Pronounced Airy structure in elastic
16
O
12
C scattering at E
lab
132 MeV
A. A. Ogloblin,
1
Dao T. Khoa,
2
Y. Kondo
¯
,
3,4
Yu. A. Glukhov,
1
A. S. Dem’yanova,
1
M. V. Rozhkov,
1
G. R. Satchler,
5,6
and S. A. Goncharov
7
1
RRC Kurchatov Institute, 123182 Moscow, Russia
2
Department of Physics, Chung Yuan Christian University, Chung Li, Taiwan 32023, Republic of China
3
Department of Natural Sciences, Kyoto Women’s University, 35 Kitahiyoshi-cho, Imakumano, Higashiyama-ku, Kyoto 605, Japan
4
Department of Theoretical Physics, RSPhysSE, The Australian National University, Canberra, ACT 0200, Australia
5
Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373
6
Department of Physics & Astronomy, University of Tennessee, Knoxville, Tennessee 37996
7
Nuclear Physics Institute, Moscow State University, Moscow, Russia
Received 24 November 1997
Measurement of elastic
16
O+
12
C scattering at E
lab
=132 MeV has been performed over the angular range
6°
c.m.
125°, which covers both the diffractive and refractive regions. A prominent minimum has been
observed at
c.m.
86°, which can be identified as an Airy minimum preceding the rainbow maximum. It thus
provides the first clear experimental evidence for the refractive rainbow scattering pattern in the
16
O+
12
C
system. This Airy structure can be well described by discrete sets of optical potentials with a relatively weak
absorption and a deep real potential. Candidates for the realistic family of
16
O+
12
C optical potentials at
E
lab
=132 MeV are discussed; those include the semimicroscopic potential given by the double-folding model.
S0556-28139805304-7
PACS numbers: 25.70.Bc, 24.10.Ht, 21.30.Fe
In recent years, our knowledge of the interaction between
heavy ions HI’s has been broadened significantly, espe-
cially through studies of the elastic scattering of certain com-
binations of light heavy ions, for which the absorption is
relatively weak and refractive effects appear. Refractive
rainbow phenomena in nuclear scattering provide a unique
source of information on the HI interaction potential at small
internuclear distances see, e.g., Refs. 1,2. In particular,
high-precision refractive scattering data have been used in
folding analyses 3,4 to place constraints upon the value of
the incompressibility of cold nuclear matter. So far, system-
atic experimental evidence of a nuclear rainbow in light HI
scattering has been found mainly in two symmetric systems
12
C+
12
C and
16
O+
16
O, with the most spectacular Airy pat-
tern exhibited in elastic
16
O+
16
O scattering at E
lab
=350
MeV 5. We note that elastic
16
O+
16
O scattering data have
been measured with extremely high accuracy at different en-
ergies 6 and show clearly the evolution of the refractive
pattern in this system, which is very helpful for the study of
the energy dependence of the HI optical potential.
While these two systems are quite ‘‘transparent’’ for re-
fractive effects to appear, the Mott interference caused by the
boson symmetry between the two identical nuclei sometimes
leads to rapidly oscillating elastic cross sections at angles
around
c.m.
=90°, which in turn obscure Airy structures in
this angular region. The whole Airy pattern might only be
seen in an optical model OM calculation which removes
the symmetrization artificially 7,8. The
16
O+
12
C system
does not have boson symmetry, and has been suggested as a
good candidate for the study of the nuclear rainbow 9.
However, available data for the
16
O+
12
C system usually do
not cover the refractive region in the angular distribution,
and therefore are of little help in revealing the rainbow struc-
ture. We note that only two data sets for the
16
O+
12
C sys-
tem, at E
lab
=608 MeV 10 and 1503 MeV 11, have been
shown to contain some refractive features which are sensitive
to the shape of real optical potential at small radii. However,
the data at the former energy do not extend to sufficiently
large angles to identify the Airy pattern 12, while the latter
energy is too high to observe the ‘‘rainbow’’ unambiguously,
since the refractive part of the angular distribution has
moved forward and mixed with the diffractive part at for-
ward angles. The present article reports on a new measure-
ment of elastic
16
O+
12
C scattering at E
lab
=132 MeV, which
was aimed to cover large scattering angles to find possible
rainbow features.
The measurement has been performed at the Kurchatov
Institute Cyclotron, where two experimental setups were
used. The first one has been used to measure scattering
events in the angular range 6°
c.m.
102°. It contained a
E - E telescope of semiconductor detectors. The thicknesses
of the E and E counters were 300 m and 13 m, respec-
tively. The solid angle to the target was 0.08 msr. The target
was a self-supporting carbon foil of 2.15 mg/cm
2
thickness.
The average beam energy in the target was 132.3 MeV, with
the energy resolution of the detector system about 1.5 MeV
determined mainly by kinematics. The angular resolution
was 0.3° in the laboratory system and was determined
mainly by multiple scattering on the target. Since the data at
forward angles are needed with high precision to determine
the absolute normalization of the data, this setup has been
used in two separate runs for repeated measurement of scat-
tering events at forward angles (
c.m.
40°).
As for the second setup, scattering events in the backward
angles (102°
c.m.
125°) have been measured with kine-
matic coincidences. Two detectors with a diameter of 25 mm
were located on either side of the beam at distances of 200
mm and 150 mm from the target. For this setup, a carbon foil
of 0.24 mg/cm
2
thickness was used for the target. The aver-
age beam energy was 132.2 MeV, and the angular resolution
PHYSICAL REVIEW C APRIL 1998 VOLUME 57, NUMBER 4
57 0556-2813/98/574/17976/$15.00 1797 © 1998 The American Physical Society