It is difficult to make quantitative estimates of strangelet production rates in heavy ion collisions. However, to set the scale, it is perhaps useful to provide rate estimates based on a conventional hadronic coalescence mechanism. This is a conservative approach which neglects other production processes that may occur in the earlier dense matter stage of the collision. The coalescence picture for the formation of ordinary non-strange nuclei is well established at BEVALAC energies (0.4 - 2 GeV/A) [21]. The number of clusters N(A,S) of baryon number A and strangeness S produced per collision is written as
where 
is the number of 
particles.
The addition of one non-strange baryon to a cluster incurs a penalty
factor P, while the conversion of a non-strange quark u, d to a
strange quark s at fixed A leads to a strangeness suppression
factor 
. Thus we have
In the thermal model [25], we have
where 
is the proton density at freezeout, 
is the
thermal wavelength and T is the temperature. From the t/p and
ratios measured in 2 GeV/A collisions at
the BEVALAC, we obtain 
[21].
For the higher energy AGS
collisions, T is larger, and we estimate 
. The factor
can be estimated in several ways: 1) from the observed
ratio at AGS energies 
; 2) from the
measured [26] probability ratio 
in
a variety of leptonic and hadronic collisions 
; 3) from the assumption of thermal and chemical equilibrium
of strange particles
All of these estimates lead us to the approximate value
, which we adopt here. Extrapolating the
observed ratio 
(Ne-Pb at 2
GeV/A), we estimate the 
or
for Au-Au collisions at the AGS. Note that
will be directly measured by E864, so this extrapolation
will ultimately be unnecessary. Our rough guess is then
An experiment with sensitivity 
could
detect fragments with
with n=11 for E864. This illustrates the importance
of high sensitivity; a change of one order of magnitude in 
shrinks the accessible domain in 
by one unit. The
region of sensitivity is enlarged somewhat if one considers N-N
collisions which produce more than one 
pair (the thresholds
for 
and 
are at 
and
4.1 GeV, respectively). With the guess 
(the additional 1/10 from the restricted
phase space for the 
), we arrive at the region of sensitivity for
E864 shown in Fig. 
.
Figure: The sensitivity of E864, expressed in (S,A) space. Strangelets
are expected to lie near S+A=0.
Strangelets are predicted to lie not far from the line S+A=0 in
Fig. , so one should be able to see such objects
with up to seven
units of strangeness. Note that E864 will also be able to find stable
dibaryon states with high strangeness 
, if such
composites exist. The strangelets are predicted to be of higher
density than ordinary nuclei, perhaps 1.5 - 2 
. Our
coalescence estimates are normalized to the which has a
central density (in a very small volume) comparable to that of a
strangelet. Thus we hope that wave function overlaps for a strangelet
are not much smaller than we have estimated. Since we have included
no explicit dependence of coalescence factors on the binding energy,
our estimates might be taken to apply to formation rates for ordinary
multi- 
hypernuclei as well. We note that the experience to
be gained from the E864 studies of the production of light nuclei and
of the antinuclei will be crucial for a realistic application of
coalescence models to strangelet production.
We emphasize that the above coalescence estimates are rather conservative.
One of the most interesting aspects of strangelet production is the
possible enhancement which could occur if ``droplets'' of quark-gluon
plasma were to be produced in the collision [27, 28].
The basic idea is that as the
quark-gluon plasma makes the transition to the final hadronic state,
the kaons it radiates are primarily those bearing the antistrange
quark, i.e. they are 
or 
rather than 
or
. This is understood in terms of the relative ease in
finding a u or d quark as compared with finding a 
or
quark in the baryon rich system formed by heavy ion
collisions at AGS energies. Reference [28] predicts
measurable probabilities for strangelet production via the
``strangeness distillation'' mechanism, starting from a droplet of
quark-gluon plasma. This mechanism preferentially produces negatively-charged
strangelets. Crawford, Desai and Shaw [29] have also estimated
production rates for strangelets from a droplet of quark-gluon plasma.
The production probability is given as a product of probabilities for:
(i) plasma droplet formation, (ii) producing a system of baryon number A,
and (iii) cooling the droplet by meson and later 
emission. The rates
obtained are substantially larger than our coalescence estimates. As an
example, they obtain strangelet formation probabilities for A=10, Z=-3
between 
for S=-4 and 
for S=-11. Thus one might
expect to detect strangelets with A as large as 20 - 25 with the high
sensitivity of E864. However, this presupposes the formation of quark-gluon
plasma in a certain sizable fraction of central Au-Au collisions at AGS
energies, which is certainly a bold assumption. Calculations of absolute
rates are clearly very uncertain. Our coalescence estimates are well
normalized to the rate for the production of 's, an observable quantity
which then serves as a calibration for the strangelet search. In any case,
we conclude that if strangelets exist and if droplets of quark-gluon plasma
with 
are formed with any appreciable frequency, the proposed
experiment will observe them. Indeed, one of the prime motivations for the
use of the heaviest possible projectile ions is the desire to enhance the
probability that regions of quark-gluon plasma will be produced in the
collisions.
One general feature of all the production models is worth noting. In
particular, they all predict that the mean transverse momentum of the
produced strangelets will scale as 
. In thermodynamic
models, this arises because the energy is the quantity which
equilibrates and at the same energy, the momentum scales as the square
root of the mass (at the temperatures reached in these collisions, the
strangelet motion in the center of mass system is non relativistic).
In the quark-gluon plasma model, the larger the size of a droplet, the
more hadrons it must radiate to reach its final state. These give rise
to a random series of transverse momentum kicks and the final
strangelet arrives at the random walk limit proportional to . A similar process occurs in the coalescence picture where the
final transverse momentum is the result of a series of transverse
momentum impulses due to the accreted constituents. We note that the
mean transverse momentum of 
produced in 200 GeV/c per
nucleon O-Au collisions [30] is 
GeV/c, and the mean transverse momentum of protons is about 0.5 GeV/c.
Indeed, there is a general tendency for the mean transverse
momentum of particles to increase as the mass increases. We thus
assume that the mean transverse momentum of strangelets produced in
AGS heavy ion collisions will be given by:
where the constant K is taken as
The range of K should account for the uncertainty in the production processes at least in so far as the mean transverse momentum is concerned.
The sensitivity of E864 is discussed in detail in the sections on
rates and backgrounds. In 1000 calendar hours of running, the
strangelet search should reach a sensitivity (90% confidence level)
of 
per interaction. This level of sensitivity was
assumed in Fig. .
A number of possible improvements are conceivable
to improve this level should that be necessary. This sensitivity
represents a factor of 
over the level achieved to date in
AGS experiment E814 [8] and a factor of
over what we believe the limit to be in E814.