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Chinese Physics B

Four-level model of ion—ion laser-induced collisional energy transfer and numerical calculations for Ca + —Sr + system

Deying Chen, Hongying Zhang, Fan Rong-Wei

Published May 1, 2010• 1 citation
Publisher

Abstract

The four-level model of laser-induced collisional energy transfer (LICET) for the ion–ion collision system is established based on the time-dependent Schrödinger equation for the electron dynamics, through which the equations of motion of the probability amplitudes and cross section of the collision system are obtained. Numerical calculations are performed for the Ca + –Sr + system, with the results showing that the peak of the LICET spectrum appears at a resonant frequency of the transfer laser. The magnitude of the obtained collision cross section is in the order of 10 −16 cm 2 , and is comparable to that obtained in atomic systems, which indicates the validity of the established four-level model.

DOI
10.1088/1674-1056/19/5/053402

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The four-level model of laser-induced collisional energy transfer (LICET) for the ion–ion collision system is established based on the time-dependent Schrödinger equation for the electron dynamics, through which the equations of motion of the probability amplitudes and cross section of the collision system are obtained. Numerical calculations are performed for the Ca + –Sr + system, with the results showing that the peak of the LICET spectrum appears at a resonant frequency of the transfer laser. The magnitude of the obtained collision cross section is in the order of 10 −16 cm 2 , and is comparable to that obtained in atomic systems, which indicates the validity of the established four-level model.
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(-13)cm(2) at a laser intensity of 8.29 × 10(9)W/cm(2) 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.
Based on the four-state model of laser-induced collisional energy transfer,the cross section of the collisional energy transfer in the Sr-Ca system is obtained.Various factors,including field intensity,relative speed,and temperature,which influence the collisional cross section,are discussed for illustrating the features of the Sr-Ca laser-induced collisional energy transfer(LICET) process.The calculated results show that the LICET spectral profiles obviously become narrower when the laser field intensity increases.The collision cross section rises with laser intensity and tends to saturate.In the vicinity of the spectral profile center,the cross section at fixed laser detuning becomes smaller as the relative speed and system temperature increase.The results indicate that the intermediate states strongly affect the spectral profile of LICET.
Based on the existing four-level model of laser-induced collisional energy transfer, the collision process in Ba-Sr system in both weak and strong fields is calculated by immediate integration of the equation of motion, and profiles of laser-induced transition probability and collision cross section under both conditions are obtained. Numerical results for the weak field are in fair to good agreement with former analytical results, while the ones for the strong field show that the effect of laser-induced collision is enhanced when the transfer laser intensity increases. Moreover, the peak of the laser-induced collisional energy transfer spectrum shows an evident shift from resonant frequency to the violet side in strong field, and full width at half maximum (i.e. tuning range) of the spectrum becomes obviously narrower compared with that in weak field.
A four-state model considering the relative velocity distribution function for calculating the cross section of laser-induced collisional energy transfer in a Sr—Li system is presented and profiles of laser-induced collision cross section are obtained. The resulting spectra obtained from different intermediate states are strongly asymmetrical in an opposite asymmetry. Both of the two intermediate states have contributions to the final state, and none of the intermediate states should be neglected. The peak of the laser-induced collisional energy transfer (LICET) profile shifts toward the red and the FWHM becomes narrower obviously with laser field intensity increasing. A cross section of 1.2 × 10−12 cm2 at a laser field intensity of 2.17 × 107 V/m is obtained, which indicates that this collision process can be an effective way to transfer energy selectively from a storage state to a target state. The existence of saturation for cross section with the increase of the laser intensity shows that the high-intensity redistribution of transition probabilities is an important feature of this process, which is not accounted for in a two-state treatment.
A laser induced quadrupole–quadrupole collisional energy transfer system of Xe–Kr is proposed, and the three-level laser induced collisional energy transfer (LICET) model is presented. Calculating results show that the peak of the LICET profile moves to the red and the FWHM becomes narrower, obviously with the laser field intensity increasing, while the resulting spectra is shifted in frequency toward the blue and the full width at half peak of the profile becomes larger as the relative velocity increases. The spectrum of the quadrupole–quadrupole LICET in the Xe–Kr system has a wider tunable range in an order of magnitude than the dipole–dipole LICET spectra. A cross section of 3.36×10−15 cm2 is obtained, which indicates that the quadrupole–quadrupole LICET process also can be an effective way to transfer energy selectively from a storage state to a target state.
We examine theoretically the behavior of cross sections for laser-induced collisional energy transfer (LICET) over a wide range of detunings and laser intensities for the two-atom pairs Li-Sr and Eu-Sr which have been previously studied experimentally. These two cases are complementary in that the laser and collisional interactions enter in opposite orders, and their level structures are such as to give weak-field line shapes of opposite asymmetry and intensity shift. A three-state model is used and the Bambini-Berman formula for the weak-field quasistatic wing is verified. At high intensities the peak cross section is found to go through a maximum and the LICET profile is found to become symmetric about a shifted center with notable departures from a uniform falloff in the far quasistatic wing, apparently arising from radiative collisional interference effects.