LASER ASSISTED CHARGE EXCHANGE IN ATOMIC COLLISIONS

We present total charge exchange cross sections for collisions of Li(ls22s 2S) with H(ls) in presence of a linear polarized laser field of intensity 0.05 < < TW/cm and wavelength 5 103 < Z < 14 103/,. Our calculation shows that the laser field can increase the cross section of this reaction by a factor of ten at impact energies E < 0.1 keV/a.m.u. The mechanism of this process is discussed and it is shown that both atomic and molecular radiative transitions can take place depending on the laser wavelength employed.

In previous papers, we have suggested that cross sections of charge exchange processes in ion-atom collisions can be increased by inducing radiative transitions between the electronic states of the quasimolecule formed during the collision.Besides that, the presence of the radiation field permits the modification of the cross section by varying two new parameters, intensity and wavelength.This additional freedom makes these processes more selective for diagnosis purposes in fusion plasmas, specially in cold regions of the reactor where the cross sections of the field-free reactions are small.
At the collision velocities considered in this work (v > 0.02 a.u.), previous calculations have shown that high (although technically accessible2) laser intensities (I 0.1 TW/cm 2) are needed to achieve a sizeable effect on the cross sections.The consequence of this requirement is that only a few experiments 3 have reported cross sections showing the effect of quasimolecular radiative transitions in ion (atom)-atom collisions.
In the present work we have calculated total cross sections for the charge exchange process" Li(lsa2s 2S) --H(ls) + he0 Li + + H- (1) which has been predicted 4 to be notably enhanced by the effect of the electromagnetic field.It is known, 5 that reaction (1) takes place in absence of external fields through non-adiabatic transitions taking place in the (ionic-covalent type) avoided crossings between the electronic molecular states.In this work we have considered the modification of these transitions by a laser frequency that is resonant with the molecular energy splitting at the avoided crossing region.Radiative transitions in pseudocrossings were previously considered 6 in the OH 8+ quasimolecule.Our calculation showed that the dynamical effect of the sharp peak of the transition dipole moment is cancelled by the Stark shift of the molecular levels in the avoided crossing region.However investigation is needed to know if these conclusions also hold for wider avoided crossings such as those arising in the LiH correlation diagram.
At the laser intensities considered in the present work, a semiclassical description of the laser is appropriate.In this application we have assumed that the field is monochromatic and linearly polarized.We have also employed a semiclassical description of the collision in which the nuclei follow rectilinear trajectories with impact parameter b and velocity v, while the electronic motion is described quantum- mechanically through a wavefunction p(r, t), solution of the semiclassical equation: with H given by H Hel + Hint (3) where Hel is the electronic Hamiltonian in the Born-Oppenheimer approximation and Hint is the Hamiltonian describing the interaction between the electromagnetic field and the colliding system.In the dipole approximation we have" Hint-" E .ri (4)   where the sum extends over the number of electrons and cos (cot + q) We employ a molecular expansion for p, in which it is developed in the basis of (approximate) eigenfunctions of Hel, b: (r, t) , a(t) c(r, R) exp E dt' (6)   where E is the electronic energy of the molecular state 2. Substitution of expression (6) in (2) yields the set of differential equations: )exp -i (E-E/)dt' (7)   Transition probabilities and cross sections are obtained from the coefficients a(t) that are a solution of (7).Inspection of (7) shows that non-adiabatic transitions take place through both radiative (due to Hint) and non-radiative (due to O/Ot) couplings.In practice, a perturbative solution 7 of ( 7) is usually carried out.In this approxi- mation dynamical couplings are also neglected.A great advantage of the perturba- tive approximation is that it permits 8 to obtain a simple expression of the average of the cross section over the orientation of the quasimolecule formed during the collision relative to the direction of polarization of the laser.However, as it will be discussed below, a simple perturbative approach is not adequate for the present calculation.This implies that the system (7) must be solved for each direction of polarization of the laser.In this calculation we have assumed that the laser propa- gates in the Y direction of the laboratory frame of reference.This direction corresponds to an electric field in the Z direction, which is expected to yield the largest radiative transitions.
We have employed a basis set of five molecular states (four 1E and one lI-I).The energies of these states 5 are shown in Figure 1.The entrance channel of reaction (1) is a statistical mixture of lie and 132 (not shown in Figure 1).However, since only one singlet state dissociates in Li + + H-, in absence of spin-orbit coupling, only the singlet subsystem is needed to treat reaction (1).
The mechanism of the charge exchange process involves a transition between the two first 12 states.As the relative nuclear velocity decreases, the effectiveness of dynamical couplings diminishes, and the lie 21E transition will take place mainly through radiative transitions.We have selected a range of values of the laser wavelength (5 103 < A < 14 103/) such that radiative transitions from the entrance channel lie to states 31E and 4]2 are negligible, therefore the state 41E, which correlates diabatically to Li + + H-, is populated through an indirect mechanism involving non-radiative transitions in the avoided crossings 2 E 31E and 31E 4-E.
A practical consequence of this mechanism, which involves both radiative and non-radiative couplings, is that a perturbative approximation is not adequate for the present calculation.
We show in Figure 2 the transition dipole moments that are relevant to the mechanism proposed.One can notice that the transition dipole moments ( 1 1E It[2 1E } and ( 11E Itl 1 I-I > do not vanish asymptotically.To see the implications of this fact, we have solved (7) assuming that the colliding system is described initially by the atomic state Li(lsa2s as).We have found that even for laser frequencies not   R (a. u.) Figure 2 Modulus of transition dipole moments as functions of the internuclear distance" kl aEI/I2 E)I" )[(1 1111 117)1"( )1(2 1111 11-I)1.
satisfying the resonance condition in the atomic limit (o 0.07 a.u.), the coefficients a(t) oscillate indefinitely reflecting the inadequacy of this approximate initial condition.To overcome this difficulty, we have solved the system (7) assuming that the Li atom is described initially by a linear combination of Li(1sZ2s 2S) and Li(1s22s 2p) atomic states, an atomic "dressed" state, 9 formed by interaction with the laser field.Physically this initial condition implies that the time of interaction of the Li atom with the field is longer than the time of interaction with the H atom.In practice we have assumed that the system is initially described for the dressed state with a larger contribution of the atomic state Li(lsZ2s 2S).To implement the new initial condition, we have transformed the molecular basis set to obtain a set of wavefunctions which dissociate in the atomic dressed states.The new basis set is formed by the following functions: ql a ci + q12 exp (-iElt) + c (cos 0 22 "}-sin0 (jl l-I) exp (-iE2t) )2 d 1 )12 exp (-iEt) + c2 (cos 0 (])22 --sin0 q)a ri) exp (-iE2t) q)3 a (--sin0 (])22 q-cos 0 1 1-i) exp (-iE2t) )5 d-" )4Z (8)  where the coefficients c + are those defining the dressed states, 9 E1,2 are the energies of the atomic states Li(1sZ2s) and Li(1sZ2p), and sin0 b/R, cos0 vt/R are the elements of the matrix that asymptotically transforms molecular wavefunctions into non-rotating ones.Substitution of the new expansion in (2) yields an alternative set of differential equations.Charge exchange cross sections are obtained in our basis set from the coefficient of s.
Charge exchange cross sections are presented in Figures 3 and 4 as functions of laser wavelength and impact energy.It must be noted that, since the coefficients are oscillating functions of t, the calculated cross section depends on the choice of the time origin.As a consequence, the cross section oscillates as a function of the phase of the field q (values given in Figures 3 and 4 are for q 0).The amplitude of this oscillation is about one third of the cross section mean value.
The calculated cross section (Figure 3) shows two maxima as a function of the laser wavelength.The first maximum at Z 9700A appears at a laser frequency that corresponds to the Li(ls:2p) Li(lsa2s) energy difference, and this peak is due to an enhancement of the cross section due to radiative transitions taking place in the Li atom before entering in the collision region.The second maximum appears at 6600, which corresponds to the 21E IE energy difference at R 7 Bohr, and may be ascribed to quasimolecular radiative transitions in the vicinity of the 212--lE avoided crossing, which in contrast with previous findings are not 0.01 ' " " , , ., , ' ' ' " " ' , , ,  E (geV/a.m.u) Figure 4 Charge exchange total cross section as a function of the impact energy for two laser wavelengths: ), 9700/; ) 7115 and laser intensity 0.1T w/cm2.Field-free charge exchange total cross sections.
completely cancelled out by the diagonal Stark terms.A similar behaviour has been found for other values of the impact energy and laser intensity.
In Figure 4 we present the dependence of the charge exchange cross section with the impact energy.It can be noted that the cross section is enhanced in the region of impact energies E < 0.1 keV/a.m.u, where dynamical transitions cease to be effective.Quantal calculations at lower velocities, where the effect of radiative transitions can be more pronounced, are underway.

Figure 1
Figure 1 Electronic energies of the states E and H of LiH.
Figure 1 Electronic energies of the states E and H of LiH.

Figure 3
Figure 3 Charge exchange total cross section as a function of the laser wavelength for two impact energies: