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Does thermalization occur in intermediate energy nucleus-nucleus collisions?
NuclearphysicsA447 (1985) 591c-602~ North-Holland,Amsterdam
59lc
DOES THERMALIZATIONOCCURIN INTERMEDIATEENERGY
NUCLEUS-NUCLEUS COLLISIONS?
Gary D. WESTFALL National Michigan
Superconducting State University,
Cyclotron Laboratory East Lansing, Michigan
48824-1321
Evidence for thermalization in intermediate energy nucleus-nucleus collisions is presented based on inclusive light particle and complex fragment spectra, light particle-complex fragment correlation measurements and p-p A consistent result is obtained that nucleons and correlation results. light nuclei emitted in these reactions display many characteristics of thermal sys terns.
1.
INTRODUCTION One of
energy tion
the
is
realized
interesting
energies
peratures energies
results
participant
by Morrissey-Benenson The
purpose
of
intermediate The
this
term,
malization observed chemical
get
with
fragmentation
particle
spectra
projectile-like particle
and
particle
data
of
in favor
defined of
this
emission
fusion
To study from
fragment light
that
these
collisions
exhibit
200
tem-
At high
equilibration A recent
is result
tnermalization.
of
in
thermalizatlon
paper
in
addressed
data
of
in this
from Jacak
particle
spectra
0375-9474/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
complex
define
one
et.
therfor
fragments, here
projectlie must
from
all i.e.
vdry smoothly
or from
orginate
energy
source
under discussion
reactions that
i will
velocity
thermalization those
intermeaiate
quantities
The particles
energy.
incomplete
The data
and triggered
purpose
property
interest
sources. complex
well
statistical
processes.
30 to
ion
such as the those
degree
by a common, intermediate
incident or
c&e
high
from
formulations.
experiments
a large
tne
not
For the
and the
of
gas
of
thermaliza-
collisions. is
particles,
from fusion
Fermi
that
to present
be signified
equilibrium,
ranging
where compound nuclei
of
multiparticle
nucleus-nucleus
participant
monotonically originate
is
collisions. to
whether
nucleons in hign multiplicity events. 2 casts doubt on the concept of et. al.
thermalization,
nucleus-nucleus
energies
barrier
demonstrated
paper
energy
in the field of
known phenomenun in heavy
in terms
from sophisticated group’
questions
the question
incident
a well
coulomb
explainable
Ball
for
at is
the
puzzling
concerns
reactlons
above
are
by the Plastic reached
in
just that
and
collisions
Thermalizat:on
MeV/nucleon. at
most
nucleus-nucleus
and
do not or tdr-
separate
the
target-like
or
paper are inclusive light 3 al., systematics of light from
Hasselquist
et.
al.
4
G. D. Westfall / Intermediate
592~
and Caskey
et.
nucleus-nucleus 2.
5
al.,
and light
collisions
energy nucleus-nucleus
particle
from Fox et.
al.
correlations 6
collisions
from
intermediate
energy
INCLUSIVE DATA Light
particle
many groups
and complex
over
projectile/target studied
one
needs
these
be defined
data
in
target-observed velocity
of
section
for
such
of
the source
Boltzmann
the
moving
data
of
0.
the
model
is
fit
will
and emits
is
three
assumed to
particles
of
extract of
in-
may have
parameterized
where each
with
T, and the
the source
range
regions
We have
by
systems
from phenomena that
The source
distribution
in way that Also
way.
source case
a large
many different
are minimized.
energy
particles
and for
the
contributions
8, temperature
have been measured
energies
to compare
energy
a single
the observed
spectra
in a compact
that
on incident
terms
incident
parameterizing
the data
particle-incident
a relativistic rest
of
dependence
of
inclusive
To be able
a method of
features
must
different
range
systems.
the essential terest
a large
fragment
projectileparameters:
production
cross
be described
isotropically
by
in its
frame. The
Fig.
inclusive
1 along
inclusive
with
spectra
data
for
p,d,
at higher
92 MeV/nucleon
*OAr+Au are
data
and
data for
tions
inclusive They display
that
is
1
solid
shown in Fig.
particles energy
of .the statistical
Fig.
30 MeV/nucleon
shown’as
shown along
light
exponential
are suggestive
fits
energies
from
nature.
and t from
the moving source
with
lines.
2 where p,d,t,
moving
in general
spectra
source appear
and smooth
nature
‘%+Au are shown in 4 An example of
of
Fig.
fits. to
2
be thermal
angular
the spectra.
3He,and *He Ir These
distribu-
in
G.D. Westfall /Intermediate
We have data for fits
applied
I%-,
include
"O-, only
that may
"Ne-,
contain
lisions However,
contributions projectile
by not
at low
incident
velocity source
energies
spectra
at forward
0, T, and g for light
are shown in Fig. 3 as a These
parameters
that high energy nucleus-nucleus
be compared
to reactions
one cannot
The
or at low energies that may
above the coulomb barrier.ll
may
targets.
velocity source and ex-
The parameters
vary col-
at 10 MeV/nucleon.
distinguish
kinematic method between light particles originating fragmentation
on heavy
fitting
fragmentation
contributions.
with incident energy suggesting at 2 CeV/nucleon
reactions
from an intermediate
emitted from an intermediate
function of energy/nucleon smoothly
and *'A?induced
contributions
have target frapentation particles
593c
the single moving source model to a large body of inclusive
plicitly exclude spectator angles
energy nucleus-nucleus collisions
easily using this
from target and projectile
and thus the results at low energies must be suspect.
Fig. 3
Inclusive that
treat
However
light paticle spectra have been explained nuclear
most
collisions
both
macroscopically
and microscopically.
of these model treat the nuclear matter in terms of nucleons Only
and do not include the fact that not nucleons but that
in terms of many models
a large
number
are emitted
of complex fragments
of complex fragment emission
is shown
in Fig.
in these
are emitted as well. 4 where
Be isotopes
reactions An example from
137
G.D. Westfall /Intermediate
594
MeV/nucleon “Ee
*‘Ar+Au
at 60° at
nucleon
scattering.
fragment
spectra
ments
with
42,
induced
and low energy
ranges
are
ments that barrier
from
surprising
to
other
heavy
ion
collisions
extracted
an intermediate obtained
are
emitted
is
target
from
that
all
The
apparent
fragment type
of
tures are
source.
in Fig.
which
source
suggesting
was
shown
velocity that
This 5 is
decrease
attributed
= 80 MeV/nucleon. in
Fig.
7 along
along to
the high
with
the
results
from
protons
scatter
flaw
t
in
mass of
originate of
section of
all
‘%I :
the detection for
a quantum
Fig.
6.
3
the observed
from
in the extracted
cutoff
cross
to
that
A possible
velocities
increasing do not
energy
The production
fragments 3 5. The
Fig.
5
source
with the
fragment.
0 137MeV/n m 92MeWn . 42MaWn
fragments with
coulomb
Ar+Au
extracted
decreases
the heavier
frag-
by the
suggests
source.
angular
target-like
in
result
be
proton-
and
complex
rdnging
This
Fig. in the
of
shown
the fragments
temperature.
4
interpretation
energy
to
are
from a common, thermalized
Fig. in this
One must
and the emitted
source
M-
seen
similar
fits
frag-
a way as to suppress
such as high energy
source
a
from complex
fragments.
peak characterized
_
is
in such
nucleus
of
nucleon-
+ Au and Ca for
the suppression
moving
velocity
have the same apparent
the fragments
*‘Ar
thdt
coulomb
of
have been extracted
experiments
important by the
the emission
the superposition
projectile-like
from
Most
is
to explain
of
have been applied and
the heavy residual
result
seem
“N
difficult
parameters
data
compared.
between
is
in terms
and 137 MeV/nucleon
can be identified
The temperatures emitted
source
92,
target-like
comparing
It
simply
These fits
from
in
sh~wn.~
Moving from
lSA514.
contributions careful
are
50 MeV/nucleon
energy nucleus-rmcleus collisions
these
the
same
temperasystem fragments
statistical
3
calculation. stood
in terms
terms
of
G.D. Westfall /Intermediate
energy nucleus-nucleus collisions
Clearly
of
of
chemical
the
these
equilibrium
as we11 a8 kinetic
137 MeV/A
again
complex
concepts
pointing
fragments
toward
can be underzation
thermali
in
equilibrium.
. Ar+Au (1 Ar+Ca
0.6
2
production
statistical
59%
4
6
6 A
Fig. 3.
Fig.
6
7
LIGHT PARTICLE-COMPLEXFRAGMENTCORRELATIONS The apparent
besides
thermal
that
appear
to
each may not
inclusive
spectra
such
as
the
that
a series
event
and
topology
pnenomena. rapidity violent
fragment which
8 for
the spectra created (322<7)
for
quite
the
similarity
of
spectra
at
for
of
angles
spectra 4 9.
cross
in this
the cross
sections
for
the
with
triggered
is
production
these
should
signify
(PLF)
a
survives
at 25O are
fragments
on IRFs with fragment
shown in Fig.
as a function are to
of
of
guide
an indication
shown
The shapes
these
inclusive
figure
of
collision.
*‘Ar+Au are
lines
we
type
which
IHF trigger
sections
average
events
an intermediate
fragment
The
of
where
on Al and Au targets.’
92 MeV/nucleon
responsible
the
types
out a given
the IRFs and indicate
Proton
as invariant
the shapes is
all
for
on the
associated
events
as a gentle
(3SZ<6)
are shown in Fig. from
spectra
effects
many separate
that
different to select
are
large
12C incident
The solid
momentum. mechanism
particle selected
other
over
spectra
over
experiments
emitted
similar
IRFs
averaging
where a projectile-like
mechanisms.
‘%+A1
have been plotted
fragment
is
30 MeV/nucleon
by similar
average
light
events
may be due to
may produce
can be characterized
fragment
are
30 MeV/nucleon
the of
and events
Tne inclusive
this
triggered
study
(IRF)
collision
tne collision in Fig.
of
The two types
fact
be thermalized
To remove
be thermal.
have undertaken
reaction
of
thermalization
events
data
nature
36226
that
for
spectra 10. the
the eye.
the various
of are
The total The
d single fragments.
G.D. Westfall / Intermediate energy nucleus-nucleus
596c
Fig. Spectra
for
in Fig.
ll.4
figures
for
have the
same general
particle
-
protons
coincident
The inclusive comparison
IRF
Fig.
8 with
light with
the
features
combinations
IRFs from
particle
9
92 MeV/nucleon
spectra
coincidence
collisions
have
spectra.
are
included
spectra
suggesting
these
for
all
shown in
The coincidence
as the inclusive that
“Ar+Au
been
measured
fragments
the
spectra light
have a common
source .
IRF+X
4oAr+Au-
92 Mev,lrJclwn
MOMENTUM
V.M’/c)
Fig. The solid triggered significantly
curves data for
10
in the Figs.
and
these
p-Li
fits
coincidences
Fig.
9 and 11 are moving describe
the
from both
11
source
data
very
targets
at
well
fits
to
the
and only
30 MeV/nucleon.
IRF-
deviate The
G.D. Westfall /Intermediate
extracted
temperatures
coincidence
values
spectra
divided
tracted inclusive
by the
inclusive
Tnere
lower
parameter
13 show
than the
decrease seems
the
differences
between
the
The inclusive
fragment
velocity.
type
statistics
‘%
One clearly
PLFs but Li and Be fraeJnents peaked at
the
30 MeV/nucleon tial
cross
for
*OAr + Au.
a function
of
mentation
those are
the
Cross
ratio
The velocity are
distributions indicate
the
for
of
presence
Figs.
other
be
of
mass.
a
There
velocity
The apparent light
isotopes
are shown in Fig.
have been plotted
near
projectile
the
the
as a function
incident
projectile
velocity
spectrum
rather
for
B and C
than one
spectra between protons and PLFs from 4 15. The inclusive double differenat
13”
are
velocity
which most
P fragments. of
and
and
the PLF trigger
are shown for
exponential
fragment
the
30
tend to
measured.
over
fragment
distributions 0 through
primarily
possible
sections
at
varia-
indications
temperature
velocity
PLF trigger
the
exthe
same
measured
are
particle of
the than
“He spectra. for
Coincidence the
the
velocities
There
the
and those the
+ Al are shown in Fig.
sections
MeV/nucleon velocity.
of light
that
significant
trigger
show an exponential
beam velocity. “C
a peak
about
spectra
10%.
particle
5% higher
fragments
The spectra
fragment
sees
are
increased
(3sZs6)
+ Al.’
the detected
but
light
the coincidence
demonstrate
be about
trigger
of
of
spectra
30 MeV/nucleon of
with
“He parameters
lower
the ratio
of
dependence
particular
of
be any statistically
by about
parameter
may be due to the
to
coincidence
velocities
be no significant on the
of
the range
.59-/C
collisions
IRF triggered
These ratios tend
to
extracted
velocity
the
92 MeV/nucleon
over
that
parameters
14 for
for
values.
not appear
inclusive
in the to
at
does
nucleus-nucleus
12 and 13 as ratios
temperatures
temperatures
in this
12 and
velocties
are shown in Figs.
IRF-triggered
MeV/nucleon. tion
and
energy
fragments to the
clearly
with
16 for
92
(3SZ~ld)
as
inciaent
projectile
show projectile
The Li ana Be fragment
in shape
projectile
shown in Fig.
with
only
fragmentation
slight
fragvelocity
shoulders
phenomena.
to
The B,
G.D. Westfall /Intermediate
598c
C, and N velocity emission
distributions
energy nucleus-nucleus collisions
show evidence
of
.
both fragmentation
and thermal
I
30 M&/nucleon
“C + AI -
p +XpLF
lo-*-
2
5
.-
10-s
~~~~
10-5
The B and C spectra tributions
in
Fig.
Fig.
14
Fig.
16
in Fig. 16 appear
1 0
40
80 ENERGY
Fig.
15
Fig.
17
14 and the S, Cl and Ar fragment to
be
dominated
by the
80
0 40 (MeV/nucleon)
few
velocity
nucleon
dis-
transfer
G.D. Westfall / Intermediate energy nucleus-nucleus collisions
mechanism tive
599c
as shown be the markedly narrower widths and higher velocities
to those
fragmentation
at sulfur in "AI' fragmentation MeV/nucleon. 7,a
to transfer reactions at 44 and 27.6
studied in reactions
Light particle spectra for coincidences in Fig. 17 for 92 MeV/nucleon
"Ar
rela-
The apparent sudden change from
of' the lighter mass fragments.
between protons
and
has
PLFs
been
are shown
The spectra for coincident fragments
+ AU.4
with 9sZ<15 have been summed together to obtain reasonable
statistics.
The in-
clusive light particle spectra have been included in this figure for comparison with the coincidence Li
through
N PLF
The light particle coincidence
spectra.
triggers
It can be seen that the proton coincidence through
P PLF
inclusive The
triggers
the coincident spectra
have
spectra,
average
the
coincidences mass
Note
true
shows
temperature.
at 13O may
sources.
In contrast,
with increasing
spectra.
An apparent
that
the
parameters
for
for
the lignt
no Variation
particle
- IRF
with the PLF trigger
contain
a large
the velocities
show
trigger fragment
in coincidence
contribution
a clear
mass
for
from
thermal
trend toward decreasing the
proton
and deutron
velocity 30% below the inclusive result is obtained for
emission from an excited residual A similar experiment
are
This constancy could reflect the fact
the average projectile mass of A=24 which
neutrons
than the
In addition, the PLF triggered spectra source temperatures
velocities
measured
the 0 and the F
of a lower source velocity.
As was
parameter
as the inclusive
that the PLF spectra
neutrons
for
with F through P fragments are plotted at an
of 24.
temperature
fragment mass. the same
over
for the
are plotted in Figs. 12 and 13 as ratios of
and velocities
values to the inclusive values.
summed
approximate
cross sections
a slightly flatter angular distribution
cross sections characteristic
temperatures
spectra
appear to be very similar to the inclusive spectra.
has
with
the
concept
of
target nucleus.
been
with
is consistent
carried
out
intermediate
from the system 35 MeV/nucleon
"N
by Caskey
rapidity
complex
5
where
the
fragments
were
spectra
for
at lOa are shown in Fig. 18.
The
+ Ho.
in coincidence with boron fragments
et. al.
The resulting
circles represent neutrons spectra measured on the same side of the beam as the complex
fragment
neutrons
emitted in coincidence
no same
side-opposite
directly
behind the complex fragment detector which detects
quential
and the squares represent neutrons on the opposite side.
emission
from
side
with intermediate
asymmetry
the observed
for the production of a thermalized 4. PROTON-PROTON
CORRELATIONS
except
for the neutron detector placed
complex fragment.
system.
The
rapidity boron fragments show
neutrons
from
se-
This constancy argues
G.D. Westfall /Intermediate
600~
Further
evidence
measurements
for
by Fox
direct
vs.
thermal
where
in-plane
et.
thermalization comes from 6 In this experiment al.
components
vs.
energy nucleus-nucleus collisions
was studied
out-of-plane
light
particle
in reactions
correlations
of
were
were placed
at
(e,@)=(45°,900)
and (45”, 180”)
from
to
120°
No peak was observed
in-
to out-of-plane
responding to
to
proton-proton
quasi-elastic
out-of-plane
@=O”.
correlations In Fig.
scattering.
p-p coincidence
spectra
at
for
the
and another
of
60 Energy
Fig. correlations scopes
are
(one
MeV.
This
parently ratio ratio
all
and one out-of-plane)
ratio
constant
this
of
free
over
in-plane
increases at
integrated
is
although
angle
in-plane
is
to
proton-proton
1.08
proton
of
the statistics k 0.01.
out-of-plane
is
coincidence
in-plane
detector
at
The out-of-plane
120 (MeV)
160
in the other
the
energy
range
up to
clearly
from
10 to
value
no peak at
spectra
two tele-
60 MeV and then
The average
are poor.
There
the
of cor-
19
energies
covering
as a function
telescope
the movable
LLLLLLLI
0
of
telescope.
Ratio of in-plane to
0.0 t
particle
and angles
19 the ratio
case
of C + C
in the ratio
energies
.n the movable
45”
Light
studied.
telescopes
at
contribution
40 MeV/nucleon
was moved
e=25O
correlation
the relative
for
160 apthe
20 MeV in the
as one would expect
from
scattering.
5. COALESCENCEMODEL Another model
method
of
where instead
kinetic by the
and chemical coalescence
Nucleons
that
are
assumed to
coalesce
the
nuclei
light
describing
complex
postulating
that
of
one assumes
equilibrium,
of
the large
emitted into
fragment
nuclei
number of
within
complex
can be described
are that
nucleons
a certain
fragments. as simply
is
from
these
the coalescence
fragments
emitted
radius This
spectra emitted
in
the
a system are
leads
the observed
created
collision.
in momentum space,
idea
po,
to the result
proton
in
spectra
are that
raised
G.D. Westfall /Intermediate
.
to the Ath power at the same energy/nucleon spectra as given spectra extracted
sees
This that
that
constancy
pendence
One can
relate values
for
source
size
6.
size
at
higher
energies.
all
a constant
applied
to
energy
the
is
measurements This
and also
system
of
and agrees
at a given
can be shown to
give
target with
the
bombarding the
same de-
model.
apparent
= 4.5 fm
21 mass
temperature
in fact
as the thermal
is
source
for
fragment
interaction
R are shown in Fig.
with
mon source
of
a common emitting
display
directly
The apparent
for
formulation
energy
The extracted
systems
independent
argues
the fragments
on fragment
Fig.
20
p0 is
The coalescence
energy.
agrees
is
complex
Fig.
result
This model
‘OAr + Au in Fig. 20 fragments from 92 and 137 MeV/nucleon 9 mormalization between the proton by the solid lines. The over all th The values of p0 gives po. power and the fragment spectra to the A 9) from 92 and 137 MeV/nucleon *‘Ar + Ca and Au are given in Fig. 21.
of
One clearly mass.
601~
energy nucleus-nucleus collisions
volume radius,
21 as a function
, is independent
from p-p correlations constant
source
size
of
R, to
fragment
of fragment from again
argues
mass.
mass,
similar
p,,.
and
sized
for
a com-
fragments.
CONCLUSION In conclusion
nucleus fragment
collisions spectra
the evidence can
for
be found
thermalizaton in
where a common, thermal
inclusive source
in intermediate light
particle
has been observed
energy and for
nucleuscomplex fragments
602~
with 15As14.
G.D. Westfall / Intermediate
energy nucleusnucleus
collisions
These fragments also show a constant coalescence
parent interaction volume radius.
radius and ap-
Correlations experiments where light
particle spectra triggered on complex fragments were measured show no dramaitc dependenceon the trigger particles which argues that all the particles are emitted from a common source. Proton-protoncorrelationmeasurementsshow no direct knock-out component at 40 MeV/nucleon arguing for the dominanceof thermal over single nucleon-nucleonscattering. ACKNOWLEDGEMENTS The author acknowledes contributions to this paper by B.V. Jacak, B.E. Hasselquist,Z.M. Koenig, and D. Fox. This work was supported by the National Science Foundation under grant no. PHY-83-12245. REFERENCES 1)
H.H. Gutbrod, H. Lahner, A.M. Poskanzer, T. Renner, H. Riedesel, H.G. Ritter, A. Warwick, F. Weik, and H. Wieman, Phys. Lett. 9. 317 (1983).
2)
D.J. Morrissey,W. Benenson,E. Kashy, B. Sherrill, A.D. Panagiotou. R.A. Blue, R.M. Ronningen, J. van der Plicht, and H. Utsunomiya, Phys. Lett. s, 423 (1984).
3)
L.H. Harwood, W.G. Lynch, D.K. B.V. Jacak, G.D. Westfall, C.K. Gelbke, H. Stoecker, M.B. Tsang, and T.J.M. Symons, Phys. Rev. Lett. 21, 1846
SCott,
(1983). 4)
B.E. Hasselquist,G.M. Crawley, B.V. Jacak, Z.M. Koenig, G.D. Westfall, J.E. 145 Yurkon, R.S. Tickle, J.P. Dufour, and T.J.M. Symons, Phys. Rev. e, (1985).
5) G. Caskey, A. Galonsky, B. Remington,M.B. Tsang, C.K. Gelbke,
A. Kiss, F. Deak, Z. Seres, J.J. Koiata, J. Hinnefeld,and J. Kasagi, Phys. Rev. w, 1597 (1985).
6) D.Fox, D.A. Cebra, Z.M. Koenig, J.J. Molitoris, P. Ugorowki, H. Stocker, and
G.D. Westfall, submitted to Phys. Rev. C, (1985). V. Borrel, D. Guerreau. J. Galin, B. Gatty, D. Jacquet, and X. Tarrago, Z. Phys. z4, 191 (1983). F. Rami, J.P. Coffin, G. Guillaume, B. Heusch, P. Wagner, A. Fahli, and P. Fintz, report CRN/PN.8407 (1984). B.V. Jacak, D. Fox, and G.D. Westfall, Phys. Rev. w,
704 (1985).
59lc
DOES THERMALIZATIONOCCURIN INTERMEDIATEENERGY
NUCLEUS-NUCLEUS COLLISIONS?
Gary D. WESTFALL National Michigan
Superconducting State University,
Cyclotron Laboratory East Lansing, Michigan
48824-1321
Evidence for thermalization in intermediate energy nucleus-nucleus collisions is presented based on inclusive light particle and complex fragment spectra, light particle-complex fragment correlation measurements and p-p A consistent result is obtained that nucleons and correlation results. light nuclei emitted in these reactions display many characteristics of thermal sys terns.
1.
INTRODUCTION One of
energy tion
the
is
realized
interesting
energies
peratures energies
results
participant
by Morrissey-Benenson The
purpose
of
intermediate The
this
term,
malization observed chemical
get
with
fragmentation
particle
spectra
projectile-like particle
and
particle
data
of
in favor
defined of
this
emission
fusion
To study from
fragment light
that
these
collisions
exhibit
200
tem-
At high
equilibration A recent
is result
tnermalization.
of
in
thermalizatlon
paper
in
addressed
data
of
in this
from Jacak
particle
spectra
0375-9474/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
complex
define
one
et.
therfor
fragments, here
projectlie must
from
all i.e.
vdry smoothly
or from
orginate
energy
source
under discussion
reactions that
i will
velocity
thermalization those
intermeaiate
quantities
The particles
energy.
incomplete
The data
and triggered
purpose
property
interest
sources. complex
well
statistical
processes.
30 to
ion
such as the those
degree
by a common, intermediate
incident or
c&e
high
from
formulations.
experiments
a large
tne
not
For the
and the
of
gas
of
thermaliza-
collisions. is
particles,
from fusion
Fermi
that
to present
be signified
equilibrium,
ranging
where compound nuclei
of
multiparticle
nucleus-nucleus
participant
monotonically originate
is
collisions. to
whether
nucleons in hign multiplicity events. 2 casts doubt on the concept of et. al.
thermalization,
nucleus-nucleus
energies
barrier
demonstrated
paper
energy
in the field of
known phenomenun in heavy
in terms
from sophisticated group’
questions
the question
incident
a well
coulomb
explainable
Ball
for
at is
the
puzzling
concerns
reactlons
above
are
by the Plastic reached
in
just that
and
collisions
Thermalizat:on
MeV/nucleon. at
most
nucleus-nucleus
and
do not or tdr-
separate
the
target-like
or
paper are inclusive light 3 al., systematics of light from
Hasselquist
et.
al.
4
G. D. Westfall / Intermediate
592~
and Caskey
et.
nucleus-nucleus 2.
5
al.,
and light
collisions
energy nucleus-nucleus
particle
from Fox et.
al.
correlations 6
collisions
from
intermediate
energy
INCLUSIVE DATA Light
particle
many groups
and complex
over
projectile/target studied
one
needs
these
be defined
data
in
target-observed velocity
of
section
for
such
of
the source
Boltzmann
the
moving
data
of
0.
the
model
is
fit
will
and emits
is
three
assumed to
particles
of
extract of
in-
may have
parameterized
where each
with
T, and the
the source
range
regions
We have
by
systems
from phenomena that
The source
distribution
in way that Also
way.
source case
a large
many different
are minimized.
energy
particles
and for
the
contributions
8, temperature
have been measured
energies
to compare
energy
a single
the observed
spectra
in a compact
that
on incident
terms
incident
parameterizing
the data
particle-incident
a relativistic rest
of
dependence
of
inclusive
To be able
a method of
features
must
different
range
systems.
the essential terest
a large
fragment
projectileparameters:
production
cross
be described
isotropically
by
in its
frame. The
Fig.
inclusive
1 along
inclusive
with
spectra
data
for
p,d,
at higher
92 MeV/nucleon
*OAr+Au are
data
and
data for
tions
inclusive They display
that
is
1
solid
shown in Fig.
particles energy
of .the statistical
Fig.
30 MeV/nucleon
shown’as
shown along
light
exponential
are suggestive
fits
energies
from
nature.
and t from
the moving source
with
lines.
2 where p,d,t,
moving
in general
spectra
source appear
and smooth
nature
‘%+Au are shown in 4 An example of
of
Fig.
fits. to
2
be thermal
angular
the spectra.
3He,and *He Ir These
distribu-
in
G.D. Westfall /Intermediate
We have data for fits
applied
I%-,
include
"O-, only
that may
"Ne-,
contain
lisions However,
contributions projectile
by not
at low
incident
velocity source
energies
spectra
at forward
0, T, and g for light
are shown in Fig. 3 as a These
parameters
that high energy nucleus-nucleus
be compared
to reactions
one cannot
The
or at low energies that may
above the coulomb barrier.ll
may
targets.
velocity source and ex-
The parameters
vary col-
at 10 MeV/nucleon.
distinguish
kinematic method between light particles originating fragmentation
on heavy
fitting
fragmentation
contributions.
with incident energy suggesting at 2 CeV/nucleon
reactions
from an intermediate
emitted from an intermediate
function of energy/nucleon smoothly
and *'A?induced
contributions
have target frapentation particles
593c
the single moving source model to a large body of inclusive
plicitly exclude spectator angles
energy nucleus-nucleus collisions
easily using this
from target and projectile
and thus the results at low energies must be suspect.
Fig. 3
Inclusive that
treat
However
light paticle spectra have been explained nuclear
most
collisions
both
macroscopically
and microscopically.
of these model treat the nuclear matter in terms of nucleons Only
and do not include the fact that not nucleons but that
in terms of many models
a large
number
are emitted
of complex fragments
of complex fragment emission
is shown
in Fig.
in these
are emitted as well. 4 where
Be isotopes
reactions An example from
137
G.D. Westfall /Intermediate
594
MeV/nucleon “Ee
*‘Ar+Au
at 60° at
nucleon
scattering.
fragment
spectra
ments
with
42,
induced
and low energy
ranges
are
ments that barrier
from
surprising
to
other
heavy
ion
collisions
extracted
an intermediate obtained
are
emitted
is
target
from
that
all
The
apparent
fragment type
of
tures are
source.
in Fig.
which
source
suggesting
was
shown
velocity that
This 5 is
decrease
attributed
= 80 MeV/nucleon. in
Fig.
7 along
along to
the high
with
the
results
from
protons
scatter
flaw
t
in
mass of
originate of
section of
all
‘%I :
the detection for
a quantum
Fig.
6.
3
the observed
from
in the extracted
cutoff
cross
to
that
A possible
velocities
increasing do not
energy
The production
fragments 3 5. The
Fig.
5
source
with the
fragment.
0 137MeV/n m 92MeWn . 42MaWn
fragments with
coulomb
Ar+Au
extracted
decreases
the heavier
frag-
by the
suggests
source.
angular
target-like
in
result
be
proton-
and
complex
rdnging
This
Fig. in the
of
shown
the fragments
temperature.
4
interpretation
energy
to
are
from a common, thermalized
Fig. in this
One must
and the emitted
source
M-
seen
similar
fits
frag-
a way as to suppress
such as high energy
source
a
from complex
fragments.
peak characterized
_
is
in such
nucleus
of
nucleon-
+ Au and Ca for
the suppression
moving
velocity
have the same apparent
the fragments
*‘Ar
thdt
coulomb
of
have been extracted
experiments
important by the
the emission
the superposition
projectile-like
from
Most
is
to explain
of
have been applied and
the heavy residual
result
seem
“N
difficult
parameters
data
compared.
between
is
in terms
and 137 MeV/nucleon
can be identified
The temperatures emitted
source
92,
target-like
comparing
It
simply
These fits
from
in
sh~wn.~
Moving from
lSA514.
contributions careful
are
50 MeV/nucleon
energy nucleus-rmcleus collisions
these
the
same
temperasystem fragments
statistical
3
calculation. stood
in terms
terms
of
G.D. Westfall /Intermediate
energy nucleus-nucleus collisions
Clearly
of
of
chemical
the
these
equilibrium
as we11 a8 kinetic
137 MeV/A
again
complex
concepts
pointing
fragments
toward
can be underzation
thermali
in
equilibrium.
. Ar+Au (1 Ar+Ca
0.6
2
production
statistical
59%
4
6
6 A
Fig. 3.
Fig.
6
7
LIGHT PARTICLE-COMPLEXFRAGMENTCORRELATIONS The apparent
besides
thermal
that
appear
to
each may not
inclusive
spectra
such
as
the
that
a series
event
and
topology
pnenomena. rapidity violent
fragment which
8 for
the spectra created (322<7)
for
quite
the
similarity
of
spectra
at
for
of
angles
spectra 4 9.
cross
in this
the cross
sections
for
the
with
triggered
is
production
these
should
signify
(PLF)
a
survives
at 25O are
fragments
on IRFs with fragment
shown in Fig.
as a function are to
of
of
guide
an indication
shown
The shapes
these
inclusive
figure
of
collision.
*‘Ar+Au are
lines
we
type
which
IHF trigger
sections
average
events
an intermediate
fragment
The
of
where
on Al and Au targets.’
92 MeV/nucleon
responsible
the
types
out a given
the IRFs and indicate
Proton
as invariant
the shapes is
all
for
on the
associated
events
as a gentle
(3SZ<6)
are shown in Fig. from
spectra
effects
many separate
that
different to select
are
large
12C incident
The solid
momentum. mechanism
particle selected
other
over
spectra
over
experiments
emitted
similar
IRFs
averaging
where a projectile-like
mechanisms.
‘%+A1
have been plotted
fragment
is
30 MeV/nucleon
by similar
average
light
events
may be due to
may produce
can be characterized
fragment
are
30 MeV/nucleon
the of
and events
Tne inclusive
this
triggered
study
(IRF)
collision
tne collision in Fig.
of
The two types
fact
be thermalized
To remove
be thermal.
have undertaken
reaction
of
thermalization
events
data
nature
36226
that
for
spectra 10. the
the eye.
the various
of are
The total The
d single fragments.
G.D. Westfall / Intermediate energy nucleus-nucleus
596c
Fig. Spectra
for
in Fig.
ll.4
figures
for
have the
same general
particle
-
protons
coincident
The inclusive comparison
IRF
Fig.
8 with
light with
the
features
combinations
IRFs from
particle
9
92 MeV/nucleon
spectra
coincidence
collisions
have
spectra.
are
included
spectra
suggesting
these
for
all
shown in
The coincidence
as the inclusive that
“Ar+Au
been
measured
fragments
the
spectra light
have a common
source .
IRF+X
4oAr+Au-
92 Mev,lrJclwn
MOMENTUM
V.M’/c)
Fig. The solid triggered significantly
curves data for
10
in the Figs.
and
these
p-Li
fits
coincidences
Fig.
9 and 11 are moving describe
the
from both
11
source
data
very
targets
at
well
fits
to
the
and only
30 MeV/nucleon.
IRF-
deviate The
G.D. Westfall /Intermediate
extracted
temperatures
coincidence
values
spectra
divided
tracted inclusive
by the
inclusive
Tnere
lower
parameter
13 show
than the
decrease seems
the
differences
between
the
The inclusive
fragment
velocity.
type
statistics
‘%
One clearly
PLFs but Li and Be fraeJnents peaked at
the
30 MeV/nucleon tial
cross
for
*OAr + Au.
a function
of
mentation
those are
the
Cross
ratio
The velocity are
distributions indicate
the
for
of
presence
Figs.
other
be
of
mass.
a
There
velocity
The apparent light
isotopes
are shown in Fig.
have been plotted
near
projectile
the
the
as a function
incident
projectile
velocity
spectrum
rather
for
B and C
than one
spectra between protons and PLFs from 4 15. The inclusive double differenat
13”
are
velocity
which most
P fragments. of
and
and
the PLF trigger
are shown for
exponential
fragment
the
30
tend to
measured.
over
fragment
distributions 0 through
primarily
possible
sections
at
varia-
indications
temperature
velocity
PLF trigger
the
exthe
same
measured
are
particle of
the than
“He spectra. for
Coincidence the
the
velocities
There
the
and those the
+ Al are shown in Fig.
sections
MeV/nucleon velocity.
of light
that
significant
trigger
show an exponential
beam velocity. “C
a peak
about
spectra
10%.
particle
5% higher
fragments
The spectra
fragment
sees
are
increased
(3sZs6)
+ Al.’
the detected
but
light
the coincidence
demonstrate
be about
trigger
of
of
spectra
30 MeV/nucleon of
with
“He parameters
lower
the ratio
of
dependence
particular
of
be any statistically
by about
parameter
may be due to the
to
coincidence
velocities
be no significant on the
of
the range
.59-/C
collisions
IRF triggered
These ratios tend
to
extracted
velocity
the
92 MeV/nucleon
over
that
parameters
14 for
for
values.
not appear
inclusive
in the to
at
does
nucleus-nucleus
12 and 13 as ratios
temperatures
temperatures
in this
12 and
velocties
are shown in Figs.
IRF-triggered
MeV/nucleon. tion
and
energy
fragments to the
clearly
with
16 for
92
(3SZ~ld)
as
inciaent
projectile
show projectile
The Li ana Be fragment
in shape
projectile
shown in Fig.
with
only
fragmentation
slight
fragvelocity
shoulders
phenomena.
to
The B,
G.D. Westfall /Intermediate
598c
C, and N velocity emission
distributions
energy nucleus-nucleus collisions
show evidence
of
.
both fragmentation
and thermal
I
30 M&/nucleon
“C + AI -
p +XpLF
lo-*-
2
5
.-
10-s
~~~~
10-5
The B and C spectra tributions
in
Fig.
Fig.
14
Fig.
16
in Fig. 16 appear
1 0
40
80 ENERGY
Fig.
15
Fig.
17
14 and the S, Cl and Ar fragment to
be
dominated
by the
80
0 40 (MeV/nucleon)
few
velocity
nucleon
dis-
transfer
G.D. Westfall / Intermediate energy nucleus-nucleus collisions
mechanism tive
599c
as shown be the markedly narrower widths and higher velocities
to those
fragmentation
at sulfur in "AI' fragmentation MeV/nucleon. 7,a
to transfer reactions at 44 and 27.6
studied in reactions
Light particle spectra for coincidences in Fig. 17 for 92 MeV/nucleon
"Ar
rela-
The apparent sudden change from
of' the lighter mass fragments.
between protons
and
has
PLFs
been
are shown
The spectra for coincident fragments
+ AU.4
with 9sZ<15 have been summed together to obtain reasonable
statistics.
The in-
clusive light particle spectra have been included in this figure for comparison with the coincidence Li
through
N PLF
The light particle coincidence
spectra.
triggers
It can be seen that the proton coincidence through
P PLF
inclusive The
triggers
the coincident spectra
have
spectra,
average
the
coincidences mass
Note
true
shows
temperature.
at 13O may
sources.
In contrast,
with increasing
spectra.
An apparent
that
the
parameters
for
for
the lignt
no Variation
particle
- IRF
with the PLF trigger
contain
a large
the velocities
show
trigger fragment
in coincidence
contribution
a clear
mass
for
from
thermal
trend toward decreasing the
proton
and deutron
velocity 30% below the inclusive result is obtained for
emission from an excited residual A similar experiment
are
This constancy could reflect the fact
the average projectile mass of A=24 which
neutrons
than the
In addition, the PLF triggered spectra source temperatures
velocities
measured
the 0 and the F
of a lower source velocity.
As was
parameter
as the inclusive
that the PLF spectra
neutrons
for
with F through P fragments are plotted at an
of 24.
temperature
fragment mass. the same
over
for the
are plotted in Figs. 12 and 13 as ratios of
and velocities
values to the inclusive values.
summed
approximate
cross sections
a slightly flatter angular distribution
cross sections characteristic
temperatures
spectra
appear to be very similar to the inclusive spectra.
has
with
the
concept
of
target nucleus.
been
with
is consistent
carried
out
intermediate
from the system 35 MeV/nucleon
"N
by Caskey
rapidity
complex
5
where
the
fragments
were
spectra
for
at lOa are shown in Fig. 18.
The
+ Ho.
in coincidence with boron fragments
et. al.
The resulting
circles represent neutrons spectra measured on the same side of the beam as the complex
fragment
neutrons
emitted in coincidence
no same
side-opposite
directly
behind the complex fragment detector which detects
quential
and the squares represent neutrons on the opposite side.
emission
from
side
with intermediate
asymmetry
the observed
for the production of a thermalized 4. PROTON-PROTON
CORRELATIONS
except
for the neutron detector placed
complex fragment.
system.
The
rapidity boron fragments show
neutrons
from
se-
This constancy argues
G.D. Westfall /Intermediate
600~
Further
evidence
measurements
for
by Fox
direct
vs.
thermal
where
in-plane
et.
thermalization comes from 6 In this experiment al.
components
vs.
energy nucleus-nucleus collisions
was studied
out-of-plane
light
particle
in reactions
correlations
of
were
were placed
at
(e,@)=(45°,900)
and (45”, 180”)
from
to
120°
No peak was observed
in-
to out-of-plane
responding to
to
proton-proton
quasi-elastic
out-of-plane
@=O”.
correlations In Fig.
scattering.
p-p coincidence
spectra
at
for
the
and another
of
60 Energy
Fig. correlations scopes
are
(one
MeV.
This
parently ratio ratio
all
and one out-of-plane)
ratio
constant
this
of
free
over
in-plane
increases at
integrated
is
although
angle
in-plane
is
to
proton-proton
1.08
proton
of
the statistics k 0.01.
out-of-plane
is
coincidence
in-plane
detector
at
The out-of-plane
120 (MeV)
160
in the other
the
energy
range
up to
clearly
from
10 to
value
no peak at
spectra
two tele-
60 MeV and then
The average
are poor.
There
the
of cor-
19
energies
covering
as a function
telescope
the movable
LLLLLLLI
0
of
telescope.
Ratio of in-plane to
0.0 t
particle
and angles
19 the ratio
case
of C + C
in the ratio
energies
.n the movable
45”
Light
studied.
telescopes
at
contribution
40 MeV/nucleon
was moved
e=25O
correlation
the relative
for
160 apthe
20 MeV in the
as one would expect
from
scattering.
5. COALESCENCEMODEL Another model
method
of
where instead
kinetic by the
and chemical coalescence
Nucleons
that
are
assumed to
coalesce
the
nuclei
light
describing
complex
postulating
that
of
one assumes
equilibrium,
of
the large
emitted into
fragment
nuclei
number of
within
complex
can be described
are that
nucleons
a certain
fragments. as simply
is
from
these
the coalescence
fragments
emitted
radius This
spectra emitted
in
the
a system are
leads
the observed
created
collision.
in momentum space,
idea
po,
to the result
proton
in
spectra
are that
raised
G.D. Westfall /Intermediate
.
to the Ath power at the same energy/nucleon spectra as given spectra extracted
sees
This that
that
constancy
pendence
One can
relate values
for
source
size
6.
size
at
higher
energies.
all
a constant
applied
to
energy
the
is
measurements This
and also
system
of
and agrees
at a given
can be shown to
give
target with
the
bombarding the
same de-
model.
apparent
= 4.5 fm
21 mass
temperature
in fact
as the thermal
is
source
for
fragment
interaction
R are shown in Fig.
with
mon source
of
a common emitting
display
directly
The apparent
for
formulation
energy
The extracted
systems
independent
argues
the fragments
on fragment
Fig.
20
p0 is
The coalescence
energy.
agrees
is
complex
Fig.
result
This model
‘OAr + Au in Fig. 20 fragments from 92 and 137 MeV/nucleon 9 mormalization between the proton by the solid lines. The over all th The values of p0 gives po. power and the fragment spectra to the A 9) from 92 and 137 MeV/nucleon *‘Ar + Ca and Au are given in Fig. 21.
of
One clearly mass.
601~
energy nucleus-nucleus collisions
volume radius,
21 as a function
, is independent
from p-p correlations constant
source
size
of
R, to
fragment
of fragment from again
argues
mass.
mass,
similar
p,,.
and
sized
for
a com-
fragments.
CONCLUSION In conclusion
nucleus fragment
collisions spectra
the evidence can
for
be found
thermalizaton in
where a common, thermal
inclusive source
in intermediate light
particle
has been observed
energy and for
nucleuscomplex fragments
602~
with 15As14.
G.D. Westfall / Intermediate
energy nucleusnucleus
collisions
These fragments also show a constant coalescence
parent interaction volume radius.
radius and ap-
Correlations experiments where light
particle spectra triggered on complex fragments were measured show no dramaitc dependenceon the trigger particles which argues that all the particles are emitted from a common source. Proton-protoncorrelationmeasurementsshow no direct knock-out component at 40 MeV/nucleon arguing for the dominanceof thermal over single nucleon-nucleonscattering. ACKNOWLEDGEMENTS The author acknowledes contributions to this paper by B.V. Jacak, B.E. Hasselquist,Z.M. Koenig, and D. Fox. This work was supported by the National Science Foundation under grant no. PHY-83-12245. REFERENCES 1)
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