Helium burning of 18O

Nuclear Physics A297 (1978) 489-519 ; ©North-RoUand PubJJshlng Co ., Amsterdam Not to be reproduced by photoprint or microfilm without written permluioa from the publisher

HELIUM BURNING OF "O t H. P. TRAUTVETTER, M . WIESCHER, K.-U. KETTNER and C. ROLFS Institut für Kernphysik, Münster, W. Germany and J. W. HAMMER Institut für Strahlenphysik, Stuttgart, W. Germany Rooeived 28 November 1977 A6atract : The '°O(a, y)"Ne capture reaction has been studied at E, = 0.6-2 .3 MeV. The known resonance at E, = 2.20 MeV has been established and fourteen new resonances have been found in the energy range covered. The E, = 1 .16, 1.32, 1.45, 1.53, 1 .87, 1 .96 and 2.15 MeV resonances correspond to resonanoes observed previously in the '°O(a, n)= 'Ne reaction . The E, = 0.77, 1 .25 and 1 .27 MeV reaonances represent new compound states in Z ~Ne. Information on branching ratios, ary values and total widths is reported . Transition strength arguments and analyses of y-ray angular distribution data together with result° from previous work resulted in the most likely J` assignments for the resonance° . The E, = 1.66 and 1 .78 MeV resonance° are good candidates for the .two J` = 8 + states predicted at E, x 11-12 MeV and are probably members of the K" = 0 + (ground °fate) and K` = 2 + rotational bands in ~ 2Ne. The investigated energy range of E, together with that of previous work corresponds to stellar temperatures of T ~ (0 .3-4.3) x 109 K. The astrophysical reaction rate determined from these data is compared with predictions basod in part on the nuclear optical model. The rate is also compared with that of the competing'°O(a, n) = 'Ne reaction .

E

NUCLEAR REACTIONS '°O(a, y), E = 0.6-2.3 MeV ; measured E Er, Ir Ir(~, I~E) . ~~Ne deducedresonances, resonance strength, T, J, a, E, y-ray branching raUOS, astrophysical reaction rate . Enriched'°O targets. Ge(Li) detector .

1. Introduction Following the exhaustion of the hydrogen fuel in the core of a star t' s~ the central region of the star contracts gradually. If the core becomes hot and dense enough, the helium ashes burn predominantly through the nuclear reactions 3a -~ t ZC and '2C(a, y)t 60. In hydrogen-depleted regions of second generation stars, there is expected to be also a significant concentration of "N from the operation of the CNO tricycle. Helium burning of t~N can produce the isotope ta0 by the reaction taN(~y)teF(ß,+y)te0 and the subsequent reaction t'O(a,y)22Ne is an important t

Supportoll in part by the Deutsche Forachungagemeinschaft (Ro 429/3]. 489

490

H . P . TRALTTVETTER et al.

22N6 Fig . 1 . Level diagram of 22Ne above the a-particle threshold. The excitation energies and J` assignments are from refs. 9- " " "). The E, = 2.19 MeV resonance is the lowest resonance of'8 0(a, y) 22 Ne observed in previous work ") . The lab energies E, of the expelled resonances are indicated . Shown are also the energy regions of astrophysical interest for different stellar temperatures T9 (in units of 109 K) .

link in one of the reaction chains by which heavier elements can be produced 1, 2) in the quiet burning phase of stellar evolution as well as in explosive nucleosynthesis. Fig. 1 contains a level diagram of 22Ne indicating the states above the a-particle threshold, which can be expected to contribute to the reaction rate in astrophysical circumstances. Black a) and subsequent investigators observed that in meteorites there is neon gas which is almost pure 22Ne and which has been given the name Ne-E. A major mystery in trying to unravel the origin of the solar system has been the question on the origin of this pure 22Ne gas. An explanation of the origin of this Ne-E gas will of course tie together any work on the nucleosynthesis of 22Ne with the origin of the solar system. In view of this puzzle and of the possible synthesis of 22 Ne through the above capture reaction, a knowledge of the stellar reaction rate of tea s, y) 22 Ne can be of importance in unraveling the mystery of Ne-E. The nucleosynthesis of 22Ne through the above sequence of a-capture reactions plays also an important role in the current understanding of the s-process nuclei. Recent stellar evolution calculations have shown a) that a key reaction for producing

HELIUM BURNING OF 's0

49 1

neutrons for the s-process is the reaction ZZNe(a, n)ZSMg. It has been found a) that all these reactions occur naturally in the course ofstellar evolution of many red giants. Considerable theoretical effort iscurrently beingdevoted') in producing a program which will predict reliable astrophysical reaction rates for the large number of cases where laboratory data are unobtainable due either to unstable target nuclei or to the importance of excited states of the target nuclei to the overall reaction rate in stellar environments . It is, however, imperative to check - wherever possible - theoretically predicted astrophysical reaction rates in part as an incentive for further improvements in theory . In the case of the te0(a, y)ZZNe reaction, the nuclear optical model s.e) has been used in part to extrapolate') the observed data s) at EQ = 2.15-3.70 MeV down to energies of astrophysical interest . While this investigated energy range e) is of interest in explosive nucleosynthesis, quiet helium burning requires cross-section data far below the Coulomb barrier (= 4.1 MeV). In order to test the predicted stellar reaction rates at low beam energies'), the ta 0(a,y) ZZNe reaction has been investigated in the present work over the energy range t Ea = O.1r2 .3 MeV (fig. 1). From a nuclear structure point of view, the nucleus ZZNe is also of interest, since it is among the most highly deformed of light nuclei. In a recent study of the t9F(a, p)ZZNe reaction, Broude et al. 9) have observed high-spin states in ZZNe and made a tentative identification of these states as members of several rotational bands. Since several of these high-spin states are expected to appear as resonances in ta0(a, y)ZZNe in the above energy range (fig. 1) and since only resonances with natural parity assignments can be formed in this capture reaction, a search for these resonances will provide additional information on their most likely J` assignments and will add therefore further evidence on their model identifications 9). One of the principal difficulties encountered in measuring (a, y) cross sections, which are usually quite small, arises from the sensitivity of the y-ray detector to neutrons . Neutrons are usually produced copiously from the (a, n) reaction on the target nucleus as well as (a, n) reactions on contaminants (in the target and beam defining collimators) such as ' 3C in natural carbon, which is a common contaminant of vacuum systems. The Q-value for the ' BO(a, n)Z1Ne reaction t°) is -0.70 MeV, therefore at all bombarding energies above EQ(lab) = 0.86 MeV, there is a background of neutrons from this reaction (fig. 1). At the higher bombarding energies and for forward angles in particular, the number of neutrons will be far greater than the number of capture y-rays . In order to detect the y-rays from t80(a, y)ZZNe in the presence of this neutron background, Adams et al. e) used in their cross-section measurements at Ea = 2.15-3.70 MeV the n-y time-of-flight difference to separate the effects of the neutrons and capture y-rays in the detector . Using the NaI(Tl) detectors, only transitions to the ground state and 1 .27 MeV first excited state in ZZNe could be observed . It was not possible to obtain significant branching ratios for the higher excited states, since these low-energy transitions gave only very small t

The low-energy end was determined by the technical features of the accelerator used .

492

H . P. TRAUTVETTER et al.

peaks on a much larger background . In the work of Chouraqui et al. t') a NaI('Tl) detector was also used in the search for resonances of t80(a, y)ZZNe at Ea = 1 .6-5 .0 MeV. For the observed resonances tt) at Ea = 2.19, 2.44 and 2.55 MeV the quoted resonance strengths could be deduced only from the observed R -" 0 and R -+ 1.27 MeV y-ray transitions. In order to improve the signal-to-noise ratio in the detection of the capture .y-rays, Ge(Li) detectors were used in the present search for resonances of te0(a,y)ZZNe at Ea 5 2.30 MeV (fig. 1). The experimental equipment and set-up is described in sect. 2 and followed by the experimental procedure, data analyses and results in sect. 3. The nuclear and astrophysical aspects of the data are discussed in sect. 4. 2. ExperimmW egdpmmt and eet-ap

The 4 MV Dynamitron accelerator at the Institut fur Strahlenphysik in Stuttgart supplied the `He+ beam of 50 to 200 ~A in the energy range Ea = .0.6-2 .3 MeV t. A description of this accelerator and the .beam-handling system is given in ref. t Z). The 90° analyzing magnet has been calibrated using the proton-induced resonances t°) of Z'Al(p, y)ZBSi at Ep = 774, 992, 1317, 1588 and 1724 keV as well as the a~apture resonances ts) of t4N(a, y)taF at EQ = 1526 and 2346 keV. The energy calibration and reproducibility was found to be bétter than 4 keV. The energy spread and stability (over a period of 2 h) was better than 1 keV at a terminal voltage of 1 MeV. A detailed description of these investigations together with the slit-feedback system will be given in a forthcoming publication ta) . The Ta20s targets were obtained by anodizing 0.2 mm thick Ta sheets in water tt enriched to 99 ~ in t SO. Targets with 20, 40 and 65 anodizing voltages were produced corresponding ts) to a thickness of 320, 640 and 1040 A, respectively . The observed thiçknesses are slightly smaller than the calculated values : e.g. at Ea = 1.9 MeV, the 40 V target should correspond to a thickness of30 keV, which has to be compared with the observed value of 27 keV. The targets were able to withstand the high beam loads for several hours without noticeable deterioration. The y-rays were detected in 80 cm s Ge(Li) detectors with an energy resolution of 1.9 keV at Eq = 1 .33 MeV. The efficiency curves of these detectors in close geometry have been obtained' 6) for Ey = 0.2-16.0 MeV using calibrated y-ray sources as well as y-rays from low-energy proton-capture resonances . Standard signal amplifying and analyzing equipment was used in conjunction with these detectors. A schematic diagram of the experimental set-up is shown in fig. 2. The beam passed through a 1 .5 cm diameter Ta collimator and was focused into a profile of 1.5 cm diameter on the target. The targets were mounted in a target holder at 90° with respect to the beam direction . Direct water cooling (demineralized water) was applied to all targets (water pressure ~ ., 5 bar). A window and a small lamp in the target chamber t For this energy range, half of the rectifier tubes in the accelerator have been bypassed . tt Purchased from Isotopenlabor der Kcrnfors~ungsanlage Karlsruhe, Germany .

HELIUM BURNING OF '°O TA-COLLIMATOR

?

LN -COOKED CU - SHROUD

49 3 7cm THICK LEAD SHIELD

3

80cm GElL11 DETECTOR 10°I

D Fig. 2. Schematic diagram of the experimental set-up.

allowed close inspection of the beam profile and the target stability during the bombardments . A LNZ cooled in-line copper tube (30 cm length) extended from the Ta collimator to within 3 mm of the target . This tube together with the target formed the Faraday cup for beam integration. With this tube and two more LNZ traps in the vacuum system (fig. 2~ no carbon build-up on the targets was observed. A beamscanner t Z) close to the 1 .5 cm diameter Ta collimator (fig. 2) was usedto guarantee a similar beam profile on the target in all measurements. For the measurements of excitation functions with thin and thick TaZOs targets, the 80 cm3 Ge(Li) detector was positioned at 0° in close geometry (1 .4 cm distance between the crystal front face and the target). A 7 cm thick lead shield surrounded the Ge(Li) detector and the target as tight as possible (fig. 2) in order to reduce the contribution of room background. In subsequent measurements of excitation functions as well as y-ray decay schemes ofthe individual resonances, a target holder at .45° to the beam direction was installed and the Ge(Li) detector placed at 45° in close geometry (without lead shielding). 3. Experimental procedure, data analysis and results Details of the experimental procedure and data analysis are described in the following subsections. The results on the properties of the te0(a, y)ZZNe resonances are summarized in tables 1 and 2. and fig. 7. 3.1 . EXCITATION FUNCITON OF THE '°O(a, y)=~Ne REACTION

Due to the existence of 49 states in ZZNe below the a-particle threshold'°) (Q = 9.67 MeV) a sizable fraction of the y-ray transition strength from the resonances should proceed via yy cascades through the J~ = 2 +, 1 .27 MeV first excited state. This reason together with the improved sensitivity of the Ge(Li) detector for the

494

T~arB 1 Summary of results on resonance properties of °O(a, y)=3Ne and comparison with previous work ~s~(a, Y)~~Ne

E, (Iab) (keV) 656t 4 755t 4 769f 4 1158 t 5 1254 t 4 1267 t 6 1323 f 4 1455 f 4 1534 t 5 1665 t 6 1785 t 5 1866 t 4 1959 f 5 2150 t 10 2200 f 5

r pab) (keV) ~ ~ ~ 5 5

5 2 1.5 5 4

510 5

5 ~ 7 25 f5 510 55 ~ 5 ~ 5 550 3

5

~eC(~ n)s' Ne ~ ary') (meV)

E, (lab)

(keV)

0.29 t 0.05 0.47 t 0.08 2 0.67 20 .41 ~ 1 .3 t0.2 20 .32 1 .0 ~ 2.2 t0.3 65 f 8 ~0.2 ~ 1 .8 t0.3 7.2 t l .l 7 .0 t 1 .1 Z 3.0 480 t70

Z

l' (lab) (keV)

1159 f3

6

1322 f3 1450 f3 1530 t3

6 6 24

1864 f 3 1955 f5 2160 f8 2195 f3

7 12 48 ~3

E.(=sNe) (ke~ present 10204t 4 10285t 4 10297t 4 10615f 5 10694t 4 10704f 6 10750f 4 10858f 4 10923f 5 11030 f 6 11128f 5 11194f 4 11270f 5 11426f 10 11468f 5

ref. 10183f20 10269f20 10634t20 10755t20 11000f20 11102fZO

') Values of ary 5 6, 9, 25 meV and ary e 2.7 f0.6 eV are reported i') for the E, = 1866, 1959, 2150 and 2200 keV resonances, respectively . Actual values are identical with the lower limits (see text). ~ Ref.'s. Values of'E,(I~ ~ 1873(7), 1961(7), 2156(47) and 2194(9) keV are reported in ref. i') . TearB 2

Summary of the angular distribution results for "O(a, y)~2Ne resonances E, (MeV)

Transition (MeV)

a= ~

1 .45

R-" 1 .27 1 .27~0 R~ 0 R~ 1 .27 1 .27 -a 0 R ~ 1 .27 R~8.90 8.90 ~ 1 .27 1 .27 -. 0 R ~ 3.36 R~6.34 6.34 ~ 3.36 3.36 ~ 1 .27 1 .27=+0 Ry0 R~ 1 .27 R~ 5.15 5.15-.1 .27 4.46 ~ 1 .27 1.27 ~ 0

0.9 f0.3 0.4 f0.3 -1 .0 f0.3 -O .15f0.13 ~ 0.35 t0.12 0.3 t 0.4 -0 .1 f0.2 0.1 f0.3 -0 .1 t0.1 1.2 f0.4 0.1 f0.4 0.8 f0.2 0.4 f0.2 0.7 f0.2 -1 .06f0.11 -0.28f0.14 -0.14f0.10 0.74f0.18 0.20f0.10 0.24t0.02

1 .53 1 .87

1 .96

2.20

~

a~'~ ~ -0 .5 t0 .5

-0.3 f0.4 0.08t0.12 -O.15f0 .11 -0.3 f0 .3 -0 .03t0.05

~ Corrected for finite solid angle of the Ge(Li) detector and finite size of the beam spot on the target . ~ A, terms are included only in the analyses, if the al teen alone could not fit the data (,~ ,~ ? 1 .4). The errors are obtained by variation of the a4 teams within the statistical errors of the data.

HELIUM BURNING OF '°O

49 5

1 .27 MeV y-ray line (compared to the sensitivity for the high-energy and Dopplerbroadened primary y-ray transitions) were the basis for a preliminary establishment of the excitation _function for t 8 0(a, y)Z ZNe via this secondary y-ray transition . At each a-particle energy, the full y-ray spectrum was recorded in the analyzer and stored on magnetic tape. Only the 1.27 MeV y-ray peak was analyzed during the course of the experiment . In order to locate the energy. regions of resonances, a preliminary run with a Ta20, target, 60 keV thick at Ea = 1.9 MeV, was carried out. Spectra at EQ = 0.7-2.2 MeV in energy steps of dEQ S 60 keV were taken at B y = 0°. In a second run, the excitation curve was repeated completely with a 27 keV thick target (at Ea = 1.9 MeV) and fine energy steps were taken around each of the resonances in order to establish the rise at the front edges of the thick-target yield curves . The results of this run are illustrated in fig. 3. In a subsequent run with a 13 keV thick target, a full excitation

Fig. 3. Excitation function for the 1 .27 MeV secondary y-ray transition, at Br = 0`, from the '°O(a, y)Z 2Ne reaction. The lines drawn through thedata points areto guide the eye. The known resonance at E, = 2.20 MeV is established and ~ 14 new resonancea were found below this resonance. Resonances with up to three orders of magnitude smaller strengths than the known resonance were detected . The E, = 1 .89, 2.01 and 2.12 MeVresonances arise from the "F(a, py)='Ne reaction due to "F contamination in the target (see text). Indicated is also the neutron threshold of the'°O(a, n)"Ne reaction .

curve was taken again and the existence of closely spaced resonanoes was investigated in more details. In the course of measurements of the resonance y-ray decay schemes (subsect . 3.3), excitation functions at each resonance were taken again at 9r = 45° in close geometry . In all the runs, frequent checks on the stability of the targets were carried out at the strongest resonances in the reaction. It should be noted that even with the improved sensitivity for the 1 .27 MeV y-ray, the counting rate for this line was quite low at most resonances. Typically, it was

496

H. P. TRAiJTVETTER et al. 8

W Z Z Q 2 U W N Z O U

CHANNEL

NUMBER

HELIUM BURNING OF '"O

497

b

CHANNEL NUMBER Fig. 4b.

Fig. 4. Gamma-ray spectra obtained at several resonances of'80(a, y)='Ne are shown together with the identification of the observed y-ray transitions. The accumulated charge at each resonance is also given. Note the increasing neutron-induced y-ray background at E, Z 1 MeV.

498

H. P. TRAUTVETTER et al.

W Z Z Q U W H Z O U

CHANNEL NUMBER Fig. Sa .

necessary to collect 0.01 C per energy step over the stronger resonances and up to 1.5 C over the weakest resonances. Since the 1.27 MeV y-ray can originate also from the 19F(a, py)ZZNe reaction (Qo = 1 .705 MeV) due to 19F contamination in the targets, a full excitation function was taken with a 25 keV thick CaFZ target . The '9F content in the Ta20, targets relative to the CaFZ target was determined at the Ep = 1.37 MeV resonance of

HELIUM BURNING OF 's0

499

b

W Z Z Q 2 U

10'

E~ =2 .20 MeV n=o.z c

u Z U

>o 103

Sis-,.27

R-S,E

1,~6 -L27

5.15 4.46 1.27 0

n n~ 55

ER 4

18

27 _ 2 2' 2' 0'

CHANNEL NUMBER

Fig. 56. Fig . S . Gamma-ray spectra obtained at several resonances of' s0(a, y)=2Ne are showy together with the identification of the observed y-ray transitions . The accumulated charge at each resonance is also given . Note the large neutron-induced y-ray background . The favoured y-ray decay of the known E, = 2.20 MeV resonance praoeeds to the high-lying state at 5 .15 MeV and not to the ground state and 1 .27 MeV first excited state as reported previously ").

500

i9

H. P. TRAUTVETTER et a!.

F(p, ay)' 60. These measurements revealed that the Ea = 1.89, 2.01 and 2.12 MeV resonace (fig. 3) are due to the '9F(a, py)ZZNe reaction. 3.2 . RESONANCE ENERGIES AND TOTAL WIDTHS

The a-particle energies and total widths (or upper limits) of the resonace ware determined from the location and slope of the front.edges ofthick-target yield curves as well as from the shape of thin-target yield curves. The results are summarized and compared with previous work in table 1 . Seven of the new resonances in '80(a, y)Z~Ne have been observed previously ") as resonace in the reaction 180(oc, n)Z1Ne. The a-particle energies for these reson~nces are in good agreement with previous work (table 1): Theexcitation energies E= of the corresponding resonance states in ZZNe were obtained with the use of the Q-value 1°) of 9667.6 f0.4 keV for 180(a, y)Z~Ne and are listed in table 1. With the exception of the 10.40 MeV state (see below the six states observed in the 19F(a, p)22Ne reaction 9) at E_ = 10.18-11 .10 MeV (table 1) are identified with states seen in the present work, since their E= values match within error. The E_ = 10.40 MeV state 9) is expected to occur as a resonance in 180(a, y)ZaNe at Ea = 0.90 MeV. The lack of this resonance in the excitation functions (fig . 3) may be due to an unnatural parity assignment for this state (subsect . 4.1.3). With the exceptions of the 1 .53 and 2.15 MeV resonances, the reported total widths for the ' 80(a, n)Z'Ne resonances l') are in poor agreement with the upper limits observed in the present work (table 1). The' 80(a,n) Z1 Ne reaction has been studied l ') at EQ z 1.9 ( 5 1 .9) MeV with a 13(6) keV thick Ta2 0, target . The reported I'-values l ') (table 1) should probably be considered as upper limits, since (i) no detailed account is given on the analysis procedures, (ü) no information is available on the uncertainties for these values and (üi) the quoted widths appear close to the thickness of the targets used. 3.3 . GAMMA-RAY DECAY SCHEMES

In order to determine the y-ray decay schemes of the resonances, spectra were taken with the Ge(Li) detector at 45° in close geometry. Primary transitions could be established for ten resonances . Sample y-ray spectra taken with an accumulated charge ofupto 2.0 C are shown in figs . 4 and 5. fllthough for the remaining resonances y-ray spectra have been taken also with an accumulatéd charge of up to 3.5 C, the resonance strengths were too weak and/or the neutron-induced y-ray background too high in order to extract . reliable information on their y-ray decay schemes. The y-ray branching ratios deduced from the 45° data are summarized in fig. 7. In the case of the Ea = 0.77 MeV resonance, the intensity of the 1.27 -" 0 MeV secondary transition was accounted for only to 60 ~ by the intensity of the R -i 1.27 MeV primary transition (fig. 7) indicating additional - yet unobserved - branching

HELIUM BURNING OF ' s 0

50 1

through the 1.27 MeV state. Branching ratios for the strongest resonances were obtained also from the y-ray angular distribution data (subsect. 3.4) and were in good agreement with the values deduced from the 45° data. The results are discussed in subsect. 3.6. 3.4 . GAMMA-RAY ANGULAR DISTRIBUTIONS

For the resonances at Ea = 1.45, 1.53, 1.87, 1.96 and 2.20 MeV, y-ray angular distributions were taken with the Ge(Li) detector at angles of 0°, 45° and 90° to the beam axis and at a distance of 7 cm from the target. The inherent anisotropy of the system was checked using the isotropic 1 .08 (J = 0) -" 0 MeV secondary y-ray transition at the Ea = 1 .53 resonance 13) of 14N(a, y)' 8F and found to be isotropic within 10 ~. The stability of the target was checked by the intensity of the 1.27 MeV y-ray line before and after each run.

z w

C7 Z Q W

oa z 0 U

cos2 cost 6i Ai

arc tan b

Fig. 6. The y-ray angular distributions for the R -. 0 and R ~ 1.27 ~ 0 transitions obtained at the E, = 1.53 MeV resonance are shown together with their analyses .

The results obtained at the EQ = 1 .53 MeV resonance for the R -" 0 and R -. 1.27 -" 0 y-ray transitions are illustrated in fig. 6. The experimental data for all five resonace are summarized in table 1. The results of the XZ analyses of these data are presented in table 3 and discussed in subsect. 3.6. 3.5 . RESONANCE STRENGTHS

The 180(a, y)ZZNe resonance strengths were determined at B,, = 45° relative to

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H. P. TRAUTVEITER et al. Summary of the X3

E, (MeV)

J,

J3

J3

X3

0 1 2 3 4 5 1 2 3 1 0 1 2

2 2 2 2 2 2 0 0 0 2 2 2 2

0 0 0 0 0 0

4.1 2.1 0.8 1 .6 0.6 11 .E 0.5 38 .0 25 .0 1 .2 0.5 0.6 0.1

4.6 5.4 5.4 5.4 4.6 4.6 6.9 6.9 6.9 5.4 6.9 10.8 10 .8

R-+1 .27

3 4 5 2 3 4 5 6 2 3 4 1 2 3 1

2 2 2 4 4 4 4 4 4 4 4 0 0 0 2

0.8 0.2 3.1 1 .0 0.8 1.2 17.3 16.0 4.2 1.8 1.6 0.4 218.0 116.0 0.1

10 .8 6.9 6 .9 4.6 5.4 5.4 5.4 4.6 6.9 10 .8 10 .8 6.9 6.9 6.9 10.8

Ry5.15

1

2

4.8

10.8

Transitio~ (Me~

1.45

R~1 .27-.0

1 .53

R~0

1 .87

R-+1 .27~0 R ~ 1 .27

1.9E

R -. 6.34 ~ 3.3E ~

R~3.36 2.20

T~ 3 analyses of the results from table 2

R~0

0

4 4 4 4 4

X3 (0.1 %~ Mixing ratio b 9 -0 .710 .4 1.310 .E 0.610 .3

0.010.2 -1 .811 .8 -0.210.3 or >1 .5 0.310.2

-0 .210.3 -0 .210.3 1w

0.110 .1or -9 14 0.110 .1or -6 13

h Phase convention of Rose and Brink 3 ~.

~ The mixing ratio of the secondary transition was varied in the allowed region of b = 0.011 .0 (~ 3!" .

the combined yield of the closely spaced doublet t3) (dEQ = 1 .9 keV) at EQ = 1.53 MeV of' 4N(a, y) te F. The combined strength of this doublet is is) coy = ~~

l'

' = 1.35 f0.10 eV. r

Targets of TiN were used in the measurements of thick-target yields for this 14N(a, Y)18 F resonance doublet. Thesetargets were fabricated by vacuum evaporation of a layer of natural Ti onto a 0.2 mm thick Ta backing. The Ti film was then converted to the nitride in an atmosphere of purified nitrogen gas by resistance

HELIUM BURNING OF '°O

50 3

heating of the coated Ta backing to a red heat for ~ 1 min. Such targets were typically 50 keV thick at E, = 1.5 MeV. The thick-target yield was then compared with the corresponding yield of the narrow (r 5 3 keV) Es = 2.20 MeV resonance of ' 80(a, y)ZZNe using a 24 keV thick TaZ03 target. The two coy values are then connected through the usual relation 1 s)

) ) d14 G) ia coy('80) = 1.16 E~iaO Y(ia~ ~, Ea( ~ Y( ~ ~ N) ~ where dle0)/e(1`N) represents the ratio of the a-particle stopping powers' 9) per reacting target nucleus at the two beam energies [Eruv(E, =1.53 MeV) = 10.7 x 10-1 ~ and e.,.o,(Ea = 2.20 MeV) = 7.9 x 10-1~ eV ~ cm2/atom]. The beam energies EQ are in the lab system and the numerical factor arises ie) from conversion of the expression to the c.m . system . The y-ray intensities Y(' BO) and Y('°N) were calculated from the observed intensities N( 180) and N( 14N) through the equation Y(isG) N(iaG) E~(ia~ ia Q( laN) Br( ~ Y(u~ = N(ia~ EYl18O) Br(leO) L~lls~)

'( 18 The iat10 E y ( 14N]/E l ~) of the detection effciency for the y-rays from the two reactions was ob~tained 16) from the efficiency curve of the Ge(Li) detector. The ratio Q('4N)/Q( 18 0) represents the relative accumulated charges at the two resonances and Bß(1°N)/By(180) the respective y-ray branching ratios. In order to minimize systematic errors in the ~ determination, several runs with fresh TiN and Ta205 targets were carried out. The results ofall runs were in agreement within statistical uncertainty and lead to a resonance strength of for the Ea = 2.20 MeV resonance of 180(a, y)22 Ne. This result was then used to calculate the corresponding strengths (or lower limits) for all the other resonances (table 1). An absolute determination of the resonance strength at the E, = 2.20 MeV resonance resulted in ury = 0.30 f0.15 eV. The large error is due mainly to the uncertainty of the eRective solid angle (in the close geometry at 45°) between the Ge(Li) detector and the finite size of the beam spot on target . Chouraqui et al.' 1) reported y-ray branches of R -~ 0 (30 ~) and R -~ 1 .27 (70 ~) MeV for the E, = 2.20 MeV resonance with a total strength of coy = 2.7 f0.6 eV. This value has to be compared with the present value of ww(yo+yl = 45 ~) _ 0.22 f 0.03 eV, where for the comparison only the observed R -. 0 (27 ~) and R -. 1.27 (18 ~) branches (figs . 5 and 7) have been taken into account. Due to the high neutron-induced (and resonant) y-ray background at this resonance (fig. 5), the use of a NaI detector in the previous work l') hampers the subtraction of the y-ray background from the spectra and may yield therefore to higher Wy values.

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H. F. TRALJTVETTER et al.

3.6. THE J` ASSIGNMENTS

Since ZZ Ne is formed in the present work through spinless particles, the observed resonance states have natural parity assignments. The J~ assignments or limits are based, furthermore, on y-ray transition strength arguments (where strengths z°) of E3(M3) >__ 50(10) W.u were considered as unacceptable) as well as on a comparison of the partial a- and neutron-particle widths with the Wigner limit. The XZ analyses of y-ray angular distribution data (table 3) lead to further limitations on the Jx assignments. The combination of the results from the present work with those of previous work 9) allows finally a deduction of the most likely J~ assignments (fig. 7). The 0.66 MeV resonance. The observed R -. 0(0 + ) y-ray transition (fig. 4) together E~ O~twl

E IM~YI

2 .20 2.15 1 .96 1.87 1.78 1.66 153 145 t32 1.27 1 .25 1 .16 Q77 0.75 0.66

11 .47 t1.43~ 11 .27 1119 11.13 1l.03 1092 f0.86 f0.75~ 10.70 1Q69 10.6l 10 .30 1Q28 10 .20

22Ne

BRANCHINGS (%)

r= : tesz

ss =:
56:6

no

e6t3

s ss=s

na~n~

n nat 2'- 4' a5" 8'IS:6'.7l 8'I6`1 _ 1 0`-4' 5n n°t 1 _ - 6. 5e 4' 0`If.2'.3- 1 1-12`.3- )

8.90 fi85 1' fi34 4` 6` fi31 534 1` _ 5.15 2 4' 3.36 1.27 2' 0' 0 results branching ratios and J` assignments to states in zzNe above the a-particle Fig. 7. Summary of on threshold. The stare on the E, values mark those resonance states, which have been established in the present work only through the 1.27 MeV secondary y-ray transition. The open circles indicate that the branching ratios for these states are taken from ref. 9). Information on E, and J` values for the bound atatea are obtained fromrefs. 9 . i° " zz, u).

HELIUM BURNING OF ' 80

50 5

with the resonance strength coy (table 1) lead to the restriction JR = 1 -, 2+ or 3 - . A state at E_ = 10.18 f 0.02 MeV has been observed in the' 9F(a, p)ZZNe réaction where the proton group leading to this state is found to be in coincidence with double y-rays (table 1 of ref. 9 )) . This observation leads to the conclusion T x l'y ~ I'a. This state is associated with the EQ = 0.66 MeV resonance on the following grounds : (i) the E x values match within error (present work : Ex = 10.20 MeV), (ü) the observed (23 ~) yy cascade R -~ 1 .27 -" 0 (figs. 4 and 7) is consistent with the above observation and (iii) for the lowest allowed value of JÂ = 1 - the upper limit of l'a = 10 -s eV [for lQ = 1, 9â = 1 and an interaction radius of 5.9 fm] together with a conservative estimate of !'y x 0.1 eV leads to T x I'Y ~ l'a. The observed y-ray decay scheme of this resonance compared with those of the JÂ = 1 - resonances at Ea = 1.53 and 2.20 MeV (fig. 7) suggests a JR(0.66) = 1assignment . The 0.75 MeV resonance. The R -~ 6.85(1 + ) MeV y-ray transition yields JR 5 3 (e.g. for JR = 4+ , M3 z 3500 W.u.). The favoured y-ray decay strengths to high-lying J~ = 1 + states (fig. 7) makes a JR = 0 + assignment most likely . A state at E_ = 10.27 f0.02 MeV with doubly coincident y-rays is reported 9) and associated with the present resonant state at E x = 10.28 MeV on the basis of similar arguments as given above. The 0.77 MeV resonance . The observed lower limit on the resonance strength, coy ? 0.67 meV, together with the R -" 1.27(2+ ) MeV transition limits JR <_- 5- . A comparison of the lower limits for the a-particle width with the Wigner limit yields Bâ(I = 5) ? 30, hence JR <_ 4+. The 1 .16 MeV resonance. From a study of the 180(a, n)Z1Ne reaction, Bair and Haas l') report a resonance at Ea = 1159 f 3 keV, in good agreement with the present work (table 1). No primary transitions could be clearly established for this ' SO(a,y)ZZNe resonance and therefore only a lower limit on ury (table 1) can be deduced from the 1 .27 -. 0 MeV secondary y-ray transition (fig. 3). This resonant state at E, = 10.61 MeV is associated with the reported state 9) at E_ = 10.63 f0.02 MeV, which decays 34 ~ to the 3.36(4+ ) and 66 ~ to the 6.31(6+ ) MeV state. Angular correlation data yield 9) a unique J = 5 assignment . These results together with the present work lead to a JR = 5- assignment and - due to the consequent 100 ~ y-ray decay through the 1 .27 MeV state - to a resonance strength of coy = 0.41 f 0.10 meV (table 1). It should be pointed out, that for this J; assignment the upper limits on the particle widths of I' <_ 200 eV (for to = 3 and 9~ = 1) together with I'a(IQ = 5, Bâ = 1) S 22 meV yield I',o, 5 200 eV. This value is not inconsistent with the present observation of T S 5 keV (table 1) but is in contrast to the reported total width ") of T = 6 keV (see, however, subsect. 3.2). The 1 .25 MeV resonance. The observed R -. 3.36(4+) MeV y-ray branch together with the resonance strength ury (table 1) restrict JR = 1 - -7-. A comparison of the lower limit for I'a with the Wigner limit yields Bâ(1= 7) z 9, hence JR = 1-~+ .

506

H. P. TRALTTVETTER et al.

The 1.27 MeV resonance . The existence ofthis resonance is inferred from the shape and width ofthe excitation functions for the 1 .27 -. 0 MeV secondary y-ray transition, observed in this energy range (fig. 3~ Only a lower limit on the ury strength (table 1) and a natural parity assignment can be reported for this resonance (fig. 7). The 1 .32 MeV resonance. The a-particle energy of this resonance (fig. 3) is in good agreement with the value of EQ = 1322 t 3 keV reported l ') for the 180(a, n)2' Ne reaction. A clear identification of primary y-ray transitions at this resonance was not achieved in the present work. This resonant state at E_ = 10.75 MeV is associated with the J = 5 state at E_ = 10.75 f 0.02 MeV observed . 9) in the 19F(a, p)ZZNe reaction (table 1) with a 48(52) ~ y-ray decay to the J~ = 4+(6+ ) state at 3.36(6.31) MeV (fig. 7). These results together with the present work imply JR = 5 - and a resonance strength of WY = 1.010.2 meV (table 1). The deduced upper limit on the total width of T S 1 keV is not in disagreement with the upper limit of T S 5 keV from the present work (table 1) but is again in conflict with the reported value l ') of T = 6 keV (subsect. 3.2). The 1.45 MeV resonance. The observed resonance at Ea = 1455 f4 keV is in good agreement with the reported value ") of Ea = 1450 f3 keV for a resonance in ' s0(a, n)Z'Ne. The strength of the R -. 1 .27(2+) MeV y-ray transition together with the Xz analyses of the y-ray angular distribution data (tables 2 and 3) limit J~ 5 4+ . The 1.53 MeV resonance. Two y-ray branches, R ~ 0(44 ~) and R -. 1 .27(56 ~~ are observed (figs. 4 and 7) at this resonance. Transition strength arguments applied to the R -" 0(0+) y-ray decay restrict JR = 1 -, 2+ or 3 -. The angular distribution data for this transition (fig. 6) yield a unique Jx = 1 - assignment. The Xs analysis of the angular distribution data for the R -~ 1.27 ~ 0 y-ray cascade determines the mixing ratio of the primary transition to 8 = 0.0 f0.2 (fig. 6 and table 3). The observed a-particle energy and total width are in good agreement with the reported results l') from the study of the 's0(a, n)Z1Ne reaction (table 1). The Wigner limit for the a-particle width is l'~(1= 1) 5 360 eV, hence T !'o = 25 f 5 keV (table 1). The 1.66 MeV resonance. This resonance (fig. 3) corresponds to a state in ZZNe at E_ = 11.03 MeV, unbound against a- and n-particle decay. This state is identified with the state at E_ = 11.00 f0.02 MeV observed 9) in the study ofthe 19F(a, p)ZZNe reaction . .A 100 ~ y-ray decay to the Jx = 6+ state at E~= 6.31 MeV is reported 9). The y-ray angular correlations 9) in the cascade to the ground state are identical and suggest- as a stretched case - a most likely assignment of J = 8. A J = 6 assignment could not be excluded, however, from .the XZ analyses 9). Although special efïorts were made in long runs (up to 3.0 G) to detect all the cascade y-ray transitions at this resonance, the intense high-energy tail of the Ea = 1.53 MeV resonance (fig. 3) as well as neutron-induced y-ray background prevented a dear identification of the expected y-ray lines. The above results together

HELIUM BURNING OF '"O

507

with the present work yield to a JR = 8+ (6 +) assignment and cay = 0.20f0.05 meV. The Wigner limit for the to = 6 partial neutron width is l'0 5 11 meV and that for the IQ = 8 partial a-particle width I'a 5 0.03 meV. Since this highly unbound state emits y-rays in favour of particles 9), one must conclude T l' r ~ l'a+1'o. This conclusion yields WY x (2J+1)I'a and hence 9â(I = 8) 0.3. The 1.78 MeV, resonance. From the study of the '9F(a, p)Z 2Ne reaction, a state at Ex = 11.10f 0.02 MeV is reported 9) with a 100 ~ y-ray branch to the J= = 6+ state at E_ = 6.31 MeV. The angular correlations of all y -ray transitions in the y~ascades to the ground state are identical and suggest 9) a most likely J = 8 assignment (an interferring background resulted 9) in less precise angular correlation measurements and consequently assignments of J = 5, 6 and 7 could not be excluded 9) from the XZ analyses). This state is associated with the Ea = 1.78 MeV resonance (Ex = 11 .13 MeV) of ' 80(a, y)ZZNe . The reported y-ray decay scheme of this state is confirmed by the present work (figs. 5 and 7). Strength arguments applied to the R -> 6.31(6 +) MeV transition (together with natural parity assignments) limit JR = 4+-8+ (e.g. for JR = 3- (9 -~ E3 ? 400 (150) W.u.). The combined information from previous and present work leads to JR = 8 + (5-, 6+, 7 -). The observation 9) of y-rays in favour of particle emission implies again T x l'r ~ l'a +1'o , hence coy (2J+ 1)I'Q and Bâ(1 = 8) x 1 . The 1.87 MeV resonance. The observed R ~ 1.27(2+ ) MeV y-ray branch (figs. 5 and 7) restricts Jx 5 5 - . No further limitations on JR can be obtained from the XZ analyses of the y-ray angular distribution data (tables 2 and 3). The a-particle energy for this resonance is in good agreement with the value deduced from the study of the'BO(a, n)Z'Ne reaction ") (table 1). The reported total width ") of T = 7 keV is, however, in conflict with the present work (T S 5 keV) (subsect. 3.2). The 1 .96 MeV resonance . Transition strength arguments as well as results of Xs analyses of y-ray angular distribution data (tables 1-3) limit JR = 2+ , 3 - or 4 +. The a-particle energy is in good agreement with previous results ") from the ' BO(a, n)Z' Ne reaction (table 1). The reported value ")for the total width of l = 12 keV is in conflict with the present result of T S 5 keV (subsect. 3.2). The 2.IS MeV resonance. The existence of this resonance is inferred from the observed energy dependence in the excitation functions for the 1 .27 -" 0 MeV secondary y-ray transition (fig. 3). Only limits on the resonance width and strength and a natural parity assignment can be reported for this resonance. From studies of the ' BO(a, n)Z'Ne reaction, a T = 48 keV broad resonance at Ea = 2.16 MeV is reported "~ ") (table 1). The 2.20 MeV resonance . The reported y-ray decay scheme ") of this strong resonance is in poor agreement with the present observation. The quoted branches of R ~ 0(30 ~) and R ~ 1.27(70 /) have to be compared (figs. 5 and 7) with the present values of R -> 0(27 ~~ R -. 1 .27(18 ~) and R -~ 5.15(55 ~). The XZ analyses of the R -" 0(0 +) transition yield (table 3) a unique JR = 1 - assignment, in agreement with previous work ").

H. P. TRAUTVETTER et a1.

508

4. Diecaeedon 4.1 . NUCLEAR STRUCTURE ASPECTS

The nucleus ZZNe liés between two nuclei, Z°Ne and 24Mg, which have been shown to have very well defined collective energy band structure and it is to be expected therefore that the levels in ZZNe can also be incorporated into rotational-like band structure similar to those found in Z°Ne and 24Mg. In the case of ZZ Ne, the classification is, however, more speculative, since it is based almost solely on level energies and J~ assignments. It is, nevertheless, instructive to try to group some ofthe known ZZNe levels into bands in part as an incentive for future experimental work. 4 .1 .1.. The K".= 0* ground-state rotational band. According to the SU(3) model Zt) the lowest states in ZZNe have spatial symmetry [42] and arise from the leading representation with (~~) _ (82). This representation gives rise to a ~*. = 0* groundstate rotational band with J` = 0 + , 2*, 4 + , 6* and 8* members. The first four members have been identified ZZ) with the states at 0, 1 .27, 3.36 and 6.31 MeV. The Jx = 8 + member (band end) has been assigned recently 9) with the state at E_ = 11 .00 MeV. The combined results of previous 9) and present work indicate the presence of two most likely J~ = 8* states (subsect. 3.6) at Ex = 11.03 and 11 .13 MeV (fig. ~. A decision, which of the two 8 + states belongs to the ground-state band, will have to be based predominantly on y-ray transition strength arguments, i.e. the S member should exhibit an enhanced E2 strength in the y-ray decay to the 6 member at E_ = 6.31 MeV. Due to the ~y x l'a dependence for these high-spin resonances in 180(a, y)ZZNe, the observed WY strengths (table 1) allow one to deduce only insignificant lower limits on the I'Y widths [(2J+1)I'ß ? ury] and consequently T~al.e 4

Measured and predicted E2 strengths (W .u.) for the K' = 0* grdünd-state band in ZZNe E2 strength (w.u.)

Transition r, ~ >i

experiment

shell model ~

truncated shell model °)

rotational model

2* y0*

13.6t1 .0')

13 .2

16.5

6* y 4*

12.8±i :i n)

14 .6

18 .3

13 .6 19 .4 21 .5 22 .4

') Ref. 1~. This value is the weighted average of a number of measurements . ") Ref. ~~). ~ Present work. The number in bracket is the lower limit for the E, = 11 .03 MeV state. Ref. as) . Effective c]tarSes of eP = 1 .Se and eo = O.Se are employed in the calculations . ~ Simple rotational model : E2 strength is proportional to (J, 200~J~0) 2 add the predictions are normalized to the experimental 2* ~ 0* transition strength.

HELIUM BURNING OF 's0

509

on the corresponding E2 strengths : E2 z 0.002 and 0.02 W.a for the R -+ 6.31 (6*) MeV transition from the E_ = 11.03 and 11 .13 MeV states, respectively . In a simple rotational model, this transition should have a strength of 22 .4 W.u (table 4). Large basis shell-model calculations zs) as well as truncated shell-model calculations using an SU(3) basis s+) predict two Jx = 8 * states at E_ = 11 .13-11 .27 and 12.12-12 .62 MeV, in close agreement with observation. The predicted E2 strengths for the 8i -~ 6i transition are collective but up to a factor 2.7 smaller than the expected strength from the simple rotational model (table 4). For the 8Z -~ 6i transition, a strength of E2 = 1.4 W.u. is predicted xs) . Since T x I'~ for these states, the expected lifetimes are 10.9, 7.4 and 4.0 fsec for the J~ = 8i model state (table 4) and 64 fsec for the J~ = 82 model state s3). A measurement of these lifetimes is of considerable importance for the identification of the 8* member of the ground-state band as well as for a sensitive test of the various model predictions (table 4). 4.1.2. The K" = 2* rotational band. The leading SU(3) representation with (~.~) _ (82) also gives rise 2e) to a K" = 2+ band with members of J~ = 2*, 3 + , . . ., 10* . Possible candidates for the K" = 2 * band head would be either the 2*, 4.46 MeV or 2+ , 5.37 MeV states . From the known levels, it is possible to suggest

Fig . 8 . Rotational bands in ~=Ne . The available experimental data do not allow a unique identification of the two J` = 8* states at E, z 11 MeV as members of either the K` ~ 0* ground-state rotational band or the K` = 2* excited rotational band. The slope of the suggested K` = 2* band favours the J` = 2* state at 5 .37 MeV as the band head. Also shown are the members of a possible K` = 2 rotational band . The cross-hatched areas indicate the region of excitation energies for the missing J` = 4 - and 6* band members .

51 0

H. P. TRAUTVETTER et al .

the 5.64(3 +), 6.34(4+) and 7.41(3 + or 5+) MeV states 9 . lo, zs) as subsequent band members. The 8 + member of this band could be 'one of the two J~ = 8+ states observed at Ex = 11 .03 and 11 .13 MeV. A plot of the excitation energies of these band members versus J(J+ 1) (fig. 8) would indicate a larger moment of inertia for this band (compared to the ground-state band) and would favour also the 2 + , 5.37 MeV state as the band head . The 7 + member of this band is expected around E_ = 9.7 MeV and a possible candidate is the state observed 9) at Ex = 9.84 MeV. A Jx = 7 + state at this excitation energy is expected to decay to the ground state via the low-lying. high-spin states through yy cascades. Broude et al. 9) have observed the 9.84 MeV state in strong coincidence with triple coincident y-rays, however, no reliable y-ray decay scheme could be extracted from the data. In order to substantiate this highly speculative identification, a reinvestigation of this state is desirable. This state is expected as a resonance at EQ = 0.21 MeV in the ls0(a, y)zzNe reaction and its contribution to the stellar helium burning at low temperatures can be of considerable importance (see subsect. 4.2.3). However, if this state has indeed a J~ = 7 + assignment, it will not be formed in the 180(a, y)zzNe reaction due to the unnatural parity assignment. The 6 + member of this band is expected at E_ ~, 8.5 MeV, but no candidate for this band member has. been found yet. 4.1.3. The K"= 2- rotational band. Some candidates 9. io.zs) for a K` = 2 - band, resulting from the (~,~) _ (84) representation and corresponding to a s4p1 '(sd)' configuration, are indicated in fig. 8. These include the 5.14(2 -~ 5.91(3- ), 8.44(5 -1), 10.40((6-)) and 11.48(7 - ~) MeV states . No suitable candidate for the 4- member has been found yet, but it is expected at Ex : ., 7.0 MeV. The 10.40 MeV state is expected to occur as a resonance in the ie0(a, y)zzNe capture reaction at EQ = 0.90 MeV. No evidence for the existence of this resonance was found, however, in the present work (fig. 3). The suggested J~ = 6 - assignment for this resonant state 9) is therefore not in disagreement with the present observation, since only states, with natural parity assignment can be populated. Additional experiments are highly desirable in order to support these speculative identifications. 4.2 . ASTROPHYSICAL ASPECTS

The observed data of the present work together with the results from previous investigations a .' 1) put the stellar reaction rates of 180(a, y)zzNe on a firm ground in the important temperature range of T9 = 0.3-4 .3. The derivation of the stellar reaction rates from the experimental data is described in the following subsections. The results . are then compared with predicted rates of Fowler, Caughlan and Zimmerman') based in part on the nuclear optical model. Finally, the two competing i s0(a, zzNe and 1s0(a, n)z'Ne reactions in the helium burning of 1 s0 are Y) compared.

HELIUM BURNING OF '°O

51 1

4.2.1 . Stellarreaction rates from the isolated narrow resonances. The reaction rate, N~(QVi,

of importance in astrophysical calculations is given by the expression s) (8/ ~)~

o{E)E exp ( -E/kTkiE, J where NA is Avogadro's number,
M~(kT)~

N~

TABLE S

Stellar reaction rate NA
0.010 0.016 0.025 0.040 0.063 0.10 0.16 0.25 0.40 0.63 1.0 1.6 2.5 4.0 6.3 10.0

Resonance at = 0.65-2.SS MeV

E,

0.22E-64 0.54E-40 0.21E-24 0.15E-14 O.IOE-08 0.77E-OS 0.17E-02 0.49E-O1 0.45E+00 0.50E+O1 0.53E+02 0.20E+03

Direct capture (El, E2 and M1) 0.39E-67 0.14E-55 0.36E-46 0.11E-37 0.11E-30 0.13E-24 0.24E-19 0.44E-15

Tail of 1 .53 MeV resonance

E, _.

Previous work °)

0.20E-67 0.73E-56 0.19E-46 0.60E-38 0.68E-31 0.10E-24 0.24E-19 0.61E-15 0.13E-03 0.10E+00 0.10E+02 0.39E+03 0.54E+04 0.36E+OS

Sum `) 0.59E-67 0.21E-55 0.55E-46 0.17E-37 0.18E-30 0.44E-24 0.15E-14 0.10E-08 0.77E-OS 0.17E-02 0.49E-01 0.47E+00 0.15E+02 0.44E+03 0.56E+04 0.36E+OS

') In units of "reactions sec- ' (mole cm -') - `" . ~ For equal grid steps in In Tq. ~ Above T9 = 0.25 the reaction rate is well determined by the experimental data . The quoted values at T9 ~ 0.25 should be rnnsidered as lower limits due to the possible contributions of unobserved resonance at the low-energy region (see text).

51 2

H. P. TRAUTVETTER et al.

for the 180(a, y)22Ne reaction is given 2) by dT9 = 0.81(E~-E~) with dT9 in units of 109 K and E,(c .m.) in MeV. The energy range investigated in the present work between E 1 (c.m.) = 0.54 MeV and E Z(c.m.) = 1.80 MeV results in avalid temperature range of T9 = 0.3 to 2.0. This temperature range has been extended to T9 = 2.4 by including the two known resonace i') at Ea(lab) = 2.46 and 2.55 MeV with respective resonance widths of T = 6 and 14 keV and respective strength of wY = 3.9 and 0.23 eV. The stellar reaction rate has been calculated in the range 0.01 5 T9 S 10 using the above equation and the resonance parameters (cuy and E~, given in table 1 . For the Ea = 0.77,1 .27 and 2.15 MeV resonace, the quoted lower limits on the coy strengths (table 1) have been increased by a factor of two in order to account roughly for other possible y-ray branches not cascading through the 1.27 MeV state (fig. 3). The results are presented in the second column of table 5 . Below T9 = 1 .0, thestellar reaction rate is controlled by the Ea = 0.66, 0.75 and 0.77 MeV resonances, while at the range of T9 = 1 .0-2 .5 the EQ = 1 .53, 2.20, 2.46 and 2.55 MeV resonances contribute predominantly ( z 95 ~) to the energy averaged stellar rate. 4.2.2. Stellar reaction rate from the direct capture process and broad resonances .

The contribution of the direct capture (- DC) process in 180(a, y)ZZNe to the lowenergy yield has been estimated(for details ofthe DC process, see ref. s')) . This process is expected to proceed strongly to those final bound states in Z ZNe, which have large a-spectroscopic factors. From a study of the a-transfer reaction 180('Lî, t)ZZNe, Scholz et al. ae) observed significant a-clustering for ten states in ZZNe between 6.24 and 8.59 MeV excitation energy . Due to the complexity ofthis a-transfer process, only relative a-spectroscopic factors for these Jx = 0+ , 1 - and 2 + states are given (table 1 of ref. se)). For the estimate of the DC process in ' 80(a, y)22Ne (see below) it has been assumed, that the process proceeds predominantly to these states and that the summed a-spectroscopic factor for these J~ = 0+ , 1 - and 2 + states has the value of one. It has been demonstrated [ref. z') and references therein] on several capture reactions, that the DC process for protons is dôminated by El transitions (with negligible contributions from E2 and M 1 transitions) giving rise to cross sections of the order of pb above the Coulomb barrier. For the El transitions, . the cross section is ruled by the "effective" charge (Z 1/M 1 -ZZ/M Z )2, where (Z 1 , M l) and (Z 2 , M Z) are the charge and mass ofthe projectile and target nucleus, respectively . For protons on any target nucleus (except protons), this effective charge is x ~. In the case of a-particles on target nuclei with ZZ x ZMZ, this effective charge is nearly zero and hence the DC process has to proceed through the higher y-ray multipolarities, E2 and M1, giving rise to small cross sections of 5 nb. In the case of the 180(a, y)ZZNe s -s reaction, however, the effective charge for El transitions ïs finite (~-~) = 3 x 10 and consequently El, E2 as well as M1 transitions have to be considered in the process. For the DC process to the final J~ = 0+ states, El and E2 capture contributions

HELIUM BURNING OF '°O

51 3

from the la = 1 and 2 incoming partial waves, respectively, have been calculated. For the final J~ = 1 - states, the contribution from El(lQ = 0), E2(la = 1) and M1(Ia = 1) capture has been considered and, finally, for the JR = 2 + states, again the three processes El(la = 1), E2(lQ = 0) and M1(!a = 2) were calculated. These calculations reveal, that the El contribution to the capture process . is of the same order as E2 and M1, ifnot dominant. The expected total cross section for all processes is x 15 nb at Ea = 2.5 MeV. The calculated DC cross section has been converted to the usual astrophysical S-factor 2) S(E) = Q(E)E exp (2>m),

where q is the usual Sommerfeld parameter. The analytic form of this non-resonant process (in usual Maclaurin series 2)) is MeV ~ b, where E is the c.m. projectile energy in MeV. This S-factor curve for the DC process = 67.0-39.6E+7.OE~

c f ,~ o ,o° H U i

(~ Q

U

N } o=

2 Q_ O ~ ~ô H (~ Q

o

as

m

ALPHA -PARTICLE

u

to

ENERGY E~Ilab) IMèi/]

~s

Fig. 9. Astrophysical S-factor curves for the observed resonances in '°O(a, y)~=Ne as wdl as for the expected direct capture process in this reaction . The 2.46 and 2.SS MeV resonances have been observed by lrhouraqui et al . ") . With the exception oî the E, = 1 .53 MeV resonance, all other resonance° have such small total widths and/or resonance strengths that their influEnce on stellar reaction rates at low a-particle energies can be nFglected. Shown is also the expelled location of possible low-energy resonances . If these expelled resonance! can be formed in the'°O(a, y)3=Ne reaction with appreciable strengths, the stellar burning rates at temperatures T9 5 0.3 will change by orders of magnitude.

51 4

H . P . 1'RAUTVETTER et al.

is illustrated in fig.. 9 and compared with the corresponding S(E) curves for the individual resonace . For the latter curves, it is necessary to include the energy dependence of the partial widths and the .total width in the Breit-Wigner expression . For these calculations, the total widths given in table 1 were used. For the cases, where only rough upper limits are known (table 1~ the observed properties of the resonance states and their most likely Jx assignments together with penetrability arguments for the particle decays were used to deduce a most probable value for the total width (e.g. for the resonace at Ea 5 1.32 MeV, T = 0.1 to 10 eV). The calculations indicate (fig. 9~ that only the low-energy tail of the T = 25 keV broad resonance at EQ = 1.53 MeV provides a significant contribution to the S-factor. This low-energy "non-resonant" contribution can be described again by a Maclaurin expansion (see above) resulting in the analytic expression Sl .s3(E) = 33.0-0.61E+ 179.2E2 MeV ~ b,

where E is again the c.m . projectile energy in MeV. The contributions of the direct capture process and the low-energy tail of the Ea = 1.53 MeV resonance to the stellar reaction rate have been calculated using the expression Z)

where Sett is defined through the equation Z) _ 5 _ kT S'(0) 1 S"(0) Z _ S~t _ S(0) + _ +~kT)+ _2 +~EokT) . (E ° 36 Eo + S(0) S(0) (E° J The coefficients S(0~ S'(0) and S"(0) are obtained from the expansion of the S-factor curves (see above) . The resulting rates are presented in the third and fourth column of table 5 and indicate, that the stellar reaction rate is dominated by these two contributions at temperatures of T9 5 0.1 . Since the direct capture calculations are based on the assumption of single-particle values for the a-particle spectroscopic factors CZS (see above), values of CZS = 0 or 0.1 would reduce the total stellar rates (table 5) at T9 = 0.01 by a factor 2.9 or 2.4 and at T9 = 0.1 by a factor 1 .4 or 1.1. 4.2.3. The total rate, its analytic expression and comparison with mortel predictions. The stellar reaction rates deduced from previous cross-section measurements a) of 180(a, y)ZZNe at Ea = 2.1 X3.70 MeV are listed in the fifth column oftable 5 along with the sum of all the teens in column 6. As a summary, the stellar reaction rate of î80(a, y)ZZNe is well determined by the available experimental data at temperatures T9 = 0.3 .3. At temperatures T9 S 0.3, the quoted values for N~<~i from the DC process and the tail of the 1.53 MeV resonance are uncertain up to a factor 2.9 (subsect. 4.2.2). Despite this uncertainty, these rates should be considered only as lower limits, since the expected resonances

Cl

1

HELIUM BURNING OF ' s0

51 5

at Ea = 0.04, 0.21 and 0.53 MeV (figs. 1 and 9) could increase by several orders of magnitude the stellar rates in this temperature region. Only the Ea = 0.53 MeV resonance is within the range of feasibt~ity to be observed directly by an experiment . Due to the ury coi' Q dependence and due to the barrier penetration factor contained in l'~, the two other expected low-energy resonannces are inaccessible to the experimenter by a direct strength measurement. Additional experiments with other nuclear reactions have to be carried out in order to obtain all the necessary parameters for a reliable estimate of their influence on the stellar reaction rates. If such experiments reveal e.g. that the E_ = 9.84 MeV state has indeed a J~ = 7+ assignment (as speculated in subsect. 4.1 .2), the Ea = 0.21 MeV resonance will be absent in the capture process due to the unnatural parity assignment . Finally, such future experiments may reveal additional - yet unobserved - states in ZZNe at Ex = 9.70-10 .10 MeV (fig. 1~ which can control the stellar rates at T9 5 0 .3. For use in stellar model calculations, the observed reaction rates are given by the following analytic expression N~
=

1.37 x 10 12 7,} (1 +O.OlOT* -0.46T} -0.034T9 +2 .46T9~3 +0 .45T9~3 ) 9

x exp ~-

40 .03

Ty 2 - (0.27) 7,9

+ ~ ~ exp ~-

+ 0.10~ 1016_

Ti/ 9 9 .IO T90 - 1 ° +(0to 1)x O expC- 1 i =1

9

7,s~6 ex ~- 4003 - C1 .6012 eff 1~ e~f

9

97I where T~ff = T9/(1.0+0.0665T9 ) and At = 7.54, 46.8,1 .59 x 103,1.25 x 104,1.01 x 10', 5.98 x 103 and B, = 6.23, 7.23, 14.56, 20.9, 23 .4, 24 .2 (i = 1, . . ., 6). The T9 cutoff term') is included in the first exponential (the non-resonant term = combined result of the DC process and the tail of the 1 .53 MeV resonance) to suppress its contribution at temperatures, where the reaction rate is controlled by the observed resonances . Since the EQ = 0.66 MeV resonance makes the largest contribution at low energies, this energy is taken as the cutoû energy for the non-resonant term t yielding a cutoti temperature') of T9~ o = 0.27. The sum gives the contribution from those observed resonannces at EQ = 0.66-2.55 MeV, which dominate (>_ 95 ~) the reaction rate . The third term represents the parametrized rate from the previous measurements e) at Ea = 2.60-3.70 MeV, where a T9 2 term is included in the exponential to suppress its contribution in the lower temperature range. The last term includes the expected EQ = 0.21 MeV resonance, which has been assumed to have JÂ = 0+ and Bâ(1 = 0) = 1 for the purpose of estimating its maximum 1 Actually, the cutoff should not apply to the DC portion of the non-resonant term but its contribution to the stellar rates above T9 = 0 .1 is negligible (table 5) .

51 6

H. P. TRAUTVETTER et al .

contribution to stellar rates at T9 S 0.3. The multiplication factor (0 to 1) reflects the present uncertainty of its actual contribution (see below) . In the recent compilation on thermonuclear reaction rates Fowler, Caughlan and Zimmerman') give an expression for the t 8 0(a, y)ZZNe reaction rate, which - due to the lack of data below Ea = 2.1 MeV - is based in part on the nuclear optical model s ~ 6). Thisstatistical model assumes of course thâtthere are plenty ofresonances ~o`

--`-' ,-,-'

I

T

T

T T T

~0 (a,?i)~Ne U Q W

H ~~ Z

W

70`

W ß_

10'

O

FCZ III)

H Ô 10= O

~MONSTER

F

10' L O.QI

n

~ 0.04

~

~

m .~ 0.1

0.4

10

STELLAR TEMPERATURE T9 110° °K

1

rate of °aa, y) =~ Ne predicted

Fig. 10. The stellar reaction by Fowler, Caughlan end Zimmerman') ie compared with observation, where - for a better comparison - only the ratio of the two rates are plotted. Indicated are also the temperature regions, for which the reaction rates are well determined by the experimental data from the present and previous work °" ") . For details, see text .

at low a-particle energies. The predicted rate is compared in fig. 10 with the experimental data, where the ratio
HELIUM BURNING OF '°O

51 7

with the model predictions. If, however, no additional states with natural parity assignments are found in future experiments and if the Ea = 0.21 MeV resonance has indeed a J~ = 7 +. assignment (subsect. 4.1 .2 the discrepancy will be real and the values given in table 5 have to be taken as the actual rates at T9 5 0.3. Since the solution ofthis open problem is important for the application ofstatistical models in predicting stellar reaction rates (especially for nuclei with a relatively low density of states), experimental investigations of the states in ZZNe at E_ = 9.7-10.1 MeV are highly desirable. 4.2.4. He burning of ' a0 and synthesis of Z 1 Ne and ZZNe. Helium burning of ' 80 proceeds through the two competing reactions '80(a, y)ZZNe (Q = 9.67 MeV) and ta0(a,n)Z 1 Ne (Q = -0.70 MeV). The latter reaction has been studied in detail l') at Ea = 1 to 5 MeV. Using the formula of the stellar reaction rate for this reaction from Fowler, Caughlan and Zimmerman') and the rates for 'BO(a, y)ZZNe from 10'

E

w a

~ 10' z 0 U 10~ C ô 10 O Z Q

0

V///////////iEXPERI MENT/////////////~/

Q tti' 0.1

0.4

1 .0

STELLAR TEMPERATURE

i.0

Ty 110° °K ]

10D

Fig. 11 . The ratio of the °teller reaction rates for the reactions '°O(a, y)==Ne and '°O(a, n) = 'Ne are plotted as a function of stellar temperature. The rates for the capture reaction are taken from table 5 and those for the (a, n) reaction from ref. '). Also indicated is the temperature region, for which the reaction rates of °O(a, y)==Ne are well determined by observation .

51 8

H. P. TRAUTVETTER et al.

table 5, the ratio of the reaction rates for the two competing reactions was calculated as a function of stellar temperature. The results (fig. 11) indicate that at temperatures of T9 5 0.6 helium burning of 18 0 proceeds predominantly through the 180(a, y)ZZNe reaction synthesizing therefore mainly the isotope ZZ Ne. If future experiments reveal low-spin resonances with natural parity assignments at E a 5 0.6 MeV (subsect. 4.2.3 the ratio of the two reaction rates increases much steeper at T9 5 0.3 hence reinforcing the above conclusion . At temperatures of T9 z 1.6 the reaction 180(a,n)Z1Ne dominates by three orders of magnitude over the capture reaction and hence the isotopes ZZNe and ZZNe are produced in a ratio of 103 :1 . The observation of strong resonances in the reaction 180( a, y)ZZNe below the neutron threshold (figs. 3 and 9) and the consequent dominance of the capture reaction in the He burning of 180 at T9 S 0.6 (fig. 11) may help to solve the mystery ofNe-E in connection with the origin ofthe solar system (sect. l). Ifthe ZZNe(a, n)ZS Mg reaction is indeed the key reaction for producing neutrons for the s-process, as expounded by Iben and Truran a), the conversion of 1aN (from the operation of the CNO tricycle) into ZZNe by the sequence of reactions 1aN(a~ 1s y)18F~+v) 0(a, Y)ZZN~ has to take place at stellar temperatures of T9 S 0.6. Above this temperature helium burning of 18 0 produces predominantly ZZNe and the subsequent reaction Z1Ne(a, n)ZaMg (Q = +2.56 MeV) would be the dominant neutron source for the s-process syntheses. 5. Concluding remarks The present work demonstrates that with the use of high-beam currents in conjunction with improved target-technologies and high-resolution Ge(Li) detectors small cross sections can be observed even in the presence ofan intense and pernicious neutron-induced y-ray background . The results show that the 180(a, y)ZZNe reaction proceeds through a relatively small number of isolated resonances. The stellar reaction rates are well determined at T9 = 0.3-4.3 from the experimental data . Further experimental investigations using other nuclear reactions are necessary to put the stellar rates at T9 = 0.06-0.3 on a firm ground. Of special importance are the states expected as resonances at Ea = 0.21 and 0.53 MeV (fig. 1). The expected resonance at Ea = 0.04 MeV (fig. 1) is not so much of importance, since the corresponding stellar reaction rate - even for a maximum strength (for lQ = 0 and Bâ = 1) corresponds to a lifetime of 180 (even for pXHe = 10') which is larger than the lifetime of the universe . The authors would like to thank Prof. K. W. Hoffmann and the technical staff of the 4 MV Dynamitron accelerator at the Institut fier Strahlenphysik in Stuttgart for their hospitality and other support given for this experiment. The help of

HELIUM BURNING OF 's0

51 9

H. W. Becker and J. Görres during the course of these experiments is highly appreciated. The authors are also grateful to the Deutsche Forschungsgemeinschaft for a travelling grant. The authors thank Profs. W. A. Fowler, D. N. Schramm, M. Arnould and Dr. F. Thielemann for the many enlightening and helpful comments on the manuscript . The Dynamitron accelerator and the high-current beam transport system have been supported by the Volkswagen Foundation . References

1) E. M. Burbidge, G. R. Burbidge, W. A. Fowler and F. Hoyle, Rev. Mod. Phys . 29 (1957) 547 2) C. A. Barnes, Advances in nuclear physics, vol. 4, ed . M. Baranger and E. Vogt (Plenum Press, NY, 1971) p. 133 3) D. Black, Geochem. et Cosmochem. Acta 36 (1972) 377 4) I. Iben, Astrophys. J. 196 (1975) 525, 549; J. W. Truran and I. Iben, Astrophys. J. 216 (1977) 797 5) S. E. Woosley, W. A. Fowler, J. A. Holmes and B. A. Zimmeruran, Caltech preprint OAP 422 (1975) 6) W. A. Fowler and F. Hoyle, Astrophys. J. Suppl. no. 91, 9 (1964) 201 7) W. A. Fowler, G. R. Caughlan and B. A. Zimmeruran, Ann. Rev. Asttun. Astrophys. 131975) 69 8) A. Adams, M. H. Shapiro, W. M. Denny, E . G. Adelberger and C. A. Barnes, Nucl . Phys . A131 (1969) 430 9) C. Broude, W. G. Davies, J. S. Forster and G. C. Hall, Phys. Rev. C13 (1976) 953 10) P. M. Endt and C. van der Leun, Nucl . Phys . A214 (1973) 1 11) G. Chouraqui, Th . Muller, M. Port and J. M. Thirion, J. de Phys. 31 (1970) 249 12) J. W. Hammer, H. M. Schtipferling, E. Bergandt and Th . Pflaum, Nucl . Instr. 128 (1975) 409 13) C. Rolfs, A. M. Charlesworth and R. E. Azuma, Nucl . Phys. A199 (1973) 252 ; I. Berka, K. P. Jackson, C. Rolfs, A. M. Charlesworth and R. E. Azuma, Nucl . Phys . A288 (1977) 317 14) H. P. Trautvetter, K. U. Kenner, M . Wiescher, C. Rolfs and J. W. Hammer, to be published 15) D. A. Vcrmilyea, Acta Metallurgica 1 (1953) 282 16) P. Schmalbrock, Staatsexamensarbeit, Universitât Monster (1976) 17) J. K. Bair and F. X. Haas, Phys . Rev. C7 (1973) 1356 18) C. Rolfs and A. E. Litherland, Nuclear spectroscopy and reactions C, ed . l. Cerny (Academic Presa, NY, 1974), p. 143 19) L. C. Northcliffe and R. F. Schilling, Nucl . Data Tables 7 (1970) 233 20) P. M. Endt and C. van der Leun, Nucl . Phys . A235 (1974) 27 21) J. P. Elliott, Proc . Roy. Soc. (London) A245 (1958) 128, 562 22) L. K. Fifield, R. W. Zurmiihle and D. P. Balamuth, Phys. Rev. C10 (1974) 1785 23) H. M. Freedom and B. H. Wildenthal, Phys . Rev. C6 (1972) 1633 24) A. Arima, M. Sakakura and T. Sebe, Nucl . Phys . A170 (1971) 273 25) L. K. Fifield, R. W. ZurmBhle, D. P. Balamuth and S. L. Tabor, Phys. Rev: C13 (1976) 1515 26) W. Scholz, P. Neogy, K. Hethge and R. Middleton, Phys. Rev. a6 (1972) 893 27) C. Rolfs, Nucl . Phys . A217 (1973) 29 28) H. J. Rose and D. M. Brink, Rev. Mod. Phys . 39.(1967) 306