Neutron capture cross sections: from theory to experiments and back

0.05 MB·English

by  Alberto Mengoni

Neutron capture cross sections:
from theory to experiments and back
A. Mengoni1
CERN,CH-1211Geneva23,Switzerland,and
5
ENEA,ViaDonFiammelli,2-40129Bologna,Italy
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0
2
Abstract. The method for an experimental determination of the stellar enhancement factor for the cross section of the
n 151Sm(n,g) reaction process is proposed. This study offered the pretext for an excursus on the interconnections between
a captureanddissociationreactionsandtheinterplaybetweentheoryandexperimentsinthedeterminationofneutroncapture
J crosssections.

1
3
INTRODUCTION ityoftheevaluatedreactionratesinstellarenvironment.

1 Thepossibilitytomeasuredirectlythecrosssectionfrom
v One of the most difficult issues for the accurate deter- nuclei in excited states is scarce if not completely null,
2
minationofstellarreactionratesistheevaluationofthe becausenucleiinexcitedstates(whicharenotisomers)
8
so-called stellar enhancement factor (SEF). This factor live a marginal fraction of seconds. It is proposed here
0
1 simply relatesthe cross section measuredin the labora- to use the inverse reaction channel of the neutron cap-
0 torytothecrosssectioninastellarenvironment,s ∗,by ture process to deduce the SEF for one important neu-
5 s ∗ ≡SEF×s lab. In capture reactions, this means that troncapturecrosssection:the151Sm(n,g ).Thisreaction
0 for the determination of the SEF, an evaluation of the cross section has been measured recently at the CERN
/
h capture cross section for nuclei in excited states needs n_TOFfacility[1]aswellasattheForschungszentrum,
t to be done.In same cases the SEF is close to unityand Karlsruhe [2]. These measurements provide confidence
-
l the effecton the stellar cross section is marginal.How- ontheexperimentaldeterminationoftheMaxwellianav-
c
ever, there are several importantcases in which excited eraged cross section (MACS) for the ground-state cap-
u
n statesofthetargetnucleiarestronglypopulatedinastel- ture.On theotherhand,the SEFforthisreactionneeds
: larenvironment.There,anaccuratedeterminationofthe to be derivedby theoreticalcalculationwhichmay pro-
v
SEFismandatory.Justtomentiononeexampleinwhich ducedifferentresults.Thepossibilityofanexperimental
i
X this is the case one can consider the SEF of the s n,g of determinationoftheSEFseemsthereforeappealing.
r the186Osand187Os.Thelatter,inparticular,hasanex-
a
citedstateatonly9.8KeVexcitationenergyandatstellar
temperatureof the orderof kT ≈ 30 KeV can be popu-
Capture Dissociation
lated up to 50 %. Thisimplies a 20 % differencein the
sotfel1l8a6rOMsatoxw18e7llOiasn. Ianveturargne,difcoanpetuuresecsrothses sReec/tOiosncrlaotciok 0.0 Jt n Jr > Sn−> ExSnEr ESrn > SnJr n Jt 0.0
AZ AZ
fortheagedeterminationofthegalacticnucleosynthesis, Jx Ex Ex Jx
oneobtainsanincreaseof2Gyrintheage.Itistherefore
necessarytoobtainanaccuratedeterminationoftheSEF. J0 0.0 0.0 J0
Thisis usuallydonein modelcalculationsbasedon the A+1Z A+1Z
Hauser-Feshbachstatisticalmodeltheory(HFSM).Mea-
surementsofthe capturecrosssectionsfortargetnuclei FIGURE1. Schematicviewoftheneutroncaptureanddis-
in theirground-stateallowforcheckingtheaccuracyof sociationprocesses
themodelcalculations.However,anexperimentaldeter-
minationoftheSEFwouldstronglyenhancethereliabil-
1 e-mail:[email protected]
DIRECT ANDINVERSE REACTION experimental data obtained for the ground-state transi-
CHANNELS tions and then the same normalization factor is used in
the evaluation of the cross section for transitions to the
The time-reversalinvarianceofnuclear reactionswhich otherexcitedstates.
leads to the detailed-balancerelation between reactions
in the "direct" and "inverse" channels has been widely
used for deriving reaction cross sections which can be SEF: FROMTHEORYTO EXPERIMENT
accessedinthelaboratoryonlyinoneofthetimedirec-
tions. A schematic view of the capturereaction process The 151Sm(n,g )152Sm reaction has important implica-
anditstime-reversalsinvariantisshowninFigure1.The tions in nuclear astrophysics as it can be used to con-
relationbetweenthecrosssectionsinthecaseofaneu- strainthetemperatureconditionsoftheHeburningphase
troncapturereactionprocess,n+AZ→A+1Z+g ,issim- ofAGBstars.Withits93yearsb -decayhalf-life,151Sm
plygivenby representsabranchingpointinthesprocesspathwhich
isinfluencingtheisotopicabundanceratioofthetwos-
s n,g = kkg2222JAJ+1++11s g,n hoanllfy-lGifedoifso15to1Spemsi1s5t2eGmdpearnadtu1r5e4dGedp.eSndinecnet,tohneceb t-hdaetciatys
n A
capture cross section is determined, a link between the
wherekn istheincidentneutronwavenumberandkg = temperatureconditionsandtheisotopicabundanceratio
eg/h¯cistheg -raywavenumberrelatedtotheg -raytran- betweenthetwoGdisotopescanbeestablished.
sitionenergyeg.Thedissociationcanbeinducedbyreal The151Sm(n,g )152Smcrosssectionhasbeenrecently
photons, or by the virtual photon field generated by a measuredattheCERNn_TOFfacility[1].Theresultfor
high-Z target as in the Coulomb dissociation process. the MACS-30 (MACS at kT = 30 keV) is 3100±160
The latter reaction process is nowadays widely used in mb. This result has been confirmed in a measurement
experiments with radioactive ion beams, in which also performedatFZK[2]inwhichtheMACS-30resultob-
thereactionkinematicsisinverted(seeforexample[3]). tainedis3031±68mb.Theoreticalestimatesofthecap-
One importantdifferenceto notice between the two re- ture cross section based on HF statistical model theory
actionprocessesisthat,whileinthecapturechannel,all producesmuchlowervalues,typicallyaround2000mb.
the states in the n+AZ compositesystem are populated, In anycase, the energydependenceof the crosssection
intheinversedissociationprocessonlytheground-state is well reproduced by the model calculation and, once
ofthecompositesystemisinvolved.Therefore,thetime- that the MACS value is obtained in the laboratory, the
reversalinvarianceisfullysymmetricalonlyforground- calculatedcrosssectioncanbenormalized.
statetransitions.Itisalsoimportanttonoteherethatex- 151Smhasseverallow-lyinglevelswhichcanbepop-
cited states in the residual nucleuscan be populatedby ulatedunderstellarconditions.Forexample,thefirstex-
the dissociation process. As will be shown in detail be- cited state at 4.8 keV is populated at a 30 % level at
low, the proposal of the present work is based on this temperaturesofkT =30KeV.Thedeterminationofthe
consideration. SEF for the 151Sm(n,g )152Sm reaction is therefore im-
On the experimental side, (g ,n) reactions have been portantfora reliableapplicationtoAGBstar modeling.
usedrecentlyforthedeterminationofsomecapturereac- AschematicviewofthesituationinreportedinFigure2.
tionratesofunstableisotopesofbranchingpointsinthe
sprocesspath,withtwodifferenttechniques.Anactiva-
n
tionmethodbasedonabremsstrahlungphotonspectrum 7/2− 8%
suchastheoneoftheS-DALINACatDarmstadtTechni- 3/2− 29%
calUniversity.Inthiscase,aphotonbeamwithdifferent
5/2− 51% 8.257
bremsstrahlung end-point energies is used to activate a
151
targetmaterialwhosedecayisdetectedoff-lineafterthe Sm
irradiation.Asecondmethodisbasedontheuseoflaser 0.685 0+
inverse-Compton scattering gamma-ray sources. In this 0.366 4+
case, a monochromatic gamma-ray beam is used to in- 0.121 2+
duce prompt photo-neutron (or photo-p, photo-a , etc.)
0.0 0+
emissioninthedissociationprocess.Bothtechniquesare
152Sm
described in a recent review paper [4] in which details
of the methods used to derive the capture reaction rate
from(g ,n)measurementsaregiven.Forbothmethods,a FIGURE 2. Schematic view of the neutron capture by
modelcalculationofthe(g ,n)crosssectionisrequired. 151Sm.Thepopulationprobabilitiesofthefirstthreeexcitated
targetstatesareindicatedforatemperatureofkT =30KeV.
The calculated cross section is then normalized to the
Asmentionedintheintroduction,theSEFcanbecal- old. As expected, the only open channel up to ≈ 100
culated.ThisisnormallydonewiththeuseoftheHauser- KeV above threshold is the dissociation leading to the
Feshbachstatistical modeltheory.Themainingredients 151Sm(Jp =3/2−)state.Therefore,inanactualexperi-
in these calculations are the optical model parameters ment,thiswouldproducetheinformationneededtode-
representingtheinteractionoftheneutronwiththetarget, rivethecapturecrosssectionof151Sm fromitsfirstex-
furnishing the neutron transmission coefficients for the citedstate.
neutron-nucleusinteraction. In addition,the representa- As the excitation energy increases, the second disso-
tionofthedensityofnuclearstatesatexcitationenergies ciation channel at E = 104.8 KeV opens up. Then, a
x
uptotheneutronseparationthresholdandupto≈1MeV measurementofthe(g ,n)crosssectionabovethisenergy
above.Finally, the electric dipoleresonance parameters range would include the effect of this state and in turn,
areusedtoevaluatetheg -raystrengthfunctions. allow for an experimental determination of the time-
The NON-SMOKER calculation of the SEF for the reversalneutroncaptureprocessfromthisstate.Onlyat
151Sm(n,g )152Sm reaction is 0.87 at kT = 30 KeV [5], higherexcitationenergies,theeffectoftheground-state
while in the calculation performed for the present startstocontribute,butonlytoafewpercentlevel.
work we have obtained 0.93. This discrepancy is most
likely due to different parameterizationsof the Hauser- 9.2
Feshbach theory which are used in model calculations.
Therefore, the accuracy of the SEF calculation cannot 9 -> 5th-> 6th-> 7th
guaranteeTdHbyEth1e5H2SFSmM(gth,eno)r1y5i1tSsemlf.CASE 8.6 8.8Gamma-ray energy [MeV] -> 2nd-> 3rd-> 4th
The 152Sm(g ,n)151Sm reaction can be measured with 8.4
boththetechniquesmentionedabove.Thereis,however,
aJpp=ecu0l+iargitryouinndt-hsitsatreeaocfti1o5n2.SmIn,foanclty, setaxrctiitnegdfsrtoamtesthine 0.07 ]b 0.06[ noi 0.05tces s 0.04sorc n 0.03ortue 0.02n-oto 0.01hP 0 8.2 Total-> gs-> 1st
151Sm can be populated by the strongest E1 transitions
FIGURE 4. HFSM calculation of the 152Sm(g,n)151Sm
and with s-wave neutronsin the continuum.In particu-
p − crosssectionfordissociationintothedifferent151Sm+nchan-
lar, the J =5/2 can only be populated with d-wave
nels.
p −
neutronsleftin the continuum.TheJ =3/2 first ex-
citedstateatE =4.82KeVin151Smispopulatedfrom The HFSM calculations have been performed using
x
the nuclear level density parametrization of reference
the neutron emission threshold and s-wave neutrons in
[6]. The parameters have been fixed to reproduce the
the continuum. The next possible excitation is the 5th
p − experimental level spacings at the neutron separation
excitedstateatE =104.8KeV,alsoaJ =3/2 state.
x
energies which, in the present case, are available for
ThissituationisschematicallyshowninFigure3.
boththeisotopesinvolved[7].TheMoldauer[8]optical
n 3/2− 0.105 modelparametershavebeenusedfortheneutrontrans-
3/2− 0.005 missionfunctioncalculationsandexperimentalparame-
8.257 > 8.257 5/2− 0.0 ters of the Giant Dipole Resonance [9] for the calcula-
tionoftheg -raystrengthfunction.Thecrosssectionhas
151Sm
been renormalized in order to reproduce the measured
0.685 0+ 151Sm(n,g )152Sm MACS-30. This normalization factor
0.366 4+ turned out to be 1.7 for the present HFSM calculations
aswellasfortheNON-SMOKERresult[5].
0.121 2+
The absolute value of the dissociation cross section
0.0 0+
is of the same order as that of measurements already
152Sm performed(seeforexamplethereportonthe186W(g ,n)
measurement [10]), making the proposal for an actual
FIGURE3. Dissociationof152Sminto151Sm+n. experimentquiterealistic.
The HFSM results of the calculation of the (g ,n) re-
action process are shown in Figure 4. There, the cross
sectionss g,nforthevariousreactionchannelsareshown
intheenergyregionabovetheneutronemissionthresh-
CONCLUSION
The experimental determination of the SEF for the
151Sm(n,g ) could be possible by a measurement
of the time-reversal invariant reaction process, the
152Sm(g ,n)151Sm reaction. This reaction can only pop-
ulateexcitedstatesinthe151Sm+nresidualchannelfor
excitation energies just above threshold. The technique
has been used for the determination of capture cross
sectionsofunstablenucleiatsprocessbranchingpoints
and could,in this specific case lead to the experimental
determinationofaSEFforthefirsttime.
ACKNOWLEDGMENTS
IwouldliketothankFranzKäppelerforseveralfruitful
discussionsonthesubjectofthepresentwork.
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