Characterization of fragment emission in ^{20}Ne (7 - 10 MeV/nucleon) +
  ^{12}C reactions
Characterization of fragment emission in 20Ne (7 - 10 MeV/nucleon) + 12C reactions
Aparajita Dey1, C. Bhattacharya1, S. Bhattacharya1, S. Kundu1, K. Banerjee1,
S. Mukhopadhyay1, D. Gupta1, T. Bhattacharjee1, S. R. Banerjee1, S. Bhattacharyya1,
T. K. Rana1, S. K. Basu1, R. Saha1, K. Krishan1∗, A. Mukherjee1†, D. Bandopadhyay1‡, C. Beck2
Variable Energy Cyclotron Centre, Sector - 1, Block - AF, Bidhan Nagar, Kolkata - 700 064, India.
Institut Pluridisciplinaire Hubert Curien, UMR7500, CNRS-IN2P3 et Universite Louis Pasteur,
23, Rue du Loess, B.P. 28, F-67037, Strasbourg Cedex 2, France.
The inclusive energy distributions of the complex fragments (3 ≤ Z ≤ 7) emitted from the bom-
bardment of 12C by 20Ne beams with incident energies between 145 and 200 MeV have been mea-
sured in the angular range 10o ≤ θlab ≤ 50
o. Damped fragment yields in all the cases have been
found to have the characteristic of emission from fully energy equilibrated composites. The binary
fragment yields are compared with the standard statistical model predictions. Whereas Li and Be
fragments yields are in agreement with statistical-model calculations, enhanced yields of entrance
channel fragments (5 ≤ Z ≤ 7) indicate the survival of orbiting-like process in 20Ne + 12C system
at these energies.
PACS numbers: 25.70.Jj, 24.60.Dr, 25.70.Lm
I. INTRODUCTION
Several experiments have been done in recent years to understand the mechanism of complex fragment emission
in low-energy (Elab <∼ 10 MeV/nucleon) light heavy-ion (Aprojectile + Atarget
∼ 60) reactions [1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13, 14, 15, 16, 17]. The origin of these fragments extends from quasi-elastic (QE)/ projectile breakup
[2, 3], deep-inelastic (DI) transfer and orbiting [4, 6, 12, 13, 14, 15, 16], to fusion-fission (FF) [18, 19, 20, 21, 22, 23]
processes; and in some cases the structure of the nuclei has been found to play an important role. In most of the
reactions studied, the observed fully energy-damped yields of the fragments have been successfully explained in terms
of fusion-fission (FF) mechanism [18, 19, 20, 21, 22, 23]. However, the reactions involving α - cluster nuclei (e.g., 20Ne
+ 12C [12, 13], 24Mg + 12C [16], 28Si + 12C [14, 24] etc.) deserved special attention, where the observations of large
enhancement in yield and/or resonance-like excitation function in a few outgoing channels have been indicative of a
competitive role played by the deep-inelastic orbiting mechanism [12, 13, 14, 15]. In the FF mechanism, a completely
equilibrated compound nucleus (CN) is formed, which decays into various exit channels. The decay probability is
governed by the available phase space and barrier penetration probabilities for the respective decay channels. The
process occurs in a similar time scale which is required for the complete relaxation of the entrance channel energy
and angular momentum. On the other hand, deep inelastic orbiting may be described in terms of the formation of
a long-lived, dinuclear molecular complex [15], which acts as a “door way to fusion”, with a strong memory of the
entrance channel. In this picture, the interacting ions are trapped in a more deformed configuration than that of the
compound nucleus (trapped in the pocket of the ion-ion interaction potential due to combined effects of Coulomb and
centrifugal barriers). Both orbiting and fusion-fission processes occur on similar time scale. In addition to that, for
the light heavy-ion systems, the shapes of the orbiting dinuclear complexes are quite similar to the saddle and scission
shapes obtained in course of evolution of the FF process. Therefore it is difficult to differentiate the signatures of the
two processes.
The enhancement of fully energy damped reaction yields in light systems was first observed in the study of 20Ne +
12C inelastic scattering at backward angles [12], where large cross sections have been observed in inelastic scattering
yields near 180o. Subsequently, orbiting was observed in 28Si + 12C [14, 24] and 24Mg + 12C [16] reactions. Detailed
study of 28Si + 12C system revealed that, at lower bombarding energies, the excitation spectra for the 12C frag-
ments were dominated by single excitation and mutual excitations of the 12C and 28Si fragments, whereas at higher
bombarding energies, the dominant strength for all these channels shifted to higher excitation energies [24]. For the
higher bombarding energies, the most probable Q-values were found to be independent of detection angles and the
resulting angular distributions were found to have dσ/dΩ ∝ 1/ sin θc.m. like angular dependence — characteristic of
a long-lived, orbiting, dinuclear complex. Similar results have been obtained for 20Ne + 12C system [12, 13], where
∗ Present address : 306, VIP Enclave, VIP Road, Kolkata - 700 059, India
† Present address : Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata - 700 064, India.
‡ Present address : TRIUMF, 4004 Westbrook Mall, Vancouver, Canada V6T2A3.
http://arxiv.org/abs/0704.1209v2
resonance-like behaviour was also found in the excitation functions for several outgoing channels, which was similar to
the observation made for symmetric 16O + 16O system [25, 26, 27, 28]. Enhancements of large angle, binary reaction
yields have also been observed in somewhat heavier 28Si + 28Si, 24Mg + 24Mg systems [1], where significant non
resonant background yield was observed at higher excitation energies. The general pattern which unfolds from these
studies clearly suggests that the enhancements are manifestations of dynamics of damped nuclear reactions involving
a large number of channels, rather than due to specific structure effect appearing only in a few select channels.
The enhancement in elastic and inelastic channels may be explained in terms of a long lived dinuclear configuration
that decays back to entrance channel due to weak absorption which inhibits the orbiting configuration from spreading
into compound nuclear states. However, the enhancement in the elastic channel can be explained with the assumption
of weak absorption of grazing partial waves only; on the contrary, deep-inelastic orbiting phenomenon in general
suggests weak absorption in the angular momentum window between the critical angular momentum of fusion, lcr,
and the reaction grazing angular momentum, lgr. Besides, substantial mass and charge transfer, due to the rapid
mass equilibration in light systems, would also occur during the evolution of the orbiting dinuclear complex. So, the
rearrangement channels are also of interest in probing the dynamics of the orbiting process involving light nuclear
systems.
It is, therefore evident that, though some qualitative understanding about the phenomenon of deep-inelastic orbiting
reaction, in general (i.e., correlation with number of open reaction channels [29], or, alternatively, to weak absorption)
has been arrived at, precise mechanism of the process is still unknown. The deep-inelastic orbiting process has been
observed in several light α-like systems, for example, 20Ne + 12C [12, 13], 24Mg + 12C [16], 28Si + 12C [14, 24], 28Si +
16O [30] systems, where the number of open channels are small (∼ 10) [29]. However, 16O (116 MeV) + 28Si reaction
[6] showed different behaviour so far as the shape of the energy distributions, variation of < Q > values with angle,
and yields of the fragments are concerned. For a better understanding of the orbiting process, it is interesting to
study how the orbiting process evolves with energy. Intuitively, survival of long lived dinuclear configuration other
than fused composite is less probable at higher excitations and there are also indications that entrance channel effect
becomes smaller at higher energies [1]. Shapira et al. [13] made detailed study of 20Ne + 12C system in the energy
range Elab = 54 – 81 MeV and showed that there was large enhancement of strongly damped yields, the characteristic
of a long-lived orbiting 20Ne + 12C dinuclear system. The aim of the present paper was to extend the investigation
on fragment yield from 20Ne + 12C reaction at higher excitation energies, which might allow us to have a better
understanding of orbiting vis-à-vis fusion-fission processes for 20Ne + 12C system. If a long-lived rotating dinuclear
complex is formed in these reactions, mass and charge transfer should also occur, which leads to typical deep-inelastic
reaction yields. Therefore, backangle measurements for rearrangement channels became of interest. In addition to
that the excitation function measurements, for the dependence of the average total kinetic energy (EtotK ) loss on
bombarding energy for each binary exit channel, would provide an important probe of the dynamical properties of the
long-lived dinuclear complex. With this motivation, we have studied the fragment emission spectra from the reaction
20Ne + 12C at Elab = 145, 158, 170, 180 and 200 MeV, respectively. A part of the present data has already been
reported [4], which showed enhancement in yield of Carbon and Boron fragments well above the standard statistical
model predictions.
The paper has been arranged as follows. Section II describes the experimental procedures. In Sec. III we present
the analysis of 20Ne + 12C data. The results have been discussed in Sec IV. Finally, the summary and conclusions
are presented in Sec. V.
II. EXPERIMENTS
The experiment was performed using accelerated 20Ne ion beams of energies 145, 158, 170, 180 and 200 MeV,
respectively, from the Variable Energy Cyclotron at Kolkata. The target used was ∼ 550 µg/cm2 self-supporting
12C. Different fragments (5 ≤ Z ≤ 13) have been detected using two solid state [Si(SB)] telescopes (∼ 10 µm ∆E,
300 µm E) mounted on one arm of the 91.5 cm scattering chamber. Two solid state telescopes (∼ 50 µm, 100 µm
∆E [Si(SB)] and 5 mm E [Si(Li)]) were mounted on the other arm of the scattering chamber for the detection of
light charged particles and light fragments (1 ≤ Z ≤ 4); the same detectors were also used as monitor detectors for
normalization purposes. Typical solid angle subtended by each detector was ∼0.3 msr. The telescopes were calibrated
using elastically scattered 20Ne ion from Au, Al targets and a Th-α source. The systematic errors in the data, arising
from the uncertainties in the measurements of solid angle, target thickness and the calibration of current digitizer have
been estimated to be ≈ 15%. Part of these uncertainties are due to the extrapolation procedures employed to extract
the fully damped yields from the sequential decay components by the use of Monte Carlo simulations described in
Sec. IV A.
III. RESULTS
A. Energy distribution
Inclusive energy distributions for various fragments (3 ≤ Z ≤ 13) have been measured in the angular range 10o -
50o for all the bombarding energies. This covered backward angles in the center-of-mass (c.m.) frame, because of the
inverse kinematics of the reactions. Typical energy spectra of the emitted fragments (3 ≤ Z ≤ 13) obtained at an
angle 10o at Elab = 170 MeV are shown in Fig. 1. It is evident that the energy spectra for lighter fragents (3 ≤ Z ≤ 6)
exhibit strong peaking in energy. The peaks are nearly Gaussian in shape having its centroid at the expected kinetic
energies for the fission fragments obtained from the Viola systematics corrected by the corresponding asymmetry
factors [31, 32] and are shown by arrows in Fig. 1. The shapes of the energy spectra for the other heavier fragments
(7 ≤ Z ≤ 13) are quite different from those obtained for the lighter ones. The additional contributions from DI and
QE processes have been seen in the higher energy part of the spectra. Moreover, there are contributions from the
recoiling nuclei (energy corresponding to vCN cos θlab, shown by dashed lines in Fig. 1). All these contibutions, other
than fission fragments, fall off rapidly as one moves away from the grazing angle. In this paper, we report the results
from the lighter fragments (Z = 3–7).
The inclusive energy distributions for the fragments Lithium (Z = 3), Beryllium (Z = 4), Boron (Z = 5), Carbon (Z
= 6) and Nitrogen (Z = 7) obtained at an angle 10o at various bombarding energies are shown in Fig. 2. It is observed
that at all bombarding energies the energy spectra of the ejectiles (Li, Be, B, C, N) are nearly Gaussian in shape
and they have been fitted with a single Gaussian. The non-Gaussian shapes at the low-energy side of the spectra
correspond to sequential decay processes – which can be simulated by Monte-Carlo statistical model calculations
(described in Sec. IV A). The Gaussian fits so obtained are shown by solid lines in Fig. 2. The centroids (shown by
arrows) are found to correspond to the scission of deformed dinuclear configuration [15, 31, 32]. This suggests that,
in all cases, the fragments are emitted from fully energy relaxed composite – as expected for both FF and orbiting
processes. The increasing yields at lower energies may also be due to the second kinematical solution, which is a
signature of binary nature of emission process.
B. Average velocity
The average velocities of the fragments have been computed from the measured energies and from the Z values
using the empirical relation proposed by Charity et al. [33]:
A = Z × (2.08 + 0.0029× Z). (1)
The average velocities of the fragments obtained at different bombarding energies have been plotted in the v‖ vs. v⊥
plane in Fig. 3. It is seen that at all energies, the average velocities of different fragments fall on a circle centered
around the respective vCN , the compound nuclear velocity. This suggests that at all bombarding energies the average
velocities (as well as kinetic energies) of the fragments are independent of the c.m. emission angles and indicates that
at all these energies the fragments are emitted from a fully equilibrated CN-like source with full momentum transfer.
The magnitude of the average fragment velocities (i.e., the radii of the circles in Fig. 3) decreases with the increase
of fragment mass, which is indicative of the binary nature of the emission.
C. Angular distribution
The center-of-mass (c.m.) angular distributions of the fragments (Li, Be, B, C, and N) emitted in the 20Ne (145,
158, 170, 180 and 200 MeV) + 12C reactions are shown in Fig. 4. The transformations from the laboratory to
center-of-mass system have been done with the assumption of a two body kinematics averaged over total kinetic
energy distributions. The c.m. angular distributions of these fragments obtained at all bombarding energies follow
the 1/sinθc.m. -like variation (shown by solid lines in Fig. 4) — which further corroborate the conjecture of emission
from fully equilibrated composite.
D. Average kinetic energy
The average total kinetic energies in the center-of-mass, EtotK , for the fragments (3 ≤ Z ≤ 7) obtained at all
bombarding energies, have been displayed as a function of scattering angle in Fig. 5. The average fragment kinetic
energies in the center-of-mass have been obtained from the respective laboratory values assuming two body kinematics.
It is observed from Fig. 5 that EtotK values are almost constant for each of the exit channel. The near constancy of
EtotK indicates that at all energies the lifetime of the dinuclear complex is longer than the time needed to completely
damp the energy in the relative motion [34, 35, 36, 37]. The predictions of Viola systematics [31] for fission fragment
kinetic energies, corrected by an asymmetric factor [32], have been shown by solid lines in Fig. 5. The EtotK values
predicted from Viola systematics are found to be in good agreement with the experimental data at all bombarding
energies.
E. Average Q-value distribution
The variations of average Q-value, < Q >, with center-of-mass emission angle for the fragments Li, Be, B, C, and N
obtained at different bombarding energies are shown in Fig. 6. It is observed that the < Q > of different fragments are
independent of the center-of-mass emission angles at all bombarding energies. This is in contrast to the observation
made earlier for other light systems (16O (116 MeV) + 27Al, 28Si, 20Ne (145 MeV) + 27Al, 59Co systems), where sharp
fall off of < Q > with angle have been seen [5, 6]. The < Q > values remain nearly constant which further suggest
that at all angles, the fragments are emitted from completely equilibrated source at all incident energies considered
here.
F. Equilibrium cross-section
The energy distributions, velocity diagrams, angular distributions and < Q > distributions indicate that the
yield of these fragments (Z = 3 – 7) originates from fully energy relaxed events associated with the decay of either
compound nucleus or long-lived, orbiting dinuclear system. A detailed investigation have been made to decipher
the role played by aforementioned processes in the fragment yield by comparing the experimental yields with the
theoretical predictions of the standard statistical model [38], extended Hauser-Feshbach model (EHFM) [20]. The
experimental angle integrated yields of the fragments emitted in the 20Ne + 12C reaction at different bombarding
energies are shown in Fig. 7 by solid circles (taken from Ref. [13]) and triangles. The theoretical predictions of the
statistical model code CASCADE [38] are shown by solid lines in Fig. 7. The calculations are done considering l
values up to the critical angular momentum of fusion, lcr, at each energy (given in Table I). It is observed that at
all energies the experimental yields of the fragments Li and Be are in fair agreement with the theoretical CASCADE
prediction. However, the yields of the fragments B, C and N (near entrance channel) obtained at different energies are
much higher than those predicted by the statistical model code CASCADE. A similar observation has been reported
by Shapira et al. [12, 13] for the same system at lower energies for Carbon fragment. The theoretical predictions
using EHFM have also been shown by dotted lines in Fig. 7 for the fragments B, C and N. The EHFM predictions also
similar to those obtained from CASCADE calculations and the experimental yields are in fair excess of the theoretical
estimates of both CASCADE and EHFM.
G. Excitation energy dependence of < Q >
The average Q values (< Q >) for the fragments Li, Be, B, C, and N have been plotted in Fig. 8 as a function of the
incident energy. The linear dependence of < Q > with energy provides strong evidence that the long life time may
be associated with an orbiting phenomenon. This linear dependence of < Q > can be expressed by simple equation
of the form < Q >= c −m ∗ Ec.m., where m is the slope and c is the intercept (for example, < Q > = (14.9 ± 1.0)
- (0.97 ± 0.02) Ec.m. for the fragment Carbon). The experimentally determined intercepts are found to be in fair
agreement with kinetic energies calculated using Viola systematics. It is interesting to note that the < Q > values
obtained in the present experiment between 145 MeV and 200 MeV fall on the same straight line extrapolated from
the lower energy (∼54 – 81 MeV) data [13]. This means that the energy relaxation is complete for the fragment
emission studied here up to the incident energy of 200 MeV. Moreover, it also means that the final kinetic energy
= < Q > + Ec.m.) is nearly independent of bombarding energy — which may be due to the limitation on the
maximum value of angular momentum beyond which the formation of di-nucleus is not allowed due to centrifugal
repulsion [24].
IV. DISCUSSIONS
In general, the energy distributions, the angular distributions and the total fragment yields measured for 20Ne +
12C reaction at incident energies between 145 MeV and 200 MeV are similar to those obtained at lower incident
energies (∼ 50 - 80 MeV) for the same system (see Refs. [12, 13]). Large energy damping, 1/sinθc.m. dependence
of angular distribution and near constancy of < Q > over a wide angular range signify that the fragment decay
originates from a long lived, fully energy equilibrated system. However, the large enhancement of fragment emission
cross section (5 ≤ Z ≤ 7) over the statistical-model predictions leads to the conjecture that the orbiting mechanism
may still play a major role at these energies. The possibility of these enhancements, either due to feeding from the
secondary deexcitation of the heavier fragments or due to orbiting mechanism, are investigated in great details and
described in the following subsections.
A. Contribution from secondary decay of heavier fragments
There is a possibility that the primary heavier fragments (formed due to the binary decay of composite system) may
have sufficient excitation energy to deexcite through the emission of light particles and γ-rays and contribute to the
yield of lighter fragments. This additional contribution from the secondary decay increases the total elemental yield
of the lighter fragments. To check whether the enhancement in B, C, and N yield could be due to feeding from the
secondary decay of heavier fragments of various possible binary breakup combinations, we have performed detailed
simulations of secondary decay using the Monte-carlo binary decay version of the statistical decay code LILITA [39]
and the statistical model code CASCADE [38] and PACE4 [40]. Secondary decay of Si∗ (binary channel 28Si +
4He), Al∗ (binary channel 26,25Al + 6,7Li), Mg∗ (binary channel 24,25,23Mg + 8,7,9Be), Na∗ (binary channel 22,21Na
+ 10,11B), Ne∗ (binary channel 20Ne + 12C), F∗ (binary channel 18F + 14N), O∗ (binary channel 16O + 16O), N∗
(binary channel 14N + 18F), C∗ (binary channel 12C + 20Ne), B∗ (binary channel 10,11B + 22,21Na) and Be∗ (binary
channel 8,7,9Be + 24,25,23Mg) have been studied. Indeed the LILITA calculations (using the parameter set proposed
in the Appendix of Ref. [13] and assuming the excitation energy division follows the mass ratio [1]) are in qualitative
agreement with the experimental results obtained at 9 MeV/nucleon by Rae et al. [41] for the sequential decay of
20Ne + 12C. It was found that even at the highest excitation energy, secondary decay of Si∗ and Al∗ do not reach
up to N; the contribution of primary Mg∗, Na∗ decay to Z ≤ 7 were estimated to be <∼ 1% of the primary yield
and that of Ne∗ decay to N, C, B yield were estimated to be ∼ 10–20%, ∼ 15–20% and ∼ 30–50% of the primary
yield, respectively. Nearly ∼ 40–45% of the primary O∗ produced through binary exit channel 16O + 16O decays
to C. The secondary decay yields from the primary excited fragments are shown in Fig. 9 for different bombarding
energies. As the binary yield of O, F are small (∼ 10% of the binary Ne yield, as estimated from CASCADE [38]),
overall secondary decay contribution from O, F are smaller than that from Ne. Moreover, the simulations of energy
distributions of the secondary decay yield of C from Ne as well as F, O using the code LILITA show that they peak
at much lower energies (typically, at ∼ 45–50 MeV for Ne, ∼ 48–55 MeV for F and ∼ 55–60 MeV for O, compared to
the peak of the experimental energy distribution at ∼ 75–95 MeV).
Now, the Gaussian fitting procedure for the extraction of primary fragment yield is fairly efficient in rejecting most
of the low energy tail (typical rejection ratio ∼ 25–40% of the total yield). The energy distributions of the secondary
decay have been shown in Fig. 10 for Carbon, in Fig. 11 for Boron and in Fig. 12 for Nitrogen. In the inset of these
figures the spectra shown are the difference spectra; the difference between the experimental spectra and the Gaussian
fitted to the spectra. It has been found that the secondary decay distributions reproduce the difference spectra very
well for all the cases. It is thus evident that the secondary decay component does not interfere with the estimated
primary yield for two reasons: firstly, total secondary decay yield is not quite large, and secondly, the Gaussian fitting
procedure for the extraction of primary yield does take care, to a large extent, of the rejection of the contributions of
the secondary decay components as their energy distributions are different from those of the primary components.
B. Fragment cross-section
It has been observed that the statistical model calculations do not reproduce most of the observed experimental
yields, therefore, an additional reaction component corresponding to the orbiting mechanism has to be considered.
The large measured cross sections for B, C and N fragments led to the suggestion that an orbiting, di-nuclear
configuration is formed that decays back to the entrance channel. After the discovery of orbiting in the 28Si + 12C
system, similar enhancements of large-angle, binary-reaction yields are also observed in the present data. It is expected
that the orbiting mechanism will retain a greater memory of the entrance channel than the fusion-fission process. The
trapped, dinuclear complex can either evolve with complete amalgamation into a fully equilibrated compound nucleus
or, alternatively, escape into a binary exit channel by way of orbiting trajectories. Orbiting can therefore be described
in terms of the formation of a long-lived di-nuclear molecular complex which acts as a “doorway” state to fusion with
a strong memory of the entrance channel. The equilibrium orbiting model has been used to successfully explain both
the observed cross sections and total kinetic energy (TKE) values of the fully damped fragments for several lighter
nuclear systems at lower energies. The theoretical prediction of the equilibrium model for orbiting and fusion [15] is
denoted by dash-dotted line in Fig. 7 for the fragment B, C and N, and it also fails to explain the large enhancement in
the fragment yield. The curve displayed in Fig. 7 represents the “best fit” that can be obtained by the orbiting model
with a reasonable choice of the Bass potential parameters (strengths, short range, and long range of the proximity
potential). It is, therefore, evident that both the equilibrium orbiting and statistical decay (CASCADE, EHFM)
models result in comparable disagreement with the data. It may be interesting to note here that Shapira et al.
studied the same reaction at lower energies [12, 13] and came to the conclusion that the large enhancements in the
energy damped fragment yield observed at those energies might be due to nuclear orbiting phenomenon.
The shortcomings of the equilibrium model for orbiting does not imply that the presence of an orbiting mechanism,
as distinct from fission, can be ruled out. On the contrary, there may be a large orbiting-like contribution from non
fusion window (in the angular momentum window lcr ≤ l ≤ lgr). This is consistent, at least qualitatively, from the
fact that, CASCADE calculation [38] performed with l values up to lgr (shown by dashed lines in Fig. 7) is found
to reproduce the data fairly well. The values of lgr at different bombarding energies are given in Table I. Yields
in the transfer channels (B, N, for example) are also found to be strongly affected by the orbiting process (yield
enhancement), which may be due to stochastic nucleon exchanges during long lifetime of the dinuclear system.
In Fig. 13, we show the ratio of Beryllium to Lithium (square), Boron to Lithium (circle), Carbon to Lithium
(triangle) and Nitrogen to Lithium (inverted triangle) yield as a function of bombarding energies and the corresponding
statistical model (CASCADE) calculations (solid lines). It is found that the observed Beryllium to Lithium ratio is well
explained with the statistical model calculations. However, the other observed ratios are higher than the theoretically
calculated ratios. This implies the dominance of orbiting yield over the compound nucleus yield.
C. Comparison of the
C and
C reactions
The large orbiting yields that account for the largest part of the fully damped yields of 20Ne + 12C can be
qualitatively understood in the framework of the Number of Open Channels (NOC) model [29, 42]. The calculated
NOC are shown in Table I for both the 20Ne + 12C and the 19F + 12C reactions [29] at several excitation energies
along with the measured and calculated (fusion-fission cross sections as predicted by CASCADE) fully damped yields.
The NOC for 20Ne + 12C exhibits the characteristic minimum for a grazing angular momentum of approximately lgr
= 30h̄ [29]. This very deep minimum (NOC = 4.5) explains: (i) why resonant structures have been observed to be
significant in 20Ne + 12C [27, 28] and, (ii) why the orbiting yields observed for C fragments are much larger than
the CASCADE predictions. The comparison with 19F + 12C is instructive at E∗ = 60 MeV [7] (the corresponding
value of the yield of fragment C for 20Ne + 12C, as given in Table I, has been extracted from Fig. 7 to permit a
direct comparison with 19F + 12C). The large NOC value for 19F + 12C [29] (almost order of magnitude bigger) is
consistent with the fact that essentially no resonances have been observed in this system [43, 44]. This was confirmed
by the times scale measurements of Suaide et al. [45] who found that fusion-fission (with high NOC values), a very
slow mechanism, is more competitive than a faster process such as orbiting (with small NOC values) in 19F + 12C. It
is worth noting from Table I that CASCADE predicts almost identical fusion-fission cross section for both reactions
at E∗ = 60 MeV. On the other hand, due to the survival of orbiting at energies larger than 7 MeV/nucleon, the fully
damped yields are much more than a factor of two bigger for the 20Ne + 12C system at E∗ = 60 MeV.
V. SUMMARY AND CONCLUSIONS
The inclusive double differential cross-section for fragments having Z = 3 – 7 emitted in the reaction 20Ne (∼ 7 – 10
MeV/nucleon) + 12C have been measured. Total emission cross-section for the fragments Li to N have been estimated
from the experimental distributions. The c.m. angular distributions for the fragments at all the bombarding energies
are found to have a 1/sin θc.m.-type of dependence which signifies the emission of these fragments from a long-lived
equilibrated composite. The average velocity plots in v‖ vs. v⊥ plane indicate that the fragments are emitted from
fully equilibrated source moving with compound nucleus velocity. The average kinetic energy and the average Q-value
of the fragments are independent of the emission angles. This also suggests the emission from a long-lived, equilibrated
composite. The angle-integrated cross-section for Li and Be fragments agree well with the theoretical predictions of
statistical model but the yield of B, C and N fragments (near to entrance channel) are in excess with the theoretically
predicted values. This indicates the presence of other type of reaction process, namely orbiting. In contrast, the study
of the nearby system 19F (96 MeV) + 12C clearly showed that the fragments are emitted in the fusion-fission process
[7]. Low values of NOC [29] obtained for 20Ne + 12C system as compared to the same obtained for 19F + 12C system
also confirms the conjecture of survival of orbiting in 20Ne + 12C system at higher excitations. It is interesting to
mention at this point that, 16O, 20Ne + 28Si systems [6, 10, 11], even though α-like, do not show the characteristics
of orbiting at these energies, but orbiting-like behaviour has been observed for 28Si + 16O reaction at lower energies
[22].
The present analysis also indicates that the enhancement in fragment yield for 20Ne + 12C reactions can not be
explained by the equilibrium orbiting model [15]. This may be due to the fact that, the equilibrium orbiting model
in its present form seems to be inadequate to explain the phenomena at higher excitations, and a more complete
understanding of orbiting and vis-a-vis the angular momentum dissipation (which plays a crucial role in defining
orbiting trajectories and yield) will be required.
Acknowledgements
The authors like to thank the cyclotron operating crew for smooth running of the machine, and H. P. Sil for the
fabrication of thin silicon detectors for the experiment. One of the authors ( A. D. ) acknowledges with thanks the
financial support provided by the Council of Scientific and Industrial Research, Government of India.
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TABLE I: The angular momentum values, NOC and C fragment yield for different energies.
System Elab E
∗ lcr lgr NOC
a C yield (mb)
(MeV) (MeV) (h̄) (h̄) expt CASCADEb
Ne + C 109.5 60 20 26 5.2 122.6c 35.7
Ne + C 145 73 24 31 4.5 151.9±26.8 62.2
Ne + C 158 78 24 33 8.2 149.7±26.5 58.7
Ne + C 170 82 24 34 11.0 131.8±23.8 56.9
Ne + C 180 86 25 36 33.0 142.9±25.4 66.0
Ne + C 200 94 25 38 73.2 178.3±30.7 51.4
F + C 96 60 21 24 97.2 47.92±4.37 [7] 34.5
a Values taken from Ref. [29]
b Calculation done using lcr values given in Table I
c Extracted from Fig. 7
Energy (MeV)
Ne + 
 = 10
 = 170 MeV
0 30 60 90 120 150
10 Mg
0 30 60 90 120 150
FIG. 1: Inclusive energy distributions of different fragments emitted in the reaction 20Ne (170 MeV) +12C at θlab = 10
o. The
arrow corresponds to the expected fission fragment kinetic energy. The dashed line indicates the average energy of the recoiling
nucleus.
(a,2)(a,1)
(a,3)
(a,4)
(a,5)
0.2 (b,1)
(b,2)
(b,3)
(b,4)
0.8(b,5)
(c,1)
(c,2)
(c,3)
(c,4)
(c,5)
(d,1)
(d,2)
(d,3)
(d,4)
(d,5)
0 40 80 120
(e,1)
0 40 80 120 160
40 80 120 160
40 80 120 160
40 80 120 160 200
Energy (MeV)
(e,5)(e,4)(e,3)(e,2)
FIG. 2: Inclusive energy distributions for the fragments Lithium (a), Beryllium (b), Boron (c), Carbon (d) and Nitrogen (e)
emitted in the reaction 20Ne +12C at an angle 10o for bombarding energies 145 MeV (1), 158 MeV (2), 170 MeV (3), 180 MeV
(4) and 200 MeV (5), respectively. The arrow corresponds to the centroid of the fitted Gaussian distribution (solid curve).
170 MeV
0.04 158 MeV
0.04 145 MeV
0.04 180 MeV
0.00 0.04 0.08 0.12 0.16 0.20
200 MeV
FIG. 3: The average velocities of the fragments plotted in v‖ vs v⊥ plane at different bombarding energies. The average
velocities are denoted by filled triangles (Li), filled circles (Be), open triangles (B), open circles (C) and filled squares (N). The
arrows correspond to the compound nucleus velocities.
Ne,Li)Al
Ne,Be)Mg
Ne,B)Na
Ne,C)Ne
Ne,N)F
30 60 90
30 60 90
30 60 90
 (degree)
30 60 90
30 60 90
FIG. 4: The c.m. angular distributions of fragments (Z = 3 – 7) obtained at different bombarding energies. Solid circles (145
MeV), triangles (158 MeV), inverted triangles (170 MeV), squares (180 MeV) and diamonds (200 MeV) correspond to the
experimental data and the solid lines are f(θc.m.) ∼ 1/ sin θc.m. fit to the data.
Lithium
Berillium
Boron
Carbon   
Nitrogen   
          
          
          
10 15 20 25 30
10 15 20 25 30
10 15 20 25 30
 (degree)
10 15 20 25 30
10 15 20 25 30
FIG. 5: Average kinetic energy of different fragments obtained at Elab = 145, 158, 170, 180 and 200 MeV (denoted by inverted
triangle, square, diamond, triangle and circle, respectively) plotted as a function of laboratory angle.
20 40 60 80 100
Carbon
Lithium
Berillium
145 MeV
158 MeV
170 MeV
180 MeV
200 MeV   
Boron
40 60 80 100
 (degree)
Nitrogen
FIG. 6: Average Q-values of different fragments obtained at Elab = 145, 158, 170, 180 and 200 MeV (denoted by inverted
triangle, square, diamond, triangle and circle, respectively) plotted as a function of c.m. emission angle.
2 Lithium
Berillium
Boron
2 Carbon
40 80 120 160 200
 (MeV)
Nitrogen
FIG. 7: The excitation functions for the angle-integrated yield of the fragments. Triangles are the present data; lower energy
data (filled circles) for Carbon fragments are taken from [13]. The solid curves are the predictions of the statistical model.
The dash-dotted curves for B, C and N are prediction of equilibrium orbiting model and the dotted curves are the same from
EHFM [20]. The dashed curves show CASCADE calculations using grazing angular momentum.
0 Fragment  C
Ec.m.(MeV)
Fragment  B
0 Fragment  Li
Fragment  Be
20 40 60 80
0 Fragment  N
FIG. 8: Bombarding energy dependence of the average Q-values. The solid line shows the linear dependence of < Q > with
bombarding energy. The < Q > values at lower energies for Carbon are taken from [13].
200 MeV
4 5 6 7 8
145  MeV
170 MeV
FIG. 9: Percentage secondary decay contribution from primary Ne∗ (circle), F∗ (square) and O∗ (triangle) to Z = 5 – 7.
145 MeV
0 40 80 120
4 180 MeV
0 40 80 120
0 40 80 120 160 200
Energy (MeV)
200 MeV
0 40 80 120
FIG. 10: Secondary decay contribution for Carbon fragments at different energies. The energy distribution at θlab = 10
o along
with the fitted Gaussian are shown. Inset: Distribution shows the difference spectra (total spectra - Gaussian) and the solid
line represents the total secondary decay contribution estimated using LILITA [39].
1.0 145 MeV
0 40 80 120
180 MeV
0 40 80 120
0.2   
0 40 80 120 160 200
1.5 200 MeV
0 40 80 120
Energy (MeV)
FIG. 11: Same as Fig. 10 for Boron fragments.
3 145 MeV
0 40 80 120
4 180 MeV
0 40 80 120
0 40 80 120 160 200
200 MeV
0 40 80 120 160
Energy (MeV)
FIG. 12: Same as Fig. 10 for Nitrogen fragments.
Be/Li
0 C/Li   
140 160 180 200
 (MeV)
FIG. 13: Bombarding energy dependence of the ratio of angle-integrated fragment yield. The Beryllium to Lithium (square),
Boron to Lithium (circle), Carbon to Lithium (triangle), and Nitrogen to Lithium (inverted triangle) ratios are shown. The
solid line shows the theoretical prediction using CASCADE.
	Introduction
	Experiments
	Results
	Energy distribution
	Average velocity
	Angular distribution
	Average kinetic energy
	Average Q-value distribution
	Equilibrium cross-section
	Excitation energy dependence of <Q>
	Discussions
	Contribution from secondary decay of heavier fragments
	Fragment cross-section
	Comparison of the 20Ne + 12C and 19F + 12C reactions
	Summary and Conclusions
	References
