Correlation functions for p-p, p-d, p-α, d-α, and α-α were measured for the 16O+27Al system at a beam energy of 72 MeV. The detector array was centered at laboratory angle of 20°. Compared to published data obtained at larger scattering angles, an unexpected dependence on angle is seen for the p-p channel. The observed anticorrelation is stronger at more forward angles, which suggests that correlation functions are sensitive to the specific reaction mechanisms producing the light-charged particles

DeYoung, Paul A.

Hinnefeld, Jerry

IUScholarWorks

 
IUScholarWorks at Indiana University South Bend 
 
 
Evidence for Nonequilibrium Proton 
Emission in a Low-Energy Heavy-Ion 
Reaction 
 
DeYoung, P. A., Goupell, M. J., Atallah, B. V., Haglund, J. A., Jolivette, P. L., 
MacDermaid, M. K., Peaslee, G. F., Kolata, J. J., Berners, E. D., Peterson, D., von 
Schwarzenberg, J., & Hinnefeld, J. D. 
 
 
 
 
 
To cite this article: DeYoung, P. A., et al. “Evidence for Nonequilibrium Proton 
Emission in a Low-Energy Heavy-Ion Reaction.” Physical Review C, vol. 61, 
no. 2, American Physical Society, Dec. 1999, p. 024603. APS, 
doi:10.1103/PhysRevC.61.024603. 
 
 
 
 
 
 
 
 
 
 
This document has been made available through IUScholarWorks repository, a 
service of the Indiana University Libraries. Copyrights on documents in 
IUScholarWorks are held by their respective rights holder(s). Contact 
iusw@indiana.edu for more information. 
PHYSICAL REVIEW C, VOLUME 61, 024603Evidence for nonequilibrium proton emission in a low-energy heavy-ion reaction
P. A. DeYoung, M. J. Goupell, B. V. Atallah, J. A. Haglund, P. L. Jolivette, M. K. MacDermaid, and G. F. Peaslee
Department of Physics, Hope College, Holland, Michigan 49422-9000
J. J. Kolata, E. D. Berners, D. Peterson, and J. von Schwarzenberg
Physics Department, University of Notre Dame, Notre Dame, Indiana 46556
J. D. Hinnefeld
Physics Department, Indiana University–South Bend, South Bend, Indiana 46615
~Received 10 May 1999; published 30 December 1999!
Correlation functions for p-p , p-d , p-a , d-a , and a-a were measured for the 16O127Al system at a beam
energy of 72 MeV. The detector array was centered at laboratory angle of 20°. Compared to published data
obtained at larger scattering angles, an unexpected dependence on angle is seen for the p-p channel. The
observed anticorrelation is stronger at more forward angles, which suggests that correlation functions are
sensitive to the specific reaction mechanisms producing the light-charged particles.
PACS number~s!: 25.70.Pq, 25.70.GhI. INTRODUCTION
A large number of previous studies have been made of
small-angle light-charged-particle ~LCP! correlation func-
tions for a variety of systems and energies @1#. A survey of
these results revealed a wide variety of results and a depen-
dence of the measured correlation functions on scattering
angle @1#. In many previous reports, where source character-
istics were inferred from correlation measurements, there is a
tacit assumption that measurements spanning a small range
of scattering angles would represent the overall behavior.
The finding that the correlation functions vary with angle
suggests that care must be taken when interpreting such mea-
surements. It seems that different sources of LCP’s contrib-
ute in differing ways to produce any particular correlation
function.
The specific purpose of the measurement reported here
was to observe the behavior of a low-energy system. These
low-energy systems are generally well understood within the
context of the statistical model allowing one to better under-
stand the correlation measurements at higher energies. The
specific system studied was 16O127Al at 72 MeV. The par-
ticular model chosen to simulate the data includes only sta-
tistical emission from an equilibrated compound nucleus
with no other nonstatistical emissions. In a similar correla-
tion study at 80 MeV @2#, this assumption served well and is
assumed to be valid here. This experiment was performed
with the expectation that there would be no angular depen-
dance observed because of the low energy of the reaction.
However, an angular dependance was again observed.
II. EXPERIMENTAL PROCEDURE AND DATA ANALYSIS
This experiment was performed at the University of Notre
Dame Nuclear Structure Laboratory. A 72 MeV 16O beam
was produced and impacted a thin 27Al target
(700 mg/cm2). Fourteen CsI detectors with a 1.5 cm diam-
eter were placed in a hexagonal close packed array, 50 cm
away from the target. The center angle of the array was0556-2813/99/61~2!/024603~4!/$15.00 61 024620.0° with respect to the beam, while the angle between
adjacent detectors was 3.27°. The most forward detector was
at an angle of 16.9°.
The 16O beam was pulsed and bunched in this measure-
ment. The time resolution of the beam pulses was 1.5 ns and
the pulse period was 100 ns. An electrostatic beam sweeper
system insured that the number of beam particles incident on
the target between the beam bunches was negligible. The
flight path from target to detector and the width of the beam
pulse was such that individual masses could not be well re-
solved from the energy versus time-of-flight ~TOF! data.
However, the TOF data did allow a thorough measurement
of the number of random coincidences between two LCP.
During the entire course of the experiment the real to random
ratio was greater than 100 to 1.
Pulse shaping techniques were used for particle identifi-
cation of protons, deuterons, tritons, and a particles @3#.
There were slow gain variations, typically less than 5%/day,
over the course of the week-long experiment. The shifts were
measured by monitoring the scattered protons from the
1H(16O,1H) reaction ~with absorbed hydrogen in the alumi-
num target! and elastically scattered 16O. The energy cali-
bration constants were then varied for each run to account for
the shift. A similar correction was applied so that the particle
identification was optimized from run to run. Resolution of
the LCP energies is 1% ~slightly larger at the very lowest
energies!. The final energy calibrations were determined
from elastic scattering of protons and a particles off gold
over a range of energies. Count rates in the detectors, includ-
ing elastic scattered beam particles, were held to less than 3
kHz to minimize acquisition deadtime and enhance detector
performance.
Coincident data were analyzed for events involving pairs
of detectors with opening angles of 3.27°, 5.66°, and 6.52°.
The relative momentum spectra were formed for the p-p ,
p-d , p-a , d-a , and a-a interactions from the coincidences.
Correlation functions were formed for these five interactions
by dividing a relative momentum spectrum by a reference
spectrum. The reference spectrum was obtained by mixing©1999 The American Physical Society03-1
P. A. DeYOUNG et al. PHYSICAL REVIEW C 61 024603events and the total counts in the reference spectra were
taken to be the same as the real relative momentum spectra.
Only events that involved the same opening angle and the
same two LCP were mixed.
III. RESULTS AND DISCUSSION
The measured correlation functions are shown in Fig. 1
for the p-p and p-d exit channel. The a-a , d-a , and p-a
results are given in Fig. 2. Also shown in these figures are
the measured correlation functions for a similar energy ~80
MeV! but obtained at a more backward angle (u lab545°)
@2#. The minimum opening angle for the more backward-
angle measurement was slightly larger (4.62°) than in this
work, but the range of opening angles included in the data is
comparable.
The general features of the data are as expected. In Fig. 1
one sees that the correlation functions are relatively feature-
less. The positive correlation due to diprotons at a relative
momentum of '20 MeV/c , often seen at higher energies, is
absent since this system is extended in size and long lived.
However, there are downward trends to anticorrelation at the
smallest values of the relative momentum. ~Compared to the
shape of a p-p correlation function measured at higher ener-
gies, the correlation function displayed may not exhibit a
‘‘normal’’ shape. At very low energies, the limited energy
range of the emitted protons and the event-mixing technique
for the construction of the reference spectrum result in a
correlation function that is not asymptotically flat at the
higher values of relative momentum. This was also observed
in Ref. @2#.! In Fig. 2, one sees the expected peak at
18 MeV/c in the a-a correlation function corresponding to
8Be breakup and the expected peak at 40 MeV/c in the d-a
correlation function from 6Li* production. The remaining
p-a correlation function is relatively featureless because the
width of the resonance in 5He is very broad. ~The small
FIG. 1. Comparison of results from forward and backward scat-
tering angles for p-p and p-d . The beam energy and laboratory
detection angle are indicated in each panel. The error bars are sta-
tistical but do include an estimate of the error associated with the
formation of the reference spectrum. The solid lines are the results
of Coulomb trajectory calculations assuming emission from an
equilibrated compound nucleus.02460positive correlation seen near 20 MeV/c is due to the
breakup of 9B.! The forward angle results look very similar
to the backward angle results.
The particular shape of any given correlation function is
due to the interplay of the repulsive long-ranged Coulomb
force, the short-ranged attractive nuclear force, and the
breakup of any unstable nuclei. At lower energies, the char-
acteristic large space-time extent of the sources results in
correlation functions which are not strongly affected by the
nuclear force and so do not have the strong positive correla-
tion peak seen in some higher-energy experiments. As the
space-time extent of the emitting system becomes smaller,
the depth of the anticorrelation becomes deeper and the posi-
tive correlation begins to become apparent and grows. In this
particular experiment, the p-p and p-d correlations show a
slight anticorrelation at the lowest values of relative momen-
tum due to the Coulomb force. The other correlation func-
tions show a significant positive correlation, not because the
source is small ~which would be inconsistent with the p-p
and p-d results!, but because there are unstable nuclei which
decay with definite kinematics. When the correlations are not
strong, as for p-p and p-d , the particular shapes of the cor-
relation functions may not have the expected asymptotic
value of unity at large relative momentum because of the
way the background relative momentum spectrum is formed.
~In this analysis the area of the foreground and background
spectra are fixed to be the same.! The surest way to correctly
interpret the functions in these cases is to compare the mea-
sured correlation functions with modeled correlation func-
tions constructed exactly in the same way as the data.
Thus, the simplest interpretation of these correlation func-
tions indicates a source with an extended space-time extent.
Given the beam energy, size of the compound nucleus, and
excitation energy of the compound nucleus, one would ex-
pect such a large space-time extent.
However, a more detailed comparison between the for-
ward angle and backward angle data for the p-p case shows
an interesting feature. The shape in this case is significantly
different from the other functions and indicates that the ob-
served p-p pairs came from a source with a smaller average
space-time size. Differences in the correlation functions
shown in Fig. 2 can be understood in terms of differences in
the production rate of 8Be and 6Li* at different angles and
energies @4#. It is more difficult to explain why the forward-
angle p-p correlation function should indicate different
source properties.
The results were also modeled ~solid lines in Fig. 1! to
check that the observed differences did not arise from simple
kinematic effects or the specifics of the detector geometry.
With a statistical model code ~MODGAN @5#! the properties of
the particle emission ~energy distributions at each decay step,
decay probabilities, lifetime of each step, etc.! were deter-
mined. This information served as input to a Monte Carlo
Coulomb trajectory calculation @6# with two important fea-
tures. First the specific detector geometry was carefully re-
produced. Second, the process of forming the reference spec-
trum for the model results was the same as that for the
measured data. In the past, when this approach has been
applied to low-energy correlation results the data have been3-2
EVIDENCE FOR NONEQUILIBRIUM PROTON EMISSION . . . PHYSICAL REVIEW C 61 024603FIG. 2. Comparison of results from forward
and backward scattering angles for p-a , d-a , and
a-a . The beam energy and laboratory detection
angle are indicated in each panel. The error bars
are statistical but do include an estimate of the
error associated with the formation of the refer-
ence spectrum.well reproduced @2,4,7#. The forward-angle p-p measure-
ment deviates from the prediction significantly and this indi-
cates the need for additional study.
The specific shape of the forward-angle p-p correlation is
not the standard one observed at higher energies where the
correlation is flat at high values of relative momentum and
exhibits a pronounced dip, due to Coulomb repulsion, at the
lowest values of relative momentum. In this case, the specific
shape of the forward-angle p-p correlation function is deter-
mined by the space-time properties of the source but is also
influenced by the limited range of proton momenta ~this is a
low-energy measurement! and the event-mixing algorithm.
However, since the model results are treated the same way as
the data, comparisons with the calculations are instructive
and valid.
When simply comparing the four correlation functions,
the downward trend at lower values of relative momentum of
the forward-angle p-p data seems more pronounced. In ad-
dition, there is good agreement between the data and model
calculations in three cases, but one sees a pronounced differ-
ence between the data and a model calculation for the for-
ward p-p result. This implies that the detected protons are
originating from a source ~or sources! that is different from
that applicable to the other three correlation functions.
Prior work suggested that the wide variety of p-p corre-
lation results arose from a variety of reaction mechanisms
which have different angular distributions and different
space-time sizes @1#. One might have expected that the the
current correlation results, at a beam energy of only 72 MeV,
would be determined by the dominant mode of evaporation
from a single equilibrated source. However, it is surprising
that other processes could have a large enough cross section
and multiplicity compared to evaporation from an equili-
brated system to significantly affect the correlation function
at this low energy. Still, even though the deviations from
unity in the correlation functions are small at both forward
and backward angles, the effect observed in the forward-
angle p-p correlation function is significant. Also, the corre-02460lation functions involving composite particles, especially
p-d , seem unaffected. This suggests that the nonstatistical
emission process manifests itself preferentially with protons
rather than composite particles ~such as d).
There is definitely something at work which causes the
correlation functions for p-p at more forward angles to indi-
cate emission from a source with a smaller space-time extent.
~Assuming emission from a compound nucleus, this would
mean a shorter lifetime.! Obviously, this single measurement
can not articulate the detailed interplay of mechanisms re-
sponsible for the observations. However, it does seem that
the story told by correlation functions and the inferences
drawn from such measurements must be interpreted with
care.
IV. CONCLUSIONS
The large number of correlation measurements done to
date have demonstrated that the space-time size of the
sources of LCP’s affect the measured correlation function.
The past low energy measurements ~at more backward
angles! of p-p and p-d correlation functions have been well
reproduced by calculations based on the statistical model
@2,4,7# and the model is expected to apply to this latest mea-
surement. This newest measurement indicates that, in addi-
tion to an energy dependence, an angular dependence has
been observed for the p-p channel where none was expected.
An explanation of the observation is that correlation func-
tions are also sensitive to the presence of multiple reaction
mechanisms and that, even at the low energy of this work, a
source of LCP other than statistical emission from an equili-
brated compound nucleus, is observed.
ACKNOWLEDGMENTS
This work was supported by the National Science Foun-
dation under Grant Nos. PHY98-70262 ~Hope College!,
PHY95-15517 ~Hope College REU program!, and PHY94-
02761 ~Notre Dame!.3-3
P. A. DeYOUNG et al. PHYSICAL REVIEW C 61 024603@1# P. A. DeYoung et al., Phys. Rev. C 56, 244 ~1997!; see also
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Evidence for nonequilibrium proton emission in a low-energy heavy-ion reaction

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Evidence for nonequilibrium proton emission in a low-energy heavy-ion reaction

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