Careful comparison of F20 and Na20, and available data on reactions leading to both, suggests that Jπ(2646)=3+. Other mirror identifications are indicated and quantities of astrophysical interest are calculated

Brown, B. A.

Champagne, A. E.

Fortune, H. T.

Sherr, R.

Carolina Digital Repository

PHYSICAL REVIEW C VOLUME 48, NUMBER 3 SEPTEMBER 1993Nature of the Na 2646-keV level and the stellar reaction rate for ' Ne(p, y ) NaB. A. BrownDepartment of Physics and Astronomy and National Superconducting Cyclotron Laboratory,Michigan State University, East Lansing, Michigan 48824A. E. ChampagneDepartment ofPhysics and Astronomy, University ofNorth Carolina at Chapel Hill, Chapel Hill, North Carolina 27599and Triangle Universities Nuclear Laboratory, Duke University, Durham, North Carolina 27706H. T. FortuneDepartment of Physics, University of Pennsylvania, 209 S. 33rd Street, Philadelphia, Pennsylvania 19l04R. SherrDepartment of Physics, Princeton University, Princeton, New Jersey 08544(Received 11 November 1992)Careful comparison of F and Na, and available data on reactions leading to both, suggests thatJ (2646) =3+. Other mirror identifications are indicated and quantities of astrophysical interest are cal-culated.PACS number(s): 27.30.+ t, 97.10.CvThe region of excitation energy just above 2.2 MeV inNa is important because of the possibility of a reso-nance in the astrophysically interesting [1—3] reaction' Ne(p, y) Na. Above the ' Ne+p threshold at 2199keV, the first known state [4—7] is at 2646 keV (see Fig.1). This state, which is presumed to be the strongest(p, y) resonance, is strongly populated [4—6] inNe( He, t) Na and has been variously and incorrectlyidentified [4—6] as the mirror of the 3173- or 3488-keV1+ states in F and even [8] as the mirror of a supposed1 state at 3173 keV in F.Despite the large Coulomb shifts observed and expect-ed for states containing significant 2s&&z strength, the3488-keV 1+ state is too far away for Na(2646) to be itsmirror. In fact, the Coulomb shift calculated using asingle-particle potential and weighted by the known [7](d,p) spectroscopic factor indicates a mirror for the3488-keV state at 3080 keV in Na. The 2986-keV statein Na has been assigned J =1+ on the basis of thebeta-delayed proton decay of Mg [9] and via ' Ne+pelastic scattering [10]. Consequently, we associate thisstate with the 3488-keV state in F.The 3173-keV state in F is probably a 1+ state andmost likely has a six-particle —two-hole (6p-2h) config-uration [11], i.e., (sd )t, ( lp ) io (where the subscriptsdenote angular momentum J and isospin T). This state isweakly populated in the Ne(t, He) F reaction [12] andin all other reactions surveyed [11,13—17], lending fur-ther support to its low-J and core-excited nature [9]. The2646-keV state in Na cannot be its mirror because sucha state would be weakly populated in theNe( He, t ) Na reaction and would also have a negligi-ble Coulomb shift. The remaining candidates for the mir-ror of Na(2646) are [7] a 3+ state at 2966 keV and prob-able (3 ) and (4 ) states at 2865 and 2968 keV, respec-tively. Although the 2857-keV state in Na has been as-signed [4,5] J =3+ on the basis of ( He, t) angular distri-butions [which would then imply negative parity forNa(2646)], the fits to these data are not particularlycompelling. With the exception of 0 and 1 states aris-ing from coupling of a p&&z hole to the —,'+ excited state of'Ne (and 'Na), other negative-parity mirror pairsshould have negligible Coulomb shifts. In fact, the shiftsmay be slightly negative, with states in Na lying slightlyabove their F counterparts. This expectation is borneout by the 2 and 3 states at 1309 (1338) and 1971(1993) keV, respectively, in F ( Na). Therefore it islikely that the 996-keV level of Na contains mirrors ofboth the 984-keV 1 and 1057-keV 1+ states of F.Similarly, the three states in Na at 1841, 1993, and 2064keV probably contain mirrors of five F levels: 1824-keV5+, 1844-keV 2, 1971-keV 3, 2044-keV 2+, and 2194-keV 3+. Consequently, the 2865-keV (3 ) state in F isprobably analogous to the 2857-keV state in Na ratherthan to the 2646-keV state. By a similar argument, the2968-keV (4 ) state in F could be the mirror to the3056-keV state in Na. However, this latter state hasbeen assigned J =0+ from ' Ne+p scattering [10]. Thefirst known [7] 0+ state in F is at 3526 keV. A calcula-tion of the Coulomb shift for this state shows it to be theanalog of the 3056-keV state in Na.By process of elimination (assuming that no statesremain to be identified below 3.5 MeV in F), the onlyF state whose mirror could be Na(2646) is at 2966 keV(3 ). Correspondence with states above 3.5 MeV in Fwould imply unphysically large Coulomb shifts. Withthis identification, the (t, He) and ( He, t) cross sectionsare consistent and the Coulomb shift is appropriate.Hence, in what follows, we take this assignment as deter-mined, viz. , J (2646)=3+. Our mirror assignments aresummarized in Fig. 1.The quantity of interest for astrophysical applicationsis the thermonuclear reaction rate0556-2813/93/48(3)/1456(4)/$06. 00 48 1456 1993 The American Physical Society48 BRIEF REPORTS 14573173 (1+ )29682966 3 (4 )2865 (3 )2646 3+2194 (3')2044 2 - - 2064 (3+)19711824 1844 2 5+ - 1841 2-+3488 3526 0+2986 1+30562857 (3- )2199Ne+ pETCrp-PROCESS24 . 25-. 26 27 . I 'iR. '=SI UI SlI JRPs . . '.', .: . .cx«~AI AI AI AIt$7F 18F1309105798482365621+14+]338996808606(2)3+14~55RNRBIimml@Ntiti Iii t m';ssmmaar@ aII I ski'B!SR~(tow. ts& e5~e~tjlt HOT CNO CYCLES20F2+NaFIG. 2. The hot CNO cycles and early rp process. More de-tailed reaction networks may be found in Ref. [3] and referencestherein.FIG. 1. Energy levels [6,7] of F and Na discussed in thetext.(o.v) = 8&P1/2(kT) ~ jo (E)E exp( EjkT )dE— ,where p is the reduced mass and k is the Boltzmann con-stant. In general, the cross section o(E) contains contri-butions from resonant and nonresonant processes. Foran isolated, narrow resonance at a center-of-mass energyE, , this expression reduces to(o'v ) =(2m IpkT) ~ A coy exp( E, IkT) —.For a (p, y) resonance, the resonance strength coy is givenbycoy = [(2Jf+ I)/2(2J, +1)]r,r, yr .Here Jf and J; are the spins of the final and initial states,respectively, while I p, I &, and I are the proton andgamma-ray partial and total widths of the resonance, re-spectively. Although the ' Ne(p, y) Na reaction has notbeen measured directly, it is possible to estimate reso-nance strengths using the known structure of the 3 =20nuclei as a guide.Resonant capture to the 2646-keV state (E, =447keV, J =3+) can proceed via a lds&2 proton coupled tothe ground state of ' Ne (J = —,'+) or via a 2si&z protoncoupled to the 238-keV first excited state (J =—', +) (inprinciple, other excited states could become important atextremely high temperatures). Proton single-particlewidths of I sp(po) =9.7 eV and I sp(p, ) =2. 1 eV were cal-culated within the framework of scattering from a realWoods-Saxon potential (ro=1.26 a =0.6 fm). The l=2spectroscopic factor for F(2966) has been measured[15,18] in the ' F(d,p) F reaction to be S=0.054. Thecorresponding shell-model value is S=0.068. For' Ne*+2s&&2, we take the shell-model value of S=0.35.Thus we obtain proton widths of I p0 0 52 eV andI &=0.73 eV. Nothing is known of the y decays ofNa(2646). Its mirror has a mean lifetime [7] of 60+40fs, decaying primarily via M1's to the 2&+, 3,+, and 4,+ lev-els. The shell-model lifetime for this state is 3.5 fs (seeTable I), more than an order of magnitude shorter thanthe measured value, but consistent within the experimen-tal uncertainty. [One prediction of the current work isthat if the F(2966) lifetime were to be better measured, amuch smaller value should result. ] Correcting for the Efactor and applying a small N, Z correction in the M1operator [19],the mean lifetime in Na should be 5.5 fs,i.e., I =0.12 eV.A similar procedure may be used to extract resonanceTABLE I. Expected M1 decays of F(2966) and Na(2646) from shell-model calculations. '(Mev)zoFE(MeV) B (M1) (fs)Ef(MeV)NaE(MeV) B(M1) (fs)213+4+Total0.00.6560.8232.9662.3102.1430.2850.1600.6767.628.78.53.50.00.6060.8082.6462.0401.8380.3000.1810.52310.236.917.55.5'The wave functions and effective operators used for the M 1 matrix elements are described in Ref. [19]. The E2 contributions are toosmall to cause appreciable changes.1458 BRIEF REPORTS 48CD 00E(h4E-6I—-8CC-10I—LU-14Q -16TOTAL(P T) Na58. 857787LUz'.0oLljCC10410~o'XNe-180.1 10parameters for the other nearby states at 2857 keV(E, =658 keV, J =3 ), 2986 keV (E, =787 keV,J =1+), and 3056 keV (E, =857 keV, J =0+). InF, neutron spectroscopic factors have been measured[15,18) for all three mirror states and mean lifetimes aretabulated [7] for the two positive-parity states. In thecase of the 2857-keV state, we assume I =I, whichleads an upper limit on the resonance strength. Forreasons that will be made clear below, we only considercapture involving the ground state of ' Ne.Explosive hydrogen burning, which accompanies su-pernovas and powers cataclysmic binaries, is expected toproceed via the hot CNO cycles or, for heavier nuclei,through the rp process [1—3] (Fig. 2). The former is con-sidered to be the energy source for novas, whereas thelatter is thought to power more energetic explosions (e.g.,x-ray bursts). An rp process may be triggered directlyfrom preexisting 3 ~ 20 nuclei or from lighter nuclei viaseveral "breakout" reactions from the hot CNO cycles.TEMPERATURE (10 K)FICx. 3. Thermonuclear reaction rate for ' Ne(p, y) Na un-der the assumption that ' Ne is in its ground state. Resonancecontributions are labeled according to their energy and werecalculated using the parameters found in Table II. The direct-capture rate (DC) is from Ref. [21].100. 1 1TEMPERATURE (10 K)FIG. 4. Mean reaction times for ' Ne(p, y ) Na and"O(a,y)' Ne versus temperature for XH =0.77 and XH, =0.20.For the purposes of illustration, a density of p=10' g/cm' waschosen. Mean lifetimes against P+ decay are also indicated.The link between the hot CNO cycles and the rp processis provided primarily by the ' O(a, y)' Ne reaction [20]and to a lesser extent by the ' F(p, y )' Ne and' Ne(a, p) 'Na reactions. These breakout reactions willoccur for temperatures T)0.4X10 K (or T9)0.4) anddensities in excess of p=10 g/cm . An rp process maythen be initiated by a subsequent ' Ne(p, y) Na reaction.The rate of the ' Ne(p, y) Na reaction has been calcu-lated using the resonance strengths listed in Table II andthe contribution from nonresonant direct capture [21]and is shown in Fig. 3. For reactions involving ' Ne inits ground state, the rate is dominated by the 447-keV res-onance (E =2646 keV). However, by T9=1, ' Ne willbe in its first excited state 15% of the time and in itssecond excited state 3% of the time. For T9&2, theground-state population falls below 50% of the total.Consequently, we have estimated the resonance strengthfor population of the 447-keV resonance from the firststate of ' Ne. The other resonances have strengths whichappear to be determined primarily by the exit channelTABLE II. Summary of resonance parameters.E '(keV)E,(keV)r,(eV)r,(ev)CO/(this study)(meV) Ref. [4]CO/(literature)Ref. [5] Ref. [6]2857298630566587878572646 44731+0+I po=0. 52I p)=0.730.021.0X10'2. 1X10'0.120.028 X10-'0.018037~202.27.511.319.228.8126.2315.9551.197.5020707.5'Ref. [6]."Assumed in order to give an upper limit on coy.BRIEF REPORTS 1459(i.e., coy=col r) and, as a result, they should not changedramatically with temperature unless the proton width isdrastically decreased (in which case they will becomeeven less important). Assuming that these latterstrengths are in fact unchanged by thermal excitation in' Ne, an approximate analytic expression for the reactionrate which includes the effects of thermal excitation tothe first excited state (for population of the 2646-keVstate) isN„( tr U ) = ( 5.45 X 10 ) T9 'Xexp( —4. 378/T9 ) cm s 'molThis approximation reproduces a more exact calculationto better than 10% over the temperature range0.25 ~ T9 ~2.0 and once again the 2646-keV state is themajor contributor to the total rate. For temperaturesbelow this range, the ground-state rate is appropriate(with the contribution from direct capture). AboveT9 2, the population of higher-lying excited states can-not be ignored and so this approximation may not be ac-curate.With our new calculations, the rate of the' Ne(p, y ) Na reaction is increased by about an order ofmagnitude over earlier results [4—6]. However, this in-crease is not astrophysically significant because the fIowinto the rp process is limited by the rate of the (slower)' O(a, y)' Ne reaction. This point is illustrated in Fig. 4where the mean reaction times for ' Ne(p, y) Na and' O(a, y)' Ne are plotted versus temperature for hydro-gen and helium mass fractions of XH =0.77 andXH, =0.20, respectively. For T9=0.4—2, the (p, y) rateis 6.0—1.6 orders of magnitude greater than the (a, y) rate(independent of density). In other words, once material isconverted into ' Ne, it will be rapidly passed along tohigher masses.Experimental verification of our results for the 2646-keV state are desirable, and here the increased resonancestrength is significant because it leads directly to a corre-sponding increase in the expected count rate for the'H(' Ne, Na)y reaction. Assuming a beam intensity of1 particlenA, the 2646-keV state will be produced at arate of 3860/h. In addition, our predictions of J =3and I /I =0.09 can be examined via indirect nuclearspectroscopy. Such studies are in progress.This work was supported in part by the National Sci-ence Foundation and for one of us (B.A.B.) under GrantNo. PHY-90-17077 with MSU. We were also supportedin part (A.E.C.) by the U.S. Department of Energy. Weare indebted to N. M. Clarke for providing us with angu-lar distributions of the levels observed in Ref. [12].[1] R. K. Wallace and S. E. Woosley, Astrophys. J. Suppl. 45,389 (1981).[2] M. Wiescher, J. Gorres, F.-K. Thielemann, and H. Ritter,Astron. Astrophys. 160, 56 (1986).[3] A. E. Champagne and M. Wiescher, Annu. Rev. Nucl.Part. Sci. 42, 39 (1992).[4] L. O. Lamm, C. P. Browne, J. Gorres, S. M. Graff; M.Wiescher, and A. A. Rollefson, Nucl. Phys. A510, 503(1990)~[5] S. Kubono et al. , Z. Phys. A 331, 359 (1989);Astrophys. J.344, 460 (1989).[6] M. S. Smith, P. V. Magnus, K. I. Hahn, A. J. Howard, P.D. Parker, A. E. Champagne, and Z. Q. Mao, Nucl. Phys.A536, 333 (1992).[7] F. Ajzenberg-Selove, Nucl. Phys. A475, 1 (1987).[8] P. Descouvemont and D. Baye, Nucl. Phys. A517, 143(1990).[9]J. Gorres et al. , Phys. Rev. C 46, R833 (1992);A. Piechac-zek et al. , in Proceedings of the 6th International Conference on Nuclei Far from Stability, Atomic Masses andFundamental Constants 1992, edited by R. Neugart andA. Wohr, Institute of Physics Conference Series 132 (IOP,Bristol, 1993).[10]R. Coszach et al. , in Proceedings of the 2nd InternationalSymposium on nuclear Astrophysics, Karlsruhe, Germany,1992, edited by F. Kappeler and K. Wissak (IOP, Bristol,1993).[11]R. Medoff, L. R. Medsker, S. C. Headley, and H. T. For-tune, Phys. Rev. C 14, 1 (1976).[12] N. M. Clarke, P. R. Hayes, M. B. Becha, C. N. Pinder,and S. Roman J. Phys. G 16, 1547 (1990).[13]H. T. Fortune and J. N. Bishop, Nucl. Phys. A293, 221(1977).[14] H. T. Fortune and J. D. Garrett, Phys. Rev. C 14, 1695(1976).[15]H. T. Fortune and R. R. Betts, Phys. Rev. C 10, 1292(1974).[16]G.-B. Liu and H. T. Fortune, Phys. Rev. C 37, 1818(1988).[17]G.-B. Liu and H. T. Fortune, Phys. Rev. C 38, 2134(1988).[18]H. T. Fortune, G. C. Morrison, R. C. Bearse, J. L. Ynte-ma, and B. H. Wildenthal, Phys. Rev. C 6, 21 (1972).[19]B. A. Brown and B. H. Wildenthal, Nucl. Phys. A474, 290(1987).[20] P. V. Magnus, M. S. Smith, A. J. Howard, P. D. Parker,and A. E. Champagne, Nucl. Phys. A506, 332 (1990).[21] K. Langanke, M. Wiescher, W. A. Fowler, and J. Gorres,Astrophys. J. 301, 629 (1986).

Nature of the Na 20 2646-keV level and the stellar reaction rate for Ne 19 ( p ,γ ) 20 Na

Brown, B.A.

Champagne, A.E.

Fortune, H.T.

Nature of the Na20 2646-keV level and the stellar reaction rate for Ne19(p,γ)20Na

https://cdr.lib.unc.edu/downloads/8623j722j

Nature of the Na 20 2646-keV level and the stellar reaction rate for Ne 19 ( p ,γ ) 20 Na

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