Drake G.W.F. (editor) Handbook of Atomic, Molecular, and Optical Physics

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972 Part E Scattering Experiment

–4

–7

–6

Liquid nitrogen feedline

–9

–10

–11

–4

beam source

Heater

Skimmer

Turning fork chopper

Synchronous motor

Cross-correlation chopper

Ultrahigh vacuum

differentially pumped

mass spectrometer

detector

Cold trapVelocity sector

Effusive F atom source

Fig. 66.1 Experimental arrangement for F+ D

→ DF+F reactive scattering. Pressure (in torr) indicated in each re-

gion. Components are (1) effusive F atom source; (2) velocity selector; (3) cold trap; (4) D

beam source; (5) heater;

(6) liquid nitrogen feedline; (7) skimmer; (8) tuning fork chopper; (9) synchronous motor; (10) cross-correlation chopper;

(11) ultrahigh vacuum differentially pumped mass spectrometer detector

traction and the detector moved to record the integrated

signal at each laboratory angle.

Two kinds of measurements are typically made in

these experiments: time-of-ﬂight spectra and angular

distributions. Usually one is interested in obtaining the

complete product-ﬂux vs. velocity contour map, since

this contains full details of the scattering process. This

is obtained by measuring a full angular distribution

as well as time-of-ﬂight data at many laboratory an-

gles. The results are then simulated using a forward

convolution ﬁtting procedure to obtain the underlying

contour map [66.41–43]. Because scattering of isotropic

reagents exhibits cylindricalsymmetry about the relative

velocity vector, it is sufﬁcient to measure products scat-

tered in any plane containing this vector to determine

the product distribution. This is not true for structured

particles (e.g. involving atoms in P states); however, this

azimuthal anisotropy has been used to explorethe impact

parameter dependence of the reaction dynamics [66.44].

In a typical reactive scattering experiment, A+

BC → AB+C, either of the two products may be de-

tected. Conservation of linear momentum requires that

the cm frame momenta of the two products must sum

to zero. It is thus only necessary to obtain the contour

map for one of the products. The choice of detected

product is usually dictated by kinematic considera-

tions, although one may choose to detect a product

that is kinematically disfavored if its partner happens

to have a mass with a large natural background in the

detector. Kinematic considerations can be critical in

assessing the suitability of a given system for study.

It is very important that one of the products be scat-

tered entirely within the viewing range of the detector

in order to obtain a complete picture of the reaction

dynamics.

The advantages of crossed-beams employed in

conjunction with an electron impact ionizer-mass spec-

trometer detector derive primarily from the universality

of the detector. No spectroscopic information is required

and there are no invisible channels, such as may occur

with spectroscopic detection methods. In addition, the

resolution of these machines may be increased almost

arbitrarily; indeed, even rotationally inelastic scattering

has been studied [66.45]. The disadvantages are comple-

mentary to the advantages: the universal detector implies

that quantum state resolution is not achieved directly, al-

Part E 66.2

Reactive Scattering 66.2 Experimental Conﬁgurations 973

though in favorable cases the product vibrational states

may be resolved in the translational energy distribu-

tions [66.21, 46]. In addition, if the product of interest

represents a mass that receives interference from one

of the beam masses, background interference may be

problematic. Kinematic considerations mentioned above

may also preclude study of certain systems. However,

the kinematic requirements for the Doppler and imaging

approach discussed below are complementary to those

of the rotatable-detector conﬁguration.

66.2.2 Doppler Techniques

Spectroscopic detection methods in crossed-beam ex-

periments allows the measurement of state-resolved

differential cross sections, and thus the ultimate level of

insight into the reaction dynamics. A method developed

by Kinsey and others [66.47,48] determines differential

cross sections by measurement of product Doppler pro-

ﬁles using LIF (called ADDS for Angular Distribution

by Doppler Spectroscopy). For a laser directed parallel

to the relative velocity vector, a particle scattered with

a cm velocity of u perceives the photon as having the

Doppler shifted frequency



= ν



1−(u+V

) ·

n/c



, (66.17)

where ν is the laser frequency and V

is the velocity

of the center of mass, both in the laboratory frame of

refernce, and

n is the unit vector in the probe laser di-

rection. For the case of a single possible recoil speed,

one may obtain the full differential cross section directly

in the cm frame by reconstruction of a single Doppler

proﬁle [66.47]. In this case, the angular resolution is

a maximum for the sideways scattered products, and

a minimum at the poles. An alternative approach is to

measure the Doppler proﬁle with a laser perpendicular to

the relative velocity vector. This approach (PADDS for

Perpendicular ADDS) affords complementary angular

resolution, but folds the forward and backward scattered

products into a single symmetric component [66.48].

For the case in which the detected product does not

possess a known recoil speed (for example if the ther-

modynamics of the process is not known,or if one probes

the atomic fragment in an A+ BC → AB+C reaction),

a single Doppler proﬁle is insufﬁcient to reconstruct the

double differential cross sections. Nevertheless, Kin-

sey’s earliest experimental results were for one such

example: the reaction H+NO

→ OH+NO [66.49].

More recently Mestdagh et al. [66.50] have studied

electronically inelastic collision processes using this ap-

proach by measuring the Doppler proﬁles over a range

of probe laser angles, as illustrated in Fig. 66.2. A beam

of barium atoms is crossed at 90 degrees by a beam

of some molecular perturber. At the interaction region,

the barium atoms are electronically excited using a nar-

row band dye laser. Scattered barium atoms that have

undergone a speciﬁc electronic transition as a result of

the collision are probed at the interaction region using

a second dye laser, which is scanned across the Doppler

proﬁle. The product-ﬂux vs. velocity contour map is

then reconstructed by means of a forward convolution

simulation procedure analogous to that described in the

preceding section.

In addition to state-resolved detection, another dif-

ference between the Doppler methods and the traditional

crossed-beam conﬁguration is that the kinematic consid-

erations favor detection of fast particles, and almost any

system that is spectroscopically suitable may be con-

sidered. The primary disadvantage of Doppler methods

is the limited angular and translational energy resolu-

tion possible. Often, however, modest angular resolution

is sufﬁcient to achieve a global picture of the reaction

dynamics. Much current work involves the study of pho-

toinitiated reactions in cells, relying on the short excited

state lifetimes to guarantee single collision conditions,

and using iterative ﬁtting procedures to probe product

velocity distributions and angular momentum polariza-

tion [66.14]. Angular momentum polarization can have

a profound effect on the measured distributions and can

afford a powerful additional means of exploring the col-

lision dynamics. Examples of 3- and 4-vector correlation

experiments approach a “complete description” of the

scattering process (Chapt. 46) [66.50–52].

66.2.3 Product Imaging

Another spectroscopic technique is based on direct

imaging of the scattered product distribution. The tech-

nique was ﬁrst used to record state-resolved angular

distributions of methyl radicals from the photodissoci-

ation of methyl iodide [66.53]. The method has since

been widely employed to study photodissociation, and

more recently to record state-resolved inelastic scatter-

ing in a crossed-beam experiment [66.54]. Recently it

has been applied to a crossed-beam reactive scattering

system [66.55]. The crossed-beam conﬁguration used

by Houston and coworkers is shown schematically in

Fig. 66.3. The two skimmed supersonic beams cross at

right angles, and scattered products are state-selectively

ionized on the axis of a time-of-ﬂight mass spectrom-

eter using resonant photoionization. The ion cloud thus

formed continues to expand with its nascent recoil vel-

Part E 66.2

974 Part E Scattering Experiment

0.5 m

Scale

Mass spectrometer

Time-of-flight arm

Pilot tube

Chopper

Atomic beam

Oven for effusive beam

Collision zone

Molecular beam source

Laser beam

Single mode optical fiber

Collection optics

Fig. 66.2 Schematic view of crossed molecular beam apparatus with LIF-Doppler detection

ocity as it drifts through the ﬂight tube. The ions then

strike a microchannel plate coupled to a phosphor screen.

The latter is viewed by a video camera gated to record

the signal at the mass of interest. The images are thus

two-dimensional projections of the nascent three dimen-

sional product distributions.

Video camera

Phosphor screen

Pulsed nozzle

NO/He beam

Skimmers

Probe laser

Ar beam

Flight tube

MCP

Pulsed

nozzle

Fig. 66.3 Schematic view of crossed molecular beam ap-

paratus with product imaging detection

There now exist two alternatives for regenerating

the three dimensional distribution from the projection.

The ﬁrst, a tomographic reconstruction using an in-

verse Abel transform, is widely used in photodissciation

studies [66.56,57]. It is a direct inversion procedure fea-

sible for cases in which the image is the projection of

a cylindrically symmetric object, with its axis of sym-

metry parallel to the image plane. This analysis yields

a unique product contour map directly from the image,

but it is difﬁcult to incorporate apparatus functions, and

is sensitive to noise in the data. The second alterna-

tive is a forward convolution ﬁtting method. A Monte

Carlo based simulation has the advantage that one may

treat the averaging over experimental parameters quite

rigorously.

The advantages of the imaging method again de-

rive from its reliance on a spectroscopic probe, so that

quantum state resolution is possible and background

interference may be avoided. In addition, it possesses

a multiplexing advantage since the velocity distribution

is recorded for all angles simultaneously. Imaging re-

lies exclusively on photoionization, unlike the Doppler

methods which may use either photoionization or LIF.

This is somewhat disadvantageous since the available

photoionization schemes are limited and often high laser

Part E 66.2

Reactive Scattering 66.2 Experimental Conﬁgurations 975

power is necessary to achieve adequate signal intensity.

As a result, background ions can be a problem. In gen-

eral, resonantly enhanced two-photon ionization, i. e.

[1+1], detection schemes are thus preferable.

66.2.4 Laboratory to Center-of-Mass

Transformation

Angular and velocity distributions measured in the

laboratory frame must be transformed to the cm frame

for theoretical interpretation. Accounts of this transfor-

mation and details concerning the material presented

below may be found in [66.58–61], among others. The

Newton diagram is useful to aid in visualizing the

transformation, and in understanding the kinematics of

a given collision system. For the scattering of F+D

for

example, shown in Fig. 66.4, a beam of ﬂuorine atoms

with a velocity v

is crossed by a beam of D

, velocity

, at 90 degrees. The relative velocity between the two

reactants is g =v

−v

, and the velocity of the cm of

the entire system is

. (66.18)

divides the g into two segments corresponding to

the cm velocities of the two reagents. The magnitude

of these vectors, u

and u

are inversely propor-

tional to the respective masses. If scattered DF products

are formed with a laboratory scattering angle Θ and

a laboratory velocity v

asshowninFig.66.4,this

corresponds to DF backscattered with respect to the in-

cident F atom, in the cm system. It is common to refer

the scattering frame direction to the atomic reagent in an

A+BC → AB+C reaction, for example, to make clear

the dynamics of the process. In this case the backscat-

tered DF arises as a result of a direct rebound collision.

Some useful kinematic quantities are summarized here.

For beams A and BC intersecting at 90 degrees, the an-

v = 1

v = 2

v = 3

Fig. 66.4 Newton diagram for collision of F with H

with

superimposed c.m. ﬂux vs. velocity contour map

gle of the cm velocity vector with respect to A is given

= arctan

. (66.19)

For an arbitrary Newton diagram with angle α between

the two beams the magnitude of the relative velocity is

= v

−2v

cos α, (66.20)

the relative velocity vector is

g = v

−v

, (66.21)

and the collision energy is

coll

, (66.22)

where µ

is the reduced mass of the initial collision

system. The magnitude of the cm frame velocity of

particle A before collision is

g . (66.23)

The ﬁnal relative velocity is



= v

−v

, (66.24)

with magnitude





avail

/µ

, (66.25)

where the available energy E

avail

= E

coll

int,reac

exo

−E

int,prod

(66.26)

in which E

int,reac

is the internal energy of the reactants,

exo

is the exoergicity of the reaction, and E

int,prod

the internal energy of the products.

One must transform the laboratory intensity

I(Ω) ≡ d

σ/ d

Ω into I(ω)



≡ d

σ/ d



,thecor-

responding cm quantity. For the crossed-beam con-

ﬁguration described in Sect. 66.2.1, the laboratory

distributions are distorted by a transformation Jacobian

that arises because the laboratory detector views differ-

ent cm frame solid angles depending on the scattering

angle and recoil velocity. For the spectroscopic experi-

ments described in Sects. 66.2.2 and 66.2.3, the Jacobian

is unity (the cm velocity represents a simple frequency

offset of the Doppler proﬁles, for example); however,

the transformation of the scattering distributions from

the recorded quantities (2-dimensional projections or

intensity vs. wavelength) to recoil velocity distributions

may be complex. Two cases must be considered for the

Part E 66.2

976 Part E Scattering Experiment

conﬁguration discussed in Sect. 66.2.1: one in which dis-

crete velocities result (such as elastic or state-resolved

scattering experiments), and one in which continuous

ﬁnal velocities are measured. For the ﬁrst case, the

laboratory and cm differential cross sections are inde-

pendent of the respective product velocities v and u and

these quantities are related by

Ω

= J

(66.27)

so that the transformation Jacobian is given by

J =

Ω

(66.28)

For discrete recoil velocities, the cm solid angle is

ω =

, (66.29)

where dA is a surface element of the product Newton

sphere. The laboratory solid angle corresponding to this

quantity is

Ω =

cos(u, v)

dA , (66.30)

so that the Jacobian for the ﬁrst case is given by

J =

cos(u, v)

(66.31)

For the case of continuous ﬁnal velocities, the σ are

velocity-dependent and are related by

Ω dv

= J

ω du

(66.32)

so that here the Jacobian is given by

J =

ω du

Ω dv

(66.33)

In this case we consider a recoil volume element dτ

(in velocity space), which must be the same in both

coordinate frames:

dτ

= u

du d

ω = dτ

lab

= v

dv d

Ω, (66.34)

so that the Jacobian is

J = v

. (66.35)

The laboratory intensity is then related to that in the cm

frame by

lab

(v, Θ) = (v

) I

(θ, u). (66.36)

Fora mass spectrometer detector with electron bombard-

ment ionizer, one measures number density of particles

rather than ﬂux, so that the recorded signal is given by

lab

(v, Θ) =

lab

(v, Θ)

(u,θ). (66.37)

The usual ﬂux vs. velocity contour map is a po-

lar plot of the quantity I

(u,θ). The product velocity

distributions are then

I(u) =



I(θ, u) sin θ dθ dφ

= 2π



I(u,θ)sin θ dθ, (66.38)

and the translational energy distributions are

I(E

) = I(u)



(66.39)

66.3 Elastic and Inelastic Scattering

When particles collide, they may exchange energy or

recouple it into different modes, they may change their

direction of motion, and they may even change their

identity. The study of these processes reveals a great

deal of information about the forces acting between the

particles and their internal structure. It is useful to begin

with a summary of the dominant features of elastic and

inelastic scattering.

66.3.1 The Differential Cross Section

Figure 66.5 illustrates the relation between the deﬂec-

tion function χ and the impact parameter b for a realistic

potential containing an attractive well and a repulsive

core. For large b there is no interaction, hence no de-

ﬂection. At smaller values of b, the attractive part of

the potential is experienced and some positive deﬂec-

tion results. At a smaller value of b, b

, the inﬂuence

of the attractive component of the potential reaches

a maximum, giving the greatest positive deﬂection:

this is the rainbow angle by analogy with the optic-

al phenomenon. There is another value of the b for

which point the attractive and repulsive parts of the

potential balance, yielding no net deﬂection. This is

the glory impact parameter b

. For yet smaller val-

ues of b, the interaction is dominated by the repulsive

core and rebound scattering gives a negative deﬂection

function.

Part E 66.3

Reactive Scattering 66.3 Elastic and Inelastic Scattering 977

–0+

Fig. 66.5 Schematic diagram showing the relation between

impact parameter b and deﬂection function χ

The important expressions related to the differential

cross section are summarized here [66.62]. For scatter-

ing involving an isotropic potential, the deﬂection angle

is Θ =|χ|. The differential cross section dσ gives the

rate of all collisions leading to deﬂection angles in the

solid angle element dω:

dN(θ)

∝ I(θ) dω = I(θ)2π sin(θ) dθ.

(66.40)

The incremental cross section is dσ = I(θ) dω =

2πb db,so

I(θ) =

sin θ(dθ/db)

(66.41)

For classical particles, the relation between the deﬂec-

tion function and the potential is

χ = π −2b

∞





1−

V(R)

−



−1/2

(66.42)

where V(R) is the potential as a function of interparticle

distance R, R

is the turning point of the collision, and

the collision energy.

In the high energy limit, for large b ≈ R

χ(b, E

) ∝ V(b)/E

. (66.43)

For a long-range potential V(R) proportional to R

−s

2/s

2(1+1/s)

I(θ) = const . (66.44)

For a potential exhibiting a minimum, the rainbow an-

gle θ

is proportional to the collision energy, and clearly

resolvedwhen the collision energy is 3 to 5 times the well

depth. In addition, supernumery rainbows and quantum

mechanical “fast osillations” occur in the dσ,andthese

provide a sensitive probe of the interaction. Accurate in-

teratomic potentials are routinely obtained from elastic

scattering experiments [66.60,63].

66.3.2 Rotationally Inelastic Scattering

Classical scattering involving an anisotropic potential

results in another rainbow phenomenon, distinct from

that seen in pure elastic scattering and notable in that it

does not require an attractive component in the poten-

tial. These rotational rainbows are equivalently seen in

a plot of integral cross section against change in rota-

tional angular momentum ∆ j, or in the differential cross

section for a particular value of ∆ j. The rotational rain-

bow peaks arise from the range of possible orientation

angles γ in a collision involving an anisotropic potential.

When there is a minimum in dγ/ dθ for a given ∆ j,the

differential cross section reaches a maximum [66.64].

The rotational rainbow peak occurs at the most forward

classically allowed value of the scattering angle, and dσ

drops rapidly at smaller angles. The rainbow moves to

more backward angles with increasing ∆ j because the

larger j-changing collisions require greater momentum

transfer, hence must arise from lower impact parameter

collisions. For heteronuclear molecules, two rainbow

peaks may be observed, corresponding to scattering off

either side of the molecule. One can relate the location

of the rainbow peak to the shape of the potential using

a classical hard ellipsoid model [66.65]:

A− B =



2sin



r,cl



−1

, (66.45)

where j is the rotational angular momentum, p

is the

inital linear momentum, θ

r,cl

is the classical rainbow po-

sition, and A and B are the semimajor and semiminor

axes of a hard ellipse potential. The classical rainbow

positions occur somewhat behind the quantum mechan-

ical and experimental rainbow positions, so the classical

rainbow may be estimated as the point at which the

peak has fallen to 44% of the experimental value. Real

molecular potentials may be far from ellipsoids, how-

ever, so detailed quantitative insight into the potential

requires a comparison of scattering data with trajectory

calculations.

66.3.3 Vibrationally Inelastic Scattering

There has been no direct observation of the differential

cross section of T–V or V–T energy transfer involving

neutral molecules owing to the small cross sections for

Part E 66.3

978 Part E Scattering Experiment

these processes. Integral cross section data are available,

however. Above threshold, the latter has shown a lin-

ear dependence of σ on collision energy for ∆ν = 1,

quadratic for ∆ν = 2 and cubic for ∆ν = 3 [66.66].

In addition, a great deal of information on vibrational

relaxation processes has been obtained in cell experi-

ments [66.67].

66.3.4 Electronically Inelastic Scattering

A wealth of information is available on electroni-

cally inelastic scattering systems, since these in general

exhibit much larger cross sections than V–T pro-

cesses [66.68, 69]. In addition, spectroscopic methods

may be used to overcome some of the background prob-

lems that hamper the study of the latter. Often, quenching

of electronically excited states involves curve crossing

mechanisms, so that very effective coupling of electronic

to vibrational energy may occur. Spin-orbit changing

collisions of Ba





with O

or NO, for example, occur

by a near-resonant process and result in almost complete

conversion of electronic energy to vibrational excitation

of the product [66.70]. The analogous collisions with

and H

, however, reveal very repulsive energy re-

lease with little concomitant vibrational excitation. Both

processes likely occur via curve crossings of the rele-

vant electronic states, but the near-resonant mechanism

occurs by way of an ionic intermediate.

66.4 Reactive Scattering

Reactive differential cross sections reveal several dis-

tinct aspects of the chemical encounter. The angular

distributions themselves may be used to infer the life-

time of the collision intermediate: long-lived complexes

exhibit forward-backward symmetry along the relative

velocity vector. In this case “long-lived” means on the

order of several rotational periods. The rotational period

of the complex may thus be used as a clock to study the

energy dependence of the intermediate’s lifetime. The

angular distributions further reveal the relation of initial

and ﬁnal orbital angular momentum. Sharply peaked an-

gular distributions generally indicate strongly correlated

initial and ﬁnal orbital angular momentum vectors. Fi-

nally, the product translational energy release contains

the details of the energy disposal, and reveals a wealth

of information about the thermodynamics of the pro-

cess, the existence of barriers, and sometimes even the

geometry of the transition state. Together, the angular

and tranlational energy distributions reveal many of the

details of the potential energy surface.

The dynamics of reactive collisions fall broadly

into three main categories characterized by distinct an-

gular and energy distributions. The three categories

are harpoon/stripping reactions, rebound reactions, and

long-lived complex formation. Some reactions may ex-

hibit more than one of these mechanisms at once, or

the dynamics may change from one to another as the

collision energy is varied.

66.4.1 Harpoon and Stripping Reactions

It was known in the 1930s that collisions of alkali

atoms with halogen molecules exhibit very large cross

sections and yield highly excited alkali halide prod-

ucts. These observations were accounted for by the

harpoon mechanism proposed by M. Polanyi. Because

alkali atoms have low ionization potentials and halo-

gen molecules large electron afﬁnities, as the alkali

atom approaches the molecule, electron transfer may

occur at long range. These processes are considered

in detail in Chapt. 49 [66.71, 72]. The harpooning dis-

tance R

at which this curve crossing takes place

may be estimated simply as the distance at which

the Coulomb attraction of the ion pair is sufﬁcient

to compensate for the endoergicity of the electron

transfer:

= e

/(I

− A

), (66.46)

where I

and A

represent the ionization potential and

electron afﬁnity of the electron donor and recipient,

respectively. For R in Å and E in eV, this relation is

= 14.4/(I

− A

). (66.47)

Owing to the large Coulombic attraction between the

ion pair, reaction proceeds immediately following elec-

tron transfer. The crossing distance may then be used

to estimate the effective reaction cross section. The ver-

tical A

is not necessarily the appropriate value to use

in estimating these crossing distances; stretching of the

halogen bond may occur during approach, so the ef-

fective A

is generally somewhere between the vertical

and adiabatic values. Often there exists some repulsion

between the atoms in the resulting halogen molecular

ion, so that electron transfer is accompanied by disso-

ciation of the molecule in the strong ﬁeld of the ion

Part E 66.4

Reactive Scattering 66.4 Reactive Scattering 979

pair. The alkali ion, having sent out the electron as the

“harpoon”, then reels in the negative ion, leaving the

neutral halogen atom nearly undisturbed as a specta-

tor. Because these events occur at long range, there is

no momentum transfer to the spectator atom, and it is

a simple matter to estimate the anticipated angular and

translational energy distributions in this spectator strip-

ping limit. The product molecule is scattered forward

(relative to the direction of the incident atom) and for

the reaction A+ BC → AB+C, the ﬁnal cm velocity

for the product AB is given by



=−M

, (66.48)

where u

is the initial cm velocity of the BC mol-

ecule. This spectator stripping mechanism may occur in

systems other than harpoon reactions, and is useful to

remember as a limiting case.

The likelihood of electron transfer at these cross-

ings may be estimated using a simple Landau–Zener

model [66.72](Chapt.49). For relative velocity g,

impact parameter b and crossing distance R

, the prob-

ability for undergoing a transition from one adiabatic

curve to another (that is, the probability for remaining

on the diabatic curve) is given by

p = 1− e

−δ

, (66.49)

where

δ =

2πH



1−



−

, (66.50)

and H

is the coupling matrix element between the two

curves. H

may be estimated from an empirical relation

which is accurate within a factor of three over a range

of 10 orders of magnitude [66.73]. In atomic units



∗

−0.86R

∗

, (66.51)

where

∗







(66.52)

is the reduced crossing distance, and I

and I

are the

initial and ﬁnal ionization potentials of the transferred

electron. One ﬁnds electron transfer probabilities near

unity for curve crossing distances below about 5 Å,

dropping to zero for crossing at distances greater

than about 8 Å. These estimates are based on electron

transfer in atom–atom collisions, and it is important to

remember that atom–molecule collisions occur on sur-

faces rather than curves, so the crossing seam may cover

a broad range of internuclear distances.

66.4.2 Rebound Reactions

Another common direct reaction mechanism is the

rebound reaction exempliﬁed by F +D

→ DF+

D [66.21]. The cm product ﬂux vs. velocity contour map

obtained for this reaction is shown in Fig. 66.4. Owing to

the favorable kinematics and energetics in this case, the

FD product vibrational distribution is clearly resolved,

and peaks at v = 2. The dominant v = 2 product peaks

at a cm angle of 180 degrees (referred to the direction of

the incident F atom). This rebound scattering is charac-

teristic of reactions exhibiting a barrier in the entrance

channel. Rebound scattering implies small b collisions,

and this serves to couple the translational energy efﬁ-

ciently into overcoming the barrier. Small b collisions

have necessarily smaller cross sections however, since

cross section scales quadratically with b.

66.4.3 Long-lived Complexes

A third important reaction mechanism involves the for-

mation of an intermediate that persists for some time

before dissociating to giveproducts. If the collision com-

plex survives for many rotational periods



∼ 10

−11



then the cm angular distribution exhibits a characteris-

tic forward–backward symmetry, usually with peaking

along the poles. The latter occurs because the initial

and ﬁnal orbital angular momenta tend to be parallel

(and perpendicular to the initial relative velocity vector).

When there exist dynamical constraints enforcing some

other relation, as in the case F +C

,thensideways

scattering may be observed, despite a lifetime of several

rotational periods [66.74–76]. For some systems exhibit-

ing this long-lived behavior, the rotational period may be

used as a molecular clock to monitor the lifetime of the

complex. By increasing the collision energy until the dis-

tribution begins to lose its forward–backward symmetry,

one can investigate the internal energy of the system just

when its lifetime is on the order of a rotational period.

Systems that have an inherent symmetry may exhibit

this forward–backward symmetry in the scattering dis-

tributions despite lifetimes that are considerably shorter

than a rotational period. This is the case for O(

reacting with H

, for example [66.77]. This reaction

involves insertion of the O atom into the H

bond result-

ing in an intermediate that accesses the deep H

Owell

and contains considerable vibrational excitation. Tra-

jectory calculations show that the complex dissociates

after a few vibrational periods, but the distribution ex-

hibits forward–backward symmetry because the O atom

is equally likely to depart with either H atom.

Part E 66.4

980 Part E Scattering Experiment

66.5 Recent Developments

Astonishing progress in reactive scattering methods has

continued in the past decade, and a few highlights are

summarized here. These advances have taken the form

of improvements in detection methods or, in some cases,

entirely new experimental approaches.

One of the most important of these is the H atom

Rydberg time-of-ﬂight (HRTOF) method [66.78,79]pi-

oneered by the late Karl Welge and coworkers for the

hydrogen exchange reaction. This approach employs

a conventional scattering geometry, and is suitable only

for experiments yielding product H or D atoms. De-

spite this narrow focus, owing to the general importance

of hydrogen elimination reactions and the remarkable

resolution of the technique, this has been an important

development. The H or D atom products are excited

to long-lived high-n Rydberg states in a 1+1



exci-

tation scheme in the interaction region. The atoms ﬂy

through a ﬁeld free region and impinge upon a rotatable

ﬁeld-ionization detector. The result is very high velocity

resolution, largely because the spreads in the beam ve-

locities make a negligible contribution to the product

velocity spread since the H atoms are moving so fast.

In addition, the dimensions of the scattering volume

and ionization region may easily be made small rela-

tive to the ﬂight length. Using this technique, Welge and

coworkers achieved fully rotationally-resolved differen-

tial cross sections for the hydrogen exchange reaction.

A second, widely-used approach is a variation of the

state-resolved Doppler probe in a bulb conﬁguration.

This strategy, pioneered by Hall at Brookhaven [66.80]

and Brouard et al. in Oxford [66.81], has been ap-

plied most notably to study excited oxygen atom

reactions. Although not a true crossed-beam approach,

through appropriate exploitation of kinematic con-

straints, energy conservation, and careful analysis,

state-resolved doubly differential cross sections may be

obtained, sometimes with additional vector properties as

well [66.82].

Another signiﬁcant new direction in detection strate-

gies is the use of near-threshold VUV product ionization.

This is a universal approach, in that little advance

spectroscopic information is required, but it is selec-

tive in that dissociative ionization is minimized and

sometimes isomer-selective detection may be achieved.

This approach has been used in synchrotron-based stud-

ies of Cl atom reactions [66.83], in transition metal

reactions [66.84], and in product imaging studies of

oxygen and chlorine atom reactions using the F

ex-

cimer at 157 nm [66.85]. Inspired by the threshold VUV

detection methods, Casavecchia and coworkers have

recently advanced the use of near-threshold electron

impact ionization in a conventional universal crossed-

beam conﬁguration [66.86]. Their recent results show

the great promise of this technique to deliver higher

signal-to-noise and to minimize fragmentation processes

in the detection step that may obscure the underlying

dynamics.

A ﬁnal note concerns advances in imaging tech-

niques applied to reactive scattering. Mention has been

made of the successful application of the VUV ex-

cimer probe for imaging radical products of reaction

of Cl and O(

P) reactions with alkanes. Two signiﬁcant

advances in imaging strategies have made it a very pow-

erful technique. The ﬁrst of these is “velocity mapping”,

developed by Eppink and Parker at Nijmegen [66.87],

a simple but important strategy that eliminates spa-

tial blurring in the images. The second is “slicing”,

or 3-D, methods that allow the velocity-ﬂux contour

map to be recorded directly [66.88–90]. This has seen

its most beautiful illustration in recent work by Liu

and coworkers at IAMS in state-resolved detection of

methyl radicals following reaction of F atoms with

methane [66.91]. Their images provide quantum state

correlated differential cross sections for this reaction

directly, allowing comparison to theory at an unprece-

dented level of detail.

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Part E 66