The reaction Ar36(p,)37K has been measured in the proton energy range of Ep=0.320.93 MeV. A new resonance was found at ER=321 keV. We have measured the branching ratios and the resonance strength. The stellar reaction rates which are dominated by this resonance for temperatures T=0.070.9 GK are calculated. Network calculations have been performed to investigate the influence of the new stellar rates on the time evolution of the Ar36 abundance during explosive H burning

Azuma, R.E.

Graff, S.M.

Görres, J.

Iliadis, C.

Ross, J.G.

Wiescher, M.

Carolina Digital Repository

PHYSICAL REVIEWS C VOLUME 45, NUMBER 6Reaction Arg, y) K in explosive hydrogen burningJUNE 1992C. Iliadis, J. G. Ross, J. Gorres, and M. WiescherUniuersity ofNotre Dame, Notre Dame, Indiana 46556S. M. GraffLos Alamos Wationa/ Laboratory, Los Alamos, ¹mMexico 87545R. E. AzumaUniuersity of Toronto, Toronto, Ontano, Canada M5S IA?(Received 10 February 1992)The reaction Ar(p, y) K has been measured in the proton energy range of E~ =0.32-0.93 MeU. Anew resonance was found at E& =321 keU. We have measured the branching ratios and the resonancestrength. The stellar reaction rates which are dominated by this resonance for temperaturesT=0.07—0.9 GK are calculated. Network calculations have been performed to investigate the influenceof the new stellar rates on the time evolution of the Ar abundance during explosive H burning.PACS number(s): 25.40.Lw, 27.30.+t, 95.30.CqI. INTRODUCTION7,= 0.4, p = lo g/cm'(c.y)(p,a)Ar37 38 39' '', 141%135 36 37 38 3935 38CI'. 14143I 32 33 34 35 36I II II28 29 30 3I 32 33 341X1X1X27 28 '29 30 3 IFICx. 1. Major nuclear flows in the rp process integrated overa period of t=1000 s for the A =30-40 mass range. The calcu-lation was performed for a constant temperature T=0.4 GKand density p=10 g/cm . Solid arrows indicate dominant nu-clear flows. Dashed arrows indicate flows roughly an order ofmagnitude weaker.Hydrogen burning, at temperatures and densities far inexcess of those attained in the interiors of ordinarymain-sequence stars, may occur in various astrophysicalsite, including novae, x-ray bursts, and supernova explo-sions. For these explosive and hydrogen-rich environ-ments, the rp process has been proposed [1] as a fast nu-cleosynthesis reaction sequence whereby CNO materialwill be transferred into the Fe-Ni mass region. The re-sulting network of nuclear reactions involves proton andalpha capture, (p, a) reactions, and P-decay processes, aswell as possible inverse reactions, and extends from theline of stability up to the proton drip line.Recent numerical network calculations [2] indicatethat the main reaction flow in the mass A =30-40 rangewill lead to the production of Ar for typical tempera-tures T=0.2-0.6 GK and densities p=10 —10 g/cm .Figure 1 shows the result of a calculation for a constanttemperature T=0.4 GK and density p= 10 glcm . Forthe initial elemental-abundance distribution, solar isoto-pic abundances have been used. The dominant reactionpath is given byCl(p, y) Ar(P+v) Cl(p, y) Ar(p, y) K(P+v) Arwith an alternative branch viaAr(P+v) 'Cl(p, y) Ar .Therefore, the stellar rate of the subsequent reactionAr(p, y) K determines the flow towards heavier massregions.The proton capture on Ar was previously investigat-ed by Goosman and Kavanagh [3] and by de Esch andvan der Leun [4] in the bombarding energy rangeE &0.9 MeV. Figure 2 shows the level diagram of Kwith the corresponding resonances in the Ar+p chan-nel and the important energy windows for different stellartemperatures. The lowest-lying resonance has been ob-served [3] at Ett =917 keV. The reaction rates forAr(p, y) K have been previously estimated by Wallaceand Woosley [1] considering this resonance only. How-ever, for temperatures of interest here ( T (1 GK), theGamow windows are located well below this proton ener-gy. In fact, there are two more states known [3,4] be-tween the proton threshold and the resonance atEz =917 keV. The corresponding resonance energies areEz =321 and 440 keV, respectively. We therefore inves-tigated the reaction Ar(p, y)37K in the astrophysicallyimportant energy range E~ =300—920 keV.Throughout this work, E is the proton bombardingenergy and Ez labels the resonance energy. Both ener-gies are given in the laboratory system unless stated oth-erwise.45 2989 1992 The American Physical Society2990 ILIADIS, ROSS, GORRES, WIESCHER, GRAFF, AND AZUMA 452J9I7440------32l2750 5+0.52ss (7 )—E (keV) E„(keV)I.OO5IO4IOIO3= 32I keVJI I IAr(p, y} K8=55I II I I~~ } I I I I Il37l l380 7440 keV37FIG. 2. Level diagram of K and proton energies of reso-nances in the reaction ' Ar(p, y)' K. The Gamow windows fordifferent stellar temperatures T9 (10 K) are also indicated.0t tIO0I I I i i I I I I i i I I I I I I320 340 430 450 900 920 940LABProton energy E (keV)FIG. 3. Excitation function for ' Ar(p, y)' K, measured at8=55' for the primary transition to the ground state in K.The data points shown are not corrected for the y-ray efficiencyof the Ge detector. The resonance at E& =321 keV has notbeen observed previously. The ratio of target thicknesses atE~ =321 and 917 keV agrees with the corresponding ratio of theeffective stopping powers. The solid line is to guide the eye.II. APPARATUSThe 1-MV Van de Graaff accelerator at the Universityof Toronto supplied proton beams of up to 70 pA on tar-get in the energy range of E =0.3-1.0 MeV, with an en-ergy resolution of EE=1 keV and an energy calibrationbetter than +2 keV. The proton beam passed through aTa collimator and was directed onto the target which wasmounted at 45' with respect to the beam direction. Aliquid-nitrogen-cooled copper tube was placed betweenthe collimator and the target to minimize carbon deposi-tion on the target. The target and chamber formed aFaraday cup for charge integration and a negative volt-age ( —300 V) was applied to the Cu tube to suppresssecondary electron emission from the target.The Ar target was made by implanting Ar ions into a0.5-mm-thick Ta backing with a charge density of 54mC/cm and an implantation energy of 80 keV, yieldinga thickness of =7 keV at E =917-keV bombarding ener-gy. The thick target yield curve for the Ez =917-keVresonance in Ar(p, y) K is shown in Fig. 3. The targetstoic hiometry was determined from the known [3]strength of this resonance, coy=0. 208+0.03 eV. Usingthe stopping power tables of Andersen and Ziegler [5], aratio of tantalum to argon of NT, /N~, =6.5+1.3 hasbeen obtained. The target was directly water cooled andwas checked several times during the course of the exper-iment. No noticeable deterioration was observed over anaccumulated charge of 6 C.The y-ray spectra was measured with a 37% Ge detec-tor. The energy resolution was 2.0 keV at E =1.3 MeV.The detector was placed at 0~=55' with respect to thebeam direction at a front-face-to-target distance of d= 1.8cm and was shielded by 5 cm of lead to reduce roombackground contributions. The y-ray efficiencies weredetermined using a calibrated Co source as well as the yrays from the resonance [6] at Ea =992 keV in theAl(p, y) Si reaction. Since the Ge detector was posi-tioned in close geometry to the target, coincidence sum-ming [7] of y rays had to be considered. We have es-timated the effect of coincidence summing on the abso-lute y-ray efficiency at E =1333 keV to be less than 9%using the calibrated Co source strength and the intensi-ties of the y lines at Er =1173and 1333 keV and of theirsumming peak. This uncertainty was included in the er-rors for the full-energy peak efficiency.III. EXPERIMENTAL RESULTS AND DISCUSSIONGamma-ray spectra were measured in the bombardingenergy range E =320-930 keV with charge accumula-tions of 0.01-1 C. Figure 3 shows the yield curve for theprimary decay to the ground state of K. Two reso-nances have been observed at E„=917and 321 keV.The resonance at Ez =917 keV was known from ear-lier work [3,4]. Our measured resonance energy andbranching ratios are listed in Tables I and II, and theyare in agreement with the values from the literature.The resonance at Ez =321 keV had not been seen pre-viously. Both the resonance energy and the observed pri-mary y energies, however, correspond within the experi-mental errors to the state at E =2170 keV (J = —,' ) inthe compound nucleus K. This state was observed intransfer reaction studies [3] and in (p, yy) work [4]. We,therefore, adopt spin and parity of J =—,' for this reso-nance. Figure 4 shows the on-resonance y spectrum tak-en at E =325 keV. In addition to the strong ground-state branching, a weak primary decay to the first excitedstate at E„=1371 keV (J =—,'+} is also observed (seeTable II). This branch has not been seen in the earlier(p, yy } work of Ref. [4] where the state at E„=2170keVwas populated by the y decay of higher-lying resonances.45 REACTION Ar(p, y) K IN EXPLOSIVE HYDROGEN BURNING 2991TABLE I. Energies and strengths for Ar(p, y) K resonances.Present321+2'917+2'ER (keV)Ref. [4]321.3+0.2439.5+0.2917.52+0.07JB'(Ref. [4])327 +2S+2Experiment(6.1+1.4) X 10(2.4X 100.208+0.030coy (eV)'Calculated'6.3X10-'(2.5 X10-'0.095'From the location of midpoint of front edge of thick target yield curve.bCalculated from known E„and Q~r =(1857.57+0.09) keV.'From the present work; the quoted values have been obtained relative to the strength of the resonanceat ER =917keV (see text).From Ref. [3];used as a reference for the calculation of the target stoichiometry.'With coy=(2J +1)r,r,nI .'Calculated from Eq. (1) by estimates of the partial widths I ~ and I ~ (see text).The corresponding secondary ground-state transition ofthe level at E =1371 keV is also indicated in Fig. 4 andagrees in intensity, after correction for the different y-rayefficiencies, with the primary decay.The strength coy of a (p, y ) resonance is defined by2J+1 r, r,(2j~+1)(2j,+1) Iwith J, j, and jt as spin of the resonance, the projectile,and the target nucleus, respectively; I is the total widthof the resonance, and I,1 are the corresponding par-tial widths. The resonance strength is related to thethick-target yield Yz of a resonance [8] by2effA +A Y~,~R t Pwhere A,~ is the proton wavelength at the resonance ener-gy, A, ( &~ ) the mass of the target (projectile) in u, andE ff the effective stopping power of the ArTa target com-pound:e,tr e«+(—NT, /N«)eT, with NT, /N«=6. 5+1.3 .The stopping power values for c~, and cT, were takenfrom Ref. [5]. For the newly observed resonance atElt =321 keV, a value of yai=(6. 1+1.4)X10 eV hasbeen obtained (see Table I). The quoted error includesthe uncertainty of the effective stopping power (+20%),the relative y-ray efficiency (+7%), and the charge mea-surement (25%).No resonance has been observed at E =440 keV, cor-responding to the state at E„=2285 keV (J =—,'+ ). Us-IO—5I IR ~ l37 II 57 I ~ 0R~OC(p, y) N+OC3I~IO=BB BBB8"RaThIIOOOChannel2000 3000FIG. 4. On-resonance y-ray spectrum, measured at 0=55' for the new observed resonance at ER =321 keV. The y-ray energiesabove peaks are in keV. Background contributions are labeled.2992 ILIADIS, ROSS, GORRES, WIESCHER, GRAFF, AND AZUMATABLE II. Gamma-ray branching ratios (in %) of K states.Exf(keV)0137113802170'From Ref. [4].E~ (keV)E., (keV)J7783+2I +27232Present87+613+4321217032Ref. [4]100&4&4Present98.6+0.91.4+0.4& 0.491727505—2Ref. [4]98.2+0.11.5%0.10.3+0.1=3 P)C S.pR' (3)Here, the quantity R denotes the nuclear channel radius,p the reduced mass, P& the penetrability at the resonanceenergy E; for the orbital angular momentum l of the reso-nance, and C the isospin Clebsch-Gordan coefficient(C = 1 for T = —,' states). The single-particle spectroscop-ic factors S were adopted from Hagen et al. [10]. The re-sulting strengths of coy=6. 3X10 and 9.5X10 eVfor the resonances at Ez =321 and 917 keV, respectively,are in the same order of magnitude as the directly Inea-sured values (see Table I). For the assumed g-wave reso-nance at Ez =440 keV, no spectroscopic factor is known.Using the Wigner limit C S=1 results in a theoreticalupper limit for the strength of ~y ~ 2. 5 X 10eV, similar to the experimentally obtained upper limit(see Table I).To search for possible direct capture (DC) transitions,an off-resonance y spectrum was taken at a proton bom-barding energy of E =895 keV with a total accumulatedcharge of 1 C. No y transitions to fina1 states in King the known branching ratio [4] of this state, an upperlimit of roy 2.4X10 eV has been determined (seeTable I).The branching ratios and coy values have been deducedfrom spectra taken at 8&=55' [where Pz(cos8)=0], as-suming that any possible P4(cos8) component in the an-gular distribution is negligible. This is clearly the casefor the J=—', resonance at Ez =321 keV. Also, the mea-sured angular distribution [4] of the resonance atE„=917keV (J = —,'+ ) indicates only an A z component.For the possible resonance at E~ =440 keV (J =—', + ), nocorrection for angular distribution efFects has been ap-plied in the calculation of the upper limit for coy.It is interesting to compare the measured resonancestrengths with the values obtained from Eq. (1) by an esti-mate of the partial widths I ~ and I . Such calculatedresonance strengths are frequently used for the derivationof stellar reaction rates if the respective values for coycannot be measured directly. The y partial width I ofunbound K states can be deduced from the known life-times [9] of the bound mirror states in Ar. The protonpartial width I can be parametrized [8] ascould be observed. The cross sections that result fromDC model calculations (see Sec. IV) are 2 orders of mag-nitude smaller than the experimentally determined upperlimits of cr & 40 nb.IV. ASTROPHYSICAL IMPLICATIONSThe stellar reaction rate N„(rrv ) of Ar(p, y) K canhave contributions from narrow resonances and thedirect capture process into the low-lying states in K.The reaction rate (in units of reactions s 'mol 'cm )for isolated narro~ resonances is given by the expression[11]N„(ov ) = 1.54X10"[pT(GK))X g (coy);exp[ —11.605E;/T(GK)], (4)where the reduced mass p is an u and the strengths my, .and c.m. energies E; of the resonances are in MeV. Fortemperatures of interest here (T ( 1 GK), all resonanceswith E; &2042 keV were considered. The E; and coy;values for resonances located in the energy range of thepresent experiment were taken from Table I. Otherwise,the values of Refs. [3,4] have been used. The reactionrate contribution for the resonances at Ez =321 and 917keV are listed in columns 2 and 4 of Table III, respective-ly. To investigate the maximum contribution of the as-sumed resonance at Ez =440 keV, the stellar rates havebeen calculated with the experimentally found upper lirn-it (see Table I). The resulting values are shown in column3 of Table III.For the calculation of the nonresonant reaction rates,the cross sections of the DC process for transitions to allbound states in K were calculated using the formalismdescribed by Rolfs [12]. The single-particle spectroscopicfactors were adopted from Ref. [10]. The sum of the as-trophysical S factors for all final states was parametrizedbelow E = 1.5 MeV by the polynomialS(E)=0.1195—4.630X 10 E+1.4996X 10 E (5)with S in MeV b and E the c.m. energy in MeV. The stel-lar reaction rates were calculated using the expressionsfor nonresonant reaction mechanisms [11]and are listedin column 5 of Table III.The total reaction rates are shown in column 6 of45 REACTION ' Ar(p, y)' K IN EXPLOSIVE HYDROGEN BURNING 2993TABLE III. Stellar reaction rates N„(o v ) of ' Ar(p, y)"K in units of (cm'/mol s).T9 (10 K) 321'N„&crv &917c DC' Total'0.050.060.070.10.30.50.80.91.01.52.02 71X10—»3.67 x 10-"1.64x10-"5.44x 10-"3.34 X 101.96X 101.472.042.604.745.642.72 X 103.16x 10-"3.39x 10-"3.42X10 "1.54x 10-'5.33x 10-'1.09 x 10-'1.82x 10-'2.69x 10-'7.67 x 10-'1.14x 10-'2.34 X 109.58 x10-"1.08x 10-"2.04x 10-"9.48 x 10-'1.11x10-'3.92 x 10-'1.061.82x 10'6.64x 10'1.46x 10-"1.32 x 10-"4.77 x10-"9.63 x 10-"8.35 x10-"4.70 X 101.46X1.68x1.68x5.44x3.34x1.96x1.582.433.662.30X7.35 x10—2410 2210—131010-'10110''Contribution of new observed resonance at Ez =321 keV.Maximum contribution of assumed resonance at E& =440 keV, calculated with the experimentallydetermined upper limit for aery {see Table I).'Contribution of resonance at E& =917keV.Contribution of direct capture into states at E„=O, 1371,and 1380 keV in K.'Total reaction rate contribution of resonances E& =321-2042 keV and DC.Table III and they are also displayed in Fig. 5 with theindividual contributions discussed above. It can be seenthat the new resonance at Ez =321 keV determines thestellar rates over the entire temperature range ofT=0.07—0.9 GK . At very low temperatures, T (0.07GK, the DC process dominates, while the resonance atEz =917 keV contributes substantially only at high tem-peratures T & 0.9 GK. The assumed resonance atEz =440 keV and all other resonances with E& &1259keV, are negligible for temperatures T & 1.5 GK.The resonance at Ez =321 keV increases Nz ( cr v ) byseveral orders of magnitude for temperatures T &0.9 GK(see Table III). To investigate the impact of our new re-suits on the expected abundance of Ar during explosiveH burning, we have performed network calculations us-ing the new and old stellar rates, respectively. Figure 6shows the time evolution of the Ar abundance, obtainedfor a constant temperature and density (T=O 4GK, .p=10 g/cm ) over a time period of 1000 s. The oldrates predicted an appreciable enrichment by nearly 2 or-ders of magnitude over the initial solar abundance ofAr. Due to its sma11 depletion rate at this temperature,Ar is not processed further towards heavier masseswithin the time scale of the calculation. The use of thenew rate, however, leads to a substantially difFerent re-sult. The initial Ar abundance is reduced by 3 orders ofIOI I I I I I I I I I 1 I I 1IIO-2IQT=04 GK, p=lO g/cm0oEAbV'Z.'IOIO-20IOIOIO~ IO0 IO~ IOIOLDI l l ! l l IIO IO IO IO IO IO IO IOTime (s)O. l I.OStellar temperature T (GK)FIG. 5. Total stellar reaction rate (solid line) and individualcontributions (dashed lines) for the reaction Ar(p, y)' K.FIG. 6. Abundance of Ar vs time for a constant tempera-ture T=0.4 GK and density p=10 g/cm'. The two curvesshown result from using the old and new stellar rates for the re-action Ar(p, y ) K, respectively.2994 ILIADIS, ROSS, GORRES, WIESCHER, GRAFF, AND AZUMAmagnitude at the end of the calculation. The new stellarreaction rate of Ar(p, y} K is large enough to guaran-tee a strong mass flow towards heavier nuclei at tempera-tures T =0.2—0.6 GK.This work was supported by U.S. National ScienceFoundation Grant No. PHY88-03035 (Notre Dame) andby the Natural Sciences and Engineering Research Coun-cil of Canada.[1]R. K. Wallace and S. E. Woosley, Astrophys. J. Suppl. 45,389 (1981).[2] L. A. van Warmer, Ph.D. thesis, University of NotreDame, 1990 (unpublished).[3] D. R. Goosman and R. W. Kavanagh, Phys. Rev. 161,1156 (1967).[4] H. P. L. de Esch and C. van der Leun, Nucl. Phys. A476,316 (1988).[5] H. H. Andersen and J. F. Ziegler, Stopping Powers andRanges in All Elements (Pergamon, New York, 1977).[6] A. Antilla, J. Keinonen, M. Hautala, and I. Forsblom,Nucl. Instrum. Methods 147, 501 (1977).[7] K. Debertin and R. G. Helmer, Gamma- and X-Ray Spectrometry with Semiconductor Detectors (North-Holland,Amsterdam, 1988).[8] H. E. Gove, in Nuclear Reactions I, edited by P. M. Endtand M. Demeur (North-Holland, New York, 1959).[9]P. M. Endt, Nucl. Phys. A521, 1 (1990).[10]M. Hagen, U. Janetzki, K.-H. Maier, and H. Fuchs, Nucl.Phys. A152, 404 (1970).[11]W. A. Fowler, G. R. Caughlan, and B. A. Zimmerman,Annu. Rev. Astron. Astrophys. 23, 69 (1975).[12]C. Rolfs, Nucl. Phys. A217, 29 (1973).

Reaction Ar36(p,)37K in explosive hydrogen burning

https://cdr.lib.unc.edu/downloads/8336hb66c

Reaction Ar36(p,)37K in explosive hydrogen burning

Abstract

Similar works

Full text

Available Versions

Carolina Digital Repository