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

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by  M. Evers

Novel insights into transfer processes in the reaction 16O+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 nuclei 16O+208Pb is a benchmark in nuclear reaction studies.
Ournewmeasurementsofback-scatteredprojectile-likefragmentsatsub-barrierenergiesshowshow
thattransferof2protons(2p)ismuchmoreprobablethanα-particletransfer. 2ptransferprobabil-
itiesarestronglyenhancedcomparedtoexpectationsforthesequentialtransferoftwouncorrelated
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 in 16O, 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.
PACSnumbers: 25.70.Hi,21.60.Gx
Collisionsofheavyionsatenergieswellbelowandclose independentparticleshellmodel,bothnucleiaredoubly-
to the fusion barrier are entirely driven by quantum me- magic with a closed shell of protons and neutrons. How-
1 chanics. For example, sub-barrier fusion occurs through ever, one and two proton knockout measurements of 16O
1
quantumtunnellingoftheprojectilenucleusthroughthe using inelastic electron scattering indicate that pairing
0
fusion barrier. This process in turn is affected by the correlations in the 16O nucleus lead to a reduction of
2
internal structure of the collision partners [1], leading to the spectroscopic factors of excited states just below the
n
a coherent superposition of reaction channels. Amongst Fermi surface [14]. Furthermore, recent results based on
a
J the possible reactions competing with fusion, transfer of the time-dependent density matrix approach [15] indi-
more than one nucleon is certainly the least well under- cate that pairing correlations may indeed lead to cluster
7
stood mechanism, and constitutes an important task to structureeffectsin16O.Varioussources[16,17]reporton

] be described both experimentally and theoretically. In excitedstatesin16Oandotheroxygenisotopes,strongly
x
particular,thedistinctionbetweensequentialandcluster supporting an α-cluster structure.
e
- transfer is a great challenge, not only in nuclear physics Extensive measurements probing different transfer
l
c [2], but also in electron transfer between ions or atomic channels for the 16O+208Pb reaction exist. It was com-
u cluster collisions [3]. In nuclear collisions, the transfer
monly believed that the dominant transfer process in-
n
of a cluster of nucleons is a clear signature of correla-
[ volvingtheexchangeoftwochargednucleonsatenergies
tions between the transferred nucleons affecting the dy- near the fusion barrier was α-particle transfer (16O,12C)
1 namics. Pairing between nucleons of the same isospin
[9]. While at energies well above the fusion barrier, 2p
v
as well as α-particle clustering have been considered as transfer(16O,14C)inthesamereactionwasalsoobserved
3
the most important correlations affecting multi-nucleon
9 [10–12], relative probabilities between α-particle and 2p
3 transfer [2]. transfer were not addressed.
1
Measurementsoftransferprobabilitiesinvariousreac- This letter presents evidence that (1) 2p transfer (and
.
1 tions and at energies near the fusion barrier have there- not α-particle transfer) is the dominant transfer process
0 fore been utilized to investigate the role of pairing corre- leading to ∆Z = 2 events in the reaction 16O+208Pb at
1
lations between the transferred nucleons. Pairing effects energieswellbelowthefusionbarrier,and(2)2ptransfer
1
: are believed to lead to a significant enhancement of pair issignificantlyenhancedcomparedtopredictionsassum-
v
and multi-pair transfer probabilities [2, 4–7]. Closely re- ing the sequential transfer of uncorrelated protons, with
i
X lated to the phenomenon of pairing correlations is the absolute probabilities as high as those of 1p transfer at
r nuclear Josephson effect [8], which is understood as the energies near the fusion barrier.
a tunneling of nucleon pairs (i.e. nuclear Cooper-pairs)
Measurements were carried out using the 14UD elec-
throughatime-dependentbarrieratenergiesnearbutbe-
trostatic accelerator of the Australian National Univer-
lowthefusionbarrier. Thiseffectisbelievedtobesimilar
sity. Beamsof16Owereincidentona208PbStargetwith
to that of a supercurrent between two superconductors
athicknessof100µg/cm2, evaporatedontoa15µg/cm2
separatedbyaninsulator. Anenhancementofthetrans-
C backing. A detector telescope consisting of a gas ion-
fer probability at sub-barrier energies is therefore com-
ization chamber and a Si detector located at a backward
monly related to the tunneling of (multi-)Cooper-pairs
angle of θ = 162◦ was used to record the energy and
lab
from one superfluid nucleus to the other [2].
energylossoftheback-scatteredprojectile-likefragments
The reaction 16O+208Pb can be considered a bench- (PLFs). Two Si monitors positioned at ±30◦ were used
mark in low-energy heavy-ion collisions [9–13]. In the to normalize the back-scattered events to the Ruther-
2
E /V
c.m. B
16O+208Pb, Ebeam = 79.00 MeV 1.00 0.95 0.90 0.85
10-1
ΔZ = 0
ΔZ = 1
10-2
208Pb(3-) Pi
ΔZ = 2 y
t
13C bili
14C oba 10-3 (P1p)2 P1p
12C Pr
208Pb(16O,15N)209Bi
10-4
25 30 35 40 45 50 55 ΔZ=2 transfer
ESi [MeV] 208Pb(16O,14C)210Po
208Pb(16O,12C)212Po
FIG. 1. (Color online) Two dimensional ∆E −E spectrum
for the reaction 16O+208Pb at the indicated beam energy,
12.5 13.0 13.5 14.0 14.5 15.0
corresponding to E /V = 0.98. The three different re-
c.m. B
r [fm]
gionsindicating∆Z =0,1,2transferarelabeled. Calculated min
energy loss curves (dashed curves) for 14C, 13C and 12C are
FIG.2. (Coloronline)Transferprobabilitiesfortheindicated
shown (see text).
transfer processes as a function of the distance of closest ap-
proach,seeEq.(1). Theasymptoticbehaviourfor1ptransfer
and sequential 2p transfer are shown by the dotted straight
TABLEI.ReactiongroundstateQ-valuesforselectedtransfer
lines. The vertical dashed line indicates the barrier position.
processes in the reaction 16O+208Pb. Processes with a plus
ThelargeopensquareanddiamondatE /V ∼1.0arethe
c.m. B
sign correspond to pickup, a minus sign indicates stripping.
measurements for N (blue) and C PLFs (black) from Vide-
Predominant processes as determined by our measurements
baek et al. [12]. The smaller open squares and diamonds
and previous work [12, 19] are highlighted in bold.
are the measurements for N (blue) and C PLFs (black) from
Timmers [18].
Reaction Process Q [MeV]
gs
0 208Pb(16O,17O)207Pb +1n -3.225
=
208Pb(16O,18O)206Pb +2n -1.918
Z angle monitor detectors. Overall normalization of the
∆ 208Pb(16O,15O)209Pb −1n -11.727 probabilities was achieved using the total quasi-elastic
1 208Pb(16O,15N)209Bi −1p -8.328 excitation function, following the procedure detailed in
=
208Pb(16O,14N)210Bi −1p−1n -14.557 Ref.[20]. Supplementarydatacomesfrommeasurements
Z
∆ 208Pb(16O,16N)208Bi −1p+1n -13.299 using only a Si detector, and by integrating the num-
208Pb(16O,14C)210Po −2p -13.553 ber of counts in the total kinetic energy loss spectrum
2 208Pb(16O,13C)211Po −2p−1n -17.178 in a fixed energy interval. This is possible because of
=
Z 208Pb(16O,12C)212Po −2p−2n -16.116 thewellseparatedreactionQ-valuesforthepredominant
∆ 208Pb(16O,15C)209Po −2p+1n -19.993 (asdeterminedbyourmeasurementsandpreviouswork)
transfer processes in the reaction 16O+208Pb (see Ta-
208Pb(16O,16C)208Po −2p+2n -22.710
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-
ford cross section. A typical two dimensional spectrum
bilitiesareplottedasafunctionofthedistanceofclosest
at a beam energy corresponding to E /V = 0.98 is
c.m. B approach assuming a Coulomb trajectory [21]
showninFig.1. Thethreedistinctregionscorrespondto
oxygen, nitrogen and carbon PLFs, which are associated Z Z e2 1 (cid:18) θ (cid:19)
with the transfer of ∆Z = 0, 1 and 2 units of charge. rmin = 4pπ(cid:15)t 2E 1+cosec c2.m. , (1)
0 c.m.
The main peak at E ∼ 50MeV corresponds to elasti-
Si
cally scattered 16O particles. Events resulting from the where Z ,Z are the atomic number of projectile and
p t
transfer of three or more charged nucleons (∆Z ≥3) are target nucleus, and E and θ are the energy and
c.m. c.m.
not observed for measurements at sub-barrier energy. scatteringangleinthecentre-of-massframe,respectively.
Transfer probabilities for processes with different ∆Z Theabsoluteprobabilitiesatanenergyaroundthefusion
are extracted by gating on the particular region of inter- barrier agree very well with previous measurements [12]
estinthe∆E−E spectra,andnormalizingthenumberof at E /V ∼ 1.0, which are shown by the large open
c.m. B
events to the total number of counts in the two forward square and diamond symbol for the N and C PLFs, re-
3
Beams of 12,13C were used in the same experiment
10-1
to determine the accuracy of the energy loss calcula-
208Pb(16O,xC)224-xPo, E = 79.00 MeV
beam tions, by scattering them from a thick tantalum target
to give empirical energy loss curves for the detector tele-
14C
]10-2 13C scope. These measurements were reproduced satisfacto-
-1V
e 12C rilybycalculationsusinganimprovedversionofthecode
M
[ STROP3, which uses stopping powers from Ref. [22].
)
Erel10-3 Based on the energy loss calculations, a new quantity,
Δ
d( the relative energy loss ∆Erel, was then defined. This
P/ quantity corresponds to the difference between the mea-
d
10-4 suredenergylossofthe∆Z =2PLFsandthecalculated
energy loss of 14C. The ∆E projections are indepen-
rel
dent of differences in kinetic energy of the PLFs, thus
theypresentausefultoolfor(1)identifyingthedominant
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 transferprocesses,and(2)determiningtheircorrespond-
ΔErel [MeV] ing absolute probabilities integrated over all final states
in the residual nuclei. Fig. 3 shows the elastically scat-
FIG. 3. (Color online) Relative energy loss ∆E of the
rel tered12Cand13Cbeamparticles, shadedgreenandred,
∆Z = 2 transfer events (thick black histogram) relative to
the calculated energy loss of 14C (see text) for an incident respectively. The centroids coincide with the calculated
oxygen beam on a lead target at the indicated energy. His- energy losses for 12C and 13C (indicated by the vertical
tograms of the relative energy losses for the elastic scatter- lines), therefore confirming the accuracy of the energy
ing measurements using beams of 12C and 13C are shown by losscalculationsasshownbythedashedcurvesinFig.1.
the green and red shaded areas. The Gaussians fits (dotted The relative energy loss spectrum for the ∆Z =2 trans-
curves)correspondto2p,2p1nandα-particletransferleading fereventsmeasuredinthe16Oinducedreactionisshown
to14C,13Cand12Cejectiles;theenvelopeofthefitsisshown
bythethickhistograminFig.3foranincident16Obeam
by the solid curve. Calculated relative energy losses for the
energy corresponding to E /V = 0.98. The major-
threeindicatedtransferreactionsareindicatedbythevertical c.m. B
lines. ity of these ∆Z = 2 events lie at ∆Erel values above
the centroids of the 12C and 13C events. This identi-
fies the majority of these events with 14C ejectiles, ex-
spectively. Earlier measurements at the ANU of the N pectedtobeproducedfollowingthe2p-strippingreaction
andCPLFsfromRef.[18]areshownbythesmalleropen 208Pb(16O,14C)210Po.
squaresanddiamonds, respectively, andalsoshowexcel- The contributions to the total ∆Z = 2 transfer prob-
lentagreement. Neithermeasurementshoweveralloweda ability from the three transfer reactions 2p, 2p1n and α-
separationinmassofthePLFs,anditwascommonlyas- particle transfer were extracted by fitting a 3-Gaussian
sumedthatα-particletransferwasthedominant∆Z =2 distribution to the ∆E spectrum. The width of each
rel
transfer process [9]. individual Gaussian is fixed to the value of the width of
In order to obtain insights into the ∆Z = 2 transfer the Gaussian-shaped elastically scattered 12C distribu-
mechanisms, an unambiguous identification of the dom- tion (green histogram in Fig. 3), and the relative energy
inant ∆Z = 2 transfer process is important. Reaction losses between the three C isotopes are fixed to the val-
Q-values for 2p and α-particle stripping are too similar ues of the calculated energy losses for these particles.
toallowforaseparationoftheseprocessessolelybasedon Theenvelopeofthe3-Gaussiandistributionaswellasits
kinematicconsiderations,asisthecasee.g. forthe1pand individual Gaussian components are shown by the black
1p1n stripping reactions (see Table I). However, 12C and solid and dotted curves in Fig. 3. Absolute probabilities
14Cionsloseadifferentamountofenergyinthegasofthe for each ∆Z =2 transfer process were then obtained by
detectortelescope. ThedashedcurvesinFig.1showthe evaluating the integral of the individual Gaussian func-
calculated energy losses for the C isotopes 12,13,14C. The tions of the 3-Gaussian distribution and normalizing the
locus of the majority of the measured ∆Z =2 events co- sum of the three transfer probability components to the
incides with the energy loss curve for 14C. This suggests total ∆Z =2 transfer probability.
thatthemajorityof∆Z =2eventsoriginatefromthe2p Extracted probabilities for the two transfer processes
transferreactionleadingto14C,withasecondarycontri- 208Pb(16O,14C)210Biand208Pb(16O,12C)212Biareshown
bution from 2p1n and α-particle transfer. However, the in Fig. 2 by the orange and green triangles, respec-
unique identification of events with a particular transfer tively. Transfer probabilities for the 2p1n stripping pro-
process depends critically on the accuracy of the energy cess208Pb(16O,13C)211Biarenotshownsincetheyareat
loss calculations, which in turn depend on the modelling least 10 times smaller than those for α-particle transfer
of the detector and the accuracy of the stopping power (see Fig. 3). At sub-barrier energies, 2p transfer (orange
tables used. triangles in Fig. 2) is the dominant process. α-particle
4
transfer probabilities (green triangles) are smaller by a correctly included in nuclear reaction model calculations
factor of ∼ 2−3 compared to that of 2p transfer. The [9,24,25]. Thismaythenleadtoafullunderstandingof
difference in probabilities between 2p and α transfer in- this reaction and the structure of its constituting nuclei.
creases with increasing beam energy, and is largest at
E /V ∼1.0. M.E. would like to thank W. von Oertzen for his in-
c.m. B
Insights into the transfer mechanisms and the signifi- sightfulremarksandcommentsafterreadingthisLetter.
cance of pairing correlations may be obtained by investi- TheauthorsacknowledgethefinancialsupportofanAus-
gatingtheradialdependenceoftheaveragetransferform tralian Research Council Discovery Grant.
factor at large separation distances (i.e. for r > r ,
min B
where r is the fusion barrier radius). The asymptotic
B
behaviouroftheprobabilityfortransferprocessiisgiven
by [2, 7]
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