{include  6_1.doc|6.	ATOMIC AND MOLECULAR CLUSTERS

6.1 	Stopping powers of atoms and atomic clusters
	J.F. Liang, R. Vandenbosch and W.G. Weitkamp
	We have continued our effort to determine vicinage effects in the stoppi
ng power of small carbon clusters.  We are particularly interested in the energy
 region where with decreasing energy electronic stopping gives way to nuclear st
opping.  In this energy region the differences in stopping are small as the nucl
ear and electronic vicinage effects tend to cancel each other.  Last year we rep
orted our results for the stopping of single carbon atom anions.1  We have exten
ded these measurements to {EMBED EQUATION |} and to a lesser extent {EMBED EQUAT
ION |} anions.  The measurements consist of comparing the energy loss of {EMBED 
EQUATION |} with {EMBED EQUATION |} at the same bombarding energy per carbon.  T
his means the degraded carbon ions exiting from the stopping foil have close to 
the same energy, with any difference reflecting vicinage effects.  Our first ser
ies of measurements were made with a surface barrier detector with a thin Au win
dow. 
	We first determined that the vicinage effects were independent of the st
opping foil thickness in the range explored, 5-25 {EMBED EQUATION |}.  This is t
o be expected as the clusters will break up and the atoms separate soon after th
ey enter the stopping foil.  In view of the independence of the vicinage effect 
on foil thickness it is more appropriate to express the effect as the difference
 in stopping power for clusters as compared to single atoms, rather than the rat
io of the stopping powers.  We have found that {EMBED EQUATION |} clusters lose 
energy faster than {EMBED EQUATION |} ions at the highest energy studied, 165 ke
V per carbon.  As the energy decreases the difference disappears.
	Since the vicinage effects are very small we have decided to explore an 
alternate detection technique based on energy analysis of the degraded ions in a
n electrostatic deflector.  We have reoriented a 90 degree bend deflector origin
ally built to deflect the polarized ion source beam into the injection line of t
he tandem accelerator.  This deflector transmits more than 70% of undegraded bea
m to a Faraday cup.  Our measurements to date with this deflector have concentra
ted on measurements with low energy beams and a 5 {EMBED EQUATION |} stopping fo
il, and have confirmed that vicinage effects are small in the 30-50 keV per carb
on energy range.
}
{include 6_2.doc|6.2 	Size distributions for RbCn clusters
	R. Vandenbosch and D.I. Will
	It has been known for some time that low-mass carbon clusters exhibit an
 odd-even intensity pattern largely independent of the method of production of t
he clusters.  The yield of negative ions, {EMBED EQUATION |}, is larger by typic
ally a factor of 2 to 3 for even mass clusters through n about 8 or 10.  This fa
voring of even-n clusters is attributed to the larger electron affinities of car
bon chains with an even number of carbons, as can be understood from the occupan
cy of delocalized pi electron orbitals.2
	Middleton3 first reported a much stronger odd-even dependence in the yie
ld of {EMBED EQUATION |} clusters, for which the enhancement of even clusters is
 typically two orders of magnitude.  No explanation of this striking effect has 
been offered.  We decided to see if it occurs for mixed clusters with other alka
li metals.  We have measured the intensity of {EMBED EQUATION |} clusters from t
he sputtering of graphite with Rb+ ions.  The results are given in Fig. 6.2-1.  
As was observed for CsCn clusters, the enhancement of even-n clusters is more th
an two orders of magnitude.
	In an attempt to understand this enormous enhancement, we have initiated
 ab initio  quantum chemical calculations of the electron affinities of Cn and R
bCn clusters.  We are using the Gaussian 92 program4 with the LANL2DZ basis func
tions.  These basis functions are capable of reproducing the odd-even alternatio
n in electron affinities of linear Cn chains.  Our preliminary results for RbCn 
indicate an odd-even variation of similar magnitude to that for Cn.  The absolut
e values of the electron affinities however are much less, with the odd-n RbCn c
lusters (with the exception of RbC) not having stable anions (not having positiv
e electron affinities).  Although the calculations may not be accurate enough to
 conclusively determine whether the odd-n clusters have negative affinities, the
 results of the calculations strongly suggest that the origin of the large enhan
cement is the much smaller absolute values of the electron affinities of RbCn as
 compared to Cn.
	In the course of these calculations we have also explored the relative e
nergies of different geometrical configurations for the RbCn clusters.  We find 
that linear clusters with the Rb on one end are appreciably more stable than lin
ear clusters with the Rb in the middle, or than for small bent clusters.



Fig. 6.2-1.  Intensity distributions for RbCn clusters produced by Rb sputtering
 of graphite.  The small yields for n=3,5 and 7 are upper limits. 
}
{include  6_3.doc|6.3	High energy fragmentation of {EMBED EQUATION |}
	R. Vandenbosch
	The unusual stability and high symmetry of {EMBED EQUATION |} results in
 a great deal of interest in the mechanisms by which this molecule dissociates w
hen sufficiently excited.  Two rather different mechanisms have been put forward
 to account for the approximately exponential fall off in yield as the heavy fra
gment mass decreases from the mass of the parent molecule.  One is the successiv
e removal of a number of {EMBED EQUATION |} molecules.  The other is a decreasin
g probability for emitting fragments of increasing mass in a binary process.  We
 report here a semi-quantitative examination of the latter mechanism.  It was mo
tivated by a recent report of the {EMBED EQUATION |} yield distribution, where b
oth the light (n < 20) and heavy (n > 40) fragments were reported.5  A remarkabl
e feature of the data, shown in Fig. 6.3-1, is the near-symmetry of the size dis
tribution.  This is exhibited by reflecting the yield of light fragments with n 
{EMBED EQUATION |} 19 and plotting them as the closed symbols at 60-n.  This sym
metry is very suggestive of a binary fragmentation mechanism, {EMBED EQUATION |}
.
	We have developed a binary fragmentation model based upon the assumption
 of unimolecular dissociation from a statistically equilibrated system.  One ing
redient in such a model is the activation energy for a particular fragmentation 
channel leading to a {EMBED EQUATION |} and a {EMBED EQUATION |} primary product
 pair.  DeMuro, Jelski, and George6 have considered the general problem of remov
ing carbon chains under a constraint to leave the resultant heavy fragment as cl
ose as possible to the original buckyball.  They find that loss of 4, 6, 8 . . .
 atoms can occur via an "unzipping" process, yielding low-energy structures down
 to 44 atoms.  The activation energy for a particular fragmentation channel shou
ld be approximately proportional to the number of bonds broken in this unzipping
 process. We have used the tabulated results of deMuro et al. for the number of 
bonds broken when chains of different length are extracted from {EMBED EQUATION 
|} to estimate the relative yields of different fragmentation channels.  A fit t
o the data yields the full curve shown in Fig. 6.3-1.  This mechanism also leads
 to a natural explanation of the dominance of even-n for the heavy fragments.  O
dd-n primary heavy fragments cannot be produced by this unzipping process.  The 
observed yields of odd-n fragments for the lighter fragments may be the conseque
nce of {EMBED EQUATION |} and {EMBED EQUATION |} evaporation from excited chains
.  The chains produced by unzipping {EMBED EQUATION |} will have considerable st
rain energy in addition to their share of the residual excitation energy. 

Fig. 6.3-1.  The open squares represent the singly positive charged yields of Le
Brun et al. for 625 MeV bombardment of {EMBED EQUATION |} vapor.  The open circl
es are the reflection of the heavy yields assuming binary fragmentation.  The fu
ll curve is a binary fragmentation fit to the heavy fragment yields.
}
1Nuclear Physics Laboratory Annual Report, University of Washington (1994) p. 59
.
2R. Middleton, Nucl. Instrum. Methods B 58, 161 (1977).
3R. Vandenbosch et al., Nucl Instrum Methods B 88, 116 (1994).
4Gaussian 92, Revision G.1, M.J. Frisch et al., Gaussian, Inc., Pittsburgh, PA, 
1992.
5T. LeBrun et al., Phys. Rev. Lett. 72, 3965 (1994).
6R.L. deMuro et al., J. Phys. Chem. 96, 10603 (1992).

36

37

38