Novel insights into transfer processes in the reaction 16O+208Pb at sub-barrier energies

Abstract

The collision of the doubly-magic nuclei $^{16}$O+$^{208}$Pb is a benchmark
in nuclear reaction studies. Our new measurements of back-scattered
projectile-like fragments at sub-barrier energies show show that transfer of 2
protons ($2p$) is much more probable than $\alpha$-particle transfer. $2p$
transfer probabilities are strongly enhanced compared to expectations for the
sequential transfer of two uncorrelated protons; at energies around the fusion
barrier absolute probabilities for two proton transfer are similar to those for
one proton transfer. This strong enhancement indicates strong $2p$ pairing
correlations in $^{16}$O, and suggests evidence for the occurrence of a nuclear
supercurrent of two-proton Cooper pairs in this reaction, already at energies
well below the fusion barrier.

Full text

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Novel insights into transfer processes in the reaction16O+208Pb at sub-barrier energies
M. Evers,∗C. Simenel, M. Dasgupta, D. J. Hinde, D. H. Luong, R. Rafiei, and R. du Rietz
Department of Nuclear Physics, Research School of Physics and Engineering,
Australian National University, Canberra, Australian Capital Territory 0200, Australia
(Dated: January 10, 2011)
The collision of the doubly-magic nuclei16O+208Pb is a benchmark in nuclear reaction studies.
Our new measurements of back-scattered projectile-like fragments at sub-barrier energies show show
that transfer of 2 protons (2p) is much more probable than α-particle transfer. 2p transfer probabil-
ities are strongly enhanced compared to expectations for the sequential transfer of two uncorrelated
protons; at energies around the fusion barrier absolute probabilities for two proton transfer are
similar to those for one proton transfer. This strong enhancement indicates strong 2p pairing cor-
relations in16O, and suggests evidence for the occurrence of a nuclear supercurrent of two-proton
Cooper pairs in this reaction, already at energies well below the fusion barrier.
PACS numbers: 25.70.Hi, 21.60.Gx
Collisions of heavy ions at energies well below and close
to the fusion barrier are entirely driven by quantum me-
chanics. For example, sub-barrier fusion occurs through
quantum tunnelling of the projectile nucleus through the
fusion barrier. This process in turn is affected by the
internal structure of the collision partners [1], leading to
a coherent superposition of reaction channels. Amongst
the possible reactions competing with fusion, transfer of
more than one nucleon is certainly the least well under-
stood mechanism, and constitutes an important task to
be described both experimentally and theoretically. In
particular, the distinction between sequential and cluster
transfer is a great challenge, not only in nuclear physics
[2], but also in electron transfer between ions or atomic
cluster collisions [3]. In nuclear collisions, the transfer
of a cluster of nucleons is a clear signature of correla-
tions between the transferred nucleons affecting the dy-
namics. Pairing between nucleons of the same isospin
as well as α-particle clustering have been considered as
the most important correlations affecting multi-nucleon
transfer [2].
Measurements of transfer probabilities in various reac-
tions and at energies near the fusion barrier have there-
fore been utilized to investigate the role of pairing corre-
lations between the transferred nucleons. Pairing effects
are believed to lead to a significant enhancement of pair
and multi-pair transfer probabilities [2, 4–7]. Closely re-
lated to the phenomenon of pairing correlations is the
nuclear Josephson effect [8], which is understood as the
tunneling of nucleon pairs (i.e.
through a time-dependent barrier at energies near but be-
low the fusion barrier. This effect is believed to be similar
to that of a supercurrent between two superconductors
separated by an insulator. An enhancement of the trans-
fer probability at sub-barrier energies is therefore com-
monly related to the tunneling of (multi-)Cooper-pairs
from one superfluid nucleus to the other [2].
nuclear Cooper-pairs)
The reaction16O+208Pb can be considered a bench-
mark in low-energy heavy-ion collisions [9–13]. In the
independent particle shell model, both nuclei are doubly-
magic with a closed shell of protons and neutrons. How-
ever, one and two proton knockout measurements of16O
using inelastic electron scattering indicate that pairing
correlations in the16O nucleus lead to a reduction of
the spectroscopic factors of excited states just below the
Fermi surface [14]. Furthermore, recent results based on
the time-dependent density matrix approach [15] indi-
cate that pairing correlations may indeed lead to cluster
structure effects in16O. Various sources [16, 17] report on
excited states in16O and other oxygen isotopes, strongly
supporting an α-cluster structure.
Extensive measurements probing different transfer
channels for the16O+208Pb reaction exist. It was com-
monly believed that the dominant transfer process in-
volving the exchange of two charged nucleons at energies
near the fusion barrier was α-particle transfer (16O,12C)
[9]. While at energies well above the fusion barrier, 2p
transfer (16O,14C) in the same reaction was also observed
[10–12], relative probabilities between α-particle and 2p
transfer were not addressed.
This letter presents evidence that (1) 2p transfer (and
not α-particle transfer) is the dominant transfer process
leading to ∆Z = 2 events in the reaction16O+208Pb at
energies well below the fusion barrier, and (2) 2p transfer
is significantly enhanced compared to predictions assum-
ing the sequential transfer of uncorrelated protons, with
absolute probabilities as high as those of 1p transfer at
energies near the fusion barrier.
Measurements were carried out using the 14UD elec-
trostatic accelerator of the Australian National Univer-
sity. Beams of16O were incident on a208PbS target with
a thickness of 100 µg/cm2, evaporated onto a 15 µg/cm2
C backing. A detector telescope consisting of a gas ion-
ization chamber and a Si detector located at a backward
angle of θlab= 162◦was used to record the energy and
energy loss of the back-scattered projectile-like fragments
(PLFs). Two Si monitors positioned at ±30◦were used
to normalize the back-scattered events to the Ruther-
arXiv:1101.1393v1 [nucl-ex] 7 Jan 2011

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25 303540 4550 55
[MeV]
gas
E
Δ
3
4
5
6
7
8
1
10
14C
12C
13C
16O+208Pb, Ebeam = 79.00 MeV
ESi [MeV]
ΔZ = 0
ΔZ = 1
ΔZ = 2
208Pb(3-)
FIG. 1. (Color online) Two dimensional ∆E − E spectrum
for the reaction
corresponding to Ec.m./VB = 0.98. The three different re-
gions indicating ∆Z = 0,1,2 transfer are labeled. Calculated
energy loss curves (dashed curves) for14C,13C and12C are
shown (see text).
16O+208Pb at the indicated beam energy,
TABLE I. Reaction ground state Q-values for selected transfer
processes in the reaction16O+208Pb. Processes with a plus
sign correspond to pickup, a minus sign indicates stripping.
Predominant processes as determined by our measurements
and previous work [12, 19] are highlighted in bold.
Reaction
208Pb(16O,17O)207Pb
208Pb(16O,18O)206Pb
208Pb(16O,15O)209Pb
208Pb(16O,15N)209Bi
208Pb(16O,14N)210Bi
208Pb(16O,16N)208Bi
208Pb(16O,14C)210Po
208Pb(16O,13C)211Po
208Pb(16O,12C)212Po −2p − 2n
208Pb(16O,15C)209Po
208Pb(16O,16C)208Po
Process
+1n
+2n
−1n
−1p
−1p − 1n
−1p + 1n
−2p
−2p − 1n
Qgs [MeV]
-3.225
-1.918
-11.727
-8.328
-14.557
-13.299
-13.553
-17.178
-16.116
-19.993
-22.710
∆Z = 0
∆Z = 1
∆Z = 2
−2p + 1n
−2p + 2n
ford cross section. A typical two dimensional spectrum
at a beam energy corresponding to Ec.m./VB = 0.98 is
shown in Fig. 1. The three distinct regions correspond to
oxygen, nitrogen and carbon PLFs, which are associated
with the transfer of ∆Z = 0, 1 and 2 units of charge.
The main peak at ESi∼ 50MeV corresponds to elasti-
cally scattered16O particles. Events resulting from the
transfer of three or more charged nucleons (∆Z ≥ 3) are
not observed for measurements at sub-barrier energy.
Transfer probabilities for processes with different ∆Z
are extracted by gating on the particular region of inter-
est in the ∆E−E spectra, and normalizing the number of
events to the total number of counts in the two forward
208Pb(16O,14C)210Po
208Pb(16O,12C)212Po
208Pb(16O,15N)209Bi
ΔZ=2 transfer
rmin [fm]
12.513.013.514.0
14.5
15.0
10-1
10-2
10-3
10-4
Probability Pi
Ec.m./VB
1.000.950.900.85
P1p
(P1p)2
FIG. 2. (Color online) Transfer probabilities for the indicated
transfer processes as a function of the distance of closest ap-
proach, see Eq. (1). The asymptotic behaviour for 1p transfer
and sequential 2p transfer are shown by the dotted straight
lines. The vertical dashed line indicates the barrier position.
The large open square and diamond at Ec.m./VB ∼ 1.0 are the
measurements for N (blue) and C PLFs (black) from Vide-
baek et al. [12]. The smaller open squares and diamonds
are the measurements for N (blue) and C PLFs (black) from
Timmers [18].
angle monitor detectors. Overall normalization of the
probabilities was achieved using the total quasi-elastic
excitation function, following the procedure detailed in
Ref. [20]. Supplementary data comes from measurements
using only a Si detector, and by integrating the num-
ber of counts in the total kinetic energy loss spectrum
in a fixed energy interval. This is possible because of
the well separated reaction Q-values for the predominant
(as determined by our measurements and previous work)
transfer processes in the reaction16O+208Pb (see Ta-
ble I). Probabilities for the ∆Z = 1 (1p-stripping) and
∆Z = 2 transfer events are shown in Fig. 2 by the filled
squares and diamonds, respectively. The transfer proba-
bilities are plotted as a function of the distance of closest
approach assuming a Coulomb trajectory [21]
rmin=ZpZte2
4π?0
1
2Ec.m.
?
1 + cosecθc.m.
2
?
,(1)
where Zp,Zt are the atomic number of projectile and
target nucleus, and Ec.m. and θc.m. are the energy and
scattering angle in the centre-of-mass frame, respectively.
The absolute probabilities at an energy around the fusion
barrier agree very well with previous measurements [12]
at Ec.m./VB ∼ 1.0, which are shown by the large open
square and diamond symbol for the N and C PLFs, re-

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208Pb(16O,xC)224-xPo, Ebeam = 79.00 MeV
10-1
10-2
10-3
10-4
dP/d(ΔErel) [MeV-1]
12C
14C
13C
-1.0 -0.8 -0.6 -0.4 -0.20.00.20.40.6 0.8
ΔErel [MeV]
FIG. 3.
∆Z = 2 transfer events (thick black histogram) relative to
the calculated energy loss of
oxygen beam on a lead target at the indicated energy. His-
tograms of the relative energy losses for the elastic scatter-
ing measurements using beams of12C and13C are shown by
the green and red shaded areas. The Gaussians fits (dotted
curves) correspond to 2p, 2p1n and α-particle transfer leading
to14C,13C and12C ejectiles; the envelope of the fits is shown
by the solid curve. Calculated relative energy losses for the
three indicated transfer reactions are indicated by the vertical
lines.
(Color online) Relative energy loss ∆Erel of the
14C (see text) for an incident
spectively. Earlier measurements at the ANU of the N
and C PLFs from Ref. [18] are shown by the smaller open
squares and diamonds, respectively, and also show excel-
lent agreement. Neither measurements however allowed a
separation in mass of the PLFs, and it was commonly as-
sumed that α-particle transfer was the dominant ∆Z = 2
transfer process [9].
In order to obtain insights into the ∆Z = 2 transfer
mechanisms, an unambiguous identification of the dom-
inant ∆Z = 2 transfer process is important. Reaction
Q-values for 2p and α-particle stripping are too similar
to allow for a separation of these processes solely based on
kinematic considerations, as is the case e.g. for the 1p and
1p1n stripping reactions (see Table I). However,12C and
14C ions lose a different amount of energy in the gas of the
detector telescope. The dashed curves in Fig. 1 show the
calculated energy losses for the C isotopes12,13,14C. The
locus of the majority of the measured ∆Z = 2 events co-
incides with the energy loss curve for14C. This suggests
that the majority of ∆Z = 2 events originate from the 2p
transfer reaction leading to14C, with a secondary contri-
bution from 2p1n and α-particle transfer. However, the
unique identification of events with a particular transfer
process depends critically on the accuracy of the energy
loss calculations, which in turn depend on the modelling
of the detector and the accuracy of the stopping power
tables used.
Beams of
to determine the accuracy of the energy loss calcula-
tions, by scattering them from a thick tantalum target
to give empirical energy loss curves for the detector tele-
scope. These measurements were reproduced satisfacto-
rily by calculations using an improved version of the code
STROP3, which uses stopping powers from Ref. [22].
Based on the energy loss calculations, a new quantity,
the relative energy loss ∆Erel, was then defined. This
quantity corresponds to the difference between the mea-
sured energy loss of the ∆Z = 2 PLFs and the calculated
energy loss of14C. The ∆Erel projections are indepen-
dent of differences in kinetic energy of the PLFs, thus
they present a useful tool for (1) identifying the dominant
transfer processes, and (2) determining their correspond-
ing absolute probabilities integrated over all final states
in the residual nuclei. Fig. 3 shows the elastically scat-
tered12C and13C beam particles, shaded green and red,
respectively. The centroids coincide with the calculated
energy losses for12C and13C (indicated by the vertical
lines), therefore confirming the accuracy of the energy
loss calculations as shown by the dashed curves in Fig. 1.
The relative energy loss spectrum for the ∆Z = 2 trans-
fer events measured in the16O induced reaction is shown
by the thick histogram in Fig. 3 for an incident16O beam
energy corresponding to Ec.m./VB = 0.98. The major-
ity of these ∆Z = 2 events lie at ∆Erel values above
the centroids of the12C and13C events. This identi-
fies the majority of these events with14C ejectiles, ex-
pected to be produced following the 2p-stripping reaction
208Pb(16O,14C)210Po.
The contributions to the total ∆Z = 2 transfer prob-
ability from the three transfer reactions 2p, 2p1n and α-
particle transfer were extracted by fitting a 3-Gaussian
distribution to the ∆Erelspectrum. The width of each
individual Gaussian is fixed to the value of the width of
the Gaussian-shaped elastically scattered12C distribu-
tion (green histogram in Fig. 3), and the relative energy
losses between the three C isotopes are fixed to the val-
ues of the calculated energy losses for these particles.
The envelope of the 3-Gaussian distribution as well as its
individual Gaussian components are shown by the black
solid and dotted curves in Fig. 3. Absolute probabilities
for each ∆Z = 2 transfer process were then obtained by
evaluating the integral of the individual Gaussian func-
tions of the 3-Gaussian distribution and normalizing the
sum of the three transfer probability components to the
total ∆Z = 2 transfer probability.
Extracted probabilities for the two transfer processes
208Pb(16O,14C)210Bi and208Pb(16O,12C)212Bi are shown
in Fig. 2 by the orange and green triangles, respec-
tively. Transfer probabilities for the 2p1n stripping pro-
cess208Pb(16O,13C)211Bi are not shown since they are at
least 10 times smaller than those for α-particle transfer
(see Fig. 3). At sub-barrier energies, 2p transfer (orange
triangles in Fig. 2) is the dominant process. α-particle
12,13C were used in the same experiment

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4
transfer probabilities (green triangles) are smaller by a
factor of ∼ 2 − 3 compared to that of 2p transfer. The
difference in probabilities between 2p and α transfer in-
creases with increasing beam energy, and is largest at
Ec.m./VB∼ 1.0.
Insights into the transfer mechanisms and the signifi-
cance of pairing correlations may be obtained by investi-
gating the radial dependence of the average transfer form
factor at large separation distances (i.e. for rmin> rB,
where rB is the fusion barrier radius). The asymptotic
behaviour of the probability for transfer process i is given
by [2, 7]
Pi∝ exp(−2κirmin), (2)
where κi is the slope parameter for transfer process i.
The asymptotic behaviour for 1p transfer P1p is shown
by the dotted blue line in Fig. 2. In the absence of pairing
correlations between the transferred nucleons, the prob-
ability for sequential two-nucleon transfer can be esti-
mated by the product of the single nucleon transfer prob-
abilities. The resulting transfer probabilities for sequen-
tial uncorrelated 2p transfer (P1p)2are shown by the dot-
ted orange line in Fig. 2. A significant enhancement of
the observed 2p transfer probability is observed, by about
one order of magnitude, which suggests a strong pairing
correlation between the two transferred protons.
In conclusion, the 1p, 2p and α transfer processes in the
reaction16O+208Pb have been investigated at energies
far below the fusion barrier. No detailed measurements
previously existed at these deep sub-barrier energies. It
is found that 2p transfer is the dominant ∆Z = 2 trans-
fer process, extending to energies Ec.m./VB∼ 0.9. Cor-
responding absolute transfer probabilities reach a max-
imum of ∼ 10% at a beam energy around the fusion
barrier energy. The 2p transfer probability is strongly
enhanced compared to predictions assuming sequential
transfer of uncorrelated nucleons. This indicates a strong
pairing correlation between the two transferred protons
and suggests the existence of a supercurrent of Cooper-
pair protons between the16O and208Pb nuclei.
enhancement of the 2p transfer probabilities is consistent
with measurements for16O-induced reactions on closed
neutron-shell and open proton-shell targets at energies
near and above the fusion barrier [23]. The significance of
2p transfer already at energies well below the fusion bar-
rier demonstrates that pairing correlations in16O may
play a more important role than generally assumed.
This will have significant implications for both model
calculations of nuclear collisions as well as nuclear struc-
ture.Regarding the former, it has been a challenge
for many decades to simultaneously reproduce all ob-
servables related to individual reaction processes (elastic
scattering, transfer, fusion, fission) for the16O+208Pb
reaction at near-barrier energies. The current measure-
ments show that cluster transfer occurs with significant
probability even at sub-barrier energies, and must be
The
correctly included in nuclear reaction model calculations
[9, 24, 25]. This may then lead to a full understanding of
this reaction and the structure of its constituting nuclei.
M.E. would like to thank W. von Oertzen for his in-
sightful remarks and comments after reading this Letter.
The authors acknowledge the financial support of an Aus-
tralian Research Council Discovery Grant.
∗maurits.evers@anu.edu.au
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