α-clustering effects in dissipative 12C+12C reactions at 95 MeV

0.29 MB·English

by  G. Baiocco

α-clustering effects in dissipative 12C+12C reactions at 95 MeV
G. Baiocco1,2, L. Morelli1, F. Gulminelli2, M. D’Agostino1, M. Bruno1, U. Abbondanno3,
S. Barlini4,5, M. Bini4,5, S. Carboni4,5, G. Casini5, M. Cinausero6, M. Degerlier7, F. Gramegna6,
V. L. Kravchuk6,8, T. Marchi6,9, A. Olmi5, G. Pasquali4,5, S. Piantelli5, and Ad. R. Raduta10
1Dipartimento di Fisica ed Astronomia dell’Universit`a and INFN, Bologna, Italy
2LPC (IN2P3-CNRS/Ensicaen et Universit´e), F-14076 Caen c´edex, France
3INFN Trieste, Italy
4Dipartimento di Fisica ed Astronomia dell’Universit`a, Firenze, Italy
3 5INFN Firenze, Italy
1 6INFN, Laboratori Nazionali di Legnaro, Italy
0 7 University of Nevsehir, Science and Art Faculty, Physics Department, Nevsehir, Turkey
2 8National Research Center “Kurchatov Institute”, Moscow, Russia
n 9Dipartimento di Fisica ed Astronomia dell’Universit`a, Padova, Italy and
a 10NIPNE, Bucharest-Magurele, POB-MG6, Romania
J
5 Dissipative 12C+12C reactions at 95 MeV are fully detected in charge with the GARFIELD and
2 RCoapparatusesatLNL.AcomparisontoadedicatedHauser-Feshbachcalculationallowstoselect
eventswhich correspond, toalarge extent,tothestatistical evaporation ofhighly excited 24Mg, as

] wellastoextractinformation ontheisotopicdistributionoftheevaporationresiduesincoincidence
x withtheircompleteevaporationchain. Residualdeviationsfromastatisticalbehaviourareobserved
e in α yields and attributed to the persistence of cluster correlations well above the 24Mg threshold
-
l for 6 α’s decay.
c
u
PACSnumbers:
n
[

Sincethe firstheuristic propositionofα-chainsaspos- excited24Mgaround30MeV.Becauseoftheremarkable
1
v sible building blocks of even-even nuclei in the late six- persistenceofclustercorrelationsathighexcitationener-
0 ties [1], the subject of α-clustering has been a central gies, the question naturally arises whether such correla-
9 issue in nuclear physics and has even witnessed a gain tions might affect other more dissipative channels which
9
of interest in recent years [2]. On the theoretical side, are typically associated to the formation of a compound
5
highly sophisticated ab-initio calculations have shown nucleus, that is a system whose decay is assumed to be
.
1
pronouncedclusterfeaturesinthegroundstateofalarge fully decoupled from the reaction entrance channel and
0
numberoflightnuclei[3]aswellasinsomeexcitedstates governedby purely statistical laws.
3
1 around the threshold energy of breakup into constituent This effect might be experimentally seen as an excess
: clusters, showing that cluster correlations are indeed an of cluster production with respect to the prediction of
v
ubiquitous feature of quantum few-body systems down the statistical model, provided that the ingredients of
i
X to the femtometer scale. Concerning experimental re- the latter are sufficiently constrained via experimental
r search, rotational bands consistent with α-cluster struc- data. To this aim, we have performed an exclusive and
a
tures have been identified in different even-even light (quasi)complete detection of the different decay prod-
nuclei and shown to persist even along their isotopic uctsemittedin12C+12Cdissipativereactionsat95MeV,
chains [2]. Exotic non-statistical decays of these cor- and compared experimental data to a dedicated Hauser-
related states have been evidenced in the recent litera- Feshbach code, with transmission coefficients and level
ture [4]. densities optimized on the A≈20 region [8].
A natural extension of the concept of nuclear clusters We will show that all the observables of dissipative
concerns nuclear molecules. Molecular states have been events are fully compatible with a standard statistical
seeked for in nuclear reactions since the early days of behaviour, with the exception of α-yields in coincidence
heavy-ion science. In particular, several interesting res- with oxygen residues. The observed anomalies are ten-
onances have been observed in the 12C+12C reaction in tatively attributed to clustering effects which appear to
theinelastic[5]andα-transferchannels[6]. Thesestudies survive even in the most dissipative events.
24
suggestthat resonantstructures persist in the Mg sys- The experiment was performed at the LNL (Labora-
temuptoaround50MeVexcitationenergy,aremarkable tori Nazionali di Legnaro), with the 12C beam provided
result as a pure statistical behaviour might be expected by the XTU TANDEM accelerator. The experimental
due to the extremely high number of available states at setup was composed by the GARFIELD detector, cov-
suchhighexcitation. Concerningthe α-transferchannel, ering almost completely the polar angular range from
◦ ◦
experimental results have been reproduced by coupled 30 to 150 , and the Ring-Counter (RCo) annular de-
◦
cluster calculations [7] where the cross section is domi- tector, centered at 0 with respect to the beam direc-
nated by a four-cluster (α+α)+(α+12C) state of highly tionand coveringforwardlaboratoryangles in the range
2
◦ ◦
5 ≤ θ ≤ 18 . Details on the apparatus and the experi-
mentaltechniquescanbefoundinRef.[9,10]. Thecom- Z =7 Z =8 Z =9 Z =10
res res res res
bination of the two devices allows a nearly-4π coverage 10-1 10-1 -1 -1
ofthesolidangle,which,combinedwithahighgranular-
ity, permits to measure the charge, the energy and the
10-2 -2 -2 -2
emission angles of nearly all charged reaction products,
allowing an excellent discrimination of different reaction
mechanisms. 10-3 -3 -3 -3
Events with a single Z ≥ 2 fragment detected in the EE
RCo(identifiedonlyincharge)incoincidencewithoneor dd
Y/
morelightchargedparticles(LCP)Z ≤3inGARFIELD d
are selected. LCP isotopic identification has been per-
10-2 -2 -2 -2
formed through Fast and Slow CsI analysis [11], with
energy thresholds [12] similar to other experimental 4π
devices employing the same identification method [13]. 10-3 -3 -3 -3
Onlyeventswhere the totalchargeofthe entrancechan-
nel Z =12isdetectedarekeptfor theanalysis,unless
det
specifiedinthetext. Weexpectthatmostoftheselected 10-40 20 40 60-4 20 40 60-4 20 40 60-4 20 40 60
eventsshouldcorrespondtofusion-evaporation,withthe E (MeV)
residue detected at forward angles in coincidence with
evaporated particles detected at central center-of-mass
FIG.1: (Coloronline)Proton(upperpart)andα(lowerpart)
angles covered by GARFIELD. Experimental data are
energyspectraincompleteZdet =12eventsdetectedincoin-
therefore compared to the predictions of a Monte Carlo
cidencewitharesidueofchargeZres,indicatedineachfigure
Hauser-Feshbachcode[8]fortheevaporationofthecom-
column. Experimentaldata(dots)arecomparedtomodelcal-
pound nucleus 24Mg, at Ef∗us = 61.4 MeV, correspond- culations(redlines). Spectraareshownforthemostabuntant
ing to complete fusion source, and filtered through a residues, 7≤Zres ≤10.
software replica of the experimental set-up. The max-
imum angular momentum for the fused system is as-
sumed J0 max = 12 ~, coming from the systematics in tum steepens the tail of the spectrum of heavy particles
PACE4 [14]. The comparison of various experimental (α’s)withrespecttolightones(protons). Onthebasisof
observables and code calculations is used to validate the suchconsiderationsitisfoundthatnocommonchoiceon
parameterizations of statistical model ingredients imple- theparameterscanbedoneinourcalculationsinorderto
mented in the code. In particular, an exclusive study reproduceatthesametimeprotonsandαenergyspectra.
of completely reconstructed decay chains has been per- The best model reproduction is obtained with standard
formed,inordertogetaninsightintothedeviationsfrom fiducialvaluesforthetransmissioncoefficients,levelden-
a statistical behaviour observed in the decay. sity parameters and angular momentum distribution [8],
Fig. 1 displays the energy spectra of protons and α asshowninFig.1. Theverygoodreproductionachieved
particlesdetectedinGARFIELDincoincidencewiththe forprotonssuggeststhatthediscrepancyfoundforαpar-
mostabundantresidues. Ifnotexplicitely stated,alldis- ticles reflects an out-of-equilibrium emission and mostly
tributionsareshownnormalizedtoaunitaryarea,sothat concernswell-definedchannelswhereoxygenisproduced.
a comparison among their shapes is easily done, and all Tounderstandthedeviation,amoreexclusivechannel
energiesaregivenin the laboratoryreferenceframe. Ex- by channel comparison is therefore needed. Fig. 2 dis-
perimental data are always shown with statistical error playstheexperimental(leftpanel)andtheoretical(right)
bars,whenvisible. Wecanseethataverygoodreproduc- correlation between the energy of the oxygen fragment
tion of the protonenergy spectra is achievedin all chan- Eres and the sum of the energies of the two α-particles
nels, while a large discrepancy in the shape of the distri- Eαi in 12C(12C,AO)αα events. The lines represent the
2
bution appears for α particles in coincidence with oxy- kinematical locus Q = E + Eα −E =
kin res Pi=1 i beam
gen residues. The shape of particle spectra produced by −15.78MeV,whereE isthebeamenergy. Thislocus
beam
2
a statistical process is determined by the interplay of all divides the (E , Eα ) plane into two regions: in
res Pi=1 i
physicalingredientsenteringinthe decay,notablytrans- the one above,we find two correlatedbands centered re-
missioncoefficients,angularmomentumdistributionand spectivelyatQ =(1.27±1.40)MeVand(−5.35±1.70)
kin
leveldensityparameters. Nevertheless,thesedifferentin- MeV, while a broader region extends below the locus
gredients can be largely disentangled [15]: transmission up to a high amount of missing energy. In the follow-
coefficients define the shape of evaporatedspectra in the ing, we will refer to these regions as respectively the
Coulomb barrier region; the level density mostly affects non-dissipativeanddissipativeeventsregion,andwewill
theslopeoftheexponentialtail;andtheangularmomen- adopt for them the notation Q and Q . In the sta-
> <
3
V) 100 (a) (b) in competion with fusion-evaporation.
e
M 80
s ( Fig.3a displaysthe comparisonbetweendataandcal-
e 60 culationsfor the energyspectrumof αparticlesdetected
Er
incoincidencewithanoxygenresidueandemittedindis-
40
sipative events (full dots). As a reference the α energy
20
distribution without any Q selection (empty dots, see
kin
0 Fig.1)isalsoplotted. Agreatimprovementintheagree-
0 20 40 60 80 0 20 40 60 80 100
∑Eαi (MeV) ment between data and calculation is achieved when we
limitthecomparisontotheQ eventclass. Nevertheless,
<
a residualdiscrepancy is observed, and the experimental
distribution is still not reproduced in its shape. To in-
FIG. 2: (Color online) Experimental (a) and theoretical (b)
vestigate the origin of this deviation, in the middle (b)
correlationbetweentheenergyoftheoxygenfragmentandthe
sum of the energies of the two α particles in 12C(12C,AO)αα and right (c) panels of Fig. 3 we show the α energy
events. The line represent the kinematical locus Qkin = distributions associated to channels where the oxygen
Eres+P2i=1Eαi−Ebeam = −15.78 MeV at the opening of residue is in coincidence with, respectively, two or only
the4-body channel 12C(12C,15O)nαα. one α(’s). We can see that the shape of the energy spec-
tradependsonthechannel. Thestatisticalcalculationis
abletosatisfactorilyreproduceseparatelytheenergydis-
tistical model interpretation, the two correlated bands tributions ofα particlesfor dissipative2α’s and1α com-
correspond to α-decay chains, starting from the 24Mg∗ pletely reconstructed decay chains, while the sum of the
compound nucleus and leaving an 16O residue either in two processes is not correctly reproduced. Experimen-
its ground state (Qkin = −0.11 MeV) or in one of its tally, (63±5)% of the total cross section for completely
excited bound states which are not resolved in the ex- reconstructeddissipativedecayswithaαparticleandan
periment, with an averageenergy expense Qkin ≈−6.55 oxygen fragment in the outgoing channel is absorbed by
MeV.ThebroadeningobservedfortheexperimentalQkin (2α,16O∗)channels,wheretheoxygenisexcitedaboveits
bands reflects the energy resolution of our setup for the neutron emission threshold, while according to the the-
energybalanceintriplecoincidencemeasurements,which oretical predictions these channels should represent only
addsup to∆E/E .4%. The locusQkin =−15.78MeV (10±1)%of this class of events. In conclusion, the resid-
gives the threshold Q-value where the 4-body channel ualdeviationobservedinthe leftmostpanelofFig.3 ap-
12C(12C,15O)nαα opens. In terms of energy, this is the pearsto originatefromabranchingratiodiscrepancyfor
less expensive channel involving an oxygen residue and the (n,2α,15O) (and, with a minor contribution, for the
particles other than α’s. Neutrons are not detected in 2n,2α,14O)) decay channel with respect to decay chan-
this experiment, and the broader distribution observed nels involving a single α emission, even if a contribution
for lower Qkin values is due to events in which neu- fromhighenergyγ emissionfromcollectivestatescannot
tron(s)emissionhastakenplace,andtheirkineticenergy be a priori excluded.
has notbeen collected. Accordingto modelcalculations, This finding indicates that cluster correlations associ-
the (n,2α,15O) channel should absorb the largest cross- ated to the 12C+12C system persist up to higher center-
section in this region. of-massenergiesthanpreviouslyexpectedfromtheanal-
Besidesthe commonpatternobservedfor the (2α,AO) ysis of the inelastic channel [16], and lead to a non-
energycorrelation,adifferenceintherelativepopulation statistical behaviour in the decay of the highly excited
24 ∗
of the Q regions is evident between experimental data Mg. Given the high excitation energy E =61.4 MeV
≶
and calculations in Fig. 2. In particular, a much higher it is not possible to associate the extra yield to a sin-
percentage of (2α,AO) events populates the Q region gle isolatedstate with a well defined angularmomentum
>
in the experimental sample: (37±5)%, with respect to and parity. Nevertheless, interesting information can be
(9±1)% according to model predictions. Also in the extracted from Fig. 4, which displays the α−α relative
following, when giving experimental percentages, the energy distribution for the Q and the Q region, in
< >
associated error is an upper limit taking into account comparison with the statistical model calculation. We
both the statistical error and the possible 3He-α con- cansee that a clear peak appearsin the most dissipative
8 16 ∗
tamination. Events falling in the Q region correspond events, which can be associated to doorway ( Be- O )
>
to exit channels with low energy dissipation. Therefore, and(9Be∗-15O)states,wheretheexcitationenergyofthe
this region can also be populated by reactions not 16O (9Be) is above the neutron emission threshold, and
proceeding through an intermediate compound nucleus which is not present in the statistical model. The ab-
state. The larger experimental branching ratio for the sence of a 8Be resonance in the less dissipative events
(2α,16O) exit channel in the Q region probably reflects suggests that these reactions do not originate from a
>
acontaminationofdirect(α-transfer/pick-up)reactions, (α+α)+(α+12C) doorway state as it was suggested to
4
10-1 (a) (b) (c) hypothesis is made on the residue mass number Ares:
Nc
10-2 Ec∗al(Ares)=XEiCM +Nn(Ares)·(cid:10)EnCM(cid:11)+Q(Ares)
E i
d
Y/ (1)
1d0-3 where Nc ( Nn ) and EiCM ((cid:10)EnCM(cid:11)) are respectively
the charged products (neutron) multiplicity and their
center-of-mass kinetic energies, and Q is the decay Q-
10-4
0 20 40 60 0 20 40 60 0 20 40 60 value. Indeed, the emitted neutron number is uniquely
E α (MeV)
determined by mass conservation and their energy can
be (in average)estimated from the measured proton en-
ergy with the subtraction of the Coulomb barrier. An
FIG. 3: (Color online) For dissipative events (as defined in
the text) with Zdet =12, experimental (black dots) and cal- estimation of the mass of the residue can thus be ob-
culated (red lines) α energy spectra in coincidence with an tained by minimizing in each event completely detected
oxygen are compared for: all channels involving at least 1α inchargethe quantityδε∗ (A )=|E∗ (A )−E∗ |.
cal res cal res fus
(a) and, separately, channels involving 2α’s (b) and only 1 α Fig. 5a displays the resulting estimated oxygen isotopic
(c). As a reference, in the leftmost panel, also the α energy
distribution. As expected, we find in the data an ex-
distributionwithout anyQkin selection (sameasinFig. 1)is
tra production of neutron-poor isotopes, coherent with
shown (emptydots).
the finding of anextra experimentalcrosssectionfor the
(xn,2α,16−xO) channel. The reconstructedexperimental
isotopic distribution for the considered residue is found
tobegenericallywiderwithrespecttomodelpredictions.
el Q Q Finally, it is important to stress that, with the ex-
Er
d < > ception of the anomalous branching ratio towards this
Y/10-2
d channel,the detectedeventswherethe dissipatedenergy
15
overcomesthefour-bodythresholdassociatedto Ofor-
10-3 mation (Q = −15.78 MeV) are fully compatible with
kin
a complete fusion pattern followedby the compoundnu-
cleus decay of 24Mg∗. Indeed the Hauser-Feshbach cal-
10-4
0 2 4 culationsatisfactorilyreproducesallthedifferentobserv-
0 10 20 30 40 10 20 30 40 50
Erel (α,α) (MeV) ables that can be constructed with the exclusion of Q>
eventsfromtheanalysis,andthatdonotdirectlyinvolve
α-oxygen coincidences. Fig. 5 displays some selected ex-
FIG. 4: (Color online) Experimental (black dots) and calcu- amples,asthe velocitydistributions ofthe heaviestfrag-
lated (red lines) relative energy distributions of the two α’s ment and the charge distribution of reaction products,
found in coincidence with an oxygen in dissipative (left) and
this latter both for complete (Z = 12) and almost-
det
non-dissipative (right) events. In the left panel, a zoom on
complete (Z ≥ 10) events, in order to show that no
thelow relative energy region is shown in the figureinset for det
important bias is induced by the stringent completeness
experimental data.
conditions. The globalquality of the agreementbetween
data and calculations makes us claim that we have been
able to select in our data-set a component which is as
close as possible to the statistical decay of a hot equi-
be the case at lower energies [7]. librated source, corresponding to the complete fusion
24Mg∗ source.
Since we have interpreted the observed extra α-yield In conclusion, in this paper we have presented an
fromdissipativeeventsasassociatedtotheproductionof exclusive analysis of dissipative 12C+12C collisions at
neutron-pooroxygenisotopes,weexpectthatasignature 95 MeV, fully reconstructed in charge. A detailed
of the anomalous branching ratio should be evidenced comparison to a dedicated Hauser-Feshbach calculation
in the isotopic residue distribution. Unfortunately the shows an abnormally high branching ratio towards
16 ∗
residuemassisnotdirectlyaccessibleinthisexperiment, the (2α, O ) channel with respect to the statistical
becauseofthelowenergyofheavierfragments. However, expectation, where the oxygen is excited above its
due to the completeness of the detection, this informa- neutron emission threshold, which corresponds in part
tioncanbeapproximatelydeducedfromthecalorimetric to the population of a doorway (8Be-16O∗) configu-
energy distribution, as explained hereafter. The excita- ration. This extra yield could be due to a failure of
∗
tion energy E can be estimated event-by-event from the Hauser-Feshbach theory for the decay of highly
fus
the calorimetric energy balance E∗ (A ), provided an excited 24Mg, possibly due to the α-correlations of this
cal res
5
coordinators.
s)10-1 (a) Z)1 (b) This work was partially supported by the European
Y(Are10-2 Y(10-1 FPurongdrsamfor- ELNarSgAeRSc2a6l2e0F10a.cilities - Seventh Framework
10-2
10-3
10-3
10-4
10-4
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12 12 creases the 3He threshold but does not affect too much
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