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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 21062–21073
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Calculations of laser induced dipole-quadrupole collisional energy transfer in Sr-Ca

Zhenzhong Lu, Deying Chen, Yuanqin Xia, Rongwei Fan, and Hongying Zhang  »View Author Affiliations


Optics Express, Vol. 18, Issue 20, pp. 21062-21073 (2010)
http://dx.doi.org/10.1364/OE.18.021062


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Abstract

A three-state model for calculating the cross section of laser-induced dipole-quadrupole collisional energy transfer in Sr-Ca system is presented. The motion equations for the probability amplitudes of the three intermediate states are obtained. The expression of the cross section is derived. Various factors including field intensity, relative speed, system temperature which influence the collisional cross section are discussed to illustrate the features of the dipole-quadrupole laser-induced collisional energy transfer (LICET)process. Calculating results show that the peak of the LICET profiles moves to the red, the tuning range of the profiles obviously becomes narrower with the laser field intensity increasing and a cross section of 1.25 × 10−13cm2 at a laser intensity of 8.29 × 109W/cm2 is obtained. Our results indicate that dipole-quadrupole LICET process can be the effective way to transfer energy selectively from a storage state of arbitrary parity to a target state of arbitrary parity.

© 2010 OSA

1. Introduction

Laser-induced collisional energy transfer (LICET) is an optical phenomenon that a pair of colliding atoms transfer to the final states by the joint action of the collisional and radiative interactions. A LICET process between two atoms can be expressed by the reaction:

A*(i)+B(i')+ωA(f)+B**(f')
(1)

As plenty of the experimental studies have been made including Sr-Ca [1

1. R. W. Falcone, R. W. Green, J. White, J. Young, and S. Harris, “Observation of laser-induced inelastic collisions,” Phys. Rev. A 15(3), 1333–1335 (1977). [CrossRef]

], Na-Ca [2

2. A. Debarre, “High-resolution study of light-induced collisional energy transfer in Na-Ca mixture,” J. Phys. B 16(3), 431–436 (1983). [CrossRef]

], Eu-Sr [3

3. C. Brechnignac, Ph. Cahuzac, and P. E. Toschek, “High-resolution studies on laser-induced collisional-energy-transfer profiles,” Phys. Rev. A 21(6), 1969–1974 (1980). [CrossRef]

], Li-Sr [4

4. F. Dorsch, S. Geltman, and P. E. Toschek, “Laser-induced collisional-energy transfer in thermal collisions of lithium and strontium,” Phys. Rev. A 37(7), 2441–2447 (1988). [CrossRef] [PubMed]

], Rb-K [5

5. B. Cheron and H. Lemery, “Observation of laser induced collisional energy transfer in a rubidium-potassium mixture,” Opt. Commun. 42(2), 109–112 (1982). [CrossRef]

], Li-Sr [6

6. D. Z. Zhang, B. Nikolaus, and P. E. Toschek, Appl. Phys. B 28, 195 (1981).

], people also have proposed many theoretical models on LICET[7,8]. The two-level model proposed by Harris et al.[9] influenced most. Gallagher and Holstein presented the first detailed calculations of LICET line shapes. The molecular-based treatment demonstrated the importance of the van der Waals interaction to the low-intensity line shape [10

10. A. Gallagher and T. Holstein, “Collision-induced absorption in atomic electronic transitions,” Phys. Rev. A 16(6), 2413–2431 (1977). [CrossRef]

]. Bambini and Berman demonstrated that a two-state treatment was not adequate and the intermediate state which may be populated must be treated as a real state [11

11. A. Bambini and P. R. Berman, “Quasistatic wing behavior of collisional-radiative line profiles,” Phys. Rev. A 35(9), 3753–3757 (1987). [CrossRef] [PubMed]

]. Agresti et al. generalized two-level model into three-level perturbative theory[12]. In 1992, Sydney Geltman reexamined the behavior of cross sections in the three-state model for the two-pairs Li-Sr and Eu-Sr previously studied experimentally [13

13. S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]

]. A. Bambini and S. Geltman gave the theory of strong-field light-induced collisional energy transfer later. They calculated the spectral profiles of LICET process induced by polarized, high-intensity laser field [14

14. A. Bambini and S. Geltman, “Theory of strong-field light-induced collisional energy transfer in Eu and Sr,” Phys. Rev. A 50(6), 5081–5091 (1994). [CrossRef] [PubMed]

]. Based on the three-level model and considering the effects of all intermediate states, Chen et al.[15-17] developed the four-level perturbative theory between two atoms.

Moreover, the early calculations on the LICET process [7

7. M. Matera, M. Mazzoni, R. Buffa, S. Cavalieri, and E. Arimondo, “Far-wing study of laser-induced collisional energy transfer,” Phys. Rev. A 36(3), 1471–1473 (1987). [CrossRef] [PubMed]

9

9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. 13(12), 972–978 (1977). [CrossRef]

,14

14. A. Bambini and S. Geltman, “Theory of strong-field light-induced collisional energy transfer in Eu and Sr,” Phys. Rev. A 50(6), 5081–5091 (1994). [CrossRef] [PubMed]

], based on the assumption that the relative velocity was fixed which obviously did not match the practical situation and adopted the simple set of product atomic basis states which included on the m = 0 substates. In this paper, the three-level dipole-quadrupole LICET model considering the relative velocity distribution function and including all the degenerate m states which may give more accurate details of the line shape is presented. Laser induced dipole-quadrupole collision process in Sr-Ca system is numerically calculated through immediate integration. Various factors including field intensity, relative speed, temperature which influence the collisional cross section are discussed to illustrate the features of the dipole-quadrupole LICET process. And our results indicate that dipole-quadrupole LICET process can be the effective way to transfer energy selectively from a storage state of arbitrary parity to a target state of arbitrary parity.

2. Theory

Figure 1
Fig. 1 Simplified energy levels for a LICET process.
shows the LICET process between two different atoms, with those energy levels of atom A, atom B and the compound AB system that are relevant to the LICET process present and those irrelevant ignored. Taking independent atomic states of atoms A and B as basis states, these three states of the compound system can be expressed as
| 1 =||B|=|A||=||B}
(2)
where | and |A denote the ground and excited states of atom A, | , |B and |B denote the ground, excited and high-excited states of atom B respectively.

The wave function can be expressed by the basis states as follows:

Ψ=n=13cn(t)|nexp(iEnt)
(3)

We assume the coordinate system as Fig. 2
Fig. 2 Coordinate system formed by two colliding atoms.
shown where atom B is fixed and atom A moves in a straight line with velocity v along the z axis. The unprimed system is fixed in space, while in the primed system, the z’ axis points the interatomic axis, and therefore rotates with respect to the unprimed system during the collision, i.e.,
{x=xsinθ+zcosθy=yz=zsinθxcosθ
where cosθ = b/R(t),and θ varies form -π/2 to π/2。

The linear trajectory is assumed for R(t) = (b 2 + v 2 t 2)1/2, where b is an impact parameter and v is the relative velocity. Assuming the E(t) = E 0 a ycos(ωt) is the laser field with frequency ω, then the interaction Hamiltonian can be written
H(t)=eyAE0cosωteyBE0cosωt+VAB
(4)
The interaction VAB can be represented by the multipole expansion [20

20. J. O. Hirschfelder and W. J. Meath, “The nature of intermolecular forces,” Adv. Chem. Phys. 12, 1 (1967).

]
VAB=j=3VjR(t)j
(5)
where
Vj=l=1j2m=1<l<F(j,l,m)Qlm(A)Qjl1m(B)
Here is the lesser of l and j-1-l, Qlm(A) and Qjl1m(B) are multipole moment operators, and F(j, l, m) is given by [20

20. J. O. Hirschfelder and W. J. Meath, “The nature of intermolecular forces,” Adv. Chem. Phys. 12, 1 (1967).

,21

21. M. E. Rose, “The Electrostatic Interaction of Two Arbitrary Charge Distributions,” J. Math. Phys. 37, 215–222 (1958).

]
F(j,l,m)=(1)jl1[(2j2)!(2j2l2)!(2l)!]12C(jl1,l,j1;m,m,0)=(1)jl1(j1)![(lm)!(l+m)!(j1lm)!(j1l+m)!]12
where C(j-l-1, l, j-1; m, -m, 0) is Clebsch-Gordan coefficient.

By making formula (3) simultaneous with the Schrödinger equation and supposing the laser field is sufficiently intense, the motion equation of formula (2) can be obtained as follows:
iC˙=HC
(6)
where
C=[c1c2c3]
H=[0V12eiω12tV13ei(ω13+ω)tV21eiω21t00V31ei(ω31ω)t00]
Vmn=m|H(t)|n
and

ωmn=(EmEn)/

Using a unitary transformation a(t)=T(t)·C(t), where
T=[eiω21t0001000ei(ω32ω)t]
Equation (6) can be simplified as
ia˙=Va
(7)
where

a=[a1a2a3]
V=[ω21V12V13V2100V310ω32ω]

σ=00|a3(b,υ,t=)|2F(υ)2πbdbdυ
(8)

The probability density function F(v) can be represented by [22

22. Z. H. C. Deying, L. Zhenzhong, X. Yuanqin, and F. Rongwei, “Impacts of Relative velocity distribution between two colliding atoms on laser-induced collisional energy transfer,” Chin. J. Lasers 35, 0077–0080 (2008).

]
F(υ)4πυ2f(υ)=4π(M2πkT)3/2υ2eMυ2/2kT
where M is the reduced mass of the two colliding atoms, T is the thermodynamic temperature and k is the Boltzmann constant.

3. Application to Sr-Ca system

Sr-Ca system LICET process can be expressed by the following formula, and Fig. 3
Fig. 3 The LICET transition in Sr-Ca system. The energy levels in the figure are given in cm−1.
illustrates those energy levels relevant to the LICET process.

Sr(5s5pP110)+Ca(4s2S10)+ω(530.7nm)Sr(5s2S10)+Ca(3d4pF130)

The states of Sr-Ca compound system shown in Fig. 3 can be defined as:
| 1 =|Sr(5s2S10) |Ca(4s3dD12)|=|Sr(5s5pP110)|Ca(4s2S10 )|=|Sr(5s2S10) |Ca(3d4pF130)}
where energy internal between state | 1  and state | is ω 21 = −151.152 cm−1 .

Assuming that the relative speed is 600m/s, the laser is at strict resonance (Δ = 0cm−1) and the impact parameter b is equal to 0.9nm and 1.15nm respectively, through an immediate integration on formula (7), the collisional transition probability |a 3(t)|2 versus time t in this Sr-Ca system is calculated as Fig. 4
Fig. 4 The time dependence of laser-induced collision transition probability |a 3(t)|2 for the Sr-Ca system with the transfer laser resonant at an intensity of 0.133MW/cm2. (a) b = 0.9nm; (b) b = 1.15 nm.
shown. The results show that |a 3(t)|2 oscillates over time, the smaller the b is, the stronger the |a 3(t)|2 oscillates. When|t|≥20ps, |a 3(t)|2 approach to a definite value, which indicate that the laser induced collision process occurs for~40ps.

In this Sr-Ca system, when the laser intensity is fixed at 0.133MW/cm2 and the relative speed between the two colliding atoms is 600m/s, the collisional transition probability |a 3( + ∞)|2 versus the impact parameter b can be obtained through numerical integrations with different laser detuning Δ and the profiles obtained are shown in Fig. 5
Fig. 5 Laser-induced collision transition probability |a 3( + ∞)|2 as a function of impact parameter for the Sr-Ca system (a) Δ = 10 cm−1; (b) Δ = 0cm−1; (c) Δ = −10cm−1.
. It appears that |a 3( + ∞)|2 oscillates over b. To the quasimolecule system formed in the collisional process, there is an effective curve crossing at some Rx, i.e., at some Rx the argument of the exponent in equation of motion for the probability amplitudes equals zero at t such that R(t) = R x. As the Landau-Zener theory of the curve crossing section, the transition probability is only large for b≤Rx. At a given impact parameter a 3(t) accumulates during each of the two times that the crossing distance is neared. And the oscillation of |a 3( + ∞)|2 results from the adding and subtracting of the phased contributions at each of the two crossing [9

9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. 13(12), 972–978 (1977). [CrossRef]

]. It is also found that in the detuning case more of the contribution to the total collision cross section occurs at small impact parameter than in the strict resonance case. When laser detuning Δ>0, the maximum amplitude increases with increasing impact parameter, and when Δ<0, amplitude maximum decreased as the impact parameter increases.

A series of cross sections at various field intensities are shown in Fig. 6
Fig. 6 LICET spectrums for Sr-Ca system at various transfer laser intensities in weak field.
and Fig. 8
Fig. 8 LICET spectrums for the Sr-Ca system at various transfer laser intensities in strong field.
. In weak field as the Fig. 6 shown, the results are characterized by a universal asymmetric line shape and the magnitude is proportion to the field intensity. The profile can be divided into two parts, the quasi-static and the anti-static wings. A qualitative understanding of this is based on the adiabatic molecular curves given in Fig. 7
Fig. 7 Schematic adiabatic quasimolecular potential for the Sr-Ca system.
. Molecular curves of state 1 and state 2 become strongly repelling van der Waals energies by the coupling between state 1 and state 2. When ω>ω 0 there is a such R where ω can equal E3(R)-E2(R), while in the wing of ω<ω 0 there is no such value of R which leads to the sharply reduce of the transition probability in anti-static wing. Furthermore, it is shown in Fig. 6 that as far as this Sr-Ca system is concerned, the peak of the cross section profiles is not found when the transfer laser is strictly resonant (i.e. Δ = 0cm−1), but it is found when the transfer laser detunes a little from Δ = 0cm−1 in the quasi-static wing (in this paper, peak of the profiles is found when Δ = 1.5cm−1).

As the field intensity is increased shown in Fig. 8, the resulting spectrum is shifted in frequency towards the anti-stable wing. An understanding of this is that as the laser intensity increases, the Rabi oscillation frequency in the Ca(3d4pF1304s3dD12) atomic transition increases and become dominant over the Van der Waals quasimolecule mechanism. It tends to enhance the LICET cross section as ω approaches to ω 31 which is <ω 32, resulting in the bathochromic shift [13

13. S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]

]. Figure 9
Fig. 9 Shift of the peak cross section as a function of transfer laser intensity for the Sr-Ca system in strong field.
gives the shift of the peak cross section as a function of transfer laser intensity. The results show that there is a good linear relation between cross section shift and laser intensity. The magnitude of this shift to be approximately given by −5.56329 × 10−9I(W/cm2)cm−1.

Form the Fig. 8 it can be seen that with the increasing field intensity the line shape tends to become more symmetrical at its center, which is because of the cross section in the quasi-static wing lowered by the presence of a combined light and collisional shift that reduces the effective time for level crossing [23

23. A. Bambini, M. Matera, A. Agresti, and M. Bianconi, “Strong-field effects on light-induced collisional energy transfer,” Phys. Rev. A 42(11), 6629–6640 (1990). [CrossRef] [PubMed]

]. It is also apparent from Fig. 8 that decreasing field intensity has the effect of increasing the transition probability in the quasi-static wing. Moreover Full width at half peak of the profile becomes smaller as the field intensity increases.

The peak cross section as a function of transfer laser intensity for the Sr-Ca system is given in Fig. 10
Fig. 10 The peak cross section as a function of transfer laser intensity for the Sr-Ca system.
. The collision cross section rises with laser intensity and tends to saturate. There is a maximum in our results which is interpreted as originating from the increased probability of populating the intermediate state and is not accounted for in a two-state model [13

13. S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]

]. It is a significant departure from the two-state treatment result that the LICET peak cross section is monotone increasing with the laser intensity which does not conform to physical reality. A cross section of 1.25 × 10−13cm2 at a laser intensity of 8.29 × 109W/cm2 is obtained which indicate that the laser induced dipole-quadrupole and dipole-dipole collision have comparable magnitude. So the dipole-quadrupole process also can be the effective way to transfer energy selectively from a storage state of arbitrary parity to a target state of arbitrary parity.

When the relative speed is taken as 950m/s, 1100 m/s and 1200 m/s, respectively, curves of cross section σ (Δ) versus laser detuning Δ through numerical integrations are shown in Fig. 11
Fig. 11 LICET cross section vs. the laser detuning at various relative speed. The laser intensity is fixed at 108 W/cm2.
. It can be seen that the variation in the LICET profile to laser detuning has a certain tunable range. Full width at half peak of the profile and cross section at fixed laser detuning become smaller as the relative speed increases. Moreover, the quasi-static wings approximately have the same trend at different relative speed, while the anti-static wings become steeper as the speed increases. A understanding of this is that based on the [9

9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. 13(12), 972–978 (1977). [CrossRef]

], relative speed is in inverse proportion to the Weisskopf radius which is in proportion to the cross section, resulting in the cross section become smaller with collisional speed reducing.

Figure 13
Fig. 13 The LICET spectrum for the Sr-Ca system at different temperatures with the transfer laser field intensity of 83MW/cm2
shows the LICET spectrum for the Sr-Ca system at different temperatures. It is found that system temperature has no obvious effect on line shape while in quasi-static wing and especially in the spectrum center the cross section increases with the decreasing temperature. Since the average velocity decreases as the temperature increases, it leads to the Weisskopf radius rises which accounts for the cross section increasing especially in the vicinity of the spectral profiles center.

4. Conclusion

In this paper, by considering multipole expansion interaction Hamiltonian, a three-state model for calculating the cross section of laser-induced dipole-quadrupole collisional energy transfer in Sr-Ca system is presented. In the present work we consider three basis states, and include all possible m states. The transition probability is found by summing over the final level populations and averaging over the initial state populations. In view of the probability density function of relative velocity between two colliding atoms in three-dimensional space under thermal equilibrium condition, the laser-induced collision cross section at given temperature is obtained, and spectral profiles of LICET are calculated through immediate integrations. It appears that the dipole-quadrupole and dipole-dipole LICET spectrum profiles [9

9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. 13(12), 972–978 (1977). [CrossRef]

,13

13. S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]

17

17. Z. Hongying, C. Deying, L. Zhenzhong, F. Rongwei, and X. Yuanqin, “Numerical calculation of laser-induced collisional energy transfer in Ba-Sr system,” Acta Phys. Sin. 57, 7600–7605 (2008).

] have some similar features. The dipole-quadrupole Sr-Ca LICET line shape has larger tunable range than dipole-dipole Sr-Ca LICET spectrums [9

9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. 13(12), 972–978 (1977). [CrossRef]

].· The dipole-quadrupole profiles are strongly asymmetrical, i.e. in the antistatic wing on one side of the peak, the cross section falls rapidly; while in the quasi-static wing on the other side, the cross section is relatively large for a wide range of transfer laser detuning. Calculations show that the statistic distribution of the relative speed between two atoms has impacts on the collision cross section, indicating that it is necessary to consider this distribution in the calculations. The laser induced dipole-quadrupole collision spectrum shows the following features: (a) in the vicinity of the spectral profiles center the cross section at fixed laser detuning become smaller as the relative speed and system temperature increases; (b) the peak of the spectrum is shifted from the resonant frequency towards the antistatic region, with the shift increasing approximately linearly with laser intensity; (c) the spectral line shape becomes narrower and less asymmetric as the laser intensity increases; (d) the peak cross section tends to saturate with increasing laser intensity, and laser induced dipole-quadrupole collision cross section has a magnitude comparable to dipole-dipole collision cross section which indicates that dipole-quadrupole LICET process also can be the effective way to transfer energy selectively from a storage state of arbitrary parity to a target state of arbitrary parity.

References and links

1.

R. W. Falcone, R. W. Green, J. White, J. Young, and S. Harris, “Observation of laser-induced inelastic collisions,” Phys. Rev. A 15(3), 1333–1335 (1977). [CrossRef]

2.

A. Debarre, “High-resolution study of light-induced collisional energy transfer in Na-Ca mixture,” J. Phys. B 16(3), 431–436 (1983). [CrossRef]

3.

C. Brechnignac, Ph. Cahuzac, and P. E. Toschek, “High-resolution studies on laser-induced collisional-energy-transfer profiles,” Phys. Rev. A 21(6), 1969–1974 (1980). [CrossRef]

4.

F. Dorsch, S. Geltman, and P. E. Toschek, “Laser-induced collisional-energy transfer in thermal collisions of lithium and strontium,” Phys. Rev. A 37(7), 2441–2447 (1988). [CrossRef] [PubMed]

5.

B. Cheron and H. Lemery, “Observation of laser induced collisional energy transfer in a rubidium-potassium mixture,” Opt. Commun. 42(2), 109–112 (1982). [CrossRef]

6.

D. Z. Zhang, B. Nikolaus, and P. E. Toschek, Appl. Phys. B 28, 195 (1981).

7.

M. Matera, M. Mazzoni, R. Buffa, S. Cavalieri, and E. Arimondo, “Far-wing study of laser-induced collisional energy transfer,” Phys. Rev. A 36(3), 1471–1473 (1987). [CrossRef] [PubMed]

8.

S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]

9.

S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. 13(12), 972–978 (1977). [CrossRef]

10.

A. Gallagher and T. Holstein, “Collision-induced absorption in atomic electronic transitions,” Phys. Rev. A 16(6), 2413–2431 (1977). [CrossRef]

11.

A. Bambini and P. R. Berman, “Quasistatic wing behavior of collisional-radiative line profiles,” Phys. Rev. A 35(9), 3753–3757 (1987). [CrossRef] [PubMed]

12.

A. Agresti, P. R. Berman, A. Bambini, and A. Stefanel, “Analysis of the far-wing behavior in the spectrum of the light-induced collisional-energy-transfer process,” Phys. Rev. A 38(5), 2259–2273 (1988). [CrossRef] [PubMed]

13.

S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]

14.

A. Bambini and S. Geltman, “Theory of strong-field light-induced collisional energy transfer in Eu and Sr,” Phys. Rev. A 50(6), 5081–5091 (1994). [CrossRef] [PubMed]

15.

C. Deying, W. Qi, and M. Zuguang, “Four-level model of laser-induced collisional energy transfer,” Acta Opt. Sin. 16, 1653–1655 (1996).

16.

C. Deying, W. Qi, and M. Zuguang, “Numerical calculation of laser-induced collisional energy transfer in Eu-Sr,” Sci. China Ser. A 27, 449 (1997).

17.

Z. Hongying, C. Deying, L. Zhenzhong, F. Rongwei, and X. Yuanqin, “Numerical calculation of laser-induced collisional energy transfer in Ba-Sr system,” Acta Phys. Sin. 57, 7600–7605 (2008).

18.

W. R. Green, M. D. Wright, J. Lukasik, J. F. Young, and S. E. Harris, “Observation of a laser-induced dipole-quadrupole collision,” Opt. Lett. 4(9), 265–267 (1979). [CrossRef] [PubMed]

19.

J. C. White, “Observation of dipole - quadrupole radiative collisional fluorescence,” Opt. Lett. 5(6), 239–241 (1980). [CrossRef] [PubMed]

20.

J. O. Hirschfelder and W. J. Meath, “The nature of intermolecular forces,” Adv. Chem. Phys. 12, 1 (1967).

21.

M. E. Rose, “The Electrostatic Interaction of Two Arbitrary Charge Distributions,” J. Math. Phys. 37, 215–222 (1958).

22.

Z. H. C. Deying, L. Zhenzhong, X. Yuanqin, and F. Rongwei, “Impacts of Relative velocity distribution between two colliding atoms on laser-induced collisional energy transfer,” Chin. J. Lasers 35, 0077–0080 (2008).

23.

A. Bambini, M. Matera, A. Agresti, and M. Bianconi, “Strong-field effects on light-induced collisional energy transfer,” Phys. Rev. A 42(11), 6629–6640 (1990). [CrossRef] [PubMed]

OCIS Codes
(020.3690) Atomic and molecular physics : Line shapes and shifts
(190.0190) Nonlinear optics : Nonlinear optics

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: June 25, 2010
Revised Manuscript: September 8, 2010
Manuscript Accepted: September 8, 2010
Published: September 21, 2010

Citation
Zhenzhong Lu, Deying Chen, Yuanqin Xia, Rongwei Fan, and Hongying Zhang, "Calculations of laser induced dipole-quadrupole collisional energy transfer in Sr-Ca," Opt. Express 18, 21062-21073 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-21062


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References

  1. R. W. Falcone, R. W. Green, J. White, J. Young, and S. Harris, “Observation of laser-induced inelastic collisions,” Phys. Rev. A 15(3), 1333–1335 (1977). [CrossRef]
  2. A. Debarre, “High-resolution study of light-induced collisional energy transfer in Na-Ca mixture,” J. Phys. B 16(3), 431–436 (1983). [CrossRef]
  3. C. Brechnignac, Ph. Cahuzac, and P. E. Toschek, “High-resolution studies on laser-induced collisional-energy-transfer profiles,” Phys. Rev. A 21(6), 1969–1974 (1980). [CrossRef]
  4. F. Dorsch, S. Geltman, and P. E. Toschek, “Laser-induced collisional-energy transfer in thermal collisions of lithium and strontium,” Phys. Rev. A 37(7), 2441–2447 (1988). [CrossRef] [PubMed]
  5. B. Cheron and H. Lemery, “Observation of laser induced collisional energy transfer in a rubidium-potassium mixture,” Opt. Commun. 42(2), 109–112 (1982). [CrossRef]
  6. D. Z. Zhang, B. Nikolaus, and P. E. Toschek, Appl. Phys. B 28, 195 (1981).
  7. M. Matera, M. Mazzoni, R. Buffa, S. Cavalieri, and E. Arimondo, “Far-wing study of laser-induced collisional energy transfer,” Phys. Rev. A 36(3), 1471–1473 (1987). [CrossRef] [PubMed]
  8. S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]
  9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. 13(12), 972–978 (1977). [CrossRef]
  10. A. Gallagher and T. Holstein, “Collision-induced absorption in atomic electronic transitions,” Phys. Rev. A 16(6), 2413–2431 (1977). [CrossRef]
  11. A. Bambini and P. R. Berman, “Quasistatic wing behavior of collisional-radiative line profiles,” Phys. Rev. A 35(9), 3753–3757 (1987). [CrossRef] [PubMed]
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