Collision Broadening of Spectral Lines

When an atom A with energy levels E. and E approaches another atom or molecule B, the energy levels of A are shifted because of the interaction between A and B. This shift depends on the electron configurations of A and B and on the distance R(A,B) between both collision partners, which, for definiteness, we define as the distance between the centers of mass of A and B. 

The energy shifts aE are in general different for the levels E. and Ej and they may be positive as well as negative. AE is positive if the interaction between A and B is repulsive and negative if it is attractive. When plotting the energy E(R) for the different energy levels as a function of the interatomic distance R the potential curves of Fig.3.8 are obtained. 

This mututal interaction of both partners at distances R 1 R is called a oottision and 2R is the collision diametev. If no internal energy of the collision partners is transferred during the collision by nonradiative tran- 

V = 5x 10 m/s, = 1 nm = 2 x lo s. During this time the electronic charge distribution generally follows the perturbation adiabatically , which justifies the potential curve model of Fig.3.8. 

If atom A undergoes a radiative transition between levels E. and E during the collision time, the frequency of absorbed or emitted radiation, satisfying 

At thermal velocities of v = S-IO m/s, and a typical collision radius of R,. = 1 nm we obtain the collision time s. During this time the 

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To consider gas molecules as isolated from interactions with their neighbors is often a useless approximation. When the gas has finite pressure, the molecules do in fact collide. When natural and collision broadening effects are combined, the line shape that results is also a lorentzian, but with a modified half-width at half maximum (HWHM). Twice the reciprocal of the mean time between collisions must be added to the sum of the natural lifetime reciprocals to obtain the new half-width. We may summarize by writing the probability per unit frequency of a transition at a frequency v for the combined natural and collision broadening of spectral lines for a gas under pressure ... 

Radiofrequency Spectroscopy of Stored Ions II Spectroscopy, FI. G. Dehmelt The Spectra of Molecular Solids, O. Schnepp The Meaning of Collision Broadening of Spectral Lines The Classical Oscillator Analog, A. Ben-Reuven The Calculation of Atomic Transition Probabilities, R. J. S. Crossley Tables of One- and Two-Particle Coefficients of Fractional Parentage for Configurations s s u Pq> U D. H. Chisholm, A. Dalgamo, and E. R. Innes... 

W.R. Hindmarsh, J.M. Farr Collision broadening of spectral lines by neutral atoms . In Progr. Quantum Electronics, Vol. 2, Part 4, ed. by J.H. Sanders, S. Stenholm (Pergamon, Oxford 1973)... 

In our account here we neglect a third aspect of a spectral line, specifically its shape, beyond its characteristic frequency and strength. A natural line shape is almost impracticable to observe and would yield on analysis little or no additional information about intrinsic molecular properties. Another shape merely reflects components of molecular velocities in a direction parallel to the direction of propagation. Apart from these effects, further broadening of spectral lines due to finite durations, between collisions, of molecules in particular quantum states is attributed to interactions between colliding molecules rather than directly to... 

Lamb dip spectroscopy provides a very sensitive tool for studying small frequency shifts and broadening of spectral lines which normally would be undetectable because they may be small compared to the doppler width. These investigations yield information about collisions at low pressures, where the effect of far distant collisions is not suppressed by the more effective close collisions. This allows the potential between the collision partners at large intermolecular distances to be examined. 

In Section 3.3 we discussed how elastic and inelastic collisions contribute to the broadening of spectral lines. In a semi classical model, where the colliding particles travel along definite paths, an impact parameter b can be defined (see Fig.12.1) and the collisions may be classified as soft collisions (impact parameter b large compared to the minimum location r of the interaction potential) and hard collisions (bsoft collisions probe the... 

In Vol. 1, Sect. 3.3. we discussed how elastic and inelastic collisions contribute to the broadening and shifts of spectral lines. In a semiclassical model of a collision between partners A and B, the particle B travels along a definite path r(t) in a coordinate system with its origin at the location of A. The path r t) is completely determined by the initial conditions r(0) and (dr/df)o and by the interaction potential V(r, Ex, E-b), which may depend on the internal energies Ex and b of the collision partners. In most models a spherically symmetric potential V r) is assumed, which may have a minimum at r = ro (Fig. 8.1). If the impact parameter b is large compared to tq the collision is classified as a soft collision, while for b hard collisions occur. 

In Sect. 3.3. we discussed how elastic and inelastic collisions contribute to the broadening and shifts of spectral lines. In a semiclassical model of a collision between partners A and B, the particle B travels along a definite path r t) in a coordinate system with its origin at the location of A. The path r t) is... 

It is important to realize that the relaxation times might depend on some factors that are properties of the atom or molecule itself and on others that are related to its environment. Thus rotational spectra of gases have linewidths (related to the rotational relaxation times) that depend on the mean times between coUisions for the molecules, which in turn depend on the gas pressure. In liquids, the collision lifetimes are much shorter, and so rotational energy is effectively non-quantized. On the other hand, if the probability of collisions is reduced, as in a molecular beam, we can increase the relaxation time, reduce linewidths, and so improve resolution. Of course, the relaxation time only defines a minimum width of spectral lines, which may be broadened by other experimental factors. 

Homogeneous broadening. The Doppler width of spectral lines decreases as we go from the visible into the infrared region of the spectrum and eventually the line profile will be dominated by collision or natural broadening. 

Spectral lines are fiirther broadened by collisions. To a first approximation, collisions can be drought of as just reducing the lifetime of the excited state. For example, collisions of molecules will connnonly change the rotational state. That will reduce the lifetime of a given state. Even if die state is not changed, the collision will cause a phase shift in the light wave being absorbed or emitted and that will have a similar effect. The line shapes of collisionally broadened lines are similar to the natural line shape of equation (B1.1.20) with a lifetime related to the mean time between collisions. The details will depend on the nature of the intemrolecular forces. We will not pursue the subject fiirther here. 

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