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REACTION RATE UNCERTAINTIES AND THE PRODUCTION OF 19 F IN ASYMPTOTIC
GIANT BRANCH STARS
Maria Lugaro
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK; mal@ast.cam.ac.uk
Claudio Ugalde
The Joint Institute for Nuclear Astrophysics and Department of Physics, University of Notre Dame, 225 Nieuwland Science Hall,
Notre Dame, IN 46556; ugalde.1@nd.edu
Amanda I. Karakas
Institute for Computational Astrophysics, Department of Astronomy and Physics, Saint Mary's University, Halifax,
NS B3H 3C3, Canada; akarakas@ap.stmarys.ca
Joachim Go �rres and Michael Wiescher
The Joint Institute for Nuclear Astrophysics and Department of Physics, University of Notre Dame, 225 Nieuwland Science Hall,
Notre Dame, IN 46556; wiescher.1@nd.edu, goerres.1@nd.edu
John C. Lattanzio
School of Mathematical Sciences, P.O. Box 28M, Monash University, Victoria 3800, Australia; j.lattanzio@sci.monash.edu.au
and
Robert C. Cannon
Institute of Adaptive and Neural Computation, Division of Informatics, 5 Forrest Hill, Edinburgh EH1 2QL, UK; robert.cannon@ed.ac.uk
Receivved 2003 November 15; accepted 2004 July 19
ABSTRACT
We present nucleosynthesis calculations and the resulting 19 F stellar yields for a large set of models with
different masses and metallicity. During the asymptotic giant branch (AGB) phase, 19 F is produced as a conse�
quence of nucleosynthesis occurring during the convective thermal pulses and also during the interpulse periods if
protons from the envelope are partially mixed in the top layers of the He intershell (partial mixing zone). We find
that the production of fluorine depends on the temperature of the convective pulses, the amount of primary 12 C
mixed into the envelope by third dredge�up, and the extent of the partial mixing zone. Then we perform a detailed
analysis of the reaction rates involved in the production of 19 F and the effects of their uncertainties. We find that the
major uncertainties are associated with the 14 C(# , #) 18 O and 19 F(# , p) 22 Ne reaction rates. For these two reactions
we present new estimates of the rates and their uncertainties. In both cases the revised rates are lower than previous
estimates. The effect of the inclusion of the partial mixing zone on the production of fluorine strongly depends on
the very uncertain 14 C(# , #) 18 O reaction rate. The importance of the partial mixing zone is reduced when using our
estimate for this rate. Overall, rate uncertainties result in uncertainties in the fluorine production of about 50% in
stellar models with mass '3 M
# and of about a factor of 7 in stellar models of mass '5 M
# . This larger effect at
high masses is due to the high uncertainties of the 19 F(# , p) 22 Ne reaction rate. Taking into account both the
uncertainties related to the partial mixing zone and those related to nuclear reactions, the highest values of 19 F
enhancements observed in AGB stars are not matched by the models. This is a problem that will have to be revised
by providing a better understanding of the formation and nucleosynthesis in the partial mixing zone, as well as in
relation to reducing the uncertainties of the 14 C(# , #) 18 O reaction rate. At the same time, the possible effect of cool
bottom processing at the base of the convective envelope should be included in the computation of AGB
nucleosynthesis. This process could, in principle, help to match the highest 19 F abundances observed by de�
creasing the C/O ratio at the surface of the star, while leaving the 19 F abundance unchanged.
Subject headinggs: nuclear reactions, nucleosynthesis, abundances --- stars: AGB and post�AGB --- stars: carbon
1. INTRODUCTION
Spectroscopic observations show that in giant stars of type
K, M, MS, S, SC, and C the fluorine abundance is enhanced by
factors of 2--30 with respect to the solar abundance (Jorissen
et al. 1992). These low�mass stars are the only astrophysical
site observationally confirmed to produce fluorine. Hence, they
are good candidates to account for the Galactic abundance of
this element, even though recent observations of 19 F in the
LMC and ! Cen, where the abundance ratio of F/O declines
with the oxygen abundance, may support the hypothesis that
most fluorine is produced instead by massive stars (Cunha et al.
2003; Renda et al. 2004). In any case, the fluorine abundances
observed in giant stars are of considerable importance in
constraining the properties of asymptotic giant branch (AGB)
models. In AGB stars H and He shell burning with subsequent
He pulse driven convection (thermal pulse) changes the abun�
dance distribution between the H� and He�burning shells (He
intershell). Partial He burning in the He intershell converts
He into 12 C. After the occurrence of a thermal pulse, the con�
vective envelope can penetrate the He intershell and dredge
up material to the surface (third dredge�up [TDU]). The stellar
atmosphere becomes progressively rich in carbon, thus ex�
plaining the observed sequence of carbon enrichment from M
to S and C stars. These stars also show enhancements of ele�
ments produced by slow neutron captures (s�process) and are
934
The Astrophysical Journal, 615:934--946, 2004 November 10
# 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.

believed to be the main site for the production of s�process
nuclei with mass above '90 (Gallino et al. 1998; Travaglio
et al. 1999, 2001; Goriely & Mowlavi 2000).
The observed enhancements of fluorine in AGB stars indi�
cate a positive correlation with the carbon enhancements. This
can be explained if 19 F is also produced in the He intershell and
then dredged up to the surface together with 12 C and s�process
elements. Jorissen et al. (1992) proposed the following nu�
cleosynthesis path for the production of 19 F in the He intershell
of AGB stars. Neutrons produced via the 13 C(# , n) 16 O reaction
can be captured by 14 N, which is enriched from the preceding
H�burning stage where the CNO cycle dominates. The reaction
14 N(n, p) 14 C has a high cross section and produces free protons
and 14 C, which is converted by # �capture to 18 O; alternatively,
18 O can also be produced by # �capture on 14 N with subsequent
#�decay of 18 F. In core He burning, 18 O is converted by further
# �capture to produce 22 Ne via the reaction 18 O(# , #) 22 Ne;
however, in the He intershell 18 O and protons are present at
the same time, triggering the alternative reaction path 18 O( p,
# ) 15 N. Subsequent # �capture on 15 N eventually leads to the
production of 19 F, via 15 N(# , #) 19 F. The 15 N( p, # ) 12 C reaction
competes with the 18 O( p, # ) 15 N reaction and removes both
protons and 15 N from the chain of production of 19 F. The
abundance of 19 F is determined by the reaction rates associated
with this rather complex production path and by the 19 F de�
struction reaction in the He intershell, 19 F(# , p) 22 Ne.
In summary, the reactions that contribute to or affect the
production of fluorine are 13 C(# , n) 16 O, 14 N(n, p) 14 C, 14 N(# ,
#) 18 F, 14 C(# , #) 18 O, 18 O(# , #) 22 Ne, 15 N( p, # ) 12 C, together
with the alternative reaction chain 18 O( p, # ) 15 N(# , #) 19 F(# ,
p) 22 Ne. The theoretical studies of Forestini et al. (1992) and
Mowlavi et al. (1996) found that the above�described chain is
activated in the convective pulse when neutrons are released by
13 C from the H�burning ashes. However, only the lowest ob�
served abundances of 19 F could be explained. An extra amount
of 13 C is required to produce the observed 19 F and also to
match the observed enhancements of s�process elements. At
the end of each TDU where the convective envelope expands
into the stable radiative intershell zone, extra mixing processes
could lead to the formation of a zone where protons and 12 C are
partially mixed ( partial mixing zone). This would lead to ad�
ditional production of 13 C by the 12 C( p, #) reaction in the top
layers of the He intershell. Models including hydrodynamical
overshoot (Herwig 2000), rotation (Langer et al. 1999), or
the effect of gravity waves (Denissenkov & Tout 2003) have
in fact produced a partial mixing zone resulting in the forma�
tion of a 13 C ``pocket.'' Straniero et al. (1995) showed that
the 13 C formed in the pocket is completely destroyed by the
13 C(# , n) 16 O reaction before the onset of the next convective
pulse. By means of a parametric representation of the partial
mixing zone, Gallino et al. (1998) and Goriely & Mowlavi
(2000) showed that this model can explain the observed
properties of the s�process in AGB stars. In the 13 C pocket 15 N
is produced at conditions where the value of the proton�to� 12 C
ratio is close to unity (see also Mowlavi et al. 1998). This 15 N
is converted into 19 F when the pocket is ingested in the follow�
ing convective pulse. Goriely & Mowlavi (2000) analyzed the
effect of the presence of the partial mixing zone on the nu�
cleosynthesis of fluorine. These authors concluded that also by
taking into account the nucleosynthesis in the partial mixing
zone only the less fluorine�enriched stars could be explained.
The possible effect on the nucleosynthesis in the partial mixing
zone due to stellar rotation also did not seem to improve the
match with observations ( Herwig et al. 2003).
The aims of this paper are to update the study of the pro�
duction of 19 F in AGB stars and to explore the impact of the
uncertainties of nuclear reaction rates on the abundance of
fluorine produced in the framework of the current AGB star
models. First, we introduce the production of 19 F in AGB
models of a large range of masses and metallicities. We cal�
culate the stellar structure and then follow the nucleosynthesis
by making use of a postprocessing code. Our computations
represent an improvement with respect to previous computa�
tions for several reasons. First, we find the TDU to occur self�
consistently after a certain number of thermal pulses; hence, we
do not parameterize this process as done in all the previous
studies. If it is true that the amount of TDU is still uncertain
(see, e.g., Frost & Lattanzio 1996; Mowlavi 1999) and hence
can be parameterized, our approach is more consistent in the
fact that we not only deal with TDU as a way of mixing
fluorine to the stellar surface but also take into account the
feedback effect of TDU on the nucleosynthesis of 19 F in the
He intershell. As we show, this feedback has a large impact on
the production of 19 F. Second, our postprocessing code follows
the nucleosynthesis throughout all the different thermal pulses
previously computed by the evolutionary code. This was done
by Mowlavi et al. (1996) for three stellar models with a limited
number of pulses, but without including a partial mixing zone.
Goriely & Mowlavi (2000) included a partial mixing zone
in their calculations but only followed the nucleosynthesis
``during one representative interpulse and pulse phase,'' hence
missing the possible effects due to variations of the thermo�
dynamic features of each thermal pulse. Finally, our post�
processing code computes abundances of nuclei up to iron,
solving simultaneously the changes due to nuclear reactions
and those due to mixing, when convection is present. This
allows us, for example, to properly model the nucleosynthesis
that occurs at the delicate moment when the H�burning ashes
are progressively ingested in the convective pulse and the 13 C
present in the ashes burns via the (# , n) reaction while the
ingestion is occurring.
We discuss and compare results from a large set of stellar
models, analyze in detail the impact of the introduction of the
partial mixing zone and of the reaction rate uncertainties on the
3 M # Z � 0:02 model, and then present upper and lower limits
for the production of fluorine in several selected models. On
top of the comparison with spectroscopic observations of AGB
stars, our results are of relevance when studying the Galactic
chemical evolution of fluorine, as done recently by Renda et al.
(2004). The evolutionary and nucleosynthesis codes are pre�
sented in x 2. The production of fluorine in a large range of
stellar models is discussed in x 3. The effect of introducing a
partial mixing zone is discussed in x 3.1. The nuclear reactions
contributing to the production of 19 F are discussed in x 4,
together with the effect of their uncertainties on the production
of 19 F. In x 5 we present a final discussion and possible
directions for future work.
2. EVOLUTIONARY AND NUCLEOSYNTHESIS CODES
We computed the stellar structure for a large range of masses
(from M � 1 to 6.5 M
# ) and metallicities (Z � 0:0001, 0.004,
0.008, and 0.02) starting from the zero�age main sequence
up through many thermal pulses during the AGB phase using
the Mount Stromlo Stellar Structure Program ( Wood & Zarro
1981; Frost & Lattanzio 1996). Mass loss is modeled on the
AGB phase following the prescription of Vassiliadis & Wood
(1993), which accounts for a final superwind phase. Using
the prescription for unstable convective/radiative boundaries
PRODUCTION OF 19 F IN AGB STARS 935

described in detail by Lattanzio (1986), we find the TDU to
occur self�consistently for masses above 2.25 M
# at Z � 0:02,
above 1.5 M # at Z � 0:008, above 1.25 M # at Z � 0:004, and
for all the computed masses at Z � 0:0001. More details re�
garding these calculations can be found in Karakas (2003) and
for the 3 M # , Z � 0:02 model in Lugaro et al. (2003).
To calculate the nucleosynthesis in detail, we have used
a postprocessing code that calculates abundance changes due
to convective mixing and nuclear reactions (Cannon 1993).
The stellar structure inputs, such as temperature, density, ex�
tent of convective zones, mixing length, and mixing velocity
as functions of mass and model number, are taken from the
stellar evolutionary computations. Between evolution models
the postprocessing code creates its own mass mesh, resolving
regions undergoing rapid changes in composition and using a
combination of Lagrangian and non�Lagrangian points. Con�
vective mixing is done time dependently, with no assumptions
of instantaneous mixing. To model this, a ``donor cell'' scheme
is adopted in which each nuclear species is stored as two var�
iables representing two streams, one moving upward and one
moving downward. At each mass shell matter flows freely
from above or below with a certain degree of mixing and is also
exchanged between adjacent cells, from one stream to the
other.
Our nucleosynthesis network is based on 74 nuclear species,
with 59 nuclei from neutrons and protons up to sulphur and
another 14 nuclei near the iron group to allow neutron capture
on iron seeds. There is also an additional ``particle'' g for
counting the number of neutron captures occurring beyond
61 Ni, which simulates the s�process as neutron sink. The initial
abundances in the postprocessing calculations are taken from
Anders & Grevesse (1989). All proton, # �, and neutron cap�
tures and #�decays involving the species listed above are in�
cluded in the nuclear network, summing up to 506 reactions.
The bulk of reaction rates are from the REACLIB Data Tables
of nuclear reaction rates based on the 1991 updated version of
the compilation by Thielemann et al. (1986). The reaction rate
table has been updated using the latest experimental results,
which are listed in the Appendix. The reaction network is
terminated by a neutron capture on 61 Ni followed by an ad hoc
decay with k � 1 s #1 producing the particle represented by the
symbol g : 61 Ni(n; #) 62 Ni ! 61 Ni � g. Following the method
of Jorissen & Arnould (1989), we model neutron captures on
the missing nuclides by neutron sinks, meaning that the 34 S(n,
#) 35 S and 61 Ni(n, #) 62 Ni reactions are given some averaged
cross section values in order to represent all nuclei from 34 S
to 55 Mn and from 61 Ni to 209 Bi, respectively (see also Lugaro
et al. 2003; Herwig et al. 2003).
3. RESULTS FOR THE PRODUCTION OF FLUORINE
Our model predictions for the final 19 F intershell abundance
are shown in Figure 1. Note that these calculations do not
include a partial mixing zone. We find that the abundance of
19 F in the intershell is mostly dependent on two model features.
The first is the temperature at the base of the convective pulse.
As discussed by Mowlavi et al. (1996), this temperature de�
termines the efficiencies of the rates of production and de�
struction of 19 F. Below '2:2 ; 10 8 K , 15 N is not efficiently
converted into 19 F, while above '2:6 ; 10 8 K 19 F starts being
destroyed by the 19 F(# , p) 22 Ne reaction. The stellar model of
3 M # and Z � 0:02 of Mowlavi et al. (1996) was shown to
have pulse temperatures around the above range and hence to
be the most efficient case for the production of fluorine with
respect to the other two models presented by these authors: a
3 M
# , Z � 0:001 star and a 6 M
# , Z � 0:02 star. In the latter
case proton captures at the hot base of the convective envelope
(hot bottom burning) contribute to the destruction of fluorine.
Also in our models the maximum abundance of 19 F in the He
intershell at the end of the computed evolution is observed to
occur at around 3 M # , even though the temperatures are higher
in our models, up to '3 ; 10 8 K.
The second parameter that determines the abundance of
19 F in the intershell is the amount of TDU. This is demon�
strated by the fact that the maximum 19 F intershell abundance
as a function of the stellar mass is about double in the case of
Z � 0:008 what it is for Z � 0:02, which could appear at first
surprising. In fact, one would expect to find a lower 19 F
abundance at Z � 0:008 because the temperature in the con�
vective pulse is slightly higher: in the Z � 0:02 case it ranges
from 2:52 ; 10 8 K in the 10th pulse to 3:05 ; 10 8 K in the last
pulse, while in the Z � 0:008 case the temperature is around
3 ; 10 8 K in the last 10 pulses. Moreover, one would expect to
find the 19 F abundance decreasing with the metallicity of the
star since, when no partial mixing zone is included, its pro�
duction depends on the amount of 13 C in the H ashes, which is
of secondary nature, i.e., depends on the CNO abundances in
the star. However, the abundance of 12 C in the envelope is
a function of the amount of TDU. Since in our Z � 0:008
models the total mass dredged up by TDU is about twice that in
the Z � 0:02 models, there is a strong effect on the production
of 19 F due to the primary contribution to 13 C in the H�burning
ashes coming from the dredged�up 12 C.
Furthermore, the reason why the abundance of 19 F decreases
for masses lower than about 3 M
# is mostly due to the lower
TDU rather than the lower temperature in the convective pulse.
This is demonstrated by the fact that the abundance of 15 N in all
cases is insignificant with respect to that of 19 F, which means
that the fraction of 15 N that has not burned into 19 F is unim�
portant. Out of all the models, a maximum value of 2:5 ; 10 #6
for the final 15 N intershell mass fraction is computed for the
1 M # Z � 0:02 star, compared to the final 19 F mass fraction of
7 ; 10 #6 .
When comparing with the previous results of Mowlavi et al.
(1996), we find major differences due to two main reasons. The
first is the fact that we have computed a much larger number of
thermal pulses than Mowlavi et al. (1996). For example, for the
stellar model of 6 M # , Z � 0:02 we have computed 38 thermal
Fig. 1.---Mass fraction of 19 F in the He intershell after the last thermal pulse
computed for each model. No partial mixing zone was included in these
calculations.
LUGARO ET AL.
936 Vol. 615

pulses, while Mowlavi et al. (1996) computed 11 thermal
pulses. Hence, the temperature at the base of the last convec�
tive pulse, which increases with pulse number in AGB models,
is higher in our calculations. In our 6 M # , Z � 0:02 model the
temperature reaches 3:5 ; 10 8 K in the last thermal pulse,
which is higher than the value of 2:8 ; 10 8 K found by
Mowlavi et al. (1996) simply because our last pulse represents
a more advanced phase of the evolution. Hence, our final 19 F
abundance in the He intershell for this case is more than an
order of magnitude lower than that calculated by Mowlavi
et al. (1996). On the other hand , because the TDU is self�
consistently included in our calculations, we take into account
the effect of the presence of primary 12 C in the envelope dis�
cussed above; thus, the final 19 F abundance for the 3 M # ,
Z � 0:02 case in our calculation is about double that presented
by Mowlavi et al. (1996). The same conclusion can be drawn
when our results are compared with those of Forestini &
Charbonnel (1997), which are very similar to the results from
Mowlavi et al. (1996).
The production of fluorine in AGB stars is of interest also in
the light of the Galactic chemical evolution. In Figure 2 and
Table 1 we present yields for 19 F calculated for the different
model shown in Figure 1. Yields are a direct function of the
amount of TDU. They are calculated as net yields: M �
R #
0
(X # X 0 )(dM=dt) dt, where # is the total lifetime of the star,
dM/dt is the mass�loss rate, and X and X 0 refer to the current
and initial mass fraction of 19 F, respectively. The yield is
positive if 19 F is produced and negative if it is destroyed.
The 15 N yields are typically negative, decreasing from #0
for stars of 1 M # to '#2 ; 10 #5 for stars of 6 M # . This means
that this isotope is destroyed in all the models, except those
with Z � 0:0001 and mass higher than 2.25 M # . The 15 N yield
reaches a positive maximum of 4 ; 10 #6 for the highest mass
model computed at this metallicity (5 M
# ). This is due to
a combination of different factors: (1) the temperature at the
base of the convective envelope is as high as 9:7 ; 10 7 K in
this model, at which temperature the 14 N( p, #) 15 O reaction
becomes as important as the 15 N( p, # ) 12 C reaction and 15 N
can actually be produced by proton captures during hot bottom
burning; (2) the abundance of 14 N is extremely high because
of the operation of strong TDU and hot bottom burning; and
(3) the initial 15 N abundance (X 0 in the formula above) is very
low. The initial 19 F abundance is also very small; hence, the 19 F
yields for this metallicity are less negative for masses above
4 M # compared to more metal�rich models of the same mass.
In Figure 3 we compare some selected model predictions
with the observations by Jorissen et al. (1992). The metallicity
of the observed stars ranges from about Z � 0:006 to about
0.04 with an average of 0.016. Hence, the 2.5 M
# , Z � 0:004
model has a metallicity too low to be considered to match the
observations, and it is included in the figure only to illustrate
the trend of our results with metallicity. The 3 M # , Z � 0:008
model, which has the highest final 19 F abundance in the
intershell, does not represent a good match to the stellar data.
This is because the final C/O abundance in this model is 5.6,
while the stellar data have C/O up to about 1.5. It follows that
Fig. 2.---Yield of 19 F for each of the models presented in Fig. 1.
TABLE 1
19 F Yields in Solar Masses from All the Computed Stellar Models
M
(M # ) Z � 0:02 Z � 0:008 Z � 0:004 Z � 0:0001
1........................... 3.65E#8 2.37E#9 9.45E#10 5.14E#9
1.25...................... 1.59E#8 1.14E#8 6.23E#9 2.12E#7
1.50...................... 2.51E#8 2.02E#8 2.29E#8 . . .
1.75...................... 3.01E#8 9.01E#8 1.73E#7 5.43E#6
1.90...................... 2.83E#8 1.87E#7 4.96E#7 . . .
2.00...................... 2.72E#8 6.41E#7 . . . 1.05E#5
2.25...................... 1.20E#7 1.49E#6 3.87E#6 1.36E#5
2.50...................... 9.95E#7 3.36E#6 8.10E#6 4.56E#6
3.00...................... 3.93E#6 9.98E#6 6.89E#6 6.20E#8
3.50...................... 6.00E#6 2.52E#6 8.17E#7 . . .
4.00...................... 2.07E#6 8.33E#7 8.90E#8 2.74E#9
5.00...................... 6.12E#7 #1.18E#6 #6.50E#7 #6.94E#9
6.00...................... #2.18E#6 #1.62E#6 #8.41E#7 . . .
6.50...................... #2.45E#6 . . . . . . . . .
Note.---As in Fig. 2; no partial mixing zone included and reaction rates
from the Appendix.
Fig. 3.---Comparison of fluorine abundances observed by Jorissen et al.
(1992) and model predictions for selected stellar models: 3 and 5 M # with
Z � 0:02; 1.75 and 3 M # with Z � 0:008; and 2.5 M # with Z � 0:004. Pre�
dictions are normalized in such a way that the initial 19 F abundance corre�
sponds to the average F abundance observed in K and M stars, to which stellar
data are normalized (see Jorissen et al. 1992). Each symbol on the prediction
lines represents a TDU episode. Note that for the 2.5 M # , Z � 0:004 model
the final C=O � 11 and � 19 F= 16 O# � 1:7 are outside the range of the plot.
Crossed MS, S symbols denote stars with large N excesses.
PRODUCTION OF 19 F IN AGB STARS 937
No. 2, 2004

since the large 19 F abundance in this model is a consequence
of the large 12 C abundance in the envelope, we cannot take
this model to explain the highest observed values. ( We note,
however, that stars with the high C/O ratio and high 19 F abun�
dance produced by this model may in principle exist but may
be obscured by their dusty envelopes.) It should also be con�
sidered that the observational data regarding SC stars require
revision. For these stars it is difficult to derive reliable abun�
dances because of the poor modeling of the atmospheres when
C=O#1.
The problem of matching the highest observed 19 F abun�
dance could be overtaken by the inclusion of extra mixing
processes at the base of the convective envelope, also referred
to as cool bottom processing. This process occurs during the
first red giant phase in stars with M # 2:5 M # (see, e.g.,
Charbonnel 1995), as well as possibly during the AGB phase
( Nollett et al. 2003), and results in a lower 12 C/ 13 C ratio than
the standard models, as required by the observations. This type
of extra mixing is described as the circulation of material from
the base of the convective envelope into the thin radiative re�
gion located on top of the H�burning shell. Here the material is
processed by proton captures and then carried back to the en�
velope, thus producing the signature of CNO processing at the
stellar surface. Some of the MS and S stars with the highest
[ 19 F/ 16 O] ratios for a given C/O ratio are also enhanced in N, up
to 2.5 times the initial value (see Fig. 3 and discussion in
Jorissen et al. 1992). This N enhancement could be due to cool
bottom processing. If this process is at work, the surface
12 C/ 16 O ratio would appear to be lower than computed in our
calculations. On the other hand, if the temperature at which the
material is carried by cool bottom processing is lower than
about 30 million degrees, at which value the 19 F( p, # ) 16 O
reaction is activated, then the 19 F abundance would be un�
changed. This is because the 19 F production depends on the
amount of 13 C in the H�burning ashes, which is a by�product of
CNO cycling, and would not in principle be different if the
CNO cycling occurs only in the H�burning shell or also at the
base of the convective envelope via cool bottom processing.
Then the theoretical curves of Figure 3 would be simply shifted
to the left, making it easier to explain the observed 19 F abun�
dances, together with the N excess. Note that WZ Cas is the
only Li�rich star of the sample and has a very low 12 C/ 13 C ratio,
a composition that is in agreement with this extra mixing. Cool
bottom processing in the AGB phase is very uncertain, and
detailed computations are not yet available. Since it has not
been included in our computations, we cannot draw any quan�
titative conclusions on its possible effects.
Limiting the discussion to our current models, as shown in
Figure 3, at C=O #1 the 3 M # , Z � 0:02 model shows a higher
19 F abundance in the envelope than the 3 M # , Z � 0:008
model. In the 5 M
# , Z � 0:02 model, hot bottom burning is at
work; hence, both 12 C and 19 F are destroyed. When comparing
to previous calculations for the 3 M # , Z � 0:02 model, we find
that our final [ 19 F/ 16 O] ratio in the envelope is about 0.25 dex
higher than that computed by Forestini & Charbonnel (1997)
and Mowlavi et al. (1996) for the same C=O ' 1:2 ratio, which
reflects our higher fluorine intershell abundance.
3.1. The Impact of the Partial Mixingg Zone
To study the effect of the introduction of a partial mixing
zone, we have included artificially in the postprocessing
calculation a partial mixing zone at the end of each TDU epi�
sode. We have made the choice to include the partial mixing
zone only when TDU occurs because during TDU a sharp
discontinuity is produced between the convective envelope and
the radiative intershell, which is a favorable condition for the
occurrence of mixing (see, e.g., Iben & Renzini 1982). Since
the question of the specific shape of the H profile and the
mixing processes leading to the partial mixing zone is still
open, we opted for a reasonable choice of the proton profile in
which the number of protons decreases exponentially with the
mass depth below the base of the convective envelope. We
define as the partial mixing zone the region where the number
of protons ranges from the envelope value to X p � 10 #4 . In this
way about 1
4 of the extent of the partial mixing zone has
a number of protons between X p � 0:002 and 0.02, corre�
sponding to the efficient range for the production of 15 N
(see Goriely & Mowlavi 2000). Note that Goriely & Mowlavi
(2000) defined the partial mixing zone with the number of
protons ranging from the envelope value to X p � 10 #6 so that
# 1
6 of its extent corresponds to the efficient range for the pro�
duction of 15 N. For the extent of the partial mixing zone we
considered a value of M pmz � 0:001 M # , i.e., 1/15 of the mass
of the last convective pulse for the 3 M # , Z � 0:02 model. The
dilution is higher for earlier pulses that have higher mass. This
is a typical value adopted in the previous nucleosynthesis
calculations (Gallino et al. 1998; Goriely & Mowlavi 2000).
In Figure 4 we show the abundance of 15 N and 19 F in the
intershell during the period of convective instability following
each thermal pulse for the 3 M # , Z � 0:02 model. The final
abundances in each pulse can be identified as those cor�
responding to the pulse number tick mark in the x�axis. At
the beginning of a thermal pulse, while the convective insta�
bility is ingesting the H�burning ashes, 15 N is produced and its
abundance sharply increases. At the same time the abundance
of 19 F decreases because of the dilution of the intershell ma�
terial with H�burning ashes where the abundance of 19 F is
solar. Subsequently, 15 N is transformed into 19 F. In thermal
pulses followed by TDU in our model, i.e., from the 10th
thermal pulse onward, almost all 15 N is destroyed. The max�
imum temperature at the base of the 10th thermal pulse is
equal to 2:52 ; 10 8 K and 15 N is reduced to about 1/10 of its
initial abundance in this pulse. In later pulses the temperature
grows, reaching 3:05 ; 10 8 K in the last thermal pulse so that
Fig. 4.---Abundance in number of 15 N (crosses) and 19 F ( filled circles) in
the He intershell as a function of the pulse number for the 3 M # , Z � 0:02
model with a partial mixing zone of mass 0.001 M # included after each TDU
episode, i.e., after the 10th thermal pulse. Abundances are plotted only during
the time when the convective shell is present. The final abundances for each
pulse are those corresponding to the pulse number tick mark in the x�axis.
LUGARO ET AL.
938 Vol. 615

15 N is destroyed with even higher efficiency. In the very last
few pulses also about 25% of the 19 F produced is destroyed.
The effect of the partial mixing zone appears after the 11th
thermal pulse where we observe large changes in the intershell
abundances. For example, the amount of 15 N and 19 F suddenly
increases: in the 11th thermal pulse the abundance of 19 F is
about 2.5 times higher than that in the 10th thermal pulse.
The final abundance of 19 F in the intershell is '70% higher
with respect to the case with no partial mixing zone included
(shown in Fig. 1).
The extent in mass and the proton profile of the partial
mixing zone are very uncertain parameters. Most studies that
have self�consistently produced a partially mixed zone find that
the extent in mass is smaller than the 0.001 M # value that we
have used. The computed M pmz is of the order of 10 #6 M # with
rotation, of 10 #5 M
# with overshoot ( but depending on the free
overshoot parameter!), and of 10 #4 M # with gravitational
waves. A partial mixing zone of larger extent, 5 ; 10 #4 M # ,
was reported to result from semiconvection in a low�metallicity
star ( Hollowell & Iben 1988). On the other hand, previous nu�
cleosynthesis studies have artificially considered partial mixing
zones of extent up to 1/10 of the mass of the convective pulse.
To check the uncertainty introduced by the extent of the par�
tial mixing zone, we varied this parameter, thus computing
three cases in total: one without the zone included, and the
other two with the mass of the zone equal to M pmz � 0:001 and
0.002 M # .
The results are presented in Figure 5 and show that the
variation of the final abundance of 19 F in the envelope is up to a
factor of #2 when the mass extent of the partial mixing zone is
varied in the range described above. This could probably be
considered as an upper limit for the uncertainty since a mass
of M pmz � 0:002 M
# is a large value to consider within the
framework of the current models. A higher mass in fact would
imply that the mixing process carrying protons into the He
intershell region involves a large fraction of the intershell mass,
which is not what the current studies indicate. We can only
make a qualitative comparison with the results obtained by
Goriely & Mowlavi (2000) since the stellar model consid�
ered and the computation procedure are different. Our case
with M pmz � 0:001 M # and the case presented by Goriely &
Mowlavi (2000) with k pm � M pmz =M convective shell � 0:1 should
have very similar values for the extent of the region where
the production of 15 N is efficient in the partial mixing zone,
corresponding to #1/60 of the total mass of the intershell.
However, for this case the increase in the [ 19 F/ 16 O] ratio that
we computed is more than 0.3 dex higher for the same C/O
value around 1.2 than that presented in Figure 12 of Goriely &
Mowlavi (2000). This is probably due to the fact that we have
self�consistently taken the TDU into account.
The introduction of a partial mixing zone in some selected
stellar models is illustrated in Table 2, where the 19 F yields are
reported from computations performed without (col. [2]) and
with (col. [3]) the inclusion of the partial mixing zone. In the
5 M # model the extent in mass of the intershell decreases from
about 0.005 M # to about 0.001 M # at the end of the evolution.
Hence for this model we have introduced a partial mixing zone
of mass 0.001 M # . Note also that in principle we do not know
if and how the formation of the partial mixing zone is a
function of the stellar properties. In the stellar models with
mass '3 M # the effect of the partial mixing zone introduces
a factor of 2.6 uncertainty in the final yield; in the 5 M
# ,
Z � 0:02 model the uncertainty is of about a factor of 4; while
in the low�mass model, 1.75 M # , the uncertainty is of a factor
of 14 in the final yield. However, as is discussed in x 4, this
effect strongly depends on the uncertainties associated with the
14 C(# , #) 18 O reaction rate.
4. SUMMARY OF REACTION RATE STUDIES
There has been a considerable effort and improvement in the
determination of the nuclear reaction rates over the last few
years since the early 19 F nucleosynthesis studies. In particular,
new measurements of key reactions such as 14 C(# , #) 18 O,
14 N(# , #) 18 F, 15 N(# , #) 19 F, and 18 O(# , #) 22 Ne provided new
information on low�energy resonances that were ignored or
only insufficiently included in previous simulations of 19 F
nucleosynthesis. The results of all these studies are summa�
rized and discussed in the following section. The main impli�
cation for the present study is that the new experimental results
put a more stringent limit on the reaction rates and therefore
reduce considerably the associated uncertainties compared to
the uncertainties listed in the NACRE compilation (Angulo
et al. 1999). There has not been much improvement in the
18 O( p, # ) 15 N rate, and there has been very little experimental
effort in the study of 19 F(# , p) 22 Ne. We therefore discuss the
present nuclear physics--related uncertainties associated with
both rates. For the latter case we also give a new reaction rate
estimate based on experimental information and nuclear struc�
ture information on the compound nucleus 23 Na rather than on
simple penetrability arguments.
4.1. The Reaction Rate of 13 C(# ; n) 16 O
For the 13 C(# , n) 16 O reaction, we have used the rate from
Drotleff et al. (1993) and Denker et al. (1995), which is about
Fig. 5.---Comparison of fluorine abundances observed by Jorissen et al.
(1992) and model predictions for the 3 M # , Z � 0:02 model and different
choices of the extent of the partial mixing zone. The bare line represents the
cases in which no partial mixing zone is included. The lines accompanied by
tiny filled and open circles refer to cases computed with a partial mixing zone
with mass extent M pmz � 0:001 and 0.002 M
# , respectively. As in Fig. 3,
crossed MS, S symbols denote stars with large N excesses, and predictions are
normalized in such a way that the initial 19 F abundance corresponds to the
average F abundance observed in K and M stars, to which stellar data are
normalized (see Jorissen et al. 1992).
PRODUCTION OF 19 F IN AGB STARS 939
No. 2, 2004

50% lower than the rate recommended by NACRE in the
temperature range of interest. Recent 13 C( 6 Li, d ) # �transfer
studies ( Kubono et al. 2003) suggest a very small spectroscopic
factor of S # � 0:01 for the subthreshold state at 6.356 MeV.
This indicates that the high�energy tail for this state is negligible
for the reaction rate, in agreement with the present lower limit.
However, a detailed reanalysis by Keeley et al. (2003) of the
transfer data leads to significantly different results for the
spectroscopic factor of the subthreshold state S # � 0:2, which
would imply good agreement with the value used in this paper.
This situation requires further experimental and theoretical
study. A reevaluation of the rate based on new experimental
results has been performed by Heil (2002) and will be published
in a forthcoming paper. The choice of the 13 C(# , n) 16 O reaction
within the current possibilities only slightly affects the pro�
duction of 15 N and 19 F. Using the rate by Denker et al. (1995) in
the 3 M # , Z � 0:02 model with a partial mixing zone of mass
0.002 M
# gives an 8% increase in the final surface 19 F with
respect to the calculation done using the NACRE rate. This
result can be understood when the 13 C(# , n) 16 O rate is com�
pared to the 14 C(# , #) 18 O reaction, as discussed in the next
subsection.
4.2. The Reaction Rate of 14 C(# ; #) 18 O
The reaction 14 C(# , #) 18 O has been studied experimentally
in the energy range of 1.13--2.33 MeV near the neutron thresh�
old in the compound nucleus 18 O by Go�rres et al. (1992). The
reaction rate is dominated at higher temperatures by the direct
capture and the single strong 4 + resonance at center�of�mass
energy E cm � 0:89 MeV. Toward lower temperatures, which
are of importance for He shell burning in AGB stars, impor�
tant contributions may come from the 3 # resonance at E cm �
0:176 MeV (E x � 6:404 MeV) and a 1 # subthreshold state at
E x � 6:198 MeV. It has been shown in detailed cluster model
simulations that neither one of the two levels is characterized
by a pronounced # cluster structure (Descouvemont & Baye
1985). The strengths of these two contributions are unknown
and have been estimated by Buchmann et al. (1988), adopt�
ing an # spectroscopic factor of # 2
# � 0:02 and 0.06 for the
6.404 and 6.198 MeV states, respectively, for determining
the 0.176 MeV resonance strength and the cross section of the
high�energy tail of the subthreshold state. While the value for
the 6.404 MeV state is in agreement with the results of a
14 C( 6 Li, d ) 18 O # �transfer experiment (Cunsolo et al. 1981),
the value for the 6.2 MeV state appears rather large since the
corresponding # �transfer was not observed. This reflects the
lack of appreciable # �strength in agreement with the theoretical
predictions. We therefore adopted an upper limit for the spec�
troscopic factor of this resonance of # 2
# � 0:02. The upper limit
for the reaction rate is based on the experimental data (Go�rres
et al. 1992) plus the low�energy resonance contributions cal�
culated from the upper limit for the # spectroscopic factor.
For the recommended reaction rate we adopted a considerably
smaller spectroscopic factor # 2
# � 0:01 for calculating the !#
strength of the 0.176 MeV resonance. In this we followed the
recommendations by Funck & Langanke (1989). The lower
limit of the reaction rate neglects the contribution of this reso�
nance altogether and corresponds directly to the experimental
results (Go�rres et al. 1992). It should be noted, however, that the
uncertainty for the resonance strength and therefore its contri�
bution to the reaction rate is up to 5 orders of magnitude as
shown in Figure 6.
The 14 C(# , #) 18 O reaction can be activated together with
the 13 C(# , n) 16 O reaction during the interpulse period, in both
the partial mixing zone and the deepest layer of the region
composed by H�burning ashes, when 14 N(n, p) 14 C occurs,
and it represents the main path to the production of 18 O and
subsequently of 15 N. The importance of the nucleosynthesis
of 15 N during the interpulse periods is very much governed
by the choice of the rate of the 14 C(# , #) 18 O reaction. The
closer, or higher, this rate is to that of the 13 C(# , n) 16 O re�
action, the more efficient is the production of 15 N because
18 O and protons are produced together. The effect of the
partial mixing zone and hence the uncertainties related to it
are in fact much less important when using our recommended
rate, since in the temperature range of interest our rate is
more than an order of magnitude lower than our standard rate
from NETGEN (Jorissen & Goriely 2001), which was also
used in the previous study by Goriely & Mowlavi (2000; see
Fig. 7). At the temperature of interest the NETGEN rate is
based on previous theoretical studies by Funck & Langanke
(1989) and Hashimoto et al. (1986). When using our rec�
ommended rate to compute the 3 M # , Z � 0:02 model with a
partial mixing zone of mass 0.002 M
# , the final [ 19 F/ 16 O] is
the same as that computed without the partial mixing zone
within 10%.
TABLE 2
19 F Yields in Solar Masses from Selected Stellar Models
Rates
(1)
Standard a
(2)
Standard a
(3)
Recommended b
(4)
Upper c
(5)
Lower d
(6)
M pmz (M # ) ............ 0 0.002 e 0.002 e 0.002 e 0.002 e
3, 0.02 .................. 3.93E#6 1.01E#5 6.49E#6 7.10E#6 4.78E#6
5, 0.02 .................. 6.12E#7 2.46E#6 3.21E#6 4.06E#6 6.18E#7
1.75, 0.008 ........... 9.01E#8 1.23E#6 5.39E#7 5.96E#7 4.37E#7
3, 0.008 ................ 9.98E#6 2.23E#5 1.94E#5 2.09E#5 1.36E#5
2.5, 0.004 ............. 8.10E#6 1.96E#5 1.60E#5 1.69E#5 1.21E#5
Notes.---Since each model run takes at least one CPU day, it is unfeasible to repeat all the calculations
presented in x 3. More calculations will be performed under specific requests.
a As listed in the Appendix.
b As described in x 4, specifically: 14 N(# , #) 18 F from Go�rres et al. (2000), 18 O(# , #) 22 Ne from Dababneh
et al. (2003), and our recommended values for 14 C(# , #) 18 O and 19 F(# , p) 22 Ne.
c Upper limit for the 14 C(# , #) 18 O rate and lower limit for the 19 F(# , p) 22 Ne rate (x 4) to obtain the upper
limit for the yields.
d Lower limit for the 14 C(# , #) 18 O rate and upper limit for the 19 F(# , p) 22 Ne rate (x 4) to obtain the lower
limit for the yields.
e But 0.001 in the 5, 0.02 models.
LUGARO ET AL.
940 Vol. 615

4.3. The Reaction Rate of 14 N(# ; #) 18 F
The low�energy resonances in 14 N(# , #) 18 F have recently
successfully been measured by Go�rres et al. (2000). Previous
uncertainties about the strengths of these low�energy reso�
nances were removed. Because of these results, the reaction
rate is reduced by about a factor of 3 compared to NACRE.
The 14 N(# , #) 18 F reaction is inefficient at the temperature
of neutron release in the partial mixing zone while it is acti�
vated in the convective pulse. Hence, its rate only affects the
production of 19 F in the pulse. Using the new rate by Go�rres
et al. (2000) with respect to the rate by Caughlan & Fowler
(1988, hereafter CF88), which is the same as NACRE within
10%, only very marginally changes the production of 19 F. For
Fig. 6.---Recommended lower and upper limits for the rates of the 14 C(# , #) 18 O, 18 O(# , #) 22 Ne, and 19 F(# , p) 22 Ne reactions.
PRODUCTION OF 19 F IN AGB STARS 941
No. 2, 2004

example, in the 3 M # Z � 0:02 model with a partial mixing
zone of mass 0.002 M
# the final abundance in the envelope is
increased by about 5% using the new rate.
4.4. The Reaction Rate of 15 N(# ; #) 19 F
The reaction rate of 15 N(# , #) 19 F was taken from NACRE.
The rate is dominated by the contribution of three low�energy
resonances. The resonance strengths are based on the analysis
of de Oliveira et al. (1996). It should be noted, however, that
there were several recent experimental studies that point toward
a significantly higher reaction rate. De Oliveira et al. (1997)
already suggested higher resonance strengths than given in
their earlier paper. Direct # �capture measurements of the two
higher energy states by Wilmes et al. (2002) also indicate higher
strengths. A recent indirect # �transfer analysis to the three res�
onance levels by Fortune & Lacaze (2003) does suggest even
higher values for the resonance strengths. Altogether the re�
action rate of 15 N(# , #) 19 F used in this work might be under�
estimated by a factor of 5.
Using the reaction rate by CF88 for 15 N(# , #) 19 F, which is
about 50 times higher with respect to the new estimate by de
Oliveira et al. (1996), did not change the results in the 3 M #
Z � 0:02 model with a partial mixing zone of mass 0.002 M
# .
The final 19 F abundance in the envelope increased by a few
percent only. This is because the temperature in the thermal
pulses is high enough that in any case all 15 N is transformed in
19 F, as shown in Figure 4. This point was discussed by de
Oliveira et al. (1996), who showed that at temperatures higher
than '2:6 ; 10 8 K, such as those in our thermal pulses followed
by TDU, the difference between using the two rates is minimal.
Hence, even if the final rate will actually be higher than the
latest estimate, this will not make a difference to the final
results. A maximum increase of 35% in the final 19 F intershell
abundance would occur in the case of the 1 M # , Z � 0:02
model, assuming that all 15 N would burn into 19 F (see x 3).
4.5. The Reaction Rate of 15 N( p; # ) 12 C
The 15 N( p, # ) 12 C reaction has been investigated by Schardt
et al. (1952), Zyskind & Parker (1979), and more recently by
Redder et al. (1982) at E p ( lab) � 78 810 keV. These results
were summarized and compiled by NACRE. The reaction
rate at T 9 # 0:2 is dominated by the J #
� 1 # resonance at E p �
334 keV. However, contributions from three other resonances
at 1027, 1639, and 2985 keV have been included as well.
Using the NACRE rate, which is up to a factor of 2 higher than
the rate by CF88, we obtain a small decrease of '8% in the
final surface abundance of 19 F in the 3 M
# , Z � 0:02 model
with a partial mixing zone of mass 0.002 M # .
4.6. The Reaction Rate of 18 O(# ; #) 22 Ne
The 18 O(# , #) 22 Ne reaction is of interest for the discussion
of 19 F production in AGB stars since it competes with the
18 O( p, # ) 15 N process. A strong rate might lead to a reduction in
19 F production. The reaction rate of 18 O(# , #) 22 Ne has been last
summarized and discussed by Ka�ppeler et al. (1994) and by the
NACRE compilation. The main uncertainties result from the
possible contributions of low�energy resonances that have been
estimated on the basis of # �transfer measurements by Giesen
et al. (1994). A recent experimental study of 18 O(# , #) 22 Ne
by Dababneh et al. (2003) led to the first successful direct
measurement of the postulated low�energy resonances at 470
and 566 keV, thus reducing to 33% the previous uncertainty
of about a factor of 30 given by NACRE at the temperature of
interest, which was given by taking the previously available
experimental upper limit for the 470 keV resonance strength
(Giesen et al. 1994). The new rate is shown in Figure 6. Not
measured still is the 218 keV resonance, which is expected to
dominate the rate at temperatures of T # 0:1 GK , well below
the temperature in typical He�burning conditions. The resulting
reaction rate is in very good agreement with the previous es�
timate by Ka�ppeler et al. (1994), which was used for our cal�
culations of 19 F production.
4.7. The Reaction Rate of 18 O( p; # ) 15 N
The reaction 18 O( p, # ) 15 N provides a major link for the
production process of 19 F. The reaction cross section has
been measured by Lorenz�Wirzba et al. (1979) down to ener�
gies of #70 keV. Possible contributions of low energy near
threshold resonances were determined by Wiescher & Kettner
(1982) and Champagne & Pitt (1986) using direct capture and
single�particle transfer reaction techniques. These results were
compiled and summarized by NACRE. The reaction rate un�
certainties are less than an order of magnitude, as well as less
than a factor of 2 in the range of temperature of interest, and are
mainly related to uncertainties in the reasonably well studied
single�particle structure of these threshold resonance states.
The NACRE rate is the same within 10% of the rate given by
CF88. Hence, we do not currently have major uncertainties on
the 19 F production coming from this rate.
4.8. The Reaction Rate of 19 F(# ; p) 22 Ne
The reaction rate of 19 F(# , p) 22 Ne is one of the most
important input parameters for a reliable analysis of 19 F nu�
cleosynthesis at AGB stars. However, there is very little ex�
perimental data available for the 19 F(# , p) 22 Ne reaction cross
section at low energies. Experiments were limited to the higher
energy range above E # � 1:3 MeV (Kuperus 1965). CF88
suggested a rate that is based on a simple barrier penetration
model previously used by Wagoner (1969). This reaction rate
is in reasonable agreement with more recent Hauser�Feshbach
estimates assuming a high level density (see Thielemann et al.
1986) and has therefore been used in most of the previous
Fig. 7.---Rate for the 13 C(# , n) 16 O reaction ( Drotleff et al. 1993; Denker
et al. 1995; solid line) compared to two different choices for the 14 C(# , #) 18 O
reaction rate: NETGEN (dot�dashed line) and our recommended rate (dashed
line) in the range of temperature at which the 13 C(# , n) 16 O reaction is acti�
vated in the 13 C pocket.
LUGARO ET AL.
942 Vol. 615

nucleosynthesis simulations. The applicability of the Hauser�
Feshbach model, however, depends critically on the level den�
sity in the compound nucleus system (Rauscher et al. 1997).
We analyzed the level density in the compound nucleus 23 Na
above the # �threshold of Q # � 10:469 MeV as compiled by
Endt & van der Leun (1978) and Endt (1990). The typical level
density is #0.02 keV #1 . This level density is confirmed di�
rectly for the 19 F(# , p) reaction channel by direct studies from
Kuperus (1965) at resonance energies above 1.5 MeV and fur�
ther confirmed by as yet unpublished low�energy 19 F(# , p)
resonance measurements of C. Ugalde (2004, unpublished).
This low resonance density translates into an averaged level
spacing of D # 50 keV, which is considerably larger than the
average resonance width of # # 8 keV in this excitation range.
Based on these estimates, the requirement of D # # for the
applicability of the Hauser�Feshbach approach (Rauscher et al.
1997) is not fulfilled. The reaction rate for 19 F(# , p) 22 Ne
therefore needs to be calculated from determining the strengths
!# for the single resonances,
!# �
(2J � 1)
2
# # # p
# tot
: �1�
We estimated the # partial width # # using a simple WKB
approximation with an average # spectroscopic factor of
C 2 S # � 0:001 . This average spectroscopic factor was deter�
mined from determining the average # �strength distribution
from the strengths of observed # �capture resonances at higher
energies ( Kuperus 1965) and from the # spectroscopic strengths
of bound states in 23 Na ( Fortune et al. 1978). The total widths
# tot of the levels correspond in all cases to the proton partial
widths #p ; therefore, the resonance strength depends entirely
on the spin J and the # partial width # # of the resonance levels.
For the higher energy range E # #1:5 MeV we used directly
the experimentally determined resonance strengths by Kuperus
(1965). The resulting reaction rate is shown in Figure 6 and
deviates considerably from the Hauser�Feshbach prediction; in
the temperature range of intershell He burning it is more than
1 order of magnitude smaller than predicted in the Hauser�
Feshbach estimate. The possibility of ``missing strength'' in as
yet unobserved resonances seems unlikely as shown by the
previous 19 F(# , p) studies but cannot be completely excluded.
However, a substantial increase in the reaction rate would
rather be associated with a large # �strength of the low�energy
unbound states in 23 Na. Therefore, an experimental confirma�
tion of the here predicted resonance strength distribution is
desirable for a wide energy range.
Using our new recommended rate, for example, in the
3 M # , Z � 0:02 model, the final [ 19 F/ 16 O] is 0.1 dex higher
than in the case computed using the CF88 rate. The effect of
this rate and its uncertainties is larger for higher mass models,
where the temperature is higher and the 19 F(# , p) 22 Ne is more
activated.
4.9. Other Rates of Interest
The 13 C( p, #) 14 N reaction is of interest regarding the for�
mation of 13 C in the partial mixing zone. The experimental rate
by King et al. (1994) is 1.29 times higher than the rate given
by CF88 at the temperature of interest, and the revision by
NACRE, which we used, gives a rate 1.20 times higher than
CF88. A higher rate will result in a lower 13 C abundance and a
lower neutron flux during the interpulse period. Calculations
for the 3 M # , Z � 0:02 model showed that the difference of
10% less between NACRE and the rate by King et al. (1994)
yields a 5% increase in the 15 N produced during the interpulse
and a 6% increase in the final surface 19 F. We also checked that
within the current uncertainties of the 14 N(n, p) 14 C rate ('10%;
Gledenov et al. 1995) and the less important 14 N(n, #) 15 N rate
(uncertainties of a factor of about 2.5; Beer et al. 1992), the
final results do not change.
5. DISCUSSION AND CONCLUSIONS
Using the new rates presented in the previous section, in
particular for the 14 C(# , #) 18 O and the 19 F(# , p) 22 Ne reactions,
we have calculated recommended upper and lower limits for
the production of 19 F in selected stellar models (Table 2). The
runs computed with no inclusion of the partial mixing zone
(col. [2]) can be considered, within our models, as absolute
lower limits for the 19 F yields. The runs computed with the
recommended rates and including the partial mixing zone
(col. [4]) show a decrease in the yield with respect to the same
runs computed with the ``standard'' rates (col. [3]), except for
the 5 M # , Z � 0:02 model. This decrease is due to our estimate
of the 14 C(# , #) 18 O reaction, which makes the contribution of
the partial mixing zone to the production of 19 F much less
significant. In the case of the 5 M # , Z � 0:02 model the yield
increases by a factor of 1.3 owing to the fact that the temper�
atures in this intermediate�mass model are higher than in the
other models and hence the effect of our lower estimate for the
19 F(# , p) 22 Ne rate is more important. The overall uncertainties
in the 19 F production due to the uncertainties in the reaction
rates are about 50% in the stellar models with mass '3 M # and
about 40% in stellar models of lower mass. For the 5 M # ,
Z � 0:02 stellar model the uncertainties are about a factor
of 7, as a result of the large uncertainties of the 19 F(# , p) 22 Ne
rate.
The 19 F(# , p) 22 Ne reaction rate also influences the produc�
tion of fluorine in the winds of Wolf�Rayet stars; hence, models
of this type of stars should also be revised to test the effect of
our revised rate and its uncertainties. It is also important to
note that our estimated lower limit for the 19 F(# , p) 22 Ne rate is
about 4 orders of magnitude lower than the 22 Ne(# , n) 25 Mg
reaction rate. In this case the 19 F(n, #) 20 F reaction has to be
taken into account as a possible destruction channel for 19 F
when a significant neutron flux is released in the convective
pulses of AGB stars and in Wolf�Rayet stars by the 22 Ne(# ,
n) 25 Mg reaction.
For the 3 M
# , Z � 0:02 model surface abundances are also
shown in Figure 8 for a given choice of the partial mixing zone
with M pmz � 0:002 M # . With the new estimate for the 14 C(# ,
#) 18 O rate the contribution of the partial mixing zone is di�
minished, making this uncertain parameter less important. In
particular, in the lower limit case, the resulting [ 19 F/ 16 O] ratio
is the same within 10% as computed without including the
partial mixing zone (compare to Fig. 5). In none of the cases
we calculated could the highest [ 19 F/ 16 O] values observed
be reproduced. As discussed in x 3, this problem should be
reviewed with the inclusion in future calculations of extra
mixing processes (cool bottom processing) at the base of the
convective envelope.
Future work should also improve our knowledge of the
formation and the nucleosynthesis in the partial mixing zone.
One hypothesis is that rotation can play a role in varying the
efficiency of the production of 19 F and of the s�process ele�
ments ( Herwig et al. 2003). It will be of much interest to
analyze the effects of this hypothesis on the correlation be�
tween fluorine and the s�process elements and to revise the
PRODUCTION OF 19 F IN AGB STARS 943
No. 2, 2004

available observational data. Using data for carbon stars from
Utsumi (1985), it appeared that these two quantities were
correlated in AGB stars; however, using more recent and
precise data from Abia et al. (2002), this correlation does not
seem to appear anymore.
Another problem is related to C(J) stars. It is still unknown if
these stars actually belong to the AGB group or if they are in
some other phase of the evolution. Moreover, it appears that
their [ 19 F/ 16 O] ratios around 0.6 are due to a low abundance of
16 O rather than a high abundance of 19 F. Finally, the observa�
tional data regarding SC stars should be updated using more
recent atmospheric models.
M. L. deeply appreciates the hospitality and support ex�
tended to her by Michael Wiescher, Joachim Go�rres, and
Claudio Ugalde during a visit to Notre Dame University,
as well as the hospitality received by John Lattanzio and
Amanda Karakas during a visit to Monash University. We
thank Roberto Gallino, Enrico Arnone, Stefano Masera, and
Richard Stancliffe for discussion and help. The manuscript
was much extended and improved following strong criticisms
by the anonymous referee. This work was supported by the
Australian Research Council and the Australian Partnership for
Advanced Computing. Computational resources used for this
study were also partly funded by the Canada Foundation for
Innovation (CFI ) and the Nova Scotia Research and Innova�
tion Trust (NSRIT ) Fund.
APPENDIX
DETAILS OF THE REACTION RATES USED IN THE REFERENCE CASE
References for proton, # �, and neutron captures that we have used in the nucleosynthesis calculations are presented in Tables 3,
4, and 5, respectively. All of the reactions not listed in the tables are taken from the REACLIB Data Tables (version 1991).
TABLE 3
Proton Captures
Reaction References
7 Be( p, #) 8 B.................................................... Hammache et al. (1998)
13 C( p, #) 14 N .................................................. Angulo et al. (1999)
14 C( p, #) 15 N .................................................. Wiescher et al. (1990)
13 N( p, #) 14 O .................................................. Decrock et al. (1993)
17 O( p, #) 18 F................................................... Blackmon et al. (1995), Landre � et al. (1990)
17 O( p, # ) 14 N ................................................. Blackmon et al. (1995), Landre � et al. (1990)
18 F( p, #) 19 Ne ................................................. Utku et al. (1998)
18 F( p, # ) 15 O .................................................. Utku et al. (1998)
21 Ne( p, #) 22 Na............................................... El Eid & Champagne (1995)
22 Ne( p, #) 23 Na............................................... El Eid & Champagne (1995)
22 Na( p, #) 23 Mg.............................................. Stegmu � ller et al. (1996), Schmidt et al. (1995), Seuthe et al. (1990)
23 Na( p, #) 24 Mg.............................................. El Eid & Champagne (1995)
23 Na( p, # ) 20 Ne .............................................. El Eid & Champagne (1995)
24 Mg( p, #) 25 Al .............................................. Powell et al. (1999)
25 Mg( p, #) 26 Al g .......................................... Iliadis et al. (1996), Iliadis et al. (1990)
26 Mg( p, #) 27 Al .............................................. Iliadis et al. (1990)
26 Al g ( p, #) 27 Si ............................................... Champagne et al. (1993), Vogelaar et al. (1996)
27 Al( p, #) 28 Si................................................. Iliadis et al. (1990), Timmermann et al. (1988)
27 Al( p, # ) 24 Mg.............................................. Timmermann et al. (1988), Champagne et al. (1988)
28 Si( p, #) 29 P .................................................. Graff et al. (1990)
Fig. 8.---Comparison of fluorine abundances observed by Jorissen et al.
(1992) and model predictions for the 3 M # , Z � 0:02 model and M pmz �
0:002 M # and different choices of the rate of the reactions involved as de�
scribed in Table 2: ``standard'' (solid line), ``recommended'' (short�dashed
line), and lower and upper limit (dotted lines). As in Fig. 3, crossed MS, S
symbols denote stars with large N excesses, and predictions are normalized in
such a way that the initial 19 F abundance corresponds to the average F
abundance observed in K and M stars, to which stellar data are normalized
(see Jorissen et al. 1992).
LUGARO ET AL.
944 Vol. 615

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14 C(# , #) 18 O .................................................. Jorissen & Goriely (2001)
15 N(# , #) 19 F................................................... de Oliveira et al. (1996)
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TABLE 5
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14 N(n, p) 14 C ............................................... Gledenov et al. (1995)
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