# Fusion of 16O+165Ho at deep sub-barrier energies

Saikat Bhattacharjee  Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar,
Kolkata - 700064, India  Homi Bhabha National Institute, Anushaktinagar,
Mumbai - 400094, India  A. Mukherjee<EMAIL_ADDRESS>Saha
Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata - 700064, India
Homi Bhabha National Institute, Anushaktinagar, Mumbai - 400094, India  Ashish
Gupta  Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata -
700064, India  Homi Bhabha National Institute, Anushaktinagar, Mumbai -
400094, India  Rajkumar Santra  Saha Institute of Nuclear Physics, 1/AF,
Bidhan Nagar, Kolkata - 700064, India  Homi Bhabha National Institute,
Anushaktinagar, Mumbai - 400094, India  D. Chattopadhyay  Present adddress:
Tata Institute of Fundamental Research, Mumbai - 400005, India  Saha Institute
of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata - 700064, India  N. Deshmukh
Present address: School of Sciences, Auro University, Surat, Gujarat - 394510,
India  Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata -
700064, India  Sangeeta Dhuri  Shilpi Gupta  V.V. Parkar  Nuclear Physics
Division, Bhabha Atomic Research Centre, Mumbai - 400085, India  Homi Bhabha
National Institute, Anushaktinagar, Mumbai - 400094, India  S.K. Pandit  K.
Ramachandran  Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai
- 400085, India  K. Mahata  A.Shrivastava  Nuclear Physics Division, Bhabha
Atomic Research Centre, Mumbai - 400085, India  Homi Bhabha National
Institute, Anushaktinagar, Mumbai - 400094, India  Rebecca Pachuau  Present
address: Department of Physics, Banaras Hindu University, Varanasi 221005,
India.  Tata Institute of Fundamental Research, Mumbai - 400005, India
S.Rathi  Vivekanand Education Society’s College of Arts, Science & Commerce,
Mumbai - 400071, India

###### Abstract

Fusion cross-sections have been measured for the asymmetric system 16O+165Ho
at energies near and deep below the Coulomb barrier with an aim to investigate
the occurrence of fusion hindrance for the system. Fusion cross sections down
to $\sim$ 700 nb have been measured using the off-beam $\gamma$-ray technique.
The fusion cross sections have been compared with the coupled channel
calculations. Although the onset of fusion hindrance could not be observed
experimentally, an indication of a small deviation of the experimental fusion
cross-sections with respect to the calculated cross-sections could be observed
at the lowest energy measured. However, the energy onset of fusion hindrance
has been obtained from the extrapolation technique and is found to be about 2
MeV below the lowest energy of the present measurement.

## I. INTRODUCTION

Extensive studies on fusion reactions at sub-barrier energies in different
mass regions have unraveled the fundamentals of quantum mechanical tunnelling
and distribution of potential barriers between two interacting nuclei. Fusion
in the vicinity of Coulomb barrier is a probe to discern the indispensable
role of different intrinsic features of the interacting nuclei on the reaction
process. Enhancement of fusion cross sections observed in heavy-ion collisions
at sub-barrier energies has been well explained by the coupled channels model
[1; 2].

On extending the measurements from sub-barrier down to deep sub-barrier
energies, for a wide range of reactions [3; 5; 6; 4; 7; 8; 9; 10; 11; 12; 13;
14; 15; 16; 17; 18; 19], a steep fall-off of fusion excitation function has
been observed compared to the standard coupled channels calculations, although
fusion cross sections are still enhanced with respect to single-barrier
penetration model calculations. This phenomenon of change of slope in the
fusion excitation function at deep sub-barrier energies is termed as "fusion
hindrance". Observation of fusion hindrance at deep sub-barrier energies,
especially in light systems like 12C+12C and 16O+16O [4] have astrophysical
implications, as some of the light systems transpire in the late evolutionary
stages of massive stars.

Fusion hindrance was initially observed in the symmetric medium-heavy system
60Ni+89Y [3], having negative Q-value. Subsequently, studies of several
symmetric and nearly-symmetric [5; 6; 7; 8; 9; 10; 11; 12; 13] and asymmetric
[14; 15] systems over a wide range of mass and fusion Q-values have also
exhibited similar observation. By contrast, fusion of weakly bound light
projectiles 6,7Li with 198Pt does not manifest hindrance at deep sub-barrier
energies [16; 17]. However, in fusion with relatively heavier projectiles 11B
and 12C on the targets 197Au [18] and 198Pt [16], respectively, hindrance has
been observed. From these studies, it appears that for asymmetric heavy
systems, fusion hindrance becomes increasingly significant with increasing
mass and charge of the projectiles.

Several models with different physical foundations have been proposed to
describe this phenomenon. Among them, the model developed by Mişicu and
Esbensen [20; 21] is based on sudden approximation. A soft repulsive core was
incorporated with the density folded M3Y potential in this model, to consider
the nuclear incompressibility in the overlapping region of the two interacting
nuclei. The adiabatic model proposed by Ichikawa et al. [22; 23] introduces an
additional damping factor on the nuclear coupling potential. The damping
factor is a function of the internuclear distance, which takes into
consideration of the smooth change from sudden to adiabatic transition while
the two nuclei are going through fusion deep below the barrier. More recently,
Simenel et al. have studied the effect of Pauli repulsion on heavy ion fusion
by implementing the density-constrained frozen Hartree-Fock method [24].
Despite having different physical origins, these models have been quite
successful in reproducing the experimental results for different systems at
deep sub-barrier energies [4].

In the light of the problem of fusion hindrance, we have recently measured
fusion cross-sections for 16O+165Ho system at energies near and deep below the
Coulomb barrier. Owing to the large deformation of nuclei in the rare-earth
region, systems involving such nuclei usually exhibit strong coupling effects
between relative motion and internal degrees of freedom in the sub barrier
fusion mechanism. The target nucleus 165Ho has a large deformation parameter
[25], whereas the projectile 16O is a tightly bound spherical nucleus and
therefore subdues the projectile effect of different coupling schemes on the
fusion mechanism. It has been perceived that stiff systems, where coupling
effects are small, typically show fusion hindrance more readily than soft
systems [4]. The dominance of the influence of different direct reaction
channels, like inelastic scattering, transfer and breakup, in reactions
involving soft nuclei are believed to be responsible for the occurrence of
fusion hindrance at much lower energies than stiff systems [4]. The system
16O+165Ho lies between stiff and soft systems having a negative Q-value
(Q=$-$23.1 MeV) for fusion. It would be interesting to study fusion mechanism
in the system of tightly bound projectile 16O on the deformed nucleus 165Ho,
especially at deep sub-barrier energies.

The complete fusion(CF) cross sections of 16O+165Ho at above-barrier energies
have been reported in the literature [26]. Present study overlaps some of the
energies of the reported measurement. The measurement has been extended
towards below barrier to deep sub-barrier energy region. An off-beam
$\gamma$-ray detection technique has been implemented to measure the cross
sections of the $\beta$-active evaporation residues. Section II recounts the
detailed experimental method that have been implemented to perform the
experiment. The procedure of data analysis have been explained in Section III.
The details of theoretical coupled channel calculations and comparison with
experimental results have been described in Section IV. Section V consists of
a discussion followed by a summary of the present work in Section VI.

Figure 1: $\gamma$-ray spectrum of the evaporation residues arising from the
complete fusion(CF) of 16O+165Ho system at 84 MeV beam energy. The red line is
the background estimated by ROOT data analysis package [28].

## II. EXPERIMENTAL DETAILS

The experiment was performed at the 14UD BARC-TIFR Pelletron-LINAC facility,
Mumbai. Self-supporting, rolled, natural foils of 165Ho, having thickness in
the range $\sim$ 1.02-1.9 mg/cm2 were irradiated by beams of 16O, in the
energy range Elab=62-85 MeV. Each target foil of 165Ho was followed by an Al
catcher foil, sufficiently thick to stop the heavy evaporation residues (ERs)
produced in the reaction. The thickness of each target and catcher foil was
measured by the $\alpha$-transmission method. For each irradiation, a fresh
target-catcher foil assembly was used. Typical beam current during the
irradiations was $\sim$ 2-10 pnA. To correct for beam fluctuations during the
irradiation, the beam current was recorded at regular intervals of 1 min using
a CAMAC scaler. The energies of the incident beam were corrected for the loss
of energy in the target material by employing SRIM [27], at half-thickness of
the target . As all the ERs were $\beta$-active and yielded delayed
$\gamma$-rays, the activation technique was employed to determine the fusion
cross sections for the system. After each irradiation, the target-catcher foil
assembly was removed from the chamber and placed in front of an efficiency
calibrated HPGe detector, which detected the delayed $\gamma$-rays emitted by
the ERs.

Figure 2: Activity of the 178Re evaporation residue as a function of
progressing time at Elab=70 MeV. The dotted line corresponds to the activity
obtained by fitting the data. The half life from the fit is mentioned in the
graph, which is consistent with the known value.

The target-catcher foil assembly was placed either at a distance of 10 cm from
the face of the detector or on the face of the detector, depending on the
activity of the irradiated sample. The energy calibration and absolute
efficiency measurement of the detector were carried out using the standard
radioactive sources, 152Eu, 133Ba and 60Co, mounted in the same geometry as
the target. The measurement was done in a low background setup with Pb-Cu
graded shielding to reduce the background $\gamma$-rays. Data were recorded
using a digital data acquisition system employing a CAEN N6724 digitizer and
the data were analyzed using the ROOT data analysis framework [28]. A typical
off-beam $\gamma$-ray spectrum, after the irradiation at Elab= 84 MeV, is
shown in Fig. 1. The complete fusion ERs 176-178Re occurring from the decay of
the compound nucleus 181Re were uniquely identified from the characteristic
$\gamma$-rays emitted by their daughter nuclei and by following the half-
lives. Half lives of the ERs were measured from the time sliced yields of the
characteristic $\gamma$-rays and compared with the previously measured values
[29], to ensure the absence of any contribution from sources other than the
complete fusion residues. The half-life plot for 178Re at Elab= 70 MeV has
been shown in Fig. 2.

## III. ANALYSIS AND RESULTS

If Nγ represents the number of counts under a particular $\gamma$-ray peak,
corresponding to a given ER in the spectrum, then from the principle of
radioactive decay the corresponding ER cross-section ($\sigma_{ER}$) is given
as [30]:

$\sigma_{ER}=\frac{N_{\gamma}\lambda e^{\lambda
t_{w}}}{N_{B}N_{T}\epsilon_{\gamma}F_{\gamma}(1-e^{-\lambda
t_{c}})(1-e^{-\lambda t_{irr}})}$ (1)

where NB is the number of incident nuclei, NT is the number of target nuclei
per unit area, $\lambda$ is the decay constant of the ER, tirr is the
irradiation time, tw is the time elapsed between the end of irradiation and
the beginning of counting, tc is the counting time, $\epsilon_{\gamma}$ is the
efficiency of the detector for a given $\gamma$-ray energy, and Fγ is the
absolute intensity of a $\gamma$-ray decay.

Figure 3: The cross-sections of different evaporation residues of compound
nucleus for 16O+165Ho system. The dotted lines are the statistical model
calculation (PACE4) results.

The $\gamma$-ray peak corresponding to 34Cl, seen in the spectrum (Fig. 1),
arises from the reaction of 16O with the Al catcher foil. Different $pxn$ and
$\alpha{xn}$ channels, corresponding to isotopes of W and Ta respectively,
populated in the reaction of 16O+165Ho are marked in the spectrum. The $pxn$
channel can be populated as an ER of compound nucleus and also from the decay
product of Re (e.g. 177Re $\xrightarrow{\epsilon}$ 177W). The procedure to
calculate the true weight of $pxn$ ERs from the cumulative cross-sections have
been discussed by Cavinato et al. [31]. In the energy region of the present
measurement, it has been found that majority of the $\gamma$-ray peaks
corresponding to $pxn$ channels are due to the decay of Re nuclei. The
contribution of $pxn$ ERs, i.e. the direct decay product of compound nucleus
falls within the error limit of respective cross-sections at different
energies and thus have not been estimated rigorously. The $\alpha{xn}$
channels are populated either by incomplete fusion (ICF) or via the decay of
compound nucleus(CF). To estimate the contribution of $\alpha{xn}$ channels
arising from the CF residues, statistical model calculation has been performed
using the PACE4 code [32].

Figure 4: Complete fusion excitation function measured in this experiment and the previous measurement has been compared with CC calculations using Woods-Saxon potential form. The solid lines are the results obtained from the CC calculations. The arrow corresponds to the Coulomb barrier for this system. (Inset) Fusion cross-section at above barrier energies are fitted with Wong formula to obtain the optical model potential parameters of the system. The solid line is the fitted result.  Table 1: Spectroscopic properties of the evaporation residues, resulting via CF process that have been used to calculate the CF cross-sections for the 16O+165Ho system.  Residue |  $T_{1/2}$(min) | $J^{\pi}$ |  $E_{\gamma}$(keV) |  $I^{\gamma}$(%)
---|---|---|---|---
178Re(3$n$) | 13.2 | 3+ | 237.0 | 44.5
|  |  | 106.0 | 23.4
177Re(4$n$) | 14.0 | 5/2- | 196.9 | 8.4
|  |  | 209.8 | 2.8
176Re(5$n$) | 5.3 | 3+ | 240.3 | 54.0
|  |  | 109.1 | 25.0
174Ta(${\alpha}3n$) | 68.4 | 3+ | 206.5 | 60.0

To obtain a relatively better agreement between theoretical and experimental
cross-sections, the neutron and alpha potentials in the code have been
modified according to Ref.[33] and Ref.[34], respectively. Fission barrier was
fixed at 21.89 MeV following Ref.[26] and the level density parameter "$k$"
was taken to be 9. The other parameters in the code were set to the default
values. Calculated cross section for each partial wave by coupled channel
calculation (detailed discussion in next section) has been fed as input to the
PACE4 calculations. The production of 174Ta via ICF is energetically possible
at higher energies (80-85 MeV) but at lower energies, it becomes unlikely that
174Ta will be populated as an ICF product. It has also been observed that
within the energy range of the measurement, the experimental cross-sections of
$\alpha{3n}$ channel (174Ta) reasonably agree with the statistical model,
which exclusively deals with CF process. The experimentally measured cross-
sections of other $\alpha{xn}$ channels are distinctly underestimated by the
statistical model calculations. Similar trend has also been observed in
Ref.[26]. As the PACE4 code has been able to reproduce the cross-sections of
$xn$ and $\alpha{3n}$ channels relatively well, it can be inferred that all
the other $\alpha{xn}$ channels, or at least an exceedingly significant part
of them have been populated via incomplete fusion(ICF). Fig.3 shows a
comparison of the statistical model calculations with the measured ER channel
cross-sections.

The total fusion cross-sections have been determined by adding the measured
cross sections of $xn$ and $\alpha{3n}$ channels and are shown in Fig. 4.
Fusion cross section down to 678 nb has been measured in this work.
Statistical errors, as well as errors ensuing from the measurement of beam
current, target thickness and detector efficiency have been taken into
account.

Figure 5: Astrophysical S-factor for 16O+165Ho system compared with S-factor
obtained from CC calculation.

The astrophysical S-factor, often used in nuclear astrophysics to study the
low-energy behavior of nuclear reactions, is defined as,

$S(E)=E\sigma(E)exp(2\pi\eta),$ (2)

where E is the center-of-mass energy, $\sigma$ is the fusion cross-section and
$\eta$=$Z_{1}Z_{2}e^{2}/\hbar v$ is Sommerfield parameter with $v$ being the
beam velocity. The experimental S-factor curve corresponding to the measured
fusion cross-sections for the present system has been plotted in Fig. 5.
Appearance of a maximum in the S-factor curve has been presented in previous
studies at an energy where the hindrance in fusion cross-section sets in. In
the present study, although no clear maximum could be seen in the S-factor
curve within the measured energy range, an indication of a change of slope at
the lowest energy could be observed. An alternative representation, the
logarithmic slope of the fusion excitation function is defined as [3],

$L(E)=d[ln(E\sigma)]/dE={\frac{1}{E\sigma}}\frac{d(E\sigma)}{dE}$ (3)

The values of $\mathrm{L(E)}$, extracted from the measured fusion cross
sections for 16O+165Ho are plotted in Fig. 6. These representations are
independent of any theoretical model and are alternative approaches to
manifest any deviation in the slope of excitation function. From eqns. (2) and
(3), one gets the relation,

$\frac{dS}{dE}=S(E)[L(E)-\frac{\pi{\eta}}{E}]$ (4)

The derivative $\frac{dS}{dE}$ becomes zero when S-factor becomes maximum, and
from eqn. (3) one finds that this corresponds to the logarithmic derivative
for constant S-factor, $\mathrm{L_{cs}(E)}$, given by:

$L_{cs}(E)=\frac{\pi{\eta}}{E}$ (5)

The dashed curve $\mathrm{L_{cs}(E)}$ for the present system is shown in Fig.
6 by the dashed line. The experimental values of $\mathrm{L(E)}$ have been
fitted with a function $A+B/E^{\frac{3}{2}}$ [36; 37], and is shown in Fig. 6
by the dotted line. The crossover point of the curves $\mathrm{L_{cs}(E)}$ and
fitted $\mathrm{L(E)}$ corresponds to the maximum of the S-factor curve and is
related to the threshold energy ($\mathrm{E_{s}}$) for the occurance of fusion
hindrance [4]. In the measured energy regime of the present work, the fitted
$\mathrm{L(E)}$ curve does not intersect the $\mathrm{L_{cs}(E)}$ curve.
However, it can be seen from Fig. 6 that an extrapolation of the fitted
$\mathrm{L(E)}$ curve intersects the curve $\mathrm{L_{cs}(E)}$ at the energy
$\mathrm{E_{s}}=$52.78$\pm$0.78 MeV. The value of $\mathrm{E_{s}}$ calculated
from the empirical equation [38] is 53.17 MeV. The estimation of
$\mathrm{E_{s}}$ obtained from the touching point configuration in adiabatic
picture [22; 23] is 56.1 MeV.The present measurement has been performed down
to E = 54.78 MeV, which is $\approx$ 2 MeV above the extrapolated
$\mathrm{E_{s}}$ value and 1.3 MeV below the prediction from adiabatic model.
This shows that the $\mathrm{E_{s}}$ value for 16O+165Ho system will be lower
than that predicted by the adiabatic model.

## IV. COMPARISON WITH COUPLED CHANNELS CALCULATIONS

Figure 6: Logarthmic derivative L(E) of the experimental fusion excitation
function compared with CC calculations(dashed dot lines). The extrapolation of
L(E) (dotted lines) intersect the $\mathrm{L_{cs}}$ curve at 52.78 MeV.

The data obtained in the present work have been analyzed in the framework of
coupled channels (CC) calculations, using the code CCFULL [39]. These
calculations require an initial set of potential parameters. They were
obtained by fitting the fusion cross sections well above the barrier using
Wong’s formula[41], as the fusion cross sections in this energy regime are
expected to be fairly insensitive to the form or magnitude of the couplings.
The nuclear potential was taken to be of Woods-Saxon form,

$V_{n}(r)=\frac{-V_{0}}{1+exp[(r-r_{0}A_{P}^{1/3}-r_{0}A_{T}^{1/3})/a]}$ (6)

where $V_{0}$ is the depth, $r_{0}$ is the radius parameter, and $a$ is the
diffuseness of the nuclear potential. The potential parameters were obtained
by fixing $a$ to be 0.63 fm, and varying $r_{0}$ and $V_{0}$ to obtain a good
fit to the high energy part of the cross sections. The parameters thus
obtained are: $V_{0}=$102 MeV, $r_{0}=$1.15 fm and $a_{0}=$0.63 fm. The inset
in Fig. 4 shows the resulting fit. The potential parameters for the same
system has also been compared with Ref. [40]; both results are found to be
identical.

The CCFULL calculations in the no-coupling limit are shown by the dotted curve
in Fig. 4, and are seen to underpredict the data, suggesting strong effects of
deformation in the target nucleus. The CCFULL code estimates the effects of
deformation by linear as well as non linear coupling to the pure rotational
bands of the deformed nucleus. The target nucleus 165Ho is deformed with a
valence proton. The rotational states of 165Ho may be considered to be built
up by the coupling of the unpaired valence proton particle (or proton hole)
with the 0+,2+,4+,…rotational states of the neighboring even-even nucleus
164Dy (or 166Er). To remain within the model space of CCFULL, the excitation
energies and deformation parameters for the target nuclues 165Ho were taken to
be the averages of those of the neighboring even-even nuclei 164Dy and 166Er
[42; 43]. The resulting ground state rotational band upto 12+ state
($\beta_{2}$=0.32 , $\beta_{4}$=0.02 ) was included in the calculations. The
results of these calculations are shown by the solid curve in the figure. They
are seen to be in fairly good agreement with the data, except the lowest
energy data which appears to be slightly below the calculated value.

The solid curve in Fig. 5 shows the calculated astrophysical S-factor values
extracted from the CC cross sections and are found to agree well with the
experimental value, except the lowest energy point. Although no clear maximum
in the experimental S-factor plot or deviation from the the CC calculations
could be observed in the measured energy range, an indication of a small
deviation could be seen at the lowest energy measured. The dot-dashed curve in
Fig. 6 shows the calculated $\mathrm{L(E)}$ values extracted from the CC cross
sections and and are also seen to agree well with the experimental values,
although the trend of the two extreme low energy points show an indication of
possible deviation at still lower energies.

Figure 7: Systematic representation of $\mathrm{E_{s}}$ as a function of
system parameter $\mathrm{\zeta}$. The solid circles are measured and hollow
circles are extrapolated values of $\mathrm{E_{s}}$, taken from the tabulated
values of Ref.[16; 4; 36]. The solid square represents the extrapolated value
in this work. The hollow squares correspond to Ref.[10; 45] where the value of
$\mathrm{E_{s}}$ can not be obtained either by extrapolation or direct
measurements and an upper bound has been mentioned in Ref.[4].

## V. DISCUSSION

For a systematic study of the energy onset of fusion hindrance, the value of
$\mathrm{E_{s}}$ predicted for the system 16O+165Ho in the present work has
been compared in Fig. 7 with the $\mathrm{E_{s}}$ values of other heavy
systems as a function of the system parameter
$\mathrm{\zeta=Z_{p}Z_{t}\sqrt{\frac{A_{p}A_{t}}{A_{p}+A_{t}}}}$. The
parameters $\mathrm{A_{p},Z_{p},A_{t},Z_{t}}$ are the mass number and atomic
number of projectile and target. In this comparison, we have considered only
the systems in the $\mathrm{\zeta}$ range $\sim$ 1500-3000, for which
$\mathrm{E_{s}}$ are available in the literature. The parameter
$\mathrm{\zeta}$ contains information of the mass and Coulomb barrier of the
target-projectile system. The dashed line in the figure corresponds to the
empirical form of $\mathrm{E_{s}}$ [38]. The extrapolated value of
$\mathrm{E_{s}}$ obtained in the present work lies very close to the result
obtained from the empirical form
$\mathrm{E_{s}^{emp}=[0.495\zeta/(2.33+580/\zeta)]^{2/3}}$; although it should
be pointed out that an actual measurement down to the predicted threshold
energy will confirm the result. On the other hand, the $\mathrm{E_{s}}$ limit,
obtained from the adiabatic model, has been crossed but hindrance for this
system was not experimentally observed within the measured energy range.

Figure 8: Comparison of normalized fusion excitation function between
16O+165Ho, 19F+165Ho [44], and 7Li+165Ho [46] system.

A systematic comparison of fusion excitation functions have been carried out
for systems involving the target nucleus 165Ho and different projectiles and
is shown in Fig. 8. The systems involving 165Ho target nucleus, for which sub-
barrier fusion cross sections have been reported in literature are 19F+165Ho
[44] and 7Li+165Ho [46]. The projectile 16O in the present system is a stiff
nucleus, while 19F is relatively heavier and less bound than 16O, and 7Li is a
well known weakly bound stable nucleus. For comparison of different
projectile-target systems, the fusion excitation functions have been plotted
in a reduced scale. Barrier radii
$\mathrm{R_{b}}$=$\mathrm{r_{0}(A_{p}^{\frac{1}{3}}+A_{t}^{\frac{1}{3}})}$ and
Coulomb barrier $\mathrm{V_{b}}$ for each system was obtained by performing
1DBPM model calculation, using the Akyüz-Winther parametrization of Woods-
Saxon potential [47].

Table 2: $V_{b}$ and $R_{b}$ of the systems that have been used in the reduced plot (Fig. 8).  | System |  |  $V_{b}$ (MeV) |  |  $R_{b}$ (fm)
---|---|---|---|---|---
|  16O+165Ho |  | 66.34 |  | 10.93
|  19F+165Ho |  | 72.24 |  | 11.26
|  7Li+165Ho |  | 25.0 |  | 10.76

Fig. 8 shows that the reduced fusion excitation functions for the three
systems overlap reasonably well with each other at above barrier energies. But
there are no reported fusion cross sections at deep-sub-barrier energies for
the systems 19F+165Ho and 7Li+165Ho. At sub-barrier energies, the fusion
cross-sections for 19F+165Ho and 16O+165Ho agree fairly well with each other;
while the fusion cross-sections for 7Li+165Ho are enhanced in the reduced
scale. It would be interesting to see how the deep sub-barrier fusion cross
sections for the two systems compare with the present 16O+165Ho system.

## VI. SUMMARY

The fusion cross-sections for 16O+165Ho have been measured down to 678 nb,
from above-barrier to deep sub-barrier energies. The present measurement
agrees with the earlier reported data [26], in the overlapping above-barrier
energy region. Statistical model calculation of different evaporation residues
occurring from CF yielded similar results with experimental data. The
experimental CF cross-sections have been well reproduced by the coupled
channels calculations. No clear evidence of fusion hindrance has been observed
in the fusion excitation function in the measured energy range of the present
work. However, the trend of the extreme low energy points in the S-factor and
$\mathrm{L(E)}$ plots show an indication of possible deviation at still lower
energies. The extrapolation of $\mathrm{L(E)}$ suggests the onset of fusion
hindrance at 52.78$\pm$0.78 MeV, approximately 2 MeV lower than the lowest
energy measured in the present work, in accordance with the prediction from
systematics. Further measurement at lower energies may confirm the result.

###### Acknowledgements.

We sincerely thank the staff of BARC-TIFR Pelletron facility for an
uninterrupted supply of beam. We would like to extend our gratitude towards
Dr. Sanjoy Pal of TIFR, Mumbai; for helping with the digital data acquisition.

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