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ISSN 1063-7788, Physics of Atomic Nuclei, 2012, Vol. 75, No. 8, pp. 984–988.
c
©
Pleiades Publishing, Ltd., 2012.
Original Russian Text
c
©
F.G. Lepekhin, L.N. Tkach, 2012, published in Yadernaya Fizika, 2012, Vol. 75, No. 8, pp. 1045–1049.
ELEMENTARY PARTICLES AND FIELDS
Experiment
Role of
8
Be
2
2
2
α
Intermediate Nuclei in the Fragmentation
of
16
O Relativistic Nuclei in Nuclear Track Emulsions
F. G. Lepekhin and L. N. Tkach
Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina, 188300 Russia
Received June 28, 2011; in
fi
nal form, October 11, 2011
Abstract
In searches along a track in the chamber irradiated at the Laboratory of High Energies at
the Joint Institute for Nuclear Research (JINR, Dubna) with oxygen ions accelerated to a momentum
of 4.5 GeV/
c
per nucleon, 215 events containing two or mor
e doubly charged fragments of the primary
nucleus were found. Emission angles in the track-emulsion plane were measured in these events. Their
distribution is consistent with that which alpha particles are expected to have in an oxygen nucleus prior
to its interaction with a track-emulsion nucleus. Events of the
16
O
2
8
Be
4
α
type were discovered for
the
fi
rst time. They are treated as events of the coherent electromagnetic dissociation of an oxygen nucleus.
Among all events, about 14
%
of the
8
Be
2
α
decays proceed through the ground state of spin
parity
0
+
;
an approximately the same fraction of such decays proceed through the
fi
rst excited state of spin
parity
2
+
.
DOI:
10.1134/S1063778812040102
1. INTRODUCTION
The fragmentation of
16
O relativistic nuclei inter-
acting with other nuclei has been investigated in a
number of studies [1
7]. In the course of time, it
became clear that the study reported in [1] yielded
results closest to the true picture. In that study, it was
shown that the variance of the angles
φ
in the track-
emulsion plane is consisten
t within the experimental
errors with the variance of the angles
α
in the vertical
plane. Moreover, the values measured for
σ
(
φ
)
agree
with the values that are ex
pected on the basis of cal-
culations employing the Fermi momentum obtained
from data on electron scattering o
ff
16
Onuclei[8].
Below, we will show that we obtained the same result
at an oxygen-nucleus momentum of 4.5 GeV/
c
per
nucleon inclusive.
However, data whose reliability is questionable
were published in some of more recent articles
for
example, in [7]. The weakest point of those studies
was that their authors employed only integrated dis-
tributions associat
ed with the angle
θ
(
φ
2
+
α
2
)
1
/
2
and did not present a proof of
the equality of the vari-
ances of angles in the vertical and horizontal planes.
In tens of studies published since that time, it was
found that the transverse-momentum (
P
(
θ
)
) distri-
bution is not a Rayleigh dist
ribution. In experiments,
there is an excess of high
P
(
θ
)
values, which is a
consequence of the fact that
the variance of the angle
in the vertical plane is substantially greater than the
variance of the angle in horizontal plane.
Those studies were criticized in the literature sev-
eral times [9, 10], as well as in the open letter of one
of the present authors [11]. However, no arguments
against this criticism appeared, and this gives su
ffi
-
cient grounds to believe in its validity.
In the present study, we abandon an analysis of
data based on estimating the spatial angle
θ
,even
though such estimates were obtained in the experi-
ment. The point is that, at our energy, it is already
impossible to ensure an experimental accuracy that is
required in estimating the angle
θ
for separating the
8
Be
2
α
channel.
Our interest in the fragmentation of the oxygen
nucleus was also motivate
d by the fact that, accord-
ing to the calculations reported in [12, 13], this is
the only nucleus in which the cascade production of
alpha particles through the
16
O
2
8
Be
4
α
chan-
nel proceeds with a probability of about 28
%
. Below,
we demonstrate that we were able to separate events
originating from this channel. Special features of the
procedure for separating this
channel, which involves
the
8
Be intermediate state [14], are considered in the
following. After that, we discuss the details of our
experiment and, in conclusion, present its result.
2. SEPARATION OF THE CHANNEL
8
Be
2
α
If all product doubly charged particles originate
from a single center and if th
eir transverse momentum
depends exclusively on the Fermi momentum before
984
ROLE OF
8
Be
2
α
INTERMEDIATE NUCLEI 985
the interaction with a track-emulsion nucleus, the
distribution of these particles with respect to the angle
φ
in the track-emulsion plane must correspond to
a normal distribution whose mean value is zero and
whose variance is readily calculable. This follows
from the results reported in [10, 15], where the authors
showed that, for relativistic nuclei of
10
B,
11
B,
32
S,
22
Ne, and
24
Mg and of lead with momenta in the
range between 2 and 200 GeV/
c
per nucleon, the
experimental values of
σ
(
φ
)
agree within the exper-
imental errors with their cou
nterparts calculated on
the basis of the Fermi mome
ntum for these nuclei,
so that one must not reject
the hypothesis of a nor-
mal distribution of experimental angles
φ
. There is
every reason to believe that this regularity survives
for oxygen nuclei as well, which we study
that is,
there are no high transverse momenta of relativistic-
nucleus fragments.
Setting the Fermi momentum to 230 MeV/
c
for
the oxygen nucleus, w
e obtain a value of
σ
(
φ
)=
7
.
2
mrad for the expected constant of a normal distri-
bution of the projection of the transverse momentum
of doubly charged fragments onto the track-emulsion
plane. For the
8
Be
2
α
channel, the maximum
angle between the directi
ons of the emission of two
alpha particles is 2 mrad if the decay process starts
from the ground state, whose spin
parity is
0
+
,and
approximately 9 mrad if the decay in question occurs
from the
fi
rst excited state, for which the respective
quantum numbers are
2
+
. This is because the energy
of this excited state is approximately 20 times as
high as the ground-state energy. Accordingly, the
momenta of particles originating from the decay of
these states are in a ratio of
20
, the distribution of
the angles
φ
1
,
2
between the particle momenta being
bound to be uniform.
If we separated, as in [14], the
8
Be
2
α
channel
by using the angle
θ
1
,
2
between the particle momenta,
the distribution with respect to this angle would have
the form of a parabola as t
he angle increases from
a zero to a maximum, where it assumes the largest
value. Here, it corresponds to the case where two
alpha particles
fl
y apart in the direction orthogonal
to the transport velocity. In our study, the accuracy
in estimating the angle
θ
is about 2 mrad. Because
of the errors, the distribution of this angle over the
region extending up to 2 mrad is uniform in this case,
not increasing from zero to a maximum, in contrast to
what was observed in [14]. This is the reason why we
abandoned the idea of
employing the angles
θ
.
3. DESCRIPTION OF THE EXPERIMENT
A track-emulsion chamber was irradiated with
oxygen ions of momentum 4.5 GeV/
c
per nucleon at
the Laboratory of High Energies at the Joint Institute
for Nuclear Research (JINR, Dubna). Searches for
events were performed b
y means of scanning along
the track of the primary particle. In all, we scanned
146.47 m of tracks. Over this length, we found
1121 events of the inelastic interaction of a primary
nucleus with a track-emulsion nucleus. In this set of
inelastic-interaction even
ts, we selected 215 events
containing two or more doubly charged fragments of
the primary nucleus. We did not
fi
xthenumberof
other particles in an event. These might be product
particles, target fragments, or projectile fragments of
charge not equal to two.
The events were measured by an MPE-11 mi-
croscope, the readings of its track-point-coordinate
sensors being directed to the memory of a PC in re-
sponse to observer’s command [16]. Each event was
measured twice in order to rule out random failures
in saving data. However, there were virtually no such
failures. (All primary dat
a and our treatment proce-
dures are available from the website quoted in [17].
They can be used by anyone who needs them under
the condition of referring to
thesourceofthesedata.)
In each event, we measured the angle
φ
0
of the
primary track in the track-emulsion plane and its
angle
α
0
in the perpendicular plane of the microscope
reference frame, whereupon we calculated the angles
φ
i
and
α
i
at
i
=1
,
2
,
...
,
n
in the event reference
frame, where, by de
fi
nition,
φ
0
=
α
0
=0
for all
n
tracks in an event.
However, this inevitably leads to an error asso-
ciated with the continuation of the primary track to
the region where one measures the coordinates of
points of
n
tracks of fragments in an event. Only
within a distance of about 1 mm can one treat tracks
in a track emulsion as straight-line segments. At
distances of about 1 cm (and these are distances over
which one can measure angles of about 1 mrad),
tracks inevitably have rand
om S-shaped distortions
both in the horizontal and in the vertical plane. In the
last case, such distortions a
re additionally enhanced
by a mechanical shrinkage of the thickness of the
track-emulsion layer by a factor of 2.5 in relation to
the thickness of an undeveloped track emulsion, in
which case undeveloped silver bromide is removed
from the layer. As a result, a track traversing the layer
looks like a parabola rather than like a straight-line
segment.
Thus, we have seen that, in order to measure
angles of
φ
1
mrad, one has to increase the distance
in the coordinate
X
to the region where there is no
primary track any longer, but where there arise dis-
tortions, which rapidly become larger than measured
values. The possible way out is to go over to relative
measurements
that is, to measuring, instead of an
angle for which the primary track does not have a
PHYSICS OF ATOMIC NUCLEI Vol. 75 No. 8 2012