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Determination of the 35Cl(n, p)35S reaction cross section and its astrophysical implications
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NUCLEAR PHYSICS A Nuclear Physics A573 (1994) 291-305
Determination of the 35Cl(n, pJ3?3 reaction cross section and its astrophysical implications S. Druyts Institute of Reference Materials and Measurements (IRMM/ CBNM), Joint Research Centre, B-2440 Geel, Belgium
C. Wagemans
’
Nuclear Physics Laboratory, University of Gent, B-9000 Gent, Belgium
P. Geltenbort Institut LawLangevin,
F-38042 Grenoble, France
Received 2 December 1993
Abstract The 35Cl(n, P)~% reaction cross section has been measured with thermal neutrons at the High Flux Reactor of the ILL (Grenoble) and with resonance neutrons at the linear accelerator GELINA of the IRMM (Gee0 For the thermal cross section, a precise value of 440 k 10 mb was obtained. In the region up to about 100 keV neutron energy, several resonances were determined with high resolution. These data were used to calculate the maxwellian averaged cross section at various temperatures. Their impact on stellar-nucleosynthesis calculations is discussed.
Key words: NUCLEAR REACTIONS 35Cl(n, p); E = thermal-100 keV; measured proton yield vs E; deduced reaction, maxwellian averaged u; calculated (n, p)/(n, y) branching ratio.
1. Introduction
Important discrepancies (up to a factor of three) exist between the 35Cl(n,,, pj3?3 reaction cross-section values reported in the literature [l-9]. These data were
’ Supported by the National Fund for Scientific Research, Belgium. 03759474/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZ 0375-9474(94)00043-M
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obtained between 25 and 50 years ago, often using less sensitive experimental methods. In view of nowadays’ strongly improved experimental conditions, we performed a new, accurate measurement of this cross section at the High Flux Reactor of the ILL (Grenoble). In the resonance region on the other hand, only three experiments are reported [lo-121; however, with fairly poor neutron energy resolution. Since these measurements are used to calculate maxwellian averaged cross sections at various stellar temperatures, needed for nucleosynthesis calculations in the s-process [13] as well as in explosive environments [14], improved resonance data will be helpful to reduce the uncertainty in the nucleosynthesis calculations. So we performed a high-resolution measurement at the accelerator GELINA of the IRMM (Gee0
2. Measurements
with thermal
neutrons
2.1. Experimental method The 35Cl(nth, p)35S reaction cross section was measured at the curved neutron guide H22 at the ILL in Grenoble (France). It provides an intense thermal neutron beam of 5 X lo8 n/s * cm2. Moreover, the beam is very pure since the y-ray flux has been reduced by a factor of lo6 and the slow neutrons outnumber the epithermal and fast neutrons by the same factor. This enables clean particle detection in low-background conditions. A variety of silver-chloride samples (prepared by the Sample Preparation Group of the IRMM) were used, containing natural chlorine as well as chlorine with (0.636 & 0.009>% of 36C1.The 35C1isotopic fraction was (75.77 f 0.07)% in the case of natural chlorine and (75.03 f 0.071% for the sample containing 36C1.Silver-chloride was used instead of other chemical compositions such as sodium- or potassium-chloride which are more hygroscopic. The samples were prepared by vacuum deposition of silver-chloride on a 20 urn thick aluminium foil. This technique ensures homogeneity of the layers. To avoid interaction of the chlorine with the aluminium backing, the latter was first coated with a 200 Fg/cm2 Pt layer. It was checked that this measure was sufficient to maintain a constant number of Cl atoms. For one sample this precaution was not taken, which resulted in a significantly deteriorated spectrum of the emitted 35Cl(n, pj3’S protons, due to more low-energy background and a larger width of the proton peak. Great care was taken of the determination of the sample thicknesses. In view of the hygroscopy, it is not advisable to determine a chlorine mass by differential weighing [151 only. Therefore, we combined this method with spectrophotometry, isotope-dilution mass spectrometry and neutron-activation analysis. The sample thicknesses obtained in this way are given in Table 1, column 1. Full details on sample preparation and assaying are given by Eykens et al. [16] The samples were mounted in a vacuum chamber together with a thin Si surface barrier detector placed outside the neutron beam. In Fig. 1 a schematic picture is shown of the experimental setup. The detectors were calibrated by means of the
S. Druyts et al. /Nuclear
Table 1 Some specifications of the 35Cl(n,r,, P)~‘S measurements containing (0.636 f 0.009)% of 36C1 Surface density (kg Cl/cm2) (a) 9.7f0.4
17.4f0.7 31.4* 1.2 33.8 f 1.3 35.8 f 1.4 (b) 41.7f 1.6 50.1+ 2.0
51.4k2.0
Detector used
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on (a) natural chlorine samples, (b) samples
35Cl(n,h, p) cross section (b)
Uncertainty on the count rate (%)
Data recording time (h)
450 300 300 200 200 300
0.316 0.436 0.406 0.428 0.454 0.454
27 22 a 2 3.3 3 4
19.1 17.2 1.0 1.0 1.8 1.3
200 200 200 300 300 200 200
0.440 0.509 0.490 0.468 0.433 0.445 0.458
1.8 1.4 2.6 1.6 4.3 2 1.9
1.6 1.6 0.3 0.7 16.6 1.0 2.2
thickness (pm)
area (mm*)
100 30 30 15 20 30 15 15 15 30 70 15 20
a In this sample there was no Pt-coating on the Al-backing.
“B(n,,, a)7Li,6Li(n,,, a)t and 14N(n,,, p)14C reactions. In the latter, protons of almost the same energy (0.584 MeV) are emitted as in the 35Cl(n,,, pj3’S reaction. The (n, p) reaction measurements were done relative to the 235U&.,, f) reaction. For that purpose the Cl samples were replaced by a u5U sample (with well-defined mass), strictly maintaining the geometry. A thermal fission cross-section value of 584.25 f 1.10 b was adopted from the ENDF-B6 file. 2.2. Measurements and results The protons emitted in the 35Cl(n,,, p)35S reaction have an energy of 0.598 MeV so that their range in Si is only - 10 urn. Several measurements were performed
SURFACE BARRIER , DETECTOR
NEUTRON BEAM #-e
-
Fig. 1. A schematic picture of the setup of the 35Cl(n,r,, P)~‘S measurement.
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ENERGY IMeW Fig. 2. Energy distribution of the protons emitted in the 35Cl(n,h, pj3jS reaction obtained with a 15 pm Si detector.
using Si detectors with thicknesses ranging from 15 pm to 100 pm. Further specifications of the measurements are summarized in Table 1 and a typical spectrum is shown in Fig. 2. Clearly, the quality of the spectra depends on the sample and the detector used. The best separation of the proton peak from the background is obtained by means of a detector with thickness 15 pm. In all the samples a correction had to be done for underlying 7Li* particles from the “B{n,,, L.u1)7Li*reaction due to “B impurities in the sample. The number of i4N(n,, p)14C protons released due to reactions induced in the air still present in the chamber at a pressure of - 10e3 Torr was negligible as was shown in a measurement with the sample removed from the beam. The 35Cl(n,,,, P)~~S cross-section value is calculated by means of the following expression
N(“U)
ql,th(35cl) = N(35Cl)
Cf35Cl) c(235u)
%h(235U)
g,(T)(235U) g(7X35Cl)
’
in which N is the number of atoms per cm*, a,, the thermal cross-section value, C the count rate after background subtraction and g(T) the Westcott g-factor at the temperature T, of the respective reactions. The g-factors have to be included in the expression to take into account possible deviations of the cross-section shapes from a l/u function [17]. With an average energy of - 18 meV for the neutron beam used (corresponding to T = 210 K), g, (210 K) = 0.995 f 0.002 for 235U [17]. In the case of 35Cl(n, pj3%, no resonances have been observed below - 400 eV. Since moreover the only negative resonance [19] is located at - 180 eV, hence far enough from zero, g(2l.O K) = 1 is a realistic estimation for this reaction. The
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Table 2 A comparison of this work with other 35Cl(n,h, p)35S reaction cross-section measurements ized to the presently adopted values of the reference cross sections used) Reference
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(renormal-
35Cl(n,,, p)35S cross section (b)
Detector used
Relative to
0.440 f 0.010 0.314 f 0.010 0.345 +0.075 a 0.451+ 0.040 0.460 f 0.060
surface barrier emulsion ionization chamber surface barrier cloud chamber
(r[235U(n,,, f)] = 584.25 b o[14N(nthr p)14C] = 1.83 b o[t4N(n,,,, PI~~C]= 1.83 b a[r4N(n,,,, P)‘~C] = 1.83 b
0.483 f 0.014 a 0.600 f 0.090 0.350 f 0.090 0.169 + 0.034 0.320
P-detector p-detector p-detector p-detector P-detector
o[39Co(nthr y)60Co] = 37.18 b a[39Co(nu,, ~l~Co]= 37.18 b ~[35Mn(n,,,, y)56Mn] = 13.3 b
Proton emission
This work
111 Dl [31 141 Activation
151 [61 171 [81 191
a The cross section has been adjusted for the presently adopted isotopic composition of “a’Cl: 75.77% 35Cl, 24.23% 37C1.
35Cl(n,,, p)35S reaction cross-section values obtained for each sample, are listed in Table 1, column 3. The weighted mean of this quantity over all the samples, all the errors taken into account, resulted in a cross-section value of 0.44 f 0.01 b. In Table 2 an overview is given of several earlier 35Cl(n,,, p)35S reaction cross-section measurements. It shows that the cross-section value obtained in this work is in agreement with the values determined in the other proton-emission measurements, except for the ancient emulsion experiment [l]. It also lies within the wide range of values determined by activation measurements. The large spread in the cross-section values determined by the activation method might be a consequence of it being a multi-step technique which is less direct a method than the straight proton detection.
3. Measurements with resonance neutrons 3.1. Experimental method The measurements were performed at two flight-path positions of the linear accelerator GELINA of the IRMM in Gee1 (Belgium). As detector a gridded gas-flow ionization chamber was used filled with 1 b of CH, gas, so that the protons, emitted in the 35Cl(n, p)35S reaction, could be detected in a 2r-geometry. For each detected proton, coincident anode (= amplitude), cathode and time-offlight signals were recorded so that both proton and neutron energy (the latter by time-of-flight) as well as the angular distribution [18] of the protons were obtained.
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By setting a window on the proton energy one can look at the corresponding reaction yield as a function of neutron energy. In the case of the 35Cl(n, p> reaction the protons have a rather low energy (EP = 0.6 MeV), which makes them hard to discriminate from the background. Therefore, only the cross section in the resonances is reliable, since the signal-to-background ratio was too low in between resonances to allow a fair cross-section determination in the valleys. Information on the angular distribution of the protons could be obtained from the ratio of the cathode-to-anode signals, as explained by Budtz-Jorgensen and Knitter [18]. During a first experimental campaign, the ionization chamber was installed at the end of an 8 m flight path; GELINA was operated at a repetition frequency of 800 Hz with an electron-burst width of 1 ns. For these measurements, two samples containing 36C1 were used with a chlorine content of 50.1 + 2.0 and 51.4 + 2.0 km/cm*, respectively (cf. Table 1). The neutron flux was calibrated by means of the “B(n, (w)‘Li, 6Li(n, a>t and 235U(n, f) reactions induced in appropriate samples, which were placed in the chamber in strictly the same geometry as the Cl samples. For the first two reactions a l/u shape of the cross section was assumed and the thermal cross sections recommended in the ENDF-B6 data file were adopted. The same data file also delivered the 235U(n, f) cross section. As a result the 35Cl(n, P)~~S reaction cross section could be determined accurately for two resonances below 5 keV. At this very short flight path, the ionization chamber was paralyzed at neutron energies above 10 keV due to the huge y-flash produced by GELINA. For comparison purposes, a short “thermal run” was also performed at an 8 m flight path, GELINA being operated at a repetition frequency of 100 Hz with an electron-burst width of 14 ns. In a second series of measurements, a self-made target consisting of an ordinary transparent PVC tape was used. Since it contained at least five times more 35C1 atoms than the AgCl samples, the detector could be moved to a 30 m flight path, which enabled the determination of the resonance cross section up to about 100 keV neutron energy, GELINA being operated at a 800 Hz repetition frequency with a 1 ns electron-burst width. Here, the neutron flux was determined via the “B(n, a)‘Li reaction, the cross-section values of which were adopted from the evaluated data file ENDF-B6. These data were normalized to the area of the largest resonance (at about 398 eV) as determined in the measurement at 8 m. 3.2. Results and discussion 3.2.1. Resonance strengths
As mentioned in the introduction, three other experiments are reported in the literature; however, with a much poorer neutron energy resolution. The first results were reported already in 1961 by Popov and Shapiro [lo]. These measurements were performed at a lead slowing-down spectrometer up to 9 keV and suffered from the very poor resolution typical of this kind of spectrometer. Moreover, these data were normalized to a thermal cross-section value of 190 mb, which is 2.3 times smaller than the value determined in this work.
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The experimental resolution was significantly improved in the experiments of Gledenov et al. [ll], who measured the 398 and 4250 eV resonances at the IBR-30 pulsed reactor of JINR, Dubna (Russia). Finally, Koehler [12] performed measurements from 25 meV up to 100 keV at the LANSCE facility, Los Alamos (USA). Here as well, the neutron energy resolution is significantly poorer than in our experiments, which is clearly illustrated in Fig, 3. In both of the latter experiments the cross-section data were normalized to a thermal value of 489 f 14 mb. In Table 3, the resonance strengths gT,T,/T as obtained by the previous authors are compared with our results. These strengths are calculated from the resonance areas A via the relation A = 2r2X2gr,,TP/T. Here, X is the reduced neutron wavelength, g the statistical spin factor and r,,r, and r the neutron, proton and total width, respectively. The data given in Table 3 are all renormalized to a 35Cl(n,,, p) cross-section value of 440 + 10 mb as determined in this work in order to permit a good intercomparison. For the two lowest resonances, the experimental data agree within two standard deviations. The evaluated value [19] for the 4.25 keV resonance strength, however, is significantly lower than all recent experimental data. At higher neutron energies only the present data and those of Koehler [12] are available. In the present work a few more resonances are distinguished and a larger value is obtained for the 16.36 keV resonance strength compared to Koehler’s experiment. This is partly due to the difference in experimental resolution, partly to anisotropy effects, since our data were taken with an ionization chamber in a 27-geometry whereas Koehler made use of a surface barrier detector in reduced geometry. The occurrence of anisotropic proton emission in the resonances is demonstrated in Fig. 4, in which the angular distributions are compared for thermal neutrons (s-wave, hence isotropic) and for the 398 eV resonance (p-wave), where the distribution is clearly anisotropic. 3.2.2. Proton widths In ref. [20] the resonance strengths and the y-widths for a series of 35Cl(n, y)35S resonances were determined. These values, combined with the proton-resonance strengths determined in this work, allowed to calculate the r,/r, ratios and the proton widths, listed in Table 4. The value for the bound level was obtained by renormalizing the proton width of ref. [19] to a thermal cross-section value of 440 f 10 mb, assuming it had been determined by a thermal cross-section value of 190 mb before. For the 0.398 keV resonance no information on the -y-resonance strength was available in ref. [20], therefore the value of ref. [19] was used. For the 90.5 keV resonance no y-width has yet been reported, and a value of 0.5 eV was assumed. In Table 4 a list of the adopted spins is also included; some of them are fairly speculative and were put in between brackets. Only the negative-energy resonance and the resonance at 14.80 keV are reported to be s-waves, all the others are expected to be p-waves. Based on these data, average proton widths can be calculated for the s- and p-wave resonances, yielding (r,(l = 0)) = 0.016 eV and (r,
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4. Calculation of the maxwellian averaged cross section For astrophysical purposes, the experimentally determined differential crosssection values a&E,) need to be transformed into maxwellian averaged cross sections, (MACS) defined as
(a) = *
‘O
> /0
mE, exp( - EJkT)
(4.1)
d E,
k being the Boltzmann constant, T the stellar temperature and E, the neutron energy. The 35Cl(n, P)~‘S reaction cross-section curve can be interpreted as a sum of Breit-Wigner curves, if one neglects interference effects. Most of the resonances are reported to be p-wave [191. Since, moreover, their widths are much smaller than kT, as shown in Fig. 5, they can be regarded as a series of delta-functions superimposed on a tail, which is negligible in the case of p-wave resonances. The maxwellian averaged cross-section value can then be written as [21]
(4.2) Here, (a)nw is the contribution to the MACS-value of the Breit-Wigner curves due to the only two resonances alleged to be s-wave, at - 0.18 keV and at 14.8 keV [19]. The second term follows from the areas Ai (in b * eV) of the p-wave resonances. N is the number of p-wave resonances and Ei the resonance energy in keV in the laboratory system. To illustrate the influence each of the resonances has on the MACS-value, e.g. at kT = 25 keV, the 35Cl(n, p> resonances determined in the present work are plotted in Fig. 5 together with the corresponding maxwellian distribution. In Fig. 6,
Table 3 Comparison of the 35Cl(n, p)35S resonance strengths gT,T,/r, as obtained by the previous authors and from this work. All data are renormalized to a thermal cross-section value of 440 f 10 mb E, (keV)
0.398 4.25 14.80 16.36 17.14 27.35 51.6 57.8 90.5 103.5
g&T, /r
(eV)
Present work
1121
1101
1111
1191
(7.9 *0.4)~10-~ (3.8 *0.3)x10-’ (1.6 &O.5)x1O-2 (11.9 *1.5)x10-* (2.4 *0.8)~10-~ (7.5 +2.0)~10-~ (7.2 +3.6)x10-* 0.56*0.11 0.15 f 0.06 0.67 + 0.24
9.0~10-~ 3.2~10-~ 5.8x10-* 6.2x10-* 0.77 -
(6.5+2.1)~10-~ (2.3+1.2)~10-~
(9.7*1.4)~10-~ (3.6&0.7)x10-2
7.1 x~O-~ 1.44~10-~
---------- Resonance
at 398
aV
Thermai neutrons
-
a
0.2
0.4
0.6 CCJS
0.8
1.0
Q
Fig, 4. Angular d~s~ibutiu~ of the 35Cfn, p) protons; B is the angle between the normal to the cathode and the direction of the proton emissSon Chorizontat axis not c~~rated~.
a comparison is given between the IG.ACS-values as a function of kT, obtained in this work, and the MAC%-values calculated from the resonance parameters of Koehler [I21 using Eq. (4,2), after re~o~ai~zatiou to a thermal (n, p) cross section of 4% r4:20 mh. Clearly, Koehkr’s values are ~ste~at~ca~~~ tower, e,g. at 12 ket’
Table 4 Proton and y-widths for 36CXresonances, obtained by combining the present 35Cl(rr,p) data with the (II, y) work of Mackfin [Xl] E,s ikeW - 0.180 0.398 4.25 14.80 f6,36 17.15 27.35 51.6 57.8 90.5 103.5
Reson;tnce spin I adopted 2 2 (1, I21 (21 (21 (21 Ci> 1
a Vaks ohtaioed 440-f IO mb.
J-, i ql1201
r, CeVStzaf
fp feVj
1OOa 3.29 a 2.61 15.8 3.B 34.6 3.57 o.gg 0.71 4.4 0.33
0.56 a 0.46 B 0.44 0.41 0.63 l.4& 8.48 0.11 0.64 (0.5) 0.59
5.56XYO’-3a 0.14 f 0.01 a 0.168fO.014 0.026 f 0.008 0.206 rt 0.026 O.#2j, OJ?13 0,133 Ifr0.036 0.12 *a.06 0.90 *0.18 0.11 1: 0,OS a 1.8 kO.7
from ref. E19g F, has been r~~orrnaIi~ed to a thermal cross-section
value of
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L
10'1
E
l=
0
25 Z
g lo-'= ti In
I g
10-z--
z 0
10-J-
1 o-4 ‘4
lb3
ENERGY
(e”;’
Fig. 5. 35Cl(n, P)~% resonances, together with the maxwellian distribution at kT = 25 keV.
._...._............. Koehler -
10
This
25
15
Work
30
kT &“, Fig. 6. Comparison of the MACS-values obtained from Koehler’s measurement [12] and this work, as a function of kT. The dashed lines above and below our result indicate a one-standard-deviation uncertainty.
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we obtain a value of 3.2 5- 0.2 mb whereas Koehler finds 2.0 mb, at 25 keV the MACS-values are 1.86 + 0.16 mb and 1.28 mb, respectively. This discrepancy is partly due to the fact that in the determination of Koehler’s MACS-values no resonance parameters above 58 keV neutron energy were available.
5. Astrophysical implications Although it is clear that the MACS-values needed in nucleosynthesis calculations are only relevant for H-values in the keV range, one should not underestimate the importance of an accurate cross-section value at thermal neutron energy. The latter value is indeed often used to normalize cross-section data at higher neutron energies, hence it has a direct impact on MACS-values, which may be very important. A very striking example are the 35Cl(n, p) measurements of Popov et al. [lo]. They were normalized to a thermal cross section of 190 f 50 mb, which is 2.3 times lower than the value determined in this work! More recently, Koehler [12] normalized his 35Cl(n, p) measurement to a thermal value of 489 + 14 mb, which is 11% higher than the value reported here. Astrophysicists are more interested in the quantity N,((+v) instead of the maxwellian averaged cross-section values, because multiplied by the matter density
I
2x10"
I
III
I
III
I
I
I
III
I
-
This Work ____...___ Koehler
4x104
I 10-4
I
III
I
I
II,
10-3
I 10-Z
I
II,
I 10-l
T (GK)
Fig. 7. Comparison of the N,(au) curves calculated present work, as a function of the stellar temperature.
from Koehler’s
renormalized
data
[12] and the
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Fig. 8. Partial nucleosynthesis network in the Cl region. Stable isotopes are put into a full square, unstable but long-living isotopes into a square with intermittent lines and short-living isotopes are surrounded by a circle. The meaning of the reaction lines without specification is the following: a full line stands for a (n, y) reaction and an intermittent line means a less probable (n, y) transition due to competition with other reactions.
and the molar fractions of the interacting particles it immediately yields the stellar reaction rate. Obviously, NA (au) is easily obtained by multiplying the MACS-values with Avogadro’s number and the thermal velocity ;? = (2kT/~)l/~, p being the reduced mass. This operation has been done for the Cl(n, p)35S reaction with the data of the present work and of Koehler [12]. Both N,(au) curves are shown in Fig. 7. There is agreement within the error bars below 4 x 10e2 GK, the deviation starts in the region of s-process temperatures. Surprisingly, there is also agreement between the NA((+v)-values calculated by us using Koehler’s (renormalized) cross-section data with the corresponding values given by Koehler [12], which are expected to be 11% higher due to this renormalization. This is probably due to the different formulas applied to calculate N,(au). In this work it was calculated in the straightforward way mentioned above, whereas Koehler calculated this quantity by means of a theoretical fit based on the resonance parameters. As illustrated in the partial nucleosynthesis network shown in Fig. 8, the 35Cl(n, p)35S reaction plays a role in the nucleosynthesis of nuclei in the S-Cl-Ar region. An interesting item to investigate is how it influences the synthesis of the rare nucleus 36S,which is a long-standing problem in nuclear astrophysics [13,14,22]. This influence is introduced via the 35Cl(n, ~)/~~Cl(n, p) branching, which determines the relative probability of the 36S nucleosynthesis via the 35Cl(n, y) 36Cl(n, pj3’?j and the 35Cl(n, p)35S(n, yj3?S path, respectively. The ratio of the MACS-values of the 35Cl(n, y)36C1 and the 35Cl(n, p)35S reactions has been calculated using the experimental data of this work and also of ref. [12] for the (n, p>
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I
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I
I
__________
,’ ,,,’ ,,,’
0
I 5
I
I
I
Macklin/Koehler
Macklin/This Work _................... Woosfey _____-_-------______ ---___ ,/* ---__---___ ,/’ ----___---_____ ,’ ,’ ---------.__________ I’
I 10
I
I
I
I
I
20
15
I 25
I 30
kT (keV)
Fig. 9. Comparison of the ratio of the MACS-values of the 35Cl(n, y) and (II, p) reactions, determined experimentally from this work, ref. [12] and ref. [20] and theoretically from ref. [23].
as
reaction and of ref. 1201for the (n, -y>reaction. Both curves are presented in Fig. 9, together with a curve deduced from theoretically obtained fitting formulas given in ref. [24]. The calculated experimental y-rate and the theoretical rates were checked for correctness with the ones given in ref. [23]. There is good agreement between this work, combined with Macklin’s (n, y) data, and the theoretical curve, indicating that the above-mentioned ratio is approximately 6. So there is a significant branching at the 35C1nucleus in the s-process with a branching factor hnp/(hnp + Any) = 0.12 at 12 keV and 0.13 at 25 keV. The impact of this branching on the nucleosynthesis path is, however, very small, since the 35S formed via the (n, p) branch rapidly P-decays back to 35C1with a half-life of 87.5 days. This value is smaller than the half-life of a 35C1nucleus against destruction through the (n, p) reaction (defined as Ti,* = (n,(o>,,~r)-~ In 2, n, being the stellar neutron density). If one assumes a value of 3 x 10s n/cm3 for II,, then T1,2(35Cl> is 148 y at kT = 12 keV and 177 y at kT = 25 keV. The authors would like to thank H. Beer and H. Weigmann for useful suggestions, and J. Van Gils and R. BarthClCmy for their technical support. References [l] H. Berthet and J. Rossel, Helv. Phys. Acta 27 (1954) 159 [2] A. Gibert, F. Roggen and J. Rossel, Helv. Phys. Acta 17 (1944) 97
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LG. Schrdder, M. McKeown and G. Scharff-Goldhaher, Phys. Rev. 165 (1968) 1184 D.J. Hughes et al., Argonne preprint No. CP-2984 (1945) G.H.E. Sims and D.G. Juhnke, J. Inorg. Nucl. Chem. (1969) 3721 R.W. Durham and F. Girardi, Nuovo Cimento Suppl. 19 (1961) 4 W. Maurer, Z. Naturforsch. 4a (1949) 150 L. Seren, H.N. Friedlander and S.H. Turkel, Phys. Rev. 72 (1947) 888 A. Langsdorf et al., Argonne preprint No. CP-2638 (1944) p. 10 Y.P. Popov and F.L. Shapiro, Sov. Phys. JETP 13 (1961) 1132 Y.M. Gledenov, L.B. Mitsina, M. Mitrikov, Y.P. Popov, J. Rigol, V.I. Salatski and Fung Van Zuan, Dubna communications JINR P3-89-351 (1989) [12] P.E. Koehler, Phys. Rev. C44 (1991) 1675 [13] H. Beer and R.-D. Penzhom, Astron. Astrophys. 174 (1987) 323 [14] W.M. Howard, W.D. Arnett, D.D. Clayton and S.E. Woosley, Astrophys. J. 175 (1972) 201 [15] C. Wagemans, Nucl. Instr. Meth. A282 (1989) 4 [16] R. Eykens, A. Goetz, A. Lamberty, J. Van Gestel, J. Pauwels, C. Wagemans, S. Druyts and P. D’hondt, Nucl. Instr. Meth. A303 (1991) 152 [17] C. Wagemans, P. Schillebeecla and J.P. Bocquet, Nucl. Sci. Eng. 101 (1989) 293 [18] C. Budtz-Jorgensen and H. Knitter, Nucl. Instr. Meth. 223 (1984) 295 [19] SF. Mughabghab, M. Divadeenam and N.E. Holden, Neutron cross-sections, vol. 1 (Academic, New York, 1981) p. 17-1 [20] R.L. Macklin, Phys. Rev. 29 (1984) 1996 1211 H. Beer, F. Voss and R.R. Winters, Astrophys. J. Suppl. 80 (1992) 403 [22] C. Wagemans, H. Weigmann and R. Barth&my, Nucl. Phys. A469 (1987) 497 [23] Z.Y. Bao and F. K;ippeler, Atomic Data Nucl. Data Tables 36 (1987) 411 [24] SE. Woosley, W.A. Fowler, J.A. Holmes and B.A. Zimmerman, Atomic Data Nucl. Data Tables 22 (1987) 371
__ i!iB
EISNIER
NUCLEAR PHYSICS A Nuclear Physics A573 (1994) 291-305
Determination of the 35Cl(n, pJ3?3 reaction cross section and its astrophysical implications S. Druyts Institute of Reference Materials and Measurements (IRMM/ CBNM), Joint Research Centre, B-2440 Geel, Belgium
C. Wagemans
’
Nuclear Physics Laboratory, University of Gent, B-9000 Gent, Belgium
P. Geltenbort Institut LawLangevin,
F-38042 Grenoble, France
Received 2 December 1993
Abstract The 35Cl(n, P)~% reaction cross section has been measured with thermal neutrons at the High Flux Reactor of the ILL (Grenoble) and with resonance neutrons at the linear accelerator GELINA of the IRMM (Gee0 For the thermal cross section, a precise value of 440 k 10 mb was obtained. In the region up to about 100 keV neutron energy, several resonances were determined with high resolution. These data were used to calculate the maxwellian averaged cross section at various temperatures. Their impact on stellar-nucleosynthesis calculations is discussed.
Key words: NUCLEAR REACTIONS 35Cl(n, p); E = thermal-100 keV; measured proton yield vs E; deduced reaction, maxwellian averaged u; calculated (n, p)/(n, y) branching ratio.
1. Introduction
Important discrepancies (up to a factor of three) exist between the 35Cl(n,,, pj3?3 reaction cross-section values reported in the literature [l-9]. These data were
’ Supported by the National Fund for Scientific Research, Belgium. 03759474/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZ 0375-9474(94)00043-M
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obtained between 25 and 50 years ago, often using less sensitive experimental methods. In view of nowadays’ strongly improved experimental conditions, we performed a new, accurate measurement of this cross section at the High Flux Reactor of the ILL (Grenoble). In the resonance region on the other hand, only three experiments are reported [lo-121; however, with fairly poor neutron energy resolution. Since these measurements are used to calculate maxwellian averaged cross sections at various stellar temperatures, needed for nucleosynthesis calculations in the s-process [13] as well as in explosive environments [14], improved resonance data will be helpful to reduce the uncertainty in the nucleosynthesis calculations. So we performed a high-resolution measurement at the accelerator GELINA of the IRMM (Gee0
2. Measurements
with thermal
neutrons
2.1. Experimental method The 35Cl(nth, p)35S reaction cross section was measured at the curved neutron guide H22 at the ILL in Grenoble (France). It provides an intense thermal neutron beam of 5 X lo8 n/s * cm2. Moreover, the beam is very pure since the y-ray flux has been reduced by a factor of lo6 and the slow neutrons outnumber the epithermal and fast neutrons by the same factor. This enables clean particle detection in low-background conditions. A variety of silver-chloride samples (prepared by the Sample Preparation Group of the IRMM) were used, containing natural chlorine as well as chlorine with (0.636 & 0.009>% of 36C1.The 35C1isotopic fraction was (75.77 f 0.07)% in the case of natural chlorine and (75.03 f 0.071% for the sample containing 36C1.Silver-chloride was used instead of other chemical compositions such as sodium- or potassium-chloride which are more hygroscopic. The samples were prepared by vacuum deposition of silver-chloride on a 20 urn thick aluminium foil. This technique ensures homogeneity of the layers. To avoid interaction of the chlorine with the aluminium backing, the latter was first coated with a 200 Fg/cm2 Pt layer. It was checked that this measure was sufficient to maintain a constant number of Cl atoms. For one sample this precaution was not taken, which resulted in a significantly deteriorated spectrum of the emitted 35Cl(n, pj3’S protons, due to more low-energy background and a larger width of the proton peak. Great care was taken of the determination of the sample thicknesses. In view of the hygroscopy, it is not advisable to determine a chlorine mass by differential weighing [151 only. Therefore, we combined this method with spectrophotometry, isotope-dilution mass spectrometry and neutron-activation analysis. The sample thicknesses obtained in this way are given in Table 1, column 1. Full details on sample preparation and assaying are given by Eykens et al. [16] The samples were mounted in a vacuum chamber together with a thin Si surface barrier detector placed outside the neutron beam. In Fig. 1 a schematic picture is shown of the experimental setup. The detectors were calibrated by means of the
S. Druyts et al. /Nuclear
Table 1 Some specifications of the 35Cl(n,r,, P)~‘S measurements containing (0.636 f 0.009)% of 36C1 Surface density (kg Cl/cm2) (a) 9.7f0.4
17.4f0.7 31.4* 1.2 33.8 f 1.3 35.8 f 1.4 (b) 41.7f 1.6 50.1+ 2.0
51.4k2.0
Detector used
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on (a) natural chlorine samples, (b) samples
35Cl(n,h, p) cross section (b)
Uncertainty on the count rate (%)
Data recording time (h)
450 300 300 200 200 300
0.316 0.436 0.406 0.428 0.454 0.454
27 22 a 2 3.3 3 4
19.1 17.2 1.0 1.0 1.8 1.3
200 200 200 300 300 200 200
0.440 0.509 0.490 0.468 0.433 0.445 0.458
1.8 1.4 2.6 1.6 4.3 2 1.9
1.6 1.6 0.3 0.7 16.6 1.0 2.2
thickness (pm)
area (mm*)
100 30 30 15 20 30 15 15 15 30 70 15 20
a In this sample there was no Pt-coating on the Al-backing.
“B(n,,, a)7Li,6Li(n,,, a)t and 14N(n,,, p)14C reactions. In the latter, protons of almost the same energy (0.584 MeV) are emitted as in the 35Cl(n,,, pj3’S reaction. The (n, p) reaction measurements were done relative to the 235U&.,, f) reaction. For that purpose the Cl samples were replaced by a u5U sample (with well-defined mass), strictly maintaining the geometry. A thermal fission cross-section value of 584.25 f 1.10 b was adopted from the ENDF-B6 file. 2.2. Measurements and results The protons emitted in the 35Cl(n,,, p)35S reaction have an energy of 0.598 MeV so that their range in Si is only - 10 urn. Several measurements were performed
SURFACE BARRIER , DETECTOR
NEUTRON BEAM #-e
-
Fig. 1. A schematic picture of the setup of the 35Cl(n,r,, P)~‘S measurement.
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ENERGY IMeW Fig. 2. Energy distribution of the protons emitted in the 35Cl(n,h, pj3jS reaction obtained with a 15 pm Si detector.
using Si detectors with thicknesses ranging from 15 pm to 100 pm. Further specifications of the measurements are summarized in Table 1 and a typical spectrum is shown in Fig. 2. Clearly, the quality of the spectra depends on the sample and the detector used. The best separation of the proton peak from the background is obtained by means of a detector with thickness 15 pm. In all the samples a correction had to be done for underlying 7Li* particles from the “B{n,,, L.u1)7Li*reaction due to “B impurities in the sample. The number of i4N(n,, p)14C protons released due to reactions induced in the air still present in the chamber at a pressure of - 10e3 Torr was negligible as was shown in a measurement with the sample removed from the beam. The 35Cl(n,,,, P)~~S cross-section value is calculated by means of the following expression
N(“U)
ql,th(35cl) = N(35Cl)
Cf35Cl) c(235u)
%h(235U)
g,(T)(235U) g(7X35Cl)
’
in which N is the number of atoms per cm*, a,, the thermal cross-section value, C the count rate after background subtraction and g(T) the Westcott g-factor at the temperature T, of the respective reactions. The g-factors have to be included in the expression to take into account possible deviations of the cross-section shapes from a l/u function [17]. With an average energy of - 18 meV for the neutron beam used (corresponding to T = 210 K), g, (210 K) = 0.995 f 0.002 for 235U [17]. In the case of 35Cl(n, pj3%, no resonances have been observed below - 400 eV. Since moreover the only negative resonance [19] is located at - 180 eV, hence far enough from zero, g(2l.O K) = 1 is a realistic estimation for this reaction. The
S. Druyts et al. /Nuclear
Table 2 A comparison of this work with other 35Cl(n,h, p)35S reaction cross-section measurements ized to the presently adopted values of the reference cross sections used) Reference
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(renormal-
35Cl(n,,, p)35S cross section (b)
Detector used
Relative to
0.440 f 0.010 0.314 f 0.010 0.345 +0.075 a 0.451+ 0.040 0.460 f 0.060
surface barrier emulsion ionization chamber surface barrier cloud chamber
(r[235U(n,,, f)] = 584.25 b o[14N(nthr p)14C] = 1.83 b o[t4N(n,,,, PI~~C]= 1.83 b a[r4N(n,,,, P)‘~C] = 1.83 b
0.483 f 0.014 a 0.600 f 0.090 0.350 f 0.090 0.169 + 0.034 0.320
P-detector p-detector p-detector p-detector P-detector
o[39Co(nthr y)60Co] = 37.18 b a[39Co(nu,, ~l~Co]= 37.18 b ~[35Mn(n,,,, y)56Mn] = 13.3 b
Proton emission
This work
111 Dl [31 141 Activation
151 [61 171 [81 191
a The cross section has been adjusted for the presently adopted isotopic composition of “a’Cl: 75.77% 35Cl, 24.23% 37C1.
35Cl(n,,, p)35S reaction cross-section values obtained for each sample, are listed in Table 1, column 3. The weighted mean of this quantity over all the samples, all the errors taken into account, resulted in a cross-section value of 0.44 f 0.01 b. In Table 2 an overview is given of several earlier 35Cl(n,,, p)35S reaction cross-section measurements. It shows that the cross-section value obtained in this work is in agreement with the values determined in the other proton-emission measurements, except for the ancient emulsion experiment [l]. It also lies within the wide range of values determined by activation measurements. The large spread in the cross-section values determined by the activation method might be a consequence of it being a multi-step technique which is less direct a method than the straight proton detection.
3. Measurements with resonance neutrons 3.1. Experimental method The measurements were performed at two flight-path positions of the linear accelerator GELINA of the IRMM in Gee1 (Belgium). As detector a gridded gas-flow ionization chamber was used filled with 1 b of CH, gas, so that the protons, emitted in the 35Cl(n, p)35S reaction, could be detected in a 2r-geometry. For each detected proton, coincident anode (= amplitude), cathode and time-offlight signals were recorded so that both proton and neutron energy (the latter by time-of-flight) as well as the angular distribution [18] of the protons were obtained.
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By setting a window on the proton energy one can look at the corresponding reaction yield as a function of neutron energy. In the case of the 35Cl(n, p> reaction the protons have a rather low energy (EP = 0.6 MeV), which makes them hard to discriminate from the background. Therefore, only the cross section in the resonances is reliable, since the signal-to-background ratio was too low in between resonances to allow a fair cross-section determination in the valleys. Information on the angular distribution of the protons could be obtained from the ratio of the cathode-to-anode signals, as explained by Budtz-Jorgensen and Knitter [18]. During a first experimental campaign, the ionization chamber was installed at the end of an 8 m flight path; GELINA was operated at a repetition frequency of 800 Hz with an electron-burst width of 1 ns. For these measurements, two samples containing 36C1 were used with a chlorine content of 50.1 + 2.0 and 51.4 + 2.0 km/cm*, respectively (cf. Table 1). The neutron flux was calibrated by means of the “B(n, (w)‘Li, 6Li(n, a>t and 235U(n, f) reactions induced in appropriate samples, which were placed in the chamber in strictly the same geometry as the Cl samples. For the first two reactions a l/u shape of the cross section was assumed and the thermal cross sections recommended in the ENDF-B6 data file were adopted. The same data file also delivered the 235U(n, f) cross section. As a result the 35Cl(n, P)~~S reaction cross section could be determined accurately for two resonances below 5 keV. At this very short flight path, the ionization chamber was paralyzed at neutron energies above 10 keV due to the huge y-flash produced by GELINA. For comparison purposes, a short “thermal run” was also performed at an 8 m flight path, GELINA being operated at a repetition frequency of 100 Hz with an electron-burst width of 14 ns. In a second series of measurements, a self-made target consisting of an ordinary transparent PVC tape was used. Since it contained at least five times more 35C1 atoms than the AgCl samples, the detector could be moved to a 30 m flight path, which enabled the determination of the resonance cross section up to about 100 keV neutron energy, GELINA being operated at a 800 Hz repetition frequency with a 1 ns electron-burst width. Here, the neutron flux was determined via the “B(n, a)‘Li reaction, the cross-section values of which were adopted from the evaluated data file ENDF-B6. These data were normalized to the area of the largest resonance (at about 398 eV) as determined in the measurement at 8 m. 3.2. Results and discussion 3.2.1. Resonance strengths
As mentioned in the introduction, three other experiments are reported in the literature; however, with a much poorer neutron energy resolution. The first results were reported already in 1961 by Popov and Shapiro [lo]. These measurements were performed at a lead slowing-down spectrometer up to 9 keV and suffered from the very poor resolution typical of this kind of spectrometer. Moreover, these data were normalized to a thermal cross-section value of 190 mb, which is 2.3 times smaller than the value determined in this work.
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The experimental resolution was significantly improved in the experiments of Gledenov et al. [ll], who measured the 398 and 4250 eV resonances at the IBR-30 pulsed reactor of JINR, Dubna (Russia). Finally, Koehler [12] performed measurements from 25 meV up to 100 keV at the LANSCE facility, Los Alamos (USA). Here as well, the neutron energy resolution is significantly poorer than in our experiments, which is clearly illustrated in Fig, 3. In both of the latter experiments the cross-section data were normalized to a thermal value of 489 f 14 mb. In Table 3, the resonance strengths gT,T,/T as obtained by the previous authors are compared with our results. These strengths are calculated from the resonance areas A via the relation A = 2r2X2gr,,TP/T. Here, X is the reduced neutron wavelength, g the statistical spin factor and r,,r, and r the neutron, proton and total width, respectively. The data given in Table 3 are all renormalized to a 35Cl(n,,, p) cross-section value of 440 + 10 mb as determined in this work in order to permit a good intercomparison. For the two lowest resonances, the experimental data agree within two standard deviations. The evaluated value [19] for the 4.25 keV resonance strength, however, is significantly lower than all recent experimental data. At higher neutron energies only the present data and those of Koehler [12] are available. In the present work a few more resonances are distinguished and a larger value is obtained for the 16.36 keV resonance strength compared to Koehler’s experiment. This is partly due to the difference in experimental resolution, partly to anisotropy effects, since our data were taken with an ionization chamber in a 27-geometry whereas Koehler made use of a surface barrier detector in reduced geometry. The occurrence of anisotropic proton emission in the resonances is demonstrated in Fig. 4, in which the angular distributions are compared for thermal neutrons (s-wave, hence isotropic) and for the 398 eV resonance (p-wave), where the distribution is clearly anisotropic. 3.2.2. Proton widths In ref. [20] the resonance strengths and the y-widths for a series of 35Cl(n, y)35S resonances were determined. These values, combined with the proton-resonance strengths determined in this work, allowed to calculate the r,/r, ratios and the proton widths, listed in Table 4. The value for the bound level was obtained by renormalizing the proton width of ref. [19] to a thermal cross-section value of 440 f 10 mb, assuming it had been determined by a thermal cross-section value of 190 mb before. For the 0.398 keV resonance no information on the -y-resonance strength was available in ref. [20], therefore the value of ref. [19] was used. For the 90.5 keV resonance no y-width has yet been reported, and a value of 0.5 eV was assumed. In Table 4 a list of the adopted spins is also included; some of them are fairly speculative and were put in between brackets. Only the negative-energy resonance and the resonance at 14.80 keV are reported to be s-waves, all the others are expected to be p-waves. Based on these data, average proton widths can be calculated for the s- and p-wave resonances, yielding (r,(l = 0)) = 0.016 eV and (r,
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4. Calculation of the maxwellian averaged cross section For astrophysical purposes, the experimentally determined differential crosssection values a&E,) need to be transformed into maxwellian averaged cross sections, (MACS) defined as
(a) = *
‘O
> /0
mE, exp( - EJkT)
(4.1)
d E,
k being the Boltzmann constant, T the stellar temperature and E, the neutron energy. The 35Cl(n, P)~‘S reaction cross-section curve can be interpreted as a sum of Breit-Wigner curves, if one neglects interference effects. Most of the resonances are reported to be p-wave [191. Since, moreover, their widths are much smaller than kT, as shown in Fig. 5, they can be regarded as a series of delta-functions superimposed on a tail, which is negligible in the case of p-wave resonances. The maxwellian averaged cross-section value can then be written as [21]
(4.2) Here, (a)nw is the contribution to the MACS-value of the Breit-Wigner curves due to the only two resonances alleged to be s-wave, at - 0.18 keV and at 14.8 keV [19]. The second term follows from the areas Ai (in b * eV) of the p-wave resonances. N is the number of p-wave resonances and Ei the resonance energy in keV in the laboratory system. To illustrate the influence each of the resonances has on the MACS-value, e.g. at kT = 25 keV, the 35Cl(n, p> resonances determined in the present work are plotted in Fig. 5 together with the corresponding maxwellian distribution. In Fig. 6,
Table 3 Comparison of the 35Cl(n, p)35S resonance strengths gT,T,/r, as obtained by the previous authors and from this work. All data are renormalized to a thermal cross-section value of 440 f 10 mb E, (keV)
0.398 4.25 14.80 16.36 17.14 27.35 51.6 57.8 90.5 103.5
g&T, /r
(eV)
Present work
1121
1101
1111
1191
(7.9 *0.4)~10-~ (3.8 *0.3)x10-’ (1.6 &O.5)x1O-2 (11.9 *1.5)x10-* (2.4 *0.8)~10-~ (7.5 +2.0)~10-~ (7.2 +3.6)x10-* 0.56*0.11 0.15 f 0.06 0.67 + 0.24
9.0~10-~ 3.2~10-~ 5.8x10-* 6.2x10-* 0.77 -
(6.5+2.1)~10-~ (2.3+1.2)~10-~
(9.7*1.4)~10-~ (3.6&0.7)x10-2
7.1 x~O-~ 1.44~10-~
---------- Resonance
at 398
aV
Thermai neutrons
-
a
0.2
0.4
0.6 CCJS
0.8
1.0
Q
Fig, 4. Angular d~s~ibutiu~ of the 35Cfn, p) protons; B is the angle between the normal to the cathode and the direction of the proton emissSon Chorizontat axis not c~~rated~.
a comparison is given between the IG.ACS-values as a function of kT, obtained in this work, and the MAC%-values calculated from the resonance parameters of Koehler [I21 using Eq. (4,2), after re~o~ai~zatiou to a thermal (n, p) cross section of 4% r4:20 mh. Clearly, Koehkr’s values are ~ste~at~ca~~~ tower, e,g. at 12 ket’
Table 4 Proton and y-widths for 36CXresonances, obtained by combining the present 35Cl(rr,p) data with the (II, y) work of Mackfin [Xl] E,s ikeW - 0.180 0.398 4.25 14.80 f6,36 17.15 27.35 51.6 57.8 90.5 103.5
Reson;tnce spin I adopted 2 2 (1, I21 (21 (21 (21 Ci> 1
a Vaks ohtaioed 440-f IO mb.
J-, i ql1201
r, CeVStzaf
fp feVj
1OOa 3.29 a 2.61 15.8 3.B 34.6 3.57 o.gg 0.71 4.4 0.33
0.56 a 0.46 B 0.44 0.41 0.63 l.4& 8.48 0.11 0.64 (0.5) 0.59
5.56XYO’-3a 0.14 f 0.01 a 0.168fO.014 0.026 f 0.008 0.206 rt 0.026 O.#2j, OJ?13 0,133 Ifr0.036 0.12 *a.06 0.90 *0.18 0.11 1: 0,OS a 1.8 kO.7
from ref. E19g F, has been r~~orrnaIi~ed to a thermal cross-section
value of
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L
10'1
E
l=
0
25 Z
g lo-'= ti In
I g
10-z--
z 0
10-J-
1 o-4 ‘4
lb3
ENERGY
(e”;’
Fig. 5. 35Cl(n, P)~% resonances, together with the maxwellian distribution at kT = 25 keV.
._...._............. Koehler -
10
This
25
15
Work
30
kT &“, Fig. 6. Comparison of the MACS-values obtained from Koehler’s measurement [12] and this work, as a function of kT. The dashed lines above and below our result indicate a one-standard-deviation uncertainty.
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we obtain a value of 3.2 5- 0.2 mb whereas Koehler finds 2.0 mb, at 25 keV the MACS-values are 1.86 + 0.16 mb and 1.28 mb, respectively. This discrepancy is partly due to the fact that in the determination of Koehler’s MACS-values no resonance parameters above 58 keV neutron energy were available.
5. Astrophysical implications Although it is clear that the MACS-values needed in nucleosynthesis calculations are only relevant for H-values in the keV range, one should not underestimate the importance of an accurate cross-section value at thermal neutron energy. The latter value is indeed often used to normalize cross-section data at higher neutron energies, hence it has a direct impact on MACS-values, which may be very important. A very striking example are the 35Cl(n, p) measurements of Popov et al. [lo]. They were normalized to a thermal cross section of 190 f 50 mb, which is 2.3 times lower than the value determined in this work! More recently, Koehler [12] normalized his 35Cl(n, p) measurement to a thermal value of 489 + 14 mb, which is 11% higher than the value reported here. Astrophysicists are more interested in the quantity N,((+v) instead of the maxwellian averaged cross-section values, because multiplied by the matter density
I
2x10"
I
III
I
III
I
I
I
III
I
-
This Work ____...___ Koehler
4x104
I 10-4
I
III
I
I
II,
10-3
I 10-Z
I
II,
I 10-l
T (GK)
Fig. 7. Comparison of the N,(au) curves calculated present work, as a function of the stellar temperature.
from Koehler’s
renormalized
data
[12] and the
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Physics A573 (1994) 291-305
303
Fig. 8. Partial nucleosynthesis network in the Cl region. Stable isotopes are put into a full square, unstable but long-living isotopes into a square with intermittent lines and short-living isotopes are surrounded by a circle. The meaning of the reaction lines without specification is the following: a full line stands for a (n, y) reaction and an intermittent line means a less probable (n, y) transition due to competition with other reactions.
and the molar fractions of the interacting particles it immediately yields the stellar reaction rate. Obviously, NA (au) is easily obtained by multiplying the MACS-values with Avogadro’s number and the thermal velocity ;? = (2kT/~)l/~, p being the reduced mass. This operation has been done for the Cl(n, p)35S reaction with the data of the present work and of Koehler [12]. Both N,(au) curves are shown in Fig. 7. There is agreement within the error bars below 4 x 10e2 GK, the deviation starts in the region of s-process temperatures. Surprisingly, there is also agreement between the NA((+v)-values calculated by us using Koehler’s (renormalized) cross-section data with the corresponding values given by Koehler [12], which are expected to be 11% higher due to this renormalization. This is probably due to the different formulas applied to calculate N,(au). In this work it was calculated in the straightforward way mentioned above, whereas Koehler calculated this quantity by means of a theoretical fit based on the resonance parameters. As illustrated in the partial nucleosynthesis network shown in Fig. 8, the 35Cl(n, p)35S reaction plays a role in the nucleosynthesis of nuclei in the S-Cl-Ar region. An interesting item to investigate is how it influences the synthesis of the rare nucleus 36S,which is a long-standing problem in nuclear astrophysics [13,14,22]. This influence is introduced via the 35Cl(n, ~)/~~Cl(n, p) branching, which determines the relative probability of the 36S nucleosynthesis via the 35Cl(n, y) 36Cl(n, pj3’?j and the 35Cl(n, p)35S(n, yj3?S path, respectively. The ratio of the MACS-values of the 35Cl(n, y)36C1 and the 35Cl(n, p)35S reactions has been calculated using the experimental data of this work and also of ref. [12] for the (n, p>
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304 I
I
I
Physics A573 (1994) 291-305 I
I
I
__________
,’ ,,,’ ,,,’
0
I 5
I
I
I
Macklin/Koehler
Macklin/This Work _................... Woosfey _____-_-------______ ---___ ,/* ---__---___ ,/’ ----___---_____ ,’ ,’ ---------.__________ I’
I 10
I
I
I
I
I
20
15
I 25
I 30
kT (keV)
Fig. 9. Comparison of the ratio of the MACS-values of the 35Cl(n, y) and (II, p) reactions, determined experimentally from this work, ref. [12] and ref. [20] and theoretically from ref. [23].
as
reaction and of ref. 1201for the (n, -y>reaction. Both curves are presented in Fig. 9, together with a curve deduced from theoretically obtained fitting formulas given in ref. [24]. The calculated experimental y-rate and the theoretical rates were checked for correctness with the ones given in ref. [23]. There is good agreement between this work, combined with Macklin’s (n, y) data, and the theoretical curve, indicating that the above-mentioned ratio is approximately 6. So there is a significant branching at the 35C1nucleus in the s-process with a branching factor hnp/(hnp + Any) = 0.12 at 12 keV and 0.13 at 25 keV. The impact of this branching on the nucleosynthesis path is, however, very small, since the 35S formed via the (n, p) branch rapidly P-decays back to 35C1with a half-life of 87.5 days. This value is smaller than the half-life of a 35C1nucleus against destruction through the (n, p) reaction (defined as Ti,* = (n,(o>,,~r)-~ In 2, n, being the stellar neutron density). If one assumes a value of 3 x 10s n/cm3 for II,, then T1,2(35Cl> is 148 y at kT = 12 keV and 177 y at kT = 25 keV. The authors would like to thank H. Beer and H. Weigmann for useful suggestions, and J. Van Gils and R. BarthClCmy for their technical support. References [l] H. Berthet and J. Rossel, Helv. Phys. Acta 27 (1954) 159 [2] A. Gibert, F. Roggen and J. Rossel, Helv. Phys. Acta 17 (1944) 97
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