The 40Ca(alpha,gamma)44Ti reaction in the energy regime of supernova nucleosynthesis

0.14 MB·English

by  H. Nassar

The 40Ca(α,γ)44Ti reaction in the energy regime of supernova nucleosynthesis
H. Nassar1, M. Paul1∗, I. Ahmad2, Y. Ben-Dov3, J. Caggiano2, S. Ghelberg1, S. Goriely4, J.P. Greene2,
M. Hass5, A. Heger6,7, A. Heinz2, D.J. Henderson2, R.V.F. Janssens2, C.L. Jiang2, Y. Kashiv1, B.S. Nara
Singh5, A. Ofan1, R.C. Pardo2, T. Pennington2, K.E. Rehm2, G. Savard2, R. Scott2 and R. Vondrasek2
1 Racah Institute of Physics, Hebrew University, Jerusalem, Israel, 91904
2 Argonne National Laboratory, Argonne, IL 60439, USA
3 Physics Div., NRC-Negev, POB 9001 Beer-Sheva, Israel 84190
4 Universit´e Libre de Bruxelles, CP-226, 1050 Brussels, Belgium
5 Dept. of Particle Physics, Weizmann Institute, Rehovot, Israel 76100
6 Los Alamos National Laboratory, Los Alamos, NM 87545, USA and
7 University of California at Santa Cruz, Santa Cruz, CA 95064, USA
(Dated: February 8, 2008)
6 The 44Ti(t1/2= 59 y) nuclide, an important signature of supernova nucleosynthesis, has recently
0 been observed as live radioactivity by γ-ray astronomy from the Cas A remnant. We investigate
0 in the laboratory the major 44Ti production reaction, 40Ca(α,γ)44Ti (Ecm ∼ 0.6–1.2 MeV/u), by
2 direct off-line counting of 44Ti nuclei. The yield, significantly higher than inferred from previous
experiments, is analyzed in terms of a statistical model using microscopic nuclear inputs. The
n
associatedstellarratehasimportantastrophysicalconsequences,increasingthecalculatedsupernova
a 44Ti yield bya factor ∼2 over previousestimates and bringing it closer toCas A observations.
J

1
PACSnumbers: 26.30.+k,25.55.-e,97.60.Bw,95.85.Pw,24.60Dr
1

2 Theradionuclide44Ti(t =59y)isconsideredanim- afactor∼3thanestimatedbystellarcalculations[2]. No
v 1/2
portant signature of explosive nucleosynthesis in core- other source of 44Ti activity has been confirmed so far,
6
0 collapsesupernovae(SN)[1],wheremultipleαcaptureis despite a number of candidates and the improved sensi-
0 the path for SN nucleosynthesis from 28Si to 56Ni(Fe). tivity of the INTEGRAL γ-ray telescope [2]. Although
9 44Ti is mainly produced during an α-rich freeze-out many nuclear reactions play roles in determining the SN
0 phase, the ratio 44Ti/56Ni being sensitive to the explo- yield of 44Ti [9, 10], the major production reaction is
5
sionconditions. Stellarproductionof44Tideterminesthe 40Ca(α,γ)44Ti and its importance has been emphasized
0
/ abundanceofstable44Caandcontributestothatof48Ti [11]. Experimentalinformation aboutthis reactionis in-
x (fedby48Crontheα-chain). Live44Tihasbeendirectly completeandtheoreticalestimatesaremadelessreliable
e
- observed from a point source identified as Cassiopeia A bythesuppressionofdipolarT =0→0transitionsinself-
cl (Cas A) by γ- and X-ray telescopes (CGRO, RXTE, conjugate (N=Z) nuclei. The reaction was studied in
u BeppoSAX) and very recently by the INTEGRAL mis- the 70’s by α bombardment of Ca targets and prompt-
n sion (see [2, 3]). Cas A is believed to be the remnant γ spectroscopy down to Ecm ∼ 3 MeV, yielding ener-
:
v of a core-collapse SN whose progenitor mass was in the gies, spins and strengths of isolated resonances [12, 13].
Xi range 22–25 M⊙ (M⊙ denotes a solar mass) [4]. Using Rauscheret al. [14]usedthis information(together with
known values of the distance and age of the remnant, thatforlighterN=Z nuclei)tobuildanempiricalmodel
ar half-life of 44Ti and the combined γ flux from all obser- and calculate an astrophysicalrate for the reaction, cur-
vations, an initial 44Ti yield of 160±60µM⊙ is implied rently adopted in SN-nucleosynthesis codes. The aim of
[3]. This value is larger by a factor of 2–10 than 44Ti thepresentworkistoprovidenewexperimentalinforma-
yields calculated in current models (e.g. [5, 6]) and var- tion on the cross section of the 40Ca(α,γ)44Ti reaction
ious explanations have been proposed [4, 7, 8, 9]. 44Ti and on the astrophysical rate of production of 44Ti in
γ-ray emission from SN1987A in the near Large Mag- the energy range of SN nucleosynthesis. We use acceler-
ellanic Cloud galaxy, the closest known SN remnant in atormassspectrometry(AMS)withwhichwedetermine
the last two centuries, is below detection limits. But its the integral number of ground-state residual nuclei pro-
present lightcurve is believed to be powered by 44Ti ra- ducedinanactivationrun. Thismethodhasbeenusedto
dioactivityandtheinferredinitial44Tiyieldisestimated measurecrosssectionsofastrophysicalinterestproducing
to be 100–200 µM⊙ (see [2]), similar to that of Cas A. long-livednuclides[15,16]. Wemeasureforthefirsttime
Using the 56Ni yield of SN1987A directly measured by the yield of the 40Ca(α,γ)44Ti reaction integrated over
γ-rayastronomy,the implied44Ti/56Niratiois largerby a large range of energies in the explosive-nucleosynthesis
regime,allowingustovalidateorscaletheresultsofcur-
rent theoretical models and derive an astrophysical rate
compatible with laboratory experiment.
∗To whom correspondence should be addressed, email address:
Our measurements were performed by bombarding a
[e-mail]
He-gas target cell with a 40Ca beam and implanting
2
forward-recoiling reaction products in a Cu catcher act- thin He a) Ar c)
1600
ing also as beam stop. This inverse-kinematicsapproach target target
has the advantage of using a high-purity target able to
)
sustainhighbeampower,wherethe thicknesscanbe ac- er
b
curately controlled by monitoring the gas pressure. In m
u1400
the conditions of our experiment, the power deposited n
in the gas (<10 mW/mm) is not expected to change its el 800 1000 800 1000
n1000
stopping power [17]. After irradiation, 44Ti atoms are an thick He b) calib. d)
rciheerm. iTcahlelyaebxutnradcatnecdefrro44m=t4h4eTci/aTtcihe(irnwtihthe 1a0n−a1t3T-1i0c−a1r2- E (ch2 target 44Ti sample
∆
range) is then measured by AMS and the total number
900 44Ca
(n44)of44Tinucleiproducedinthecatcherisobtainedby tail
therelationn44 =r44nTi,wherenTi denotesthenumber 700 800 700 800
of Ti carrier atoms used. Importantly, this result, based E (channel number)
on the 44Ti/Ti isotopic ratio, is independent of chemical
or counting efficiencies [15]. The experimental scheme FIG.1: Identificationspectraof44Ti: Eand∆E2 areenergy
wastested by producing a copiousnumber of 44Tinuclei and energy-loss signals, respectively. The data shown have
(∼2.7×109) via the reaction 34S(12C,2n)44Ti [18]. The been filtered through a software condition set by additional
44Ti yield measured by AMS analysis and the derived energy-loss signals (∆E1, ∆E4) and correspond to runs: a)
R1; b) R2, R3; c) B1; d) S1(see Table 1).
cross section are consistent with those calculated by the
evaporation code PACE2 [19].
The 40Ca irradiations were performed at two different
accelerators. Usingtheelectron-cyclotronionsourceand whichwasusedthroughoutourworkto estimatespecific
theATLASlinacatArgonneNationalLaboratory,anin- energy loss. Irradiations under different conditions (see
tense 40Ca11+ beam (∼ 1 eµA on target) was produced. Table1,Fig. 1)wereperformedtoverifythatproduction
The irradiation was set up in a 32 cm-diameter cham- of 44Ti by backgroundreactions is negligible: in run B1,
ber used as a gas cell. The vacuum window, made of theHegaswasreplacedbypureAr(withsimilarincident
a 1.5 mg/cm2 pinhole-free Ni foil mounted eccentrically energyloss)andinrunB2(withHegas)theincidenten-
to the beam, was rotated at ∼1 Hz using a ferrofluidic ergy was shifted downward (∆Ecm= –0.25 MeV) off the
vacuum seal to dissipate the power loss of the beam. He resonance. The other irradiationswere performed at the
gas(99.995%)wascirculatedatroomtemperatureinthe Koffler Tandem accelerator (Weizmann Institute), using
large-volumechamberatconstantpressure(12Torr)dur- a(isobaricallypure)40Ca8+ beamwithanaverageinten-
ingthe 40Cairradiation. Thecatcher,atadistanceof18 sityof∼120enAontarget. TheHe(99.999%)gastarget
cmfromtheentranceNifoil,wasmadeofa6.4mmthick, and the water-cooled Cu catcher were contained in an
4.5cmdiameterCu(99.99%)disk,clampedtoachilled- electrically insulated and secondary-electron suppressed
water cooled housing. The beam intensity was periodi- chamberactingasaFaradaycupforbeamchargeintegra-
cally measuredduring the irradiationrunin anelectron- tion. Catchersmadeofthesamehigh-purityCumaterial
suppressedFaradaycupsituated2mupstreamofthegas andavacuumwindow madeofthe sameNifoilas inthe
cell and continuously monitored by a beam scanner in ATLAS experiment, were used. In order to dissipate the
front of the gas cell. In addition, a small Bragg-chamber power loss, the beam was magnetically steered onto the
detectorviewedtheNiwindowthrougha0.8mmdiame- vacuumwindowinaperiodic(∼1Hz)spiralmotion. The
tercollimatoratascatteringangleof49◦ tomonitorions incidentenergyofthe beamwassetto72.0MeVandthe
elasticallyscatteredoffthefoil. Ionidentificationallowed thickness of the 4He gas target (110Torr, 23cm) was se-
for the discrimination between the main 40Ca beam and lectedtointegratethereactionyieldfromEcm=4.2MeV
a(8.3±0.4)%contaminationof40Ar. Acorrectiontothe (afterthevacuumwindow)downtoEcm=2.1MeV,cov-
ion beam charge was applied, using the monitored 40Ca eringalargepartoftheSNnucleosynthesisenergyrange.
fraction. Itshouldbenotedthatthe40Arprojectilescan- Two independent irradiationruns were performed under
notproduce44Tifromthe4Hetarget. Theincidentlabo- thesameconditions,usingdifferentcatchers(R2,R3,see
ratoryenergy(70.9MeV)andHepressure(runR1,Table Table 1).
1)weretunedtopopulateastrongresonance(Ecm=4.10 After activation, a 10 µm-thick layer was etched off
MeV, Jπ =2+) in 44Ti, knownfrom prompt γ-raystudy each Cu catcher in a HNO3 solution containing 3 mg
[13]. Using an Enge magnetic spectrograph available on of Ti carrier. Ti4+ ions were separated from Cu by
anotherbeamline,theenergyofthe40Cabeamafterthe ion-exchange techniques and Ti was finally converted to
Ni foil was measured before the irradiation (46.1 MeV, TiO2. The44Tianalysisandmeasurementoftheisotopic
FWTM= 2.8 MeV). The energy loss is well reproduced ratios r44 were performed using the Hebrew University
bycalculationsperformedwiththeSRIM-2003code[20], AMSfacility[21]attheKoffleraccelerator. 44,46Ti− ions
3
(at least in part) been investigated by prompt-γ spec-
TABLE I:40Ca irradiations and 44Ti AMS analysis results
troscopy. The additional yield measured in the present
run Elab target/ irr. 40Ca 44Ti 44Ti/Ti n44 experiment may result from unobserved resonances but
(MeV) µg/cm2 acc. dose AMS (10−13) (106) more likely from closely spaced states in the 44Ti com-
(1) (2) (1016) counts (3) pound nucleus (Ex(44Ti)=7.2–9.3 MeV), unresolved in
previous experiments. We derive the experimental aver-
R1 46.1 He/51 L 6.9(14) 20 1.7(5) 6.4(17)
agecrosssection(thick Hetarget)overthemeasureden-
B1 46.1 Ar/106 L 3.9(8) 0 <0.1 <0.3
B2 42.5 He/42 L 2.6(5) 1 0.1(1) 0.3(3) ergyrangeσaexvep =n44/(NprojnT) = (8.0±1.1)µb(Nproj
isthenumberofincidentprojectilesandn theHetarget
B34 - - L - 0 <0.1 - thickness in atoms/cm2) and compare it iTn Fig. 2a with
R2 46.4 He/590 T 3.06(12) 33 5.6(10) 21(4) the expression σ =REmaxσ(E)(dE/dx)−1dE/∆x, us-
R3 46.4 He/590 T 4.00(20) 28 7.7(15) 30(6) ave Emin
ing values from current models for σ(E). The present
S15 - - - - 377 380(20) -
data strongly support the BRUSLIB model [25] which
B46 - - - - 0 <0.1 -
incorporates a microscopic model of nuclear level densi-
1 40Caincidentenergyafterpressurefoil ties [26] and of the γ-ray strength function [27], and a
2 irradiationaccelerator : L=linac,T=tandem global α-nucleus optical-model potential [28]; the NON-
3 3.0mgnatTicarrierusedforeachcatcher SMOKER [29] and empirical [14] models underestimate
4 unirradiatedcatcher the average cross section. In the BRUSLIB model, the
5 calibrationsample(44Ti/Ti=(3.66±0.12)×10−11)
6 blankAMScathode (natTi) γ widths (Γγ) are determined on the basis of a Quasi-
Random Phase Approximation calculation (for details,
see[27])builtonaHartree-Fockdescriptionoftheground
state, assuming complete isospin mixing. For N=Z nu-
were alternately accelerated at a terminal voltage of 12
clei, the standard prescription of ref.[30] is adopted to
MVandATi10+ionstransportedtothedetectionsystem.
account for the suppression of dipolar T =0→0 tran-
44Ti was discriminated from the dominant 44Ca isobaric
sitions by reducing the corresponding Γ ’s by a factor
γ
backgroundinamulti-anodeionizationchamber(Fig.1)
f =5. The scaled BRUSLIB calculation (Fig. 2a) was
andthe 46Ti10+ chargecurrentwasmeasured,leadingto iso
modifiedtoreproducetheexperimentalaveragecrosssec-
the44Ti/Tiratio. Inordertoreducesystematicerrorsin
tion by adjusting the suppressionfactor to f =8. This
iso
the final r44 values, the ratios were normalized to those value,anexperimentalmeasureofthedegreeofmixingof
measured for a calibration sample (Table 1; see [18, 22]
the T=0 into the T =1 states, confirmsthe largereduc-
forinformationonthe44Tisourcematerial). Blanksam-
tionof E1 strengthina N=Z nucleus. It is close to the
ples(havinggonethroughthesamechemicalprocedures, value(f =6−8)derivedinref.[31]forthe24Mgand32S
butcontainingno44Ti)wereusedtoensurethatnoback- iso
compoundnucleifromacomparativeanalysisofthecross
ground is present in the measurements. More details on
sections of (α,γ) reactions on N=Z and (Z,N=Z +2)
the AMS analysis and the experiments can be found in
target nuclei. The cross section σ(E) obtained from the
[21, 23, 24].
scaled BRUSLIB calculation was integrated to yield the
The experimental results are summarized in Table 1. astrophysical rate of the 40Ca(α,γ)44Ti reaction (Fig.
We derivefromrunR1 aresonancestrengthωγ (see e.g. 2b). The rate is higher by a factor 5-10 than that calcu-
[23] for a relationbetween yield and ωγ) of 8.8±3.0 eV, latedwith the model[14]overthe rangeoftemperatures
consistent with the results of prompt-γ measurements of SN nucleosynthesis. It is well fitted by the expres-
[13]for the twoclose-byresonancesin44TiatEx=9.227 sion NAhσvi(cm3s−1mole−1) = exp(107.92−2.254x−1+
and9.239MeV(ωγ=5.8and2.0eV,respectively). Runs 34.19x−1/3−167.81x1/3+6.867x−0.2649x5/3+82.15ln(x))
R2 and R3 (thick He target) give consistent 44Ti yields. where x=T9 in the range 0.1<T9<10 (T9 denotes the
If we interpret these yields as the sum over isolated res- temperature (K) divided by 109K).
onances in the experimental range of energies, we derive
lower and upper limits for the total resonance strength We have used this new rate in SN nucleosynthesis
of 30 eV and63 eV, respectively,depending onthe ener- models and performed calculations as those described in
giesoftheresonances. Experimentallyknownresonances ref.[32] with the KEPLER code [33]. For 15 and 25M⊙
[12,13]inthisenergyrange,andthoseusedintheempir- stars (Models S15 and S25), we find that, while the 56Ni
ical model [14], sum to a total strength of 12.5 eV only. yield is kept at 0.1M⊙, the SN 44Ti yield in the ejecta
Considerations based on the energy dependence of the increases by a factor ∼ 2 from 14µM⊙ to 27µM⊙, and
Wigner limit for the α widths and ofWeisskopf units for from 16µM⊙ to 24µM⊙, respectively. Due solely to the
γ transition intensities, require that isolated resonances new reaction rate, both the absolute 44Ti yield and the
with total strength of the order 30 to 60 eV ought to 44Ti/56Ni ratio are thus brought closer to the values in-
be centered above Ecm∼3.6 MeV. Such resonances have ferred from γ-ray astronomy observations. The higher
not been observedso far,although this energyrange has estimated44Ti/56Ni ratiois particularlyimportantsince
4
tribute to the yield. The associatedastrophysicalrate of
2
10 a) thereactionissignificantlylargerthantheoneadoptedin
previous stellar calculations and increases the predicted
100 σthis w= o8r.k0 + 1.1 µb SN 44Ti yield by a factor of ∼2. The new estimates may
) ave
arn BfR=U 5S,L σIB= 10 µb therefore account for the measured yield for the Cas A
b iso ave
σ (µ 10-2 sfNicsOoa=lNe 8d-, S BσMRavOUe=KS L8E IRµB b rtieomnnaaln44tTainldocsaulipzpedorstouthrecesprionsptheectGoaflaixdye.ntifying addi-
Rauscher et al.
10-4 eσmavpe i=ri c3a.l4 m µobdel We gratefully acknowledge the participation of J.
Rauscher et al. G¨orres,S.K. Hui and M. Wiescher in early stages of this
σ = 1.9 µb
-6 ave experiment. We thank J.P. Schiffer, J. Truran and S.
10
0 1 2 3 4 5 6 7 8 9 10 WoosleyforstimulatingdiscussionsandC.Feldsteinand
E (MeV)
cm N. Trubnikovfor their workonthe chemistry procedure.
This workwas supported in part by the US-DOE, Office
-1e) 102 b) ofNuclear Physics,underContractNo. W-31-109-ENG-
ol
m 38, the DOE Program for Scientific Discovery through
3-1ms 10-1 40Ca(α,γ)44Ti Advanced Computing (SciDAC; DE-FC02-01ER41176),
by DOE contract W-7405-ENG-36 to the Los Alamos
c
> ( 10-4 scaled BRUSLIB National Laboratory, and by the USA-Israel Binational
ν this work Science Foundation (BSF).
σ empirical model
< 10-7 Rauscher et al.
A
N
-10
10
0 1 2 3 4 5 6 7 8 9 10
T
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