Clustering features of $^9$Be, $^{14}$N, $^7$Be, and $^8$B nuclei in
  relativistic fragmentation
Clustering features of 9Be, 14N, 7Be, and 8B nuclei in relativistic
fragmentation
D. A. Artemenkov,∗ T. V. Shchedrina, R. Stanoeva, and P. I. Zarubin†
Joint Insitute for Nuclear Research, Dubna, Russia
(Dated: November 10, 2021)
Abstract
Recent studies of clustering in light nuclei with an initial energy above 1 A GeV in nuclear treack
emulsion are overviewed. The results of investigations of the relativistic 9Be nuclei fragmentation
in emulsion, which entails the production of He fragments, are presented. It is shown that most
precise angular measurements provided by this technique play a crucial role in the restoration of the
excitation spectrum of the α particle sysytem. In peripheral interactions 9Be nuclei are dissociated
practically totally through the 0+ and 2+ states of the 8Be nucleus.
The results of investigations of the dissociation of a 14N nucleus of momentum 2.86 A GeV/c in
emulsion are presented as example of more complicated system. The momentum and correlation
characteristics of α particles for the 14N→3α +X channel in the laboratory system and the rest
systems of 3α particles were considered in detail.
Topology of charged fragments produced in peripheral relativistic dissociation of radioactive 8B,
7Be nuclei in emulsion is studied.
PACS numbers: 21.45.+v, 23.60+e, 25.10.+s
∗Electronic address: artemenkov@lhe.jinr.ru
†Electronic address: zarubin@lhe.jinr.ru; URL: http://becquerel.lhe.jinr.ru
http://arxiv.org/abs/0704.0384v1
mailto:artemenkov@lhe.jinr.ru
mailto:zarubin@lhe.jinr.ru
http://becquerel.lhe.jinr.ru
I. INTRODUCTION
The peripheral fragmentation of light relativistic nuclei can serve as a source of infor-
mation about their exitations above particle decay thresholds including many-body final
states. The interactions of this type are provoked either in electromagnetic and diffraction
processes, or in nucleon collisions at small overlapping of the colliding nucleus densities. A
fragmenting nucleus gains an excitation spectrum near the cluster dissociation thresholds.
In the kinetic region of fragmentation of a relativistic nucleus there are produced nuclear
fragment systems the total charge of it is close to the parent-nucleus charge. A relative
intensity of formation of fragments of various configurations makes it possible to estimate
the importance of different cluster modes.
The opening angle of the relativistic fragmentation cone is determined by the Fermi-
momenta of the nucleon clusters in a nucleus. Being normalized to the mass numbers
they are concentrated with a few percent dispersion near the normalized momentum of
the primary nucleus. When selecting events with dissociation of a projectile into a narrow
fragmentation cone we see that target-nucleus non-relativistic fragments either are absent
(“white”stars in Ref.[1]), or their number is insignificant. The target fragments are easily
separated from the fragments of a relativistic projectile since their fraction in the angular
relativistic fragmentation cone is small and they possess non-relativistic momentum values.
In the peripheral fragmentation of a relativistic nucleus with charge Z the ionization
induced by the fragments can decrease down to a factor Z, while the ionization per one
track – down to Z2. Therefore experiment should provide an adequate detection range. In
order to reconstruct an event, a complete kinematic information about the particles in the
relativistic fragmentation cone is needed which, e.g., allows one to calculate the invariant
mass of the system. The accuracy of its estimation decisively depends on the exactness of
the track angular resolution. To ensure the best angular resolution, it is necessary that the
detection of relativistic fragments should be performed with the best spacial resolution.
The nuclear emulsion technique, which underlies the BECQUEREL project at the JINR
Nuclotron [2], well satisfies the above-mentioned requirements. It is aimed at a systematic
search for peripheral fragmentation modes with statistical provision at a level of dozens
events, their classification and angular metrology. Emulsions provide the best spacial res-
olution (about 0.5 µm) which allows one to separate the charged particle tracks in the
FIG. 1: An event of the type of “white”star from the fragmentation of a relativistic 9Be nucleus into
two He fragments in emulsion. The photograph was obtained on the PAVIKOM(FIAN) complex.
three-dimensional image of an event within one-layer thickness (600 µm) and ensure a high
accuracy of angle measurements. The tracks of relativistic H and He nuclei are separated
by sight. As a rule, in the peripheral fragmentation of a light nucleus its charge can be
determined by the sum of the charges of relativistic fragments. Multiple-particle scattering
measurements on the light fragment tracks enable one to separate the H and He isotopes.
The analysis of the products of the relativistic fragmentation of neutron-deficient isotopes
has some additional advantages owing to a larger fraction of observable nucleons and min-
imal Coulomb distortions. Irradiation details and a special analysis of interactions in the
BR-2 emulsion are presented in Ref. [3, 4]. In what follows, we give the first results of
the study of the 9Be,8B, 7Be 14N nuclei fragmentation with a few A GeV energy which are
obtained with the use of a part of the material analyzed.
II. FRAGMENTATION OF 9BE NUCLEI
The 9Be nucleus is a loosely bound n+α+α system. The energy threshold of the
9Be→n+α+α dissociation channel is 1.57 MeV. The study of the 9Be fragmentation at
relativistic energies gives the possibility of observing the reaction fragments, which are the
decay products of unbound 8Be and 5He nuclei.
The method of nuclear emulsions used in the present paper allows one to observe the
charged component of the relativistic 9Be→2He+n fragmentation channel. Owing to a
good angular resolution of this method it is possible to separate the 9Be fragmentation
events, which accompanied by the production of an unstable 8Be nucleus with its subsequent
breakup to two a particles. In this case, the absence of a combinatorial background (of three
and more α particles) for 9Be, which is typical for heavier Nα nuclei 12C and 16O makes it
possible to observe distinctly this picture.
Nuclear emulsions were exposed to relativistic 9Be nuclei at the JINR Nuclotron. A
beam of relativistic 9Be nuclei was obtained in the 10B→9Be fragmentation reaction using a
polyethylene target. The 9Be nuclei constituted about 80% of the beam, the remaining 20%
fell on Li and He nuclei.[5]
Events were sought by microscope scanning over the emulsion plates. In total 362 events
of the 9Be fragmentation involving the two He fragment production in the forward fragmen-
tation cone within a polar angle of 6◦(0.1 rad) were found. The requirement of conservation
of the fragment charge in the fragmentation cone was fulfilled for the detected events. In
event selection 5 - 7 tracks of various types were allowed in a wide (larger than 6◦) cone to
increase statistics. An example of the 9Be→2He fragmentation event in emulsion is given in
Fig. 1 [2]. This event belongs to the class of “white”stars as far as it contains neither target
nucleus fragments, nor produced mesons. This event sample includes 144 “white ”stars. The
angles of the tracks in emulsion for the detected events were obtained using a fine measuring
microscope. Angular measurements for the 362 events were carried out with an accuracy
not worse then 4.5×10−3 rad.
In analyzing the data both He fragments observed in the 9Be→2He+n channel were
supposed to be a particles. This assumption is motivated by the fact that at small angles the
9Be→ 24He+n fragmentation channel with an energy threshold of 1.57 MeV must dominate
the 9Be→3He+4He+n channel whose energy threshold is 22.15 MeV. The 3He fraction will
not exceed a few percent in this energy range [6] and all the He fragments in the detected
events may be thought of as α particles.
In Fig. 2a the PT transverse momentum distribution of α particles in the laboratory
frame of reference is calculated without the account of particle energy losses in emulsion by
the equation
PT = p0 · A · sinθ (1)
where p0, A and θ are the momentum per nucleon, the fragment mass and the polar emission
angle, respectively. The outer contour corresponds to all events. The inner histogram is
obtained for events accompanied by protons recoil of emulsion target (dashed area). The
mean value of the transverse momentum for the total event sample in the laboratory system
is equal to < PT >≈103 MeV/c with FWHM σ ≈72 MeV/c. This may be an indication
of the fact that the experimental data are not of the same kind which can be pronounced
when going over to the c.m.s. of two α particles.
The P∗T transverse momentum distribution of α particles in the c.m.s. of two α particles
, MeV/cTP
0 50 100 150 200 250 300 350
, MeV/c
0 50 100 150 200 250 300 350
FIG. 2: The PT transverse momentum distribution of α particles in the laboratory system (a),
and the P∗T momentum distribution in the c.m.s. of an α particle pair (b). The outer contour
corresponds to all events. The inner histogram is obtained for events, which accompanied by
protons recoil of emulsion target (dashed area).
described by the equation
∼= PT i −
where PT i is the transverse momentum of an i-th α particle in the laboratory system nα=2
is given in Fig. 2b. There is observed a grouping of events around two peaks with the values
< P ∗T i >≈24 MeV/c and < P
T i >≈101 MeV/c. In Ref [7] the appropriate mean values of the
α fragment transverse momenta are < P ∗T i >≈121 MeV/c for
16O→4α,< P ∗T i >≈141 MeV/c
[8] for 12C→3α and < P ∗T i >≈200 MeV/ for
22Ne→5α (processing of the available data).
There by we clearly see a tendency toward an increase of the mean α particle momentum
with increasing their multiplicity. This implies a growth of the total Coulomb interaction of
alpha clusters arising in nuclei.
In the opening angle Θ distribution (Fig. 3) one can also see two peaks with mean values
4.6×10−3rad. and 26.8×10−3rad. The ratio of the numbers of the events in the peaks is
close to unity.
The Θ distribution entails the invariant energy Q2α distribution, which is calculated as a
difference between the effective invariant mass M2α of an α fragment pair and the doubled
α particle mass by the equations
M22α = −(
Q2α = M2α − 2 ·mα (3)
rad.-310×, Θ
0 10 20 30 40 50 60 70 80
FIG. 3: The opening Θ angle distribution of α particles in the 9Be→2α fragmentation reaction at
1.2 A GeV energy. The outer contour corresponds to all events. The inner histogram is obtained
for events, which accompanied by protons recoil of emulsion target (dashed area).
where Pj is the α particle 4-momentum.
In the invariant energy Q2α distribution (Fig. 4) there are two peaks in the ranges 0 to
1 MeV and 2 to 4 MeV. The shape of the distribution does not contradict the suggestion
about the 9Be fragmentation involving the production of an unstable 8Be nucleus which
decays in the 0+ and 2+ states. The values of the peaks of the invariant energy Q2α and
the transverse momenta P∗T in the c.m.s. relate to each other. To the Q2α range from 0 to
1 MeV with a peak at 100 keV there corresponds a peak P∗T with < P
T i >≈24 MeV/c , and
to the Q2α range from 2 to 4 MeV there corresponds a peak with < P
T i >≈101 MeV/c.
III. FRAGMENTATION OF 14N NUCLEI
A stack of layers of BR-2 emulsion was exposed to a beam of 14N nuclei accelerated
[9] to a momentum of 2.86 A GeV/c at the Nuclotron of the Laboratory of High Energy
Physics (JINR). Already been found amoung 950 inelastic events in which the total fragment
charge was equal to the Z0=7 fragment charge and there were no produced particles. Events
were sought by viewing over the track length which provided the accumulation of statistics
, MeVα2Q
0 2 4 6 8 10 12
, keV
0 100 200 300 400 500 600 700 800 900 10000
FIG. 4: The invariant energy Q2α distribution of α particle pairs in the
9Be→2α fragmentation
reaction at 1.2 A GeV energy. On the intersection: the Q2α range from 0 to 1 MeV. Arrows
mark the 8Be nucleus levels (0+ and 2+). The outer contour corresponds to all events. The inner
histogram is obtained for events, which accompanied by protons recoil of emulsion target (dashed
area).
without selection. The selected events are divided in two classes. The events of the type
of “white”star and the interactions involving the production of one or a few target-nucleus
fragments belong to the first class.
Table I shows the charge multi-fragmentation topology which was studied for the events
satisfying the above-mentioned conditions. The upper line is the Z>2 fragment charge, the
second line is the number of single-charged fragments , the third one the number of two-
charged fragments, and the fourth and fifth lines are the number of the detected events
with a given topology for “white”stars and events with target-nucleus excitation for each
channel, respectively. The two last lines present the total number of interactions calculated
in absolute values and in percent.
The analysis of the data of Table I shows that the number of channels involving Z>3
fragments for the “white”stars is larger by about a factor of 1.5 than that for the events
accompanied by a target breakup. On the contrary, for the 2+2+2+1 charge configuration
TABLE I: The charge topology distribution of the “white”stars and the interactions involving the
target-nucleus fragment production in the 14N dissociation at 2.86 A GeV/c momentum.
Zfr 6 5 5 4 3 3 – –
NZ=1 1 – 2 1 4 2 3 1
NZ=2 – 1 – 1 – 1 2 3
NW.S. 13 4 3 1 1 1 6 17
Nt.f. 15 1 3 3 – 2 5 32
NP 28 5 6 4 1 3 11 49
NP,% 26 5 5 4 1 3 10 46
channel this number is smaller by about a factor of 1.5. Thus, in the events with target
breakup, the projectile fragments more strongly than in the “white”stars. The data of Table
I points to the predominance of the channel with the 2+2+2+1 charge configuration (49
events) which has been studied in more detail. The obtained results show that the 14N
nucleus constitutes a very effective source for the production of 3α system.
In order to estimate the energy scale of production of 3α particle systems in the
14N→3α+X channel, we present the invariant excitation energy Q3α distribution with re-
spect to the 12C ground state:
M23α = −(
Q3α = M
3α −M(
12C) (4)
where M(12C) is the mass of the ground state corresponding to the charge and the weight
of the system being analyzed, M∗3α the invariant mass of the system of fragments. Statistics
was increased to 132 events 14N→3α+X including 50 “white ”stars by scanning over the
emulsion plates.
The main part of the events is concentrated in the Q3α area from 10 to 14 MeV, covering
the known 12C levels (Fig. 5). Softening of the conditions of the 3He + H selection, for which
the target fragment production is allowed, does not result in a shift of the 3α excitation peak.
This fact suggests the universality of the 3α state population mechanism.
To estimate the fraction of the events involving the production of an intermediate 8Be
nucleus in the reactions 14N→8Be+X→3α+X we present the invariant excitation energy
Q3α, MeV
0 10 20 30 40 50
FIG. 5: The invariant excitation energy Q3α distribution of three α particles with respect to the
12C ground state for the process 14N→3α+X. The following notation is used: 1) all the events of
the given dissociation, 2) “white”stars.
distribution for an α particle pair with respect to the 8Be ground state (Fig. 6). The first
distribution peak relates to the value to be expected for the decay products of an unstable
8Be nucleus in the ground state 0+. The distribution centre is seen to coincide well with the
decay energy of the 8Be ground state. The fraction of the α particles originating from the
8Be decay is 25-30%.
IV. FRAGMENTATION OF 7BE, AND 8B NUCLEI
The results of investigations dealing with the charge topology of the fragments produced
in peripheral dissociation of relativistic 8B, 7Be nuclei in emulsion are presented in Ref [2,
10, 11, 12].
Table II presents the numbers of the events detected in various channels of the 7Be
, MeVα2Q
0 2 4 6 8 10 12 14 16 18 20
, keVα2Q
0 50 100 150 200 250 300 350 400 450 500
FIG. 6: The invariant excitation energy Q2α distribution of α particle pairs for the process
14N→3α+X. In the inset: a fraction of the distribution at 0-500 keV.
fragmentation. Of them, the 3He+4He channel noticeably dominates, the channels 4He+d+p
and 6Li+p constitute 10% each. Two events involving no emission of neutrons in the three-
body channels 3He+t+p and 3He+d+d were registered. The reaction of charge-exchange
of 7Be nuclei to 7Li nuclei was not detected among the events not accompanied by other
secondary charged particles.The events involving no target fragments (nb=0) are separated
from the events involving one or a few fragments (nb >0).
For the first time, nuclear emulsions were exposed to a beam of relativistic 8B nuclei.
We have obtained data on the probabilities of the 8B fragmentation channels in peripheral
interactions. 55 events of the peripheral 8B dissociation which do not involve the produc-
tion of the target-nucleus fragments and mesons (“white” stars ) were selected. A leading
contribution of the 8B→7Be+p mode having the lowest energy threshold was revealed on
the basis of these events. Information about a relative probability of dissociation modes
with larger multiplicity have been obtained. Among the found events there are 320 stars in
which the total charge of the relativistic fragments in a 8◦ fragmentation cone ΣZfr satisfies
the condition ΣZfr >3. These stars were attributed to the number of peripheral dissocia-
tion events Npf . The Npf relativistic fragment distribution of over charges NZ is given in
TABLE II: 7Be fragmentation channel (number of events)
Channel 2He 2He He+2H He+2H 4H 4H Li+H Li+H Sum
nb =0 nb >0 nb =0 nb >0 nb =0 nb >0 nb =0 nb >0
3He+4He 30 11 41
3He+3He 11 7 18
4He+2p 13 9 22
4He+d+p 10 5 15
3He+2p 9 9 18
3He+d+p 8 10 18
3He+2d 1 1
3He+t+p 1 1
3p+d 2 2
2p+2d 1 1
6Li+p 9 3 12
Sum 41 18 42 33 2 1 9 3 149
Table III. There are given the data for 256 events containing the target-nucleus fragments
- Ntf , as well as for 64 events which contain no target-nucleus fragments (“white” stars )–
Npf . The role of the channels with multiple relativistic fragments NZ >2 is revealed to be
dominant for the N“white” stars. Of peripheral events, the “white” stars Nws (Table III)
are of very particular interest. They are not accompanied by the target-nucleus fragment
tracks and makes it possible to clarify the role of different cluster degrees of freedom at a
minimal excitation of the nuclear structure.
Table IV gives the relativistic fragment charge distribution in the “white” stars for 7Be
and 8B nuclei. The 8B events are presented without one single-charged relativistic fragment,
that is a supposed proton halo. The identical fraction of the two main 2He and He+2H
dissociation channels is observed for 7Be and 8B nuclei which points out that the 8Be core
excitation is independent of the presence of an additional loosely bound proton in the 8B
nucleus.
TABLE III: The charge topology distribution of the number of interactions of the peripheral Npf
type (Npf=Ntf+Nws), which were detected in an emulsion exposed to a second
8B nucleus beam.
Here Zfr is the total charge of relativistic fragments in a 8
◦ angular cone in an event, NZ the
number of fragments with charge Z in an event, Nws the number of “white”stars, Ntf the number
of events involving the target fragments, Nws the number of “white” stars.
Zfr N5 N4 N3 N2 N1 Ntf Nws
7 - - - 1 5 1 -
6 - - - 2 2 8 2
6 - - - 1 4 6 4
6 - - - - 6 1 -
5 - - - 1 3 61 14
5 - - - 2 1 44 12
5 - - 1 - 2 8 -
5 - - 1 1 - 1 -
5 - 1 - - 1 17 24
5 1 - - - - 17 1
5 - - - - 5 21 4
4 - - - - 4 5 1
4 - - - 2 - 24 1
4 - - - 1 2 42 -
TABLE IV: The charged dissociation mode distribution of the “white” stars produced by the 7Be
and 8B nuclei. To make the comparison more convenient, for the 8B nucleus one H nucleus is
eliminated from the charged mode and the channel fractions are indicated.
ΣZfr=4
7Be % 8B (+H) %
2He 41 43 12 40
He+2H 42 45 14 47
4H 2 2 4 13
V. CONCLUSIONS
The degree of the dissociation of the relativistic nuclei in peripheral interactions can reach
a total destruction into nucleons and singly and doubly charged fragments. The emulsion
technique allows one to observe these systems to the smallest details and gives the possibility
of studying them experimentally.
New experimental observations are reported from the emulsion exposures to 14N, 9Be,
8B, 7Be nuclei with energy above 1 A GeV. The main features of 9Be→2He relativistic frag-
mentation are presented. For the particular case of the relativistic 9Be nucleus dissociation
it is shown that precise angular measurements play a crucial role in the restoration of the
excitation spectrum of the alpha particle fragments. This nucleus is dissociated practically
totally through the 0+ and 2+ states of the 8Be nucleus. The data obtained from 9Be angular
measurements can be employed for the estimation of the role of 8Be in more complicated
Nα systems.
The results of the study of the dissociation of 14N nuclei of a primary momentum of
2.86 A GeV/c in their interactions with the emulsion nuclei are also presented. The present
investigation indicates the leading role of the 2+2+2+1 charge configuration channel. The
energy scale of the 3α system production has been estimated. According to the avail-
able statistics 80% of interactions are concentrated at 10-14 MeV. The fraction of the
14N→8Be+X→3α+X channel involving the production of an intermediate 8Be nucleus is
about 25%.
Advantages of emulsion technique are exploited most completely in the study of peripheral
fragmentation of light stable and neutron deficient nuclei. The results of investigations
dealing with the charge topology of the fragments produced in peripheral dissociation of
relativistic 7Be, 8B nuclei in emulsion are presented. Information on the relative probability
of dissociation modes with a larger multiplicity was obtained. The dissociation of a 7Be core
in 8B indicates an analogy with that of the free 7Be nucleus.
[1] N. P. Andreeva, et al., Phys. At. Nucl. 68, 455–465 (2005).
[2] Web site of the BECQUEREL Project: http://becquerel.jinr.ru (2006).
[3] M. I. Adamovich, et al., Phys. At. Nucl. 62, 1378–1387 (1999).
[4] M. I. Adamovich, et al., Phys. At. Nucl. 62, 514–517” (2004).
[5] D. A. Artemenkov, arXiv:nucl-ex/0605018 (2006).
[6] V. V. Belaga, et al., Phys. At. Nucl. 59, 869–877 (1996).
[7] F. A. Avetyan, et al., Phys. At. Nucl. 59, 110–116 (1996).
[8] V. V. Belaga, et al., Phys. At. Nucl. 58, 2014–2020 (1995).
[9] T. V. Shchedrina, et al., arXiv:nucl-ex/0605022 (2006).
[10] R. Stanoeva, et al., arXiv:nucl-ex/0605013 (2006).
[11] N. G.Peresadko, et al., arXiv:nucl-ex/0605014 (2006).
[12] N. P. Andreeva, et al., arXiv:nucl-ex/0604003 (2006).
http://becquerel.jinr.ru
	Introduction
	Fragmentation of 9Be nuclei
	Fragmentation of 14N nuclei
	Fragmentation of 7Be, and 8B nuclei
	 Conclusions
	References
