# Investigation of reaction and $\alpha$ production cross sections with 9Be
projectile

Satbir Kaur  V. V. Parkar  Corresponding author<EMAIL_ADDRESS>S. K.
Pandit  A. Shrivastava  K. Mahata  K. Ramachandran  Sangeeta Dhuri  P. C. Rout
A. Kumar  Shilpi Gupta  Nuclear Physics Division, Bhabha Atomic Research
Centre, Mumbai - 400085, India  Homi Bhabha National Institute,
Anushaktinagar, Mumbai - 400094, India

###### Abstract

In order to investigate the contribution of $\alpha$ production in the
reaction cross sections, measurements of elastic scattering and inclusive
$\alpha$ particle angular distributions have been carried out with the 9Be
projectile on 89Y, 124Sn, 159Tb, 198Pt, and 209Bi targets over a wide angular
range at energies near the Coulomb barrier. The measured elastic scattering
angular distributions were fitted with optical model calculations, and
reaction cross sections were extracted. The same data were also analysed using
both global optical model potentials (Global OMP) and microscopic
S$\tilde{a}$o Paulo potentials (SPP), to obtain the reaction cross sections.
The data available in the literature for 9Be projectile includes the elastic
scattering angular distributions, $\alpha$ production cross sections, and
complete fusion cross sections on these and other targets at several energies
are also utilised for comparative studies. The reaction cross section
extracted from the three potentials (Best Fit, Global OMP and SPP) are in
reasonable agreement for all the targets except for the energies below the
barrier where the results from SPP deviate by 30-50 %. Inclusive $\alpha$
particle production cross sections were also extracted by integrating the
$\alpha$ particle angular distributions. The present data and data available
from literature of reaction and $\alpha$-particle production cross sections
were utilised to make systematic studies. Systematics of reaction and
$\alpha$-particle production cross sections revealed their universal
behaviour. The ratio of complete fusion (CF), inclusive $\alpha$ cross
sections, and their sum (CF+$\alpha$) to reaction cross sections show that at
sub-barrier energies inclusive $\alpha$ dominates and above barrier CF
dominates, and cumulative of these two processes almost explains the reaction
cross section at all energies over a wide range of target mass. A comparative
study of $\alpha$ production with other weakly bound projectiles is also
performed and a clear distinction between projectile types is observed, which
is found to correlate well with $\alpha$ separation energies of the
projectiles.

###### keywords:

Weakly bound nuclei, elastic scattering, alpha production, reaction mechanism

††journal: Nuclear Physics A

##  1 Introduction

In recent times, study of nuclear reactions with nuclei having a predominant
weakly bound $\alpha$+x cluster structure (6,7Li, 9Be), have renewed interest
to probe the origin of large $\alpha$ production cross sections and the role
of coupling to low-lying states in the continuum on various reaction channels
[1, 2, 3, 4]. For understanding the mechanism of large $\alpha$ production,
detailed measurements of energy and angular distributions as well as
integrated inclusive $\alpha$ cross sections have been investigated with 6,7Li
projectiles [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21].
Complete and incomplete fusion as well as exclusive particle coincidence
measurements along with detailed calculations have been performed to
investigate the origin of large $\alpha$ production cross sections [5, 6, 7,
8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. Recent
studies with 7Li have revealed the dominance of direct $t$-stripping mechanism
over breakup fusion for large $\alpha$ production [24, 25]. The systematics
and mechanisms of $\alpha$ particle production with weakly and strongly bound
projectiles have also been reported recently [26].

In the case of 9Be, there are several elastic scattering measurements
available in the literature [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46]. From the elastic scattering measurements,
optical model potentials and reaction cross sections were extracted. The
global optical model potential for the 9Be projectile was also developed using
the available elastic scattering angular distribution data [47]. Although
there are several elastic scattering measurements, very few measurements of
$\alpha$ particle angular distributions and hence its production cross section
have been reported [28, 31, 43, 48, 49]. It will be interesting to study the
contribution of $\alpha$ production in the reaction cross section to
understand the complete reaction mechanism. In the studies with 6,7Li
projectiles, it is demonstrated that the $\alpha$ production along with
complete fusion (CF) cross sections almost exhausts the reaction cross
sections [1, 15, 18]. However, similar study does not exist with 9Be
projectile. Due to the low neutron as well as $\alpha$ separation energies and
also the Borromean cluster structure in 9Be [50], the mechanism of $\alpha$
production can be different as compared to 6,7Li projectiles. Neutron transfer
assisted breakup process could be a significant part of $\alpha$ production
for projectiles having low neutron separation energies like 9Be [51, 52, 53,
54].

The present work aims to study the contribution of inclusive $\alpha$
production cross section to the reaction cross section for 9Be induced
reaction, for a wide range of targets, at energies around the Coulomb barrier.
The reaction cross section can be estimated from the optical model analysis of
the elastic scattering angular distributions. Further, the potential
parameters obtained using elastic scattering data could be an important input
to entrance channel potential in the coupled channel calculations. Hence,
these potential parameters can be used to investigate the influence of
different inelastic, transfer, and breakup channels on elastic and fusion
cross sections and to estimate the cross sections of these non-elastic
channels as well.

In this work, we have measured elastic scattering angular distributions with
9Be projectile on various targets (89Y, 124Sn, 159Tb, 198Pt, and 209Bi) to
extract the reaction cross sections and the angular distribution of the
$\alpha$ particles to obtain the inclusive $\alpha$ production cross sections.
A systematic study has been performed using present data along with available
literature data for $\alpha$ production and complete fusion. The paper is
organized as follows: The experimental details are described in Sec. 2. The
measured elastic scattering angular distributions along with the optical model
calculations using Global OMP, SPP are discussed in Sec. 3.1. The measured
energy spectra and inclusive $\alpha$ particle angular distributions are
reported in Sec. 3.2. Systematic studies of the reaction cross sections, CF
and $\alpha$ production cross sections with 9Be projectile are described in
Sec. 4. The summary is given in Sec. 5.

##  2 Experimental Details

Figure 1:  Photograph of the experimental setup consisting of seven Si-strip
detector telescopes (T1-T7), three silicon surface barrier (SSB) detector
telescopes (S1-S3), and four Si-integrated detector telescopes (D1-D4) inside
a 1.5 m diameter scattering chamber. Two SSB detectors (M1, M2) kept at
$\pm$20∘ for absolute normalization and beam monitoring are also denoted.

The measurements were performed using the 9Be beam at the BARC-TIFR Pelletron-
LINAC Facility, Mumbai, India. The list of self-supporting targets used along
with beam energies are given in Table 1. Beam energies were corrected for the
energy loss at half the target thickness and were further used in the
analysis. The corrected beam energies are denoted as Elab in the table. The
corresponding Ec.m./VB values are also listed where, VB values are estimated
from Ref. [55]. A photograph of the experimental setup is shown in Fig. 1. As
can be seen, the experimental setup consisted of seven Si-strip detector
(Micron Semiconductors make) telescopes (T1-T7), three silicon surface barrier
(SSB) detector (ORTEC make) telescopes (S1-S3), four Si-integrated detector
(monolithic silicon $\Delta$E-E) telescopes (D1-D4) (developed by Electronics
Division, BARC, Mumbai [56]) along with two monitor detectors (M1,M2) inside a
1.5 m diameter scattering chamber. For the Si-strip detector telescopes
(T1-T7), the $\Delta$E detectors were single-sided with 16 vertical strips,
and the E detectors were double-sided with 16 strips on front (vertical) and
16 strips on the back (horizontal). Typical thicknesses of $\Delta$E strip
detectors were 50 $\mu$m (T1, T2, T5, T6 and T7) and 20 $\mu$m (T3, T4). While
the E strip detectors were of thicknesses 1.5 mm (T1-T5 and T7) and 1 mm (T6).
The active area of the Si-strip detectors was 50 x 50 mm2 and the width of
each strip was 3.1 mm. For SSB detectors (S1-S3), the thicknesses of the
$\Delta$E detectors were 45 $\mu$m (S1, S2) and 25 $\mu$m (S3). In the case of
E detectors, the thicknesses were 1mm (S2, S3) and 5 mm (S1). For the Si-
integrated detectors (D1-D4), the thicknesses were 15 $\mu$m and 300 $\mu$m
for $\Delta$E and E layers, respectively. Two SSB detectors (M1, M2) with
thicknesses $\sim$ 300 $\mu$m were kept at $\pm$20∘ for absolute normalization
and beam monitoring. The angular range covered with the detector setup was
from $\theta_{lab}$ = 16∘ to 160∘. The data were collected in an event-by-
event mode using a VME data acquisition system. The triggers for the strip
telescopes (T1-T7) were taken from the Mesytec make MSCF16 modules of the E
detectors, which correspond to ”OR” of all 16 strips. Final master gate was
generated as the ”OR” of the triggers from the strip telescopes, E of SSB
telescopes and monitor detectors. The detectors were calibrated using the
energy of $\alpha$ particles emitted from the 229Th source and the elastic
scattering data from different targets listed above. A typical two-dimensional
energy calibrated spectrum of $\Delta$E vs Etotal for 9Be+159Tb system at
Elab=35.3 MeV and $\theta_{lab}$ = 86∘ is shown in Fig. 2(a). The x-projection
of the $\alpha$ band is shown in Fig. 2(b).

Table 1:  Details of targets used, beam energies, corrected lab energies at half thickness of the target, and Ec.m/VB values. The VB values used are calculated from Ref. [55]. Target | thickness | Ebeam | Elab | Ec.m/VB
---|---|---|---|---
| (mg/cm2) | (MeV) | (MeV) |
209Bi | 0.5 | 35.8 | 35.7 | 0.85
198Pt | 1.5 | 35.8 | 35.4 | 0.89
159Tb | 1.7 | 35.8 | 35.3 | 1.02
124Sn | 1.7 | 29.7 | 29.1 | 1.03
|  | 35.8 | 35.2 | 1.25
89Y | 1.0 | 29.7 | 29.3 | 1.24

##  3 Results and Discussion

###  3.1  Elastic scattering angular distributions

Figure 2:  (a) Typical two-dimensional energy calibrated spectrum of $\Delta$E
vs Etotal for 9Be+159Tb reaction at energy Elab=35.3 MeV and $\theta_{lab}$ =
86∘. (b) x-projection of $\alpha$ band.  Figure 3:  Elastic scattering angular
distributions for (a)209Bi, (b) 198Pt, (c) 159Tb, (d) 89Y, (e,f) 124Sn
targets. The solid lines are the results of the optical model fit, the dotted
lines represents the optical model calculations using global optical model
potentials and the dashed lines represent the calculations with SPP.

The experimental elastic scattering cross sections normalized to the
Rutherford cross sections for the 9Be projectile on 89Y, 124Sn, 159Tb, 198Pt,
and 209Bi targets are shown in Fig. 3. The cross section of the corresponding
reaction channels (elastic scattering or $\alpha$ particle) was obtained by
taking the ratio of the yields of the corresponding reaction channel (elastic
scattering or $\alpha$ particle) to the yield of the monitor detector. In this
method, the uncertainties arising due to the target thickness and beam current
were eliminated. The ratio of the two monitor counts was found to be around 1
throughout the run. Thus, the effect of beam wandering was not significant.
Hence, the error bars in the cross sections are due to statistical errors
only. Optical model (OM) calculations were performed using both the
phenomenological optical model potentials [47] and microscopic S$\tilde{a}$o
Paulo potentials [57, 58] with the code FRESCO (version FRES 2.9) [59]. For
phenomenological optical model potential, the recently developed global
optical model potential (Global OMP) for the 9Be projectile [47] was used.
This optical potential has a Woods-Saxon form: V(r,E) = VR(r,E) +
i[WS(r,E)+WV(r,E)] + VC(r) where VR denotes the real part of the potential, WS
and WV are the surface and volume imaginary parts of potential, respectively,
and VC(r) is the Coulomb potential. Based on this potential, the energy-
dependent parameters defined in Ref. [47] were used for the calculations. The
calculations using the global optical model potential are shown as dotted
lines in Fig. 3. The optical model calculations were also performed using the
microscopic double-folding S$\tilde{a}$o Paulo potential (SPP), which takes
into account the effects of Pauli non-locality related to the exchange of
nucleons between the projectile and target [57, 58]. In the context of OM
analysis (VOM = VSPP (NR+iNI)), the imaginary potential has the same form as
the real part with some normalization constant. For real and imaginary parts
of the optical potential, the strength coefficients are NR = 1.0 and NI =
0.78. This procedure has been shown to be suitable for describing the elastic
scattering cross sections for many systems in wide energy range [60]. The
calculations using SPP are shown with dashed lines in Fig. 3. The elastic
scattering angular distributions were also fitted using the SFRESCO module of
the FRESCO code [59], utilizing Woods-Saxon forms for both real and imaginary
potentials. The calculations using SFRESCO are shown as solid lines in Fig. 3.
The extracted reaction cross sections from all three (Best fit, Global OMP and
SPP) different calculations are given as $\sigma_{R}$ (Ref.), $\sigma_{R}$
(Global OMP) and $\sigma_{R}$ (SPP) respectively in Table 2. The available
elastic scattering data for 28Si, 51V, 89Y, 124Sn, 208Pb and 209Bi targets at
various energies were also utilized for which the global OMP and SPP
calculations were performed, and the reaction cross sections are listed in
Table 2. The reaction cross sections were also derived from the given set of
optical model potential parameters in [28, 31, 34, 43, 61] and are listed as
$\sigma_{R}$ (Ref) in Table 2. As can be seen from the table, three listed
reaction cross sections are in reasonable agreement with each other at all the
energies except for the energies below the barrier where the results from SPP
deviate by 30-50 %.

###  3.2  $\alpha$ particle energy and angular distributions

Figure 4:  Energy spectra for $\alpha$ particles at two (grazing and backward)
angles for (a,b) 209Bi, (c,d) 198Pt, (e,f) 159Tb at 35.8 MeV and (g,h) 124Sn,
(i,j) 89Y at 29.7 MeV. The compound nuclear contribution from PACE2 is
represented by solid line in (i,j).

Energy distributions of $\alpha$ particles at two (grazing and backward)
angles are shown for all the targets in Fig. 4(a-j). Statistical model
calculations for compound nuclei were carried out using the code PACE2 [62] to
estimate the compound nuclear contribution in the $\alpha$ spectra. The level
density parameter of a = A/10 MeV-1 was used. The default optical potentials
available in PACE2 for neutrons and protons [63] and for $\alpha$ particles
[64] emission was used. For the present data, it was found that the compound
nuclear contributions for $\alpha$ particles with heavier targets (Z=83, 78,
65, and 50) were negligible (about 1% or less), while for medium mass 89Y
target at Ec.m. = 1.2 VB it was around 7%, which is shown by solid line in
Fig. 4(i-j).

Figure 5:  Angular distributions of inclusive $\alpha$ particles for reactions
induced by 9Be projectile on different targets at beam energies (a-d) 35.8 MeV
and (e-f) 29.7 MeV along with compound nuclear contribution (dashed lines)
calculated using PACE2. The hollow symbols in (d,f) represents $\alpha$
angular distribution after subtracting the compound nuclear contribution.
Continuous lines are guide to an eye.

Next, the energy integrated $\alpha$ particle yields were obtained at
different angles, and the angular distributions at different beam energies for
various targets are plotted in Fig. 5. The errors in the cross sections are
statistical only. These angular distributions are found to peak at their
respective grazing angles. Also, the grazing angle is shifting towards the
backward angles with the increasing atomic number of the target as expected
due to the change in the Coulomb barrier.

These angular distributions were then fitted with a Gaussian distribution, and
an angle integrated total inclusive $\alpha$ cross section was obtained
following the method given in Ref. [21]. Negligible compound nuclear
contributions were then subtracted from total inclusive $\alpha$ cross
sections to get the non CF $\alpha$ cross sections and are listed as
$\sigma_{\alpha}$ in Table 2. The available non CF $\alpha$ production cross
sections and the CF cross sections available with 51V, 89Y, 124Sn, 208Pb and
209Bi targets at various energies are also listed in Table 2.

Table 2:  The measured $\alpha$ ($\sigma_{\alpha}$) and CF ($\sigma_{CF}$)
cross sections are listed along with reaction cross sections obtained from
Global OMP, SPP, and using potential parameters from those available in the
references as (Ref.) for various targets and lab energies ($E_{lab}$) with 9Be
projectile. Also, the reaction cross section extracted by fitting the present
data is listed under ($\sigma_{R}$ (Ref.)). The Coulomb barrier VB for 9Be
projectile with 209Bi, 208Pb, 198Pt, 159Tb, 124Sn, 89Y, 51V and 28Si targets
are 40.1 MeV, 39.5 MeV, 37.9 MeV, 32.9 MeV, 26.2 MeV, 21.5 MeV, 13.6 MeV, and
8.9 MeV respectively, estimated from Ref. [55]. (see text for more details)

Targets | Elab | Ec.m./VB | $\sigma_{\alpha}$ | $\sigma_{CF}$ | $\sigma_{R}$ | $\sigma_{R}$ | $\sigma_{R}$ |  $\sigma_{R}$ \- $\sigma_{CF}$
---|---|---|---|---|---|---|---|---
|  |  |  |  | Ref. | Global OMP | SPP |
| (MeV) |  | (mb) | (mb) | (mb) | (mb) | (mb) | (mb)
| 35.7 | 0.85 | 203 $\pm$ 47 | 0.62 $\pm$ 0.12b | 55$\pm$18 | 41 | 25 | 54$\pm$18
| 36.2 | 0.90 | 74.7 $\pm$ 7.5a | 1.17 $\pm$ 0.13b |  | 52 | 34 | 51 $\pm$ 0.13
| 37.2 | 0.93 | 114.2 $\pm$ 11.4a | 4.74 $\pm$ 0.28b | 116d | 79 | 57 | 111 $\pm$ 0.28
| 38.3 | 0.96 | 229.3 $\pm$ 23a | 14.91 $\pm$ 0.42b | 138d | 132 | 98 | 123 $\pm$ 0.42
| 39.2 | 0.98 | 242.5 $\pm$ 24a | 27.41 $\pm$ 1.11b | 189d | 175 | 148 | 162 $\pm$ 1.11
| 40.3 | 1.01 | 282.3 $\pm$ 28a | 57.34 $\pm$ 0.57b | 285d | 254 | 227 | 228 $\pm$ 0.57
| 41.3 | 1.03 | 419.9 $\pm$ 42a | 103.4 $\pm$ 0.74b | 382d | 342 | 314 | 279 $\pm$ 0.74
209Bi | 42.3 | 1.06 | 509.1 $\pm$ 51a | 202.3 $\pm$ 4.13b | 492d | 438 | 407 | 290 $\pm$ 4.13
| 43.3 | 1.08 | 509.9 $\pm$ 51a | 250.7 $\pm$ 6.05b |  | 537 | 502 | 286 $\pm$ 6.05
| 44.3 | 1.11 | 532.2 $\pm$ 53a | 236 $\pm$ 7c | 714d | 635 | 595 | 478 $\pm$ 7
| 45.3 | 1.13 | 504.8 $\pm$ 51a | 347.2 $\pm$ 3.78b |  | 731 | 684 | 384 $\pm$ 3.78
| 46.3 | 1.16 | 423.5 $\pm$ 42a | 374.4 $\pm$ 9.1b | 832e | 823 | 770 | 458 $\pm$ 9.1
| 47.2 | 1.18 | 460.4 $\pm$ 46a | 452.9 $\pm$ 6.34b |  | 903 | 845 | 450 $\pm$ 6.34
| 48.3 | 1.21 | 550.7 $\pm$ 55a | 521.2 $\pm$ 8.03b | 1024e | 995 | 931 | 503 $\pm$ 8.03
| 35.9 | 0.87 | 166 $\pm$ 8f | 0.56 $\pm$ 0.22g |  | 54 | 36 | 53 $\pm$ 0.22
| 38 | 0.92 | 207 $\pm$ 13f | 9.5 $\pm$ 0.9g | 156d | 129 | 105 | 147 $\pm$ 0.9
| 40 | 0.97 | 309 $\pm$ 7f | 55.6 $\pm$ 2.1g | 313d | 265 | 240 | 257 $\pm$ 2.1
| 42 | 1.02 | 437 $\pm$ 6f | 142.5 $\pm$ 4g | 513d | 452 | 424 | 371 $\pm$ 4
208Pb | 44.1 | 1.07 | 445 $\pm$ 10f | 243.7 $\pm$ 4.9g | 722d | 660 | 612 | 478 $\pm$ 4.9
| 46.1 | 1.12 | 413 $\pm$ 10f | 351.4 $\pm$ 6.6g |  | 849 | 797 | 498 $\pm$ 6.6
| 48 | 1.16 | 515 $\pm$ 10f | 453.8 $\pm$ 8.6g |  | 1016 | 949 | 562 $\pm$ 8.6
| 50.2 | 1.21 | 585 $\pm$ 10f | 570 $\pm$ 12g | 1263d | 1188 | 1096 | 693 $\pm$ 12
198Pt | 35.4 | 0.89 | 264 $\pm$ 4.1 |  | 66$\pm$14 | 81 | 59 |
159Tb | 35.3 | 1.02 | 609 $\pm$ 7.8 |  | 447$\pm$50 | 390 | 377 |
124Sn | 29.1 | 1.03 | 460 $\pm$ 3.7 | 129.3 $\pm$ 5.3h | 425$\pm$31 | 396 | 390 | 296 $\pm$ 31
| 35.2 | 1.25 | 663 $\pm$ 16 | 517 $\pm$ 11h | 1037$\pm$15 | 1018 | 988 | 520 $\pm$ 19
| 22.7 | 0.96 | 169.9 $\pm$ 60.9i | 33.2 $\pm$ 1.9j | 124 $\pm$ 18i | 173 | 153 | 91 $\pm$ 18
| 24.7 | 1.04 | 377.8 $\pm$ 129.2i | 132 $\pm$ 7j | 293 $\pm$ 27i | 372 | 364 | 161 $\pm$ 28
| 26.7 | 1.13 | 513.3 $\pm$ 49.5i | 265 $\pm$ 14j | 583 $\pm$ 35i | 591 | 586 | 318 $\pm$ 38
89Y | 28.7 | 1.21 | 533.6 $\pm$ 38.5i | 361 $\pm$ 20j | 716 $\pm$ 27i | 792 | 782 | 355 $\pm$ 34
| 29.3 | 1.24 | 566 $\pm$ 4.8 | 495 $\pm$ 35i | 813$\pm$78 | 844 | 832 | 318 $\pm$ 85
| 33.2 | 1.40 | 604.7 $\pm$ 31.19i | 559 $\pm$ 32j | 1156 $\pm$ 81i | 1172 | 1131 | 597 $\pm$ 87
51V | 25.3 | 1.58 | 460 $\pm$ 58k |  | 1070k | 1175 | 1147 |
| 27.3 | 1.70 | 576 $\pm$ 45k |  | 1293k | 1303 | 1263 |
28Si | 14 | 1.19 | 330 $\pm$ 50l | 310 $\pm$ 31l | 580 $\pm$ 29l | 535 | 509 | 270 $\pm$ 42
| 20 | 1.69 | 390 $\pm$ 40l | 680 $\pm$ 68l | 1140 $\pm$ 57l | 1084 | 1058 | 460 $\pm$ 89

* The measured $\sigma_{R}$ (Ref.), $\alpha$ ($\sigma_{\alpha}$) and CF ($\sigma_{CF}$) cross sections are from a[49], b[66], c[67], d[34], e[61], f[48], g[68], h[69], i[31], j[70], k[28],l[43]

Figure 6:  (a) Reaction cross sections $\sigma_{R}$ and (b) Reduced reaction
cross sections $\sigma_{red}$ as a function of reduced energy ($E_{red}$) for
heavy and medium-mass targets with 9Be projectile and for light mass
projectiles with 9Be target. The filled data represents the present work and
the unfilled/semi-filled data are from Refs.[27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]

##  4 Systematic study of reaction and $\alpha$ production cross sections

In the following subsections, the systematics of reaction cross sections,
inclusive $\alpha$ cross sections, and the ratios of inclusive $\alpha$ and
measured CF cross sections to reaction cross sections are shown. In order to
remove the effect of the barrier height, the x-axis is chosen as reduced
energy Ered = Ec.m. ($A_{P}$1/3 \+ $A_{T}$1/3)/($Z_{P}Z_{T}$) as used in Ref.
[65] where $Z_{P}$ $(Z_{T})$ and $A_{P}$ $(A_{T})$ are the atomic numbers and
atomic masses of the projectile (target), respectively.

###  4.1 Reaction cross sections

The reaction cross sections obtained from the optical model calculations for
the present work, along with those reported in the literature involving the
9Be nucleus [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,
43, 44, 45, 46] are shown in Fig. 6 (a). It is found that the reaction cross
sections ($\sigma_{R}$) involving 9Be nucleus and nuclei lighter than 12C
nucleus show a slightly different trend from the other nuclei as seen in Fig.
6 (a). To understand this, these reaction cross sections were reduced as
$\sigma_{red}$ = $\sigma_{R}$/($A_{P}$1/3 \+ $A_{T}$1/3)2 [65] to exclude the
effects due to geometrical size as shown in Fig. 6 (b) which follows a
universal trend.

###  4.2 $\alpha$ production cross sections

The inclusive $\alpha$ cross sections with the 9Be projectile presented in
Fig. 7 (a) are from the present work and those available in the literature
[28, 31, 43, 48, 49]. A systematic universal behaviour in $\alpha$ cross
sections is seen, similar to those observed with 6,7Li projectiles [6, 7, 11,
13, 15, 18, 21, 26]. To understand this trend, the difference between reaction
cross sections $\sigma_{R}$ and measured CF cross sections $\sigma_{CF}$ for
the 9Be+208Pb system (as a representative case) are compared and found to give
a good description with the measured inclusive $\alpha$ cross sections as
shown in Fig. 7 (a). Same is observed with other targets (209Bi, 89Y and
124Sn). The $\sigma_{R}$ and $\sigma_{CF}$ are listed in Table 2. From the
ratio of $\alpha$ cross sections to reaction cross sections (Fig. 7(b)), it is
observed that the $\alpha$ cross sections are more than 100% of the reaction
cross sections at sub-barrier energies, which then decreases up to 40% at
above-barrier energies. At the sub-barrier energies, it can be interpreted
that the contribution to the inclusive $\alpha$ from the reaction channels
e.g. 1n-transfer, breakup of 9Be leading to two $\alpha$ particles are
dominant over the reaction channels e.g. $\alpha$/5He capture, which leads to
only one $\alpha$ particle in the outgoing channel. Similar conclusions were
drawn in Ref. [71] in the study of 9Be+169Tm,181Ta,187Re and 197Au systems. As
a result, at sub-barrier energies, the $\alpha$ production cross section is
larger than the reaction cross section.

Figure 7:  (a) Systematical behaviour of inclusive $\alpha$ cross sections for
different targets with 9Be projectile as a function of reduced energy. The
filled data represents present work and the unfilled data are from Ref.[28,
31, 43, 48, 49]. The dashed line shows $\sigma_{R}-\sigma_{CF}$ data for
9Be+208Pb system. Ratio of (b) $\sigma_{\alpha}$ to $\sigma_{R}$, (c)
$\sigma_{CF}$ to $\sigma_{R}$ and (d) ($\sigma_{CF}$+$\sigma_{\alpha}$) to
$\sigma_{R}$, as a function of reduced energy ($E_{red}$) for various targets
with 9Be projectile. List of data used is given in Table 2. (see text for
details) Figure 8:  Systematic comparison of inclusive $\alpha$ cross sections
due to non-CF processes for different targets with 6,7Li [6, 7, 9, 11, 13, 15,
17, 19, 72, 73, 74, 75, 76, 77], 9Be [28, 31, 43, 48, 49], 6He [78, 79, 80,
81, 82, 83, 84, 85] and 7Be [86, 87] projectiles as a function of reduced
energy. (see text for details) Figure 9:  Non-CF inclusive $\alpha$ cross
section for with various targets for projectiles 6He [80, 82], 6,7Li [15, 75],
7Be [87], 9Be [48], 12C [88, 89], and 14N [90] around 1.2 Vb as a function of
$\alpha$ separation energies for projectiles (Sα) is shown. The line is fit to
the data (see text for details).

To compare the individual and cumulative contributions of CF and $\alpha$
cross sections in reaction cross sections, we have plotted the fraction of
$\alpha$, CF, and cumulative CF+$\alpha$ cross sections over reaction cross
sections in Fig. 7(b), Fig. 7(c) and Fig. 7(d) respectively. The data
available in the literature for CF and $\alpha$ cross sections with various
targets are given in Table 2. As shown in Fig. 7(c), the ratio of CF to
reaction cross sections increases with energy and saturates around 50-60% at
energies above the barrier for all targets. According to Fig. 7(b) and Fig.
7(c), it can be interpreted that the inclusive $\alpha$ is dominant at sub-
barrier energies and CF is dominant at above-barrier energies. The sum of
these two cross sections (CF+$\alpha$), shown in Fig. 7(d), is found to be
greater than the reaction cross sections, owing primarily to the double
$\alpha$ events from the 1n-transfer and breakup of the 9Be projectile, as
discussed in Sec. 3.2 and Sec. 4.2.

Inclusive $\alpha$ cross sections with other weakly bound stable and unstable
projectiles are also compared in Fig. 8. Lines are shown to guide the eye. Non
CF inclusive $\alpha$ production data available with 6,7Li [6, 7, 9, 11, 13,
15, 17, 19, 72, 73, 74, 75, 76, 77], 9Be [28, 31, 43, 48, 49], 6He [78, 79,
80, 81, 82, 83, 84, 85] and 7Be [86, 87] projectiles are utilised for making
this systematic study. As can be seen, an increase in $\sigma_{\alpha}$ with
incident energy is observed for all the projectiles. There is a distinction
between 6He compared with 6,7Li and 9Be induced reactions. Among 6,7Li and 9Be
projectiles, the $\alpha$ production with 6Li and 9Be is higher than 7Li
projectile. Surprisingly limited data available with 7Be projectile on 28Si
and 58Ni targets are similar to 7Li projectile. Further investigation is
required to understand the systematic trend.

In order to investigate further, the dependence of non-CF $\alpha$ cross
sections at around 1.2 Vb for 6He [80, 82], 6,7Li [15, 75], 7Be [87], 9Be
[48], and 12C [88, 89] 14N [90] projectiles with various targets on $\alpha$
separation energies $S_{\alpha}$ of the projectiles are shown in Fig. 9.
Earlier, $\alpha$ production cross sections was shown to correlate with both
$\alpha$ and neutron separation energies [26, 91]. As can be seen, all the
systems, except 7,9Be, show a systematic behaviour. The line represents a fit
to the data (excluding 7,9Be data) with the function a+(b/xc), where a=32,
b=1010, and c= 1.96. While the 9Be shows enhancement in $\alpha$ yields, 7Be
exhibits suppression with respect to the systematic behaviour. The breakup and
1n-transfer of 9Be projectiles lead to double $\alpha$ events. Therefore, it
might be a reason for enhanced $\alpha$ yields. In fact, it is observed that
the measured cross sections of $\alpha$ producing channels (Direct+Incomplete
fusion) for 9Be projectile with 238U [92] and 197Au [93] targets at around 1.2
Vb are about 263-340 mb, which are close to the value according to the
systematics of Fig. 9. There are very few measurements using the 7Be
projectile. In the present study, the 7Be data point was obtained by
interpolating the available experimental data [87], and was found to be
significantly lower as compared to the systematics. However, the sum of
measured cross sections of Direct+Incomplete fusion ($\alpha$ producing
channels ) at around 1.2 Vb is about 344 mb for 7Be+238U [92], which is in
good agreement with the systematics of Fig. 9. Therefore, more studies are
required to understand the behaviour of Be projectiles.

##  5 Summary

The elastic scattering and inclusive $\alpha$ particle angular distributions
have been measured with 9Be projectile on 89Y, 124Sn, 159Tb, 198Pt, and 209Bi
targets at energies around the Coulomb barrier. To obtain the reaction cross
section, the elastic scattering angular distribution has been compared with
the optical model calculations using both, phenomenological global optical
model potential (Global OMP) and microscopic S$\tilde{a}$o Paulo potentials
(SPP). The systematic study of reaction and inclusive $\alpha$ cross sections
for the present work and those reported in the literature were found to follow
a universal behavior. It is observed that for energies below the barrier, the
$\alpha$ production cross sections are larger than the reaction cross section
mainly due to the 1n-transfer and breakup processes which contribute to two
$\alpha$ particles. At sub-barrier energies inclusive $\alpha$ is dominant,
and for above-barrier, CF is dominant, and the sum of these two processes
(CF+$\alpha$) almost explains the reaction cross sections at all the energies
over a wide range of target mass. The $\alpha$ production cross sections with
weakly bound projectiles 6He, 6,7Li and 7,9Be have also been compared. It is
observed that the $\alpha$ production with 6He projectile is larger than
others at all the energies. Among 6,7Li and 9Be projectiles, $\alpha$
production with 6Li and 9Be projectile are similar and larger than 7Li.
Further, the non-CF $\alpha$ cross sections were found to correlate well with
separation energies $S_{\alpha}$ of the projectiles.

##  6 Acknowledgments

We would like to thank the Pelletron Linac Facility staff of BARC-TIFR,
Mumbai, India, for smooth operation during the experi- ment. We are also
thankful to Mr. P. Patale for his help during the experiment. We also thank
target lab staff of TIFR for their help in the target preparation. One of the
authors (S.K.) acknowledges the fellowship through the CSIR-UGC India through
NET-JRF scheme. S.D. acknowledges the funding from DST-INSPIRE Fellowship
scheme of Govt. of India.

## References

  * Jha et al. [2020] V. Jha, V. V. Parkar, and S. Kailas, Phys. Rep. 845, 1 (2020), and references therein.
  * Kolata et al. [2016] J. J. Kolata, V. Guimarães, and E. F. Aguilera, Eur. Phys. J. A 52, 123 (2016).
  * Canto et al. [2015] L. F. Canto, P. R. S. Gomes, R. Donangelo, J. Lubian, and M. S. Hussein, Phys. Rep. 596, 1 (2015).
  * Keeley et al. [2009] N. Keeley, N. Alamanos, K. Kemper, and K. Rusek, Prog. Part. Nucl. Phys. 63, 396 (2009).
  * Signorini et al. [2003] C. Signorini, A. Edifizi, M. Mazzocco, M. Lunardon, D. Fabris, A. Vitturi, P. Scopel, F. Soramel, L. Stroe, G. Prete, et al., Phys. Rev. C 67, 044607 (2003).
  * Pakou et al. [2003] A. Pakou, N. Alamanos, A. Gillibert, M. Kokkoris, S. Kossionides, A. Lagoyannis, N. G. Nicolis, C. Papachristodoulou, D. Patiris, D. Pierroutsakou, et al., Phys. Rev. Lett. 90, 202701 (2003).
  * Pakou et al. [2005] A. Pakou, N. G. Nicolis, K. Rusek, N. Alamanos, G. Doukelis, A. Gillibert, G. Kalyva, M. Kokkoris, A. Lagoyannis, A. Musumarra, et al., Phys. Rev. C 71, 064602 (2005).
  * Pakou et al. [2006] A. Pakou, N. Alamanos, N. Clarke, N. Davis, G. Doukelis, G. Kalyva, M. Kokkoris, A. Lagoyannis, T. Mertzimekis, A. Musumarra, et al., Phys. Lett. B 633, 691 (2006), ISSN 0370-2693.
  * Shrivastava et al. [2006] A. Shrivastava, A. Navin, N. Keeley, K. Mahata, K. Ramachandran, V. Nanal, V. V. Parkar, A. Chatterjee, and S. Kailas, Phys. Lett. B 633, 463 (2006).
  * Pakou et al. [2007] A. Pakou, K. Rusek, N. Alamanos, X. Aslanoglou, S. Harissopulos, M. Kokkoris, A. Lagoyannis, T. J. Mertzimekis, A. Musumarra, N. G. Nicolis, et al., Phys. Rev. C 76, 054601 (2007).
  * F.A. Souza et al. [2009] F.A. Souza, C. Beck, N. Carlin, N. Keeley, R. Liguori Neto, M. de Moura, M. Munhoz, M. D. Santo, A. Suaide, E. Szanto, et al., Nucl. Phys. A 821, 36 (2009).
  * Santra et al. [2009] S. Santra, V. V. Parkar, K. Ramachandran, U. K. Pal, A. Shrivastava, B. J. Roy, B. K. Nayak, A. Chatterjee, R. K. Choudhury, and S. Kailas, Phys. Lett. B 677, 139 (2009).
  * Kumawat et al. [2010] H. Kumawat, V. Jha, V. V. Parkar, B. J. Roy, S. Santra, V. Kumar, D. Dutta, P. Shukla, L. M. Pant, A. K. Mohanty, et al., Phys. Rev. C 81, 054601 (2010).
  * Souza et al. [2010] F. A. Souza, N. Carlin, C. Beck, N. Keeley, A. Diaz-Torres, R. Liguori Neto, C. Siqueira-Mello, M. M. de Moura, M. G. Munhoz, R. A. N. Oliveira, et al., Eur. Phys. J. A 44, 181 (2010).
  * Santra et al. [2012] S. Santra, S. Kailas, V. V. Parkar, K. Ramachandran, V. Jha, A. Chatterjee, P. K. Rath, and A. Parihari, Phys. Rev. C 85, 014612 (2012).
  * Luong et al. [2013] D. H. Luong, M. Dasgupta, D. J. Hinde, R. du Rietz, R. Rafiei, C. J. Lin, M. Evers, and A. Diaz-Torres, Phys. Rev. C 88, 034609 (2013).
  * Pandit et al. [2016] S. K. Pandit, A. Shrivastava, K. Mahata, N. Keeley, V. V. Parkar, P. C. Rout, K. Ramachandran, I. Martel, C. S. Palshetkar, A. Kumar, et al., Phys. Rev. C 93, 061602 (R) (2016).
  * Pandit et al. [2017] S. K. Pandit, A. Shrivastava, K. Mahata, V. V. Parkar, R. Palit, N. Keeley, P. C. Rout, A. Kumar, K. Ramachandran, S. Bhattacharyya, et al., Phys. Rev. C 96, 044616 (2017).
  * Chattopadhyay et al. [2016] D. Chattopadhyay, S. Santra, A. Pal, A. Kundu, K. Ramachandran, R. Tripathi, D. Sarkar, S. Sodaye, B. K. Nayak, A. Saxena, et al., Phys. Rev. C 94, 061602(R) (2016).
  * Chattopadhyay et al. [2018] D. Chattopadhyay, S. Santra, A. Pal, A. Kundu, K. Ramachandran, R. Tripathi, B. J. Roy, Y. Sawant, B. K. Nayak, A. Saxena, et al., Phys. Rev. C 98, 014609 (2018).
  * Joshi et al. [2022] C. Joshi, H. Kumawat, V. V. Parkar, D. Dutta, S. V. Suryanarayana, V. Jha, R. K. Singh, N. L. Singh, and S. Kailas, Phys. Rev. C 105, 034615 (2022).
  * Jin Lei and Moro [2015] Jin Lei and A. M. Moro, Phys. Rev. C 92, 044616 (2015).
  * Jin Lei and Antonio M. Moro [2017] Jin Lei and Antonio M. Moro, Phys. Rev. C 95, 044605 (2017).
  * Pandit et al. [2021] S. K. Pandit, A. Shrivastava, K. Mahata, N. Keeley, V. V. Parkar, R. Palit, P. C. Rout, K. Ramachandran, A. Kumar, S. Bhattacharyya, et al., Phys. Lett. B 820, 136570 (2021).
  * Cook et al. [2019] K. J. Cook, E. C. Simpson, L. T. Bezzina, M. Dasgupta, D. J. Hinde, K. Banerjee, A. C. Berriman, and C. Sengupta, Phys. Rev. Lett. 122, 102501 (2019).
  * Parkar et al. [2023] V. V. Parkar, V. Jha, and S. Kailas, Eur. Phys. J. A (Lett.) 59, 88 (2023).
  * Umbelino et al. [2022] U. Umbelino, R. Lichtenthäler, O. C. B. Santos, K. C. C. Pires, A. S. Serra, V. Scarduelli, A. L. de Lara, E. O. N. Zevallos, J. C. Zamora, A. Lépine-Szily, et al., Phys. Rev. C 106, 054602 (2022).
  * Kumawat et al. [2022] H. Kumawat, Prasanna M. , V. V. Parkar, C. Joshi, A. Kundu, A. Pal, K. Ramachandran, D. Dutta, S. Santra, and S. Kailas, Phys. Rev. C 106, 024602 (2022).
  * Arazi et al. [2018] A. Arazi, J. Casal, M. Rodríguez-Gallardo, J. M. Arias, R. Lichtenthäler Filho, D. Abriola, O. A. Capurro, M. A. Cardona, P. F. F. Carnelli, E. de Barbará, et al., Phys. Rev. C 97, 044609 (2018).
  * J. C. Morales-Rivera et al. [2016] J. C. Morales-Rivera, E. Martinez-Quiroz, T. L. Belyaeva, E. F. Aguilera, D. Lizcano, and P. Amador-Valenzuela, Eur. Phys. J. Web Conf. 117, 07027 (2016).
  * Palshetkar et al. [2014] C. S. Palshetkar, S. Santra, A. Shrivastava, A. Chatterjee, S. K. Pandit, K. Ramachandran, V. V. Parkar, V. Nanal, V. Jha, B. J. Roy, et al., Phys. Rev. C 89, 064610 (2014).
  * Zamora et al. [2011] J. C. Zamora, V. Guimarães, A. Barioni, A. Lépine-Szily, R. Lichtenthäler, P. N. de Faria, D. R. Mendes, L. R. Gasques, J. M. B. Shorto, V. Scarduelli, et al., Phys. Rev. C 84, 034611 (2011).
  * Di Pietro et al. [2010] A. Di Pietro, G. Randisi, V. Scuderi, L. Acosta, F. Amorini, M. J. G. Borge, P. Figuera, M. Fisichella, L. M. Fraile, J. Gomez-Camacho, et al., Phys. Rev. Lett. 105, 022701 (2010).
  * Yu et al. [2010] N. Yu, H. Q. Zhang, H. M. Jia, S. T. Zhang, M. Ruan, F. Yang, Z. D. Wu, X. X. Xu, and C. L. Bai, J. Phys. G: Nucl. Part. Phys. 37, 075108 (2010).
  * P. R. S. Gomes et al. [2009] P. R. S. Gomes, J. Lubian, B. Paes, V. N. Garcia, D. S. Monteiro, I. Padrón, J. M. Figueira, A. Arazi, O. A. Capurro, L. Fimiani, et al., Nucl. Phys. A 828, 233 (2009).
  * E. A. Benjamim et al. [2007] E. A. Benjamim, A. Lépine-Szily, D. R. Mendes Junior, R. Lichtenthäler, V. Guimarães, P. R. S. Gomes, L. C. Chamon, M. S. Hussein, A. M. Moro, A. Arazi, et al., Phys. Lett. B 647, 30 (2007).
  * Gomes et al. [2006] P. R. S. Gomes, I. Padron, E. Crema, O. A. Capurro, J. Niello, A. Arazi, G. V. Martí, J. Lubian, M. Trotta, A. J. Pacheco, et al., Phys. Rev. C 73, 064606 (2006).
  * Martí et al. [2005] G. V. Martí, P. R. S. Gomes, M. D. Rodríguez, J. O. Fernández Niello, O. A. Capurro, A. J. Pacheco, J. E. Testoni, M. Ramírez, A. Arazi, I. Padron, et al., Phys. Rev. C 71, 027602 (2005).
  * Gomes et al. [2005] P. R. S. Gomes, M. D. Rodríguez, G. V. Martí, I. Padron, L. C. Chamon, J. O. Fernández Niello, O. A. Capurro, A. J. Pacheco, J. E. Testoni, A. Arazi, et al., Phys. Rev. C 71, 034608 (2005).
  * Gomes et al. [2004] P. R. S. Gomes, R. M. Anjos, C. Muri, J. Lubian, I. Padron, L. C. Chamon, R. Liguori Neto, N. Added, J. O. Fernández Niello, G. V. Martí, et al., Phys. Rev. C 70, 054605 (2004).
  * Signorini et al. [2000] C. Signorini, A. Andrighetto, M. Ruan, J. Y. Guo, L. Stroe, F. Soramel, K. E. G. Löbner, L. Müller, D. Pierroutsakou, M. Romoli, et al., Phys. Rev. C 61, 061603 (2000).
  * Jarczyk et al. [1981] L. Jarczyk, B. Kamys, A. Magiera, J. Sromicki, A. Strzałkowski, G. Willim, Z. Wróbel, D. Balzer, K. Bodek, M. Hugi, et al., Nucl. Phys. A 369, 191 (1981).
  * Bodek et al. [1980] K. Bodek, M. Hugi, J. Lang, R. Müller, E. Ungricht, K. Jankowski, W. Zipper, L. Jarczyk, A. Strzałkowski, G. Willim, et al., Nucl. Phys. A 339, 353 (1980).
  * J. S. Eck et al. [1980] J. S. Eck, T. R. Ophel, P. D. Clark, and D. C. Weisser, Nucl. Phys. A 334, 519 (1980).
  * Balzer et al. [1977] R. Balzer, M. Hugi, B. Kamys, J. Lang, R. Müller, E. Ungricht, J. Unternährer, L. Jarczyk, and A. Strzałkowski, Nucl. Phys. A 293, 518 (1977).
  * Stahel et al. [1977] D. P. Stahel, G. J. Wozniak, M. S. Zisman, B. D. Jeltema, and Joseph Cerny, Phys. Rev. C 16, 1456 (1977).
  * Yongli Xu et al. [2019] Yongli Xu, Yinlu Han, Haiying Liang, Zhendong Wu, Hairui Guo, and Chonghai Cai, Phys. Rev. C 99, 034618 (2019).
  * Woolliscroft et al. [2003] R. J. Woolliscroft, N. M. Clarke, B. R. Fulton, R. L. Cowin, M. Dasgupta, D. J. Hinde, C. R. Morton, and A. C. Berriman, Phys. Rev. C 68, 014611 (2003).
  * Signorini et al. [2004] C. Signorini, T. Glodariu, Z. H. Liu, M. Mazzocco, M. Ruan, and F. Soramel, Progress of Theoretical Physics Supplement 154, 272 (2004).
  * Pandit et al. [2011] S. K. Pandit, V. Jha, K. Mahata, S. Santra, C. S. Palshetkar, K. Ramachandran, V. V. Parkar, A. Shrivastava, H. Kumawat, B. J. Roy, et al., Phys. Rev. C 84, 031601 (R) (2011).
  * Rafiei et al. [2010] R. Rafiei, R. du Rietz, D. H. Luong, D. J. Hinde, M. Dasgupta, M. Evers, and A. Diaz-Torres, Phys. Rev. C 81, 024601 (2010).
  * Cook et al. [2016] K. J. Cook, E. C. Simpson, D. H. Luong, Sunil Kalkal, M. Dasgupta, and D. J. Hinde, Phys. Rev. C 93, 064604 (2016).
  * Papka et al. [2007] P. Papka, T. A. D. Brown, B. R. Fulton, D. L. Watson, S. P. Fox, D. Groombridge, M. Freer, N. M. Clarke, N. I. Ashwood, N. Curtis, et al., Phys. Rev. C 75, 045803 (2007).
  * Brown et al. [2007] T. A. D. Brown, P. Papka, B. R. Fulton, D. L. Watson, S. P. Fox, D. Groombridge, M. Freer, N. M. Clarke, N. I. Ashwood, N. Curtis, et al., Phys. Rev. C 76, 054605 (2007).
  * [55] http://nrv.jinr.ru/nrv/.
  * Topkar et al. [2011] A. Topkar, A. Singh, S. Santra, P. Mukhopadhyay, A. Chatterjee, R. Choudhury, and C. Pithawa, Nucl. Inst. Meth. Phys. Res. A 654, 330 (2011).
  * M. A. G. Alvarez et al. [2003] M. A. G. Alvarez, L. C. Chamon, M. S. Hussein, D. Pereira, L. R. Gasques, E. S. Rossi, and C.P. Silva, Nucl. Phys. A 723, 93 (2003).
  * Chamon et al. [2002] L. C. Chamon, B. V. Carlson, L. R. Gasques, D. Pereira, C. De Conti, M. A. G. Alvarez, M. S. Hussein, M. A. Cândido Ribeiro, E. S. Rossi, and C. P. Silva, Phys. Rev. C 66, 014610 (2002).
  * Thompson [1988] I. J. Thompson, Comput. Phys. Rep. 7, 167 (1988).
  * Gasques et al. [2006] L. R. Gasques, L. C. Chamon, P. R. S. Gomes, and J. Lubian, Nucl. Phys. A 764, 135 (2006).
  * Signorini et al. [2002] C. Signorini, A. Andrighetto, J. Guo, M. Ruan, L. Stroe, F. Soramel, K. Löbner, L. Müller, D. Pierroutsakou, M. Romoli, et al., Nuclear Physics A 701, 23 (2002).
  * Gavron [1980] A. Gavron, Phys. Rev. C 21, 230 (1980).
  * Perey and Perey [1976] C. M. Perey and F. G. Perey, At. Data Nucl. Data Tables 17, 1 (1976).
  * Huizenga and Igo [1962] J. R. Huizenga and G. Igo, Nucl. Phys. 29, 462 (1962).
  * Gomes et al. [2005a] P. R. S. Gomes, J. Lubian, I. Padron, and R. M. Anjos, Phys. Rev. C 71, 017601 (2005a).
  * Signorini et al. [1999] C. Signorini, Z.H. Liu, Z.-C. Li, K.E.G. Löbner, L. Müller, M. Ruan, K. Rudolph, F. Soramel, C. Zotti, A. Andrighetto, et al., Eur. Phys. J. A 5, 7 (1999).
  * Dasgupta et al. [2010] M. Dasgupta, D. J. Hinde, S. L. Sheehy, and B. Bouriquet, Phys. Rev. C 81, 024608 (2010).
  * Dasgupta et al. [2004] M. Dasgupta, P. R. S. Gomes, D. J. Hinde, S. B. Moraes, R. M. Anjos, A. C. Berriman, R. D. Butt, N. Carlin, J. Lubian, C. R. Morton, et al., Phys. Rev. C 70, 024606 (2004).
  * Parkar et al. [2010] V. V. Parkar, R. Palit, Sushil K. Sharma, B. S. Naidu, S. Santra, P. K. Joshi, P. K. Rath, K. Mahata, K. Ramachandran, T. Trivedi, et al., Phys. Rev. C 82, 054601 (2010).
  * Palshetkar et al. [2010] C. S. Palshetkar, S. Santra, A. Chatterjee, K. Ramachandran, Shital Thakur, S. K. Pandit, K. Mahata, A. Shrivastava, V. V. Parkar, and V. Nanal, Phys. Rev. C 82, 044608 (2010).
  * Prasanna M. et al. [2023] Prasanna M., V. V. Parkar, V. Jha, A. Parmar, Bhushan A. Kanagalekar, and B. G. Hegde, Nucl. Phys. A 1029, 122570 (2023).
  * K.O. Pfeiffer et al. [1973] K.O. Pfeiffer, E. Speth, and K. Bethge, Nucl. Phys. A 206, 545 (1973).
  * Hugi et al. [1981] M. Hugi, J. Lang, R. Müller, E. Ungricht, K. Bodek, L. Jarczyk, B. Kamys, A. Magiera, A. Strzałkowski, and G. Willim, Nucl. Phys. A 368, 173 (1981).
  * Ost et al. [1972] R. Ost, E. Speth, K. O. Pfeiffer, and K. Bethge, Phys. Rev. C 5, 1835 (1972).
  * Signorini et al. [2001] C. Signorini, M. Mazzocco, G.F. Prete, F. Soramel, L. Stroe, A. Andrighetto, I.J. Thompson, A. Vitturi, A. Brondi, M. Cinausero, et al., Eur. Phys. J. A 10, 249 (2001).
  * Pradhan et al. [2013] M. K. Pradhan, A. Mukherjee, Subinit Roy, P. Basu, A. Goswami, R. Kshetri, R. Palit, V. V. Parkar, M. Ray, M. Saha Sarkar, et al., Phys. Rev. C 88, 064603 (2013).
  * Pandit et al. [2019] S. K. Pandit, A. Shrivastava, K. Mahata, V. V. Parkar, N. Keeley, P. C. Rout, K. Ramachandran, C. S. Palshetkar, I. Martel, A. Kumar, et al., Phys. Rev. C 100, 014618 (2019).
  * Navin et al. [2004] A. Navin, V. Tripathi, Y. Blumenfeld, V. Nanal, C. Simenel, J. M. Casandjian, G. de France, R. Raabe, D. Bazin, A. Chatterjee, et al., Phys. Rev. C 70, 044601 (2004).
  * Chatterjee et al. [2008] A. Chatterjee, A. Navin, A. Shrivastava, S. Bhattacharyya, M. Rejmund, N. Keeley, V. Nanal, J. Nyberg, R. G. Pillay, K. Ramachandran, et al., Phys. Rev. Lett. 101, 032701 (2008).
  * Di Pietro et al. [2004] A. Di Pietro, P. Figuera, F. Amorini, C. Angulo, G. Cardella, S. Cherubini, T. Davinson, D. Leanza, J. Lu, H. Mahmud, et al., Phys. Rev. C 69, 044613 (2004).
  * Scuderi et al. [2011] V. Scuderi, A. Di Pietro, P. Figuera, M. Fisichella, F. Amorini, C. Angulo, G. Cardella, E. Casarejos, M. Lattuada, M. Milin, et al., Phys. Rev. C 84, 064604 (2011).
  * Yu. E. Penionzhkevich et al. [2007] Yu. E. Penionzhkevich, R. A. Astabatyan, N. A. Demekhina, G. G. Gulbekian, R. Kalpakchieva, A. A. Kulko, S. M. Lukyanov, E. R. Markaryan, V. A. Maslov, Yu. A. Muzychka, et al., Eur. Phys. J. A 31, 185 (2007).
  * Standyło et al. [2013] L. Standyło, L. Acosta, C. Angulo, R. Berjillos, J. A. Duenas, M. S. Golovkov, N. Keeley, T. Keutgen, I. Martel, M. Mazzocco, et al., Phys. Rev. C 87, 064603 (2013).
  * Aguilera et al. [2000] E. F. Aguilera, J. J. Kolata, F. M. Nunes, F. D. Becchetti, P. A. DeYoung, M. Goupell, V. Guimarães, B. Hughey, M. Y. Lee, D. Lizcano, et al., Phys. Rev. Lett. 84, 5058 (2000).
  * Kolata [2002] J. J. Kolata, Eur. Phys. J. A 13, 117 (2002).
  * Mazzocco et al. [2015] M. Mazzocco, D. Torresi, D. Pierroutsakou, N. Keeley, L. Acosta, A. Boiano, C. Boiano, T. Glodariu, A. Guglielmetti, M. La Commara, et al., Phys. Rev. C 92, 024615 (2015).
  * Sgouros et al. [2016] O. Sgouros, A. Pakou, D. Pierroutsakou, M. Mazzocco, L. Acosta, X. Aslanoglou, Ch. Betsou, A. Boiano, C. Boiano, D. Carbone, et al., Phys. Rev. C 94, 044623 (2016).
  * Jin Gen-Ming et al. [1980] Jin Gen-Ming, Xie Yuan-Xiang, Zhu Yong-Tai, Shen Wen-Ging, Sun Xi-Jun, Guo Jun-Sheng, Liu Guo-Xing, Yu Ju-Sheng, Sun Chi-Chang, and J.D. Garrett, Nucl. Phys. A 349, 285 (1980).
  * Zhang Li et al. [1988] Zhang Li, Wang Da-yan, Jin Gen-ming, Zhang Bao-guo, and Wang Xi-ming, Phys. Rev. C 37, 669 (1988).
  * Nomura et al. [1978] T. Nomura, H. Utsunomiya, T. Motobayashi, T. Inamura, and M. Yanokura, Phys. Rev. Lett. 40, 694 (1978).
  * Kolata [2001] J. J. Kolata, Phys. Rev. C 63, 061604 (2001).
  * Raabe et al. [2006] R. Raabe, C. Angulo, J. L. Charvet, C. Jouanne, L. Nalpas, P. Figuera, D. Pierroutsakou, M. Romoli, and J. L. Sida, Phys. Rev. C 74, 044606 (2006).
  * Malika Kaushik et al. [2021] Malika Kaushik, S. K. Pandit, V. V. Parkar, G. Gupta, Swati Thakur, V. Nanal, H. Krishnamoorthy, A. Shrivastava, C. S. Palshetkar, K. Mahata, et al., Phys. Rev. C 104, 024615 (2021).