.003 cmy1 w7x., and for comparative purposes G s 3 = 10 9 Hz w14x. Here we did not take account of the influence of line shape of the incident light since the laser linewidth can be ; 1 MHz w15x. The calculated results are in Tables 1 and 2 and Figs. 2 and 3. To obtain a detailed look at the light shifts of the different hyperfine lines as resonance is approached,
we consider only the frequency range near the D 1 line. For the frequency range near the D 2 line similar conclusions can be deduced. Tables 1 and 2 show the values of the modulated circularly polarized shift Ž D nyy D nq . and the linearly polarized shift D n near the D 1 frequency for the different linewidths G s 1 = 10 8 and 3 = 10 9 Hz, where the four hyperfine lines are represented by their respective nuclear spin magnetic quantum number m I . Also the behavior of the modulated shift Ž D nyy D nq . of the four hyperfine lines at resonance is plotted in Figs. 2 and 3 focusing on the frequency range 5.08304 = 10 14 to
Table 2 The ESR shifts Ž D nyy D nq . and D n related to the different hyperfine lines for a sodium atom at a frequency near D1 line in an external magnetic field of 1.25 T
n Ž10 14 Hz.
5.075000 5.082800 5.082950 5.083000 5.083037 5.083050 5.083095 5.083096 5.083100 5.083101 5.083105 5.083106 5.083110 5.083111 5.083120 5.083138 5.083250 5.083500 5.083517 5.083561 5.083562 5.083566 5.083567 5.083570 5.083571 5.083575 5.083577 5.083581 5.083600 5.083618 5.083650 5.083800 5.084500
Ž D nyy D nq . ŽMHz.
D n ŽMHz.
m I s 3r2
1r2
y1r2
y3r2
3r2
1r2
y1r2
y3r2
0.023 1.08 2.02 2.92 4.42 5.39 0.43 y0.69 y4.35 y5.14 y7.22 y7.50 y7.95 y7.93 y6.97 y4.78 y0.94 2.45 3.27 7.75 7.74 7.22 6.92 5.41 4.69 0.86 y1.37 y5.94 y8.21 y5.97 y3.85 y1.58 y0.58
0.023 1.07 1.97 2.80 4.14 4.98 5.50 4.64 0.81 y0.31 y4.34 y5.13 y7.21 y7.49 y7.62 y5.29 y0.98 2.64 3.58 7.21 6.90 4.68 3.86 0.85 y0.26 y4.53 y6.21 y8.48 y7.52 y5.51 y3.66 y1.56 y0.58
0.023 1.06 1.93 2.70 3.91 4.65 8.10 7.74 5.51 4.65 0.45 y0.67 y4.60 y5.36 y7.92 y5.84 y1.02 2.85 3.91 4.92 4.13 0.10 y1.02 y4.22 y5.14 y7.79 y8.49 y9.02 y6.91 y5.14 y3.49 y1.54 y0.58
0.023 1.05 1.88 2.60 3.69 4.34 8.83 8.81 8.22 7.88 5.52 4.66 0.46 y0.66 y7.29 y6.51 y1.07 3.10 4.32 0.090 y1.03 y5.15 y5.98 y7.80 y8.20 y8.98 y9.03 y8.67 y6.32 y4.79 y3.34 y1.52 y0.58
y0.00072 y0.26 y0.66 y1.07 y1.79 y2.26 0.26 0.82 2.66 3.05 4.10 4.24 4.47 4.46 3.99 2.92 1.19 1.89 2.28 4.46 4.46 4.20 4.04 3.29 2.93 1.01 y0.11 y2.40 y3.56 y2.45 y1.42 y0.38 y0.045
y0.00070 y0.25 y0.63 y1.00 y1.64 y2.05 y2.27 y1.84 0.080 0.64 2.66 3.06 4.11 4.25 4.32 3.18 1.22 2.00 2.44 4.20 4.05 2.93 2.52 1.01 0.46 y1.68 y2.52 y3.67 y3.20 y2.22 y1.32 y0.37 y0.044
y0.00067 y0.25 y0.60 y0.95 y1.52 y1.88 y3.56 y3.38 y2.26 y1.83 0.27 0.83 2.81 3.18 4.48 3.46 1.26 2.11 2.62 3.06 2.67 0.65 0.086 y1.52 y1.98 y3.31 y3.66 y3.93 y2.89 y2.04 y1.23 y0.36 y0.043
y0.00064 y0.24 y0.57 y0.89 y1.41 y1.72 y3.92 y3.91 y3.61 y3.44 y2.25 y1.82 0.28 0.84 4.17 3.80 1.29 2.25 2.83 0.65 0.092 y1.97 y2.39 y3.30 y3.50 y3.90 y3.92 y3.75 y2.59 y1.85 y1.55 y0.34 y0.042
The laser intensity is 10 W cmy2 and G s 3 = 10 9 Hz. The four hyperfine lines are labeled by their respective nuclear spin magnetic quantum number m I .
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
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Fig. 2. The ESR shift Ž D nyy D nq . of the different hyperfine lines for a sodium atom on modulating from left to right circularly polarized light at a frequency range 5.08304 = 10 14 to 5.08316 = 10 14 Hz in an external magnetic field of 1.25 T. The laser intensity is 10 W cmy2 and G s 1 = 10 8 Hz. The curves a, b, c and d present the behavior of the shifts for the four hyperfine lines m I s 3r2, 1r2, y1r2 and y3r2, respectively.
5.08316 = 10 14 Hz for the different linewidths G s 1 = 10 8 and 3 = 10 9 Hz, respectively.
From Tables 1 and 2, we can deduce that in non-resonant regions the light shifts of the four
Fig. 3. The ESR shift Ž D nyy D nq . of the different hyperfine lines for a sodium atom on modulating from left to right circularly polarized light at a frequency range 5.08304 = 10 14 to 5.08316 = 10 14 Hz in an external magnetic field of 1.25 T. The laser intensity is 10 W cmy2 and G s 3 = 10 9 Hz. The curves a, b, c and d present the behavior of the shifts for the four hyperfine lines m I s 3r2, 1r2, y1r2 and y3r2, respectively.
434
L. Li et al.r Chemical Physics Letters 303 (1999) 427–434
hyperfine lines are nearly equal and the ESR shifts can be considered as a translation of the whole hfs spectrum under the action of the optical field. In fact, in this case the influence of the hyperfine interaction can be neglected and the behaviour of the shifts are as in the previous theory w1–3x, which is in agreement with the qualitative discussion for the complex ion wIrBr6 x 2y in Ref. w17x. However, as resonance is approached the influence of the hyperfine interaction complicates the ESR shifts. As shown in Figs. 2 and 3, the four hyperfine lines are produced distinguishable different shifts under the action of the optical field. Acknowledgements This work was supported by the National Science Foundation of China. References w1x A.D. Buckingham, L.C. Parlett, Chem. Phys. Lett. 243 Ž1995. 15.
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