Cross-section measurement for 45Sc(p, γ)46Ti

2.A.I

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Nuclear Physics A312 (1978) 1 4 0 - 148: ( ~ North-HollandPublishin9 Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

CROSS-SECTION M E A S U R E M E N T FOR 4SSc(p, ~')46Ti S. B. S O L O M O N t and D. G. S A R G O O D

School ~[' Physics, University o[' Melbourne, Parkville, Victoria 3052, Australia tt Received 14 August 1978

Abstract: The cross section of the reaction ¢5Sc(p,7)46Ti has been measured over the bombarding energy range 0.74.2 MeV. This energy range is appropriate for calculating the interaction rate in a stellar interior over the temperature range [0 9 l010 K. The results are compared with predictions of the statistical model of nuclear reactions. Stellar interaction rates are calculated. N U C L E A R R E A C T I O N S 45Sc(p, 7), E - 0.7 4.2 MeV: measured ~(E). Statistical model

analysis. Natural target.

1. Introduction In calculations of nuclear abundances in supernova and pre-supernova stars, extensive networks of nuclear reactions arc used 1-3). In many cases the reaction cross sections have not been determined experimentally or are inaccessible to experimental measurement as they involve short-lived radioactive targets. In such cases theoretical cross sections calculated with statistical model codes are customarily used. It is therefore of great importance to the astrophysical calculations that whereever possible laboratory measurements of cross sections be made, particularly for key reactions in the network, and that extensive testing of the statistical model by comparison with laboratory measurements be carried out to improve its reliability in those cases where theoretical cross sections have to be used. Perhaps the most stringent test of the ability of the statistical model to predict cross sections reliably is to compare measured and calculated values of the amount by which the cross section of a given reaction drops when a competing channel, notably the neutron channel, opens up, and there are several cases of such measurements already reported in the literature 4, 5). The reaction 45Sc(p, 7)46Ti is a key reaction in the explosive oxygen and silicon burning networks as it constitutes the dominant reaction t) in bridging the bottleneck at mass 45 in the flow of nucleosynthesis from 288i to the elements of the iron group 6), and is therefore a reaction for which it is particularly important to have experimentally determined cross sections. It is also a reaction for which the neutron channels open up right in the Present address: Australian Radiation Laboratories, Parkville 3052, Australia. ,t Work supported in part by the Australian Research Grants Committee [B72/15018]. 140

45Sc(p,y)46Ti

141

range of proton energies of importance in explosive nucleosynthesis calculations, namely at Ep = 2.84 MeV, and therefore measurements of the cross section in the astrophysically interesting energy range also provide data for use in testing the statistical model. For these reasons, absolute measurements of the cross section of the reaction 45Sc(p, 7)46Ti have been carried out over the proton energy range 0.74.2 MeV. Only relative y-ray yield curves for 45Sc(p, ~)46Ti have been measured previously. These measurements involved the use of NaI(T1) detectors and covered the bombarding energy ranges 0.9 1.4 MeV [ref. v)] and 1.3-2.5 MeV [ref. 8)].

2. Experimental details 2.1. MEASUREMENT OF y-RAY YIELD

Since it is the total 7-ray yield which is required for both of the analyses for which the data were being collected, and since the decay schemes of the 46Ti states excited by this reaction are dominated by multiple cascades with three or more members, the use of two large NaI(T1) detectors located at _+90° in the close sum geometry of Lyons et al. 9) was first considered. The detector efficiency of this system is high and can be reliably calculated, the reliability of the calculation increasing, and its sensitivity to branching ratios decreasing, the greater the complexity of the cascades 9). However, the method is useful only if other channels, such as (p, p' y) are either closed, very weak, or give rise only to 7-rays of lower energy than the lowest (p, y) y-ray, and is certainly of no use above the neutron threshold because of neutron activation of the NaI(Tl) crystals and the large flux of y-rays arising from the (p, n),) reaction itself. For the present measurement~ it was necessary to carry the observations to more than 1 MeV above the neutron threshold, and well above the energy at which (p, p' y) was a serious contaminant reaction. It was therefore necessary to seek an alternative method of measuring the total y-ray yield. In every case where branching ratios of 46Ti resonances excited in the 45Sc(p, y)46Ti reaction were available, it was evident that nearly 90 % of all cascades passed through the 889 keV first excited state of 46Ti,'and it therefore seemed likely that an excitation function, measured by observing only the 889 keV peak in the y-ray spectrum obtained with a Ge(Li) detector, would reproduce reliably the energy dependence of of the y-ray yield. This hypothesis was tested by making a high resolution excitation function measurement covering a total of sixteen resonances at energies below 2 MeV, where the NaI(TI) detection technique could validly be used, and comparing the NaI(T1) yield with that of the 889 keV peak in the Ge(Li) detector spectrum. The excellent agreement between the two measurements, as typified by the partial excitation function shown in fig. 1, showed that this was indeed a valid method of measuring the excitation function, and since NaI(TI) detector measurements can be used to give an absolute measure of the y-ray yield 9), comparisons such as that shown in

S. B. S O L O M O N A N D D. G. S A R G O O D

142

fig. 1 constitute a means of providing an absolute calibration of the Ge(Li) measurement. Observation of the 889 keV peak was a useful means of measuring the y-ray yield for bombarding energies up to 2.5 MeV. At higher energies the presence of the 890 keV y-ray, resulting from the population and subsequent de-excitation of the 1.433 MeV state in 45Sc via the (p, p') reaction, made extraction of the 889 keV yield impossible. For higher energy bombardment, the 1120 keV peak, corresponding to

I-ZD >rr < n-" I--

•

Nal (TI)

x

Ge(Li}

rr" U3 I--

Z :D 0 L.) >no

(D

I 1230

I 1240

I 1250

i.~l, 1260

I

i

I

1500

PROTON

i 1510

ENERGY

I

i 1520

iJ •

I

' v1540

I

1560

(keV)

Fig. 1. Portions o f the excitation function o f the 4SSc(p, ),)*6Ti reaction measured with NaI(TI) and Ge(Li) detectors. Crosses refer to the 889 keV photopeak yield observed with Ge(Li) counter a s described in the text. The filled circles are integrated ~,-ray yields measured with the NaI detector. The solid line joins these points as an aid to the eye. The two relative yield curves have been normalised to each other for comparison.

the transition between the 2.009 and 0.889 MeV states in 46Ti, was used. This y-ray was k n o w n to have a relative intensity which varied significantly from one resonance to another, but since both the astrophysical use and statistical model analysis of the data call for average cross sections rather than cross sections of individual resonances, it was anticipated that this variation would prove unimportant. To verify this, the ratio o f the yields o f the 889 and 1120 keV y-rays averaged over some ten resonances at a time was determined over the whole energy range 0.9-2.5 MeV. The ratio o f yields was found to be essentially constant thereby demonstrating that the 1120 keV peak could be used as a valid measure o f the total y-ray yield, in this experiment.

45Sc(p, 7)46Ti

143

2.2. EXCITATION FUNCTION MEASUREMENT A target of thickness 50 #g. c m - 2 was prepared by evaporating 99.99 ~o pure Sc from a tungsten wire basket on to a 0.25 mm thick tantalum backing in a vacuum of pressure 10- 6 Torr, and was bombarded by proton beams from the Melbourne 5 MV Pelletron accelerator. Beam currents were typically 10/~A at 1 MeV, falling to 1 #A at 4 MeV. Although the targets were prepared from scandium metal under vacuum, later analysis showed that they were in fact oxidised. The beam lines and target chambers are stainless steel with all metal seals, and the whole system was pumped by ion pumps which held the pressure at less than 5 x 10 -8 Torr throughout the bombardment. The tantalum target backings were clamped directly on to a stainless steel knife edge thereby forming an integral part of the vacuum system, and were cooled by liquid freon in a closed circulatory system which included a heat exchanger. The targets were angled at 55 ° to the incident beam and the Ge(Li) detector was located 11 mm from the target in this 55 ° orientation. Lead sheet of thickness 3 mm shielded the detector from the very intense 136 keV 7-ray arising from Coulomb excitation of the tantalum target backing. The last 20 cm of the beam line constituted the target chamber, which was insulated from the rest of the beam line by a plate glass annulus 1.3 cm thick and sealed on both faces by indium wire rings. The whole of the target chamber acted as a Faraday cup for beam collection. The beam was collimated to a spot of diameter 3 mm by a collimator consisting of two apertures of this diameter separated by a distance of 10 cm and followed by a wire ring held at - 4 5 0 V which acted as an electron suppressor for both the collimator and the Faraday cup. i

I

3,C

I

I

I

I

l'5Sc(p,a)t'6T i

Ai/ ~ 1.C 0"[

I

'

. ~I ~i~;]'~J''

tO

I 1.5

i*SSc(P'nI' 5Ti t I'¢ esh°~d I I I l 2.0 2.5 3.0 PROTON ENERGY (MeV)

I 3.5

" I KO

Fig. 2. Absolute cross section for the 4~Sc(p, "g)46Ti reaction. The statistical uncertainty per point is smaller than the size o f the point while the absolute uncertainty is ___20 9/o. The solid curve is a guide to the eye.

144

S. B. S O L O M O N A N D D. G. S A R G O O D

The target thickness was only 4 keV to 4 MeV protons. Allowing for the angle at which the target was mounted, the effective thickness was 7 keV. A thicker target would have been more appropriate to the aims of the measurement, but this thin target was used owing to difficulties experienced in producing robust targets of greater thickness. The excitation function was traced out in energy steps of 3 keV, and is shown in fig. 2. The data points in the energy range 0.9 2.5 MeV correspond to measurements involving the 889 keV y-ray peak, and those above 2.5 MeV to the 1120 keV peak normalised to the average behaviour of the yields of the two 7-rays in the 0 . 9 - 2.5 MeV region. Finally, the yield of the 889 keV peak in the Ge(Li) spectrum was compared with the total yield in a 12.7 x 15.2 cm NaI(TI) detector placed 11 mm from the target. also in the 55 ° direction. This comparison was made on the resonances between 1.04 and 1.11 MeV. The detection efficiency calculation for the NaI(T1) detector used the photon cross sections of Storm and Israel lo), and took into account the reduction in efficiency due to the absorption ofT-rays due to interactions with the target backing, the liquid freon cooling chamber, and the aluminium can and MgO packing around the NaI crystal, and also the enhancement of the detection efficiency due to electrons and positrons produced in these interactions and having sufficient energy to penetrate to the crystal and so initiate pulses. Individual points of the excitation function have an uncertainty of less than 3 '~,. The calibration of the Ge(Li) as a detector of total 7-ray yield is believed accurate to 13 o£. This comprises statistical errors of 2 5,; and 1 ')0 for the Ge(Li) and Na(T1) detector yields respectively, a 2 ~;, error from the extrapolation of the NaI(T1) spectrum to zero energy and an 8 ~0 uncertainty in the NaI(T1) detection efficiency due to differences in cascade structure of individual resonances. At bombarding energies below 0.9 MeV, the 7-ray yield from the thin target was prohibitively small. Accordingly, the target used for the energy range 0.7 0.9 MeV was 99.99 ~,, pure scandium foil of thickness 0.25 mm, a stopping thickness for the proton beam. The y-ray yield was measured With the Ge(Li) detector, because the 889 keV line provides an unambiguous signature of the 45Sc(p, ~')46Ti reaction at low energies, and yield from contaminant reactions poses serious difficulties for NaI(T1) detectors when the yield o f interest is low. The contribution to the stellar interaction rate was extracted from the yield data by the method of Roughton et al. J ~). 2.3. M E A S U R E M E N T O F T A R G E T T H I C K N E S S

To obtain absolu~,e cross section values it was necessary to have an accurate knowledge of the amount of scandium in the thin Sc-containing target. Two different methods of determining the scandium content were used. The more fundamental of these was by direct Rutherford scattering of c~-particles. A beam of c~-particles was collimated to a diameter of 1 mm before striking the target.

45Sc(p, 7)46Ti

145

Secondary electrons from the collimator, and from the target, were suppressed by a tantalum shield held at - 450 V. The insulation of the target assembly was checked for leakage current, and an upper limit of 0.1 hA, or 1 ~o of the current measured, was established. The scattered a-particle yield was measured with a silicon surface barrier detector, at 01ab = 135 °, whose aperture was limited by a stainless steel shield with a circular hole of 1.01 _+0.01 mm diameter in it. The diameter of the hole was measured with a travelling microscope and its distance from the target, 4.775_+ 0.020 cm, was measured with vernier calipers. Taking the finite size of the beam spot into account also, led to an uncertainty of 2 ~o in the calculated value of the detector solid angle. The 45Sc peak in the Rutherford scattering spectrum stood on the much higher plateau of the spectrum from the thick tantalum backing, and counting was continued until the statistics on the 45Sc peak area were better than 3 ~o after subtraction of this background. The measurement was carried out at a-particle energies of 2 MeV and 3.8 MeV, energies which were known to fall in the Rutherford domain for 45Sc, and which were appropriate for the second method of determining the 45Sc content of the target. The Rutherford scattering cross sections were determined to an accuracy of 1 ~o, and since the errors in beam current integration were below 0.5 ~o, the final estimated error for the scandium content, as determined by this method, was 6 ~o. The second method was less direct. From the Rutherford scattering of c~-particles at 2 MeV, an energy at which the scattering from 160 was known' to follow the Rutherford law, and at 3.8 MeV, at which the scattering cross section, although not Rutherford, was nevertheless known lz), the ratio of 45Sc to 160 was determined. The thickness of the target in energy units was then found by two independent methods. The first was by measuring, at each energy, the full width at half-height of the elastic scattering peaks from 45Sc and deconvoluting the intrinsic resolution of the detector, which had already been determined at both energies from the shape of the high energy edge of the elastic scattering spectrum from a thick tantalum sheet. The thickness, in energy units, was determined to better than 3 ~o by this method. The second was by measuring the shift in position of the high energy edge of the scattering spectrum from tantalum when both 2 and 3.8 MeV a-particles were scattered from clean thick tantalum and from the target on its thick tantalum backing. The target composition data, .together with the tables of atomic stopping cross section of Northcliffe and Schilling ~3), were used to convert the target thickness measurements to units of mass per unit area, and the target composition data was then used again, to give the scandium content. Uncertainties in the target composition data produced a 7 ~o error in the total atomic stopping power of the scandium containing layer. Taking the error in the tabulated atomic stopping powers as 5 gave an overall error in the Sc content of 15 ~ and 16 ~ , respectively, for the two methods of measuring the thickness in energy units. Hence, in all, six determinations of 45Sc in the target were made, and these agreed

S. B. SOLOMON AND D. G. SARGOOD

146

to within 7 ~o- The finally adopted value for the Sc content was 38_+ 2 gg • cm 2 Combining the errors in the y-ray yield and the target thickness measurement gives an estimated error of 20 ~,, for the absolute cross section shown in fig. 2. Errors arising from beam current integration and system deadtime were below 0.5 o/,,.

3. Discussion 3A. COMPARISON WITH STATISTICAL MODEL CALCULATIONS In the notation o f W o o s l e y et al. 14) and Holmes et al. 1~), the cross section of the reaction I~(1", k)L ~' is given for the statistical model by the equation 7z22 -uv u ~ ( 2 J + 1) T]'(J'~)TkV(J'~) ark (E j) = t2Jf + l)(2J s + 1) j,= Trot(J;) - ' where # and v refer to discrete energy states of the nuclei I and L respectively, and J, are the spin and parity of resonance states in the compound nucleus. When comparison is made with experimental data, the superfix p will be zero, since the target is necessarily in its ground state. In the aSSc(p, y)46Ti cross section measurements reported in this paper, the total y-ray yield to all states of a6Ti was measured, rather than the yield to individual states, implying a summation over v. The cross-section expression for this reaction then becomes

apO?(Ep)

7[)~2

= (2)oc-+l)~-jp + l ) E (2J + 1) T°(J'~)T'(J') s,, Trot(J'~) '

where

L ( J ~) = ~ T~(J'). v

Woosley et al. 14) and Holmes et aL 15) calculate the transmission coefficients, T(J'), for particle channels by using the equivalent square well representation of a Woods-Saxon optical potential developed by Michaud et al. L6,17), and for the y-ray channel by considering only dipole transitions from each resonance level. For comparison with the statistical model predictions, the experimental data were averaged over energy intervals of 165 keV to smooth out the structure. The smoothed data are plotted in fig. 3~ The full line in fig. 3 is the calculated cross section of Woosley et aLia). The broken line is the same calculated cross section multiplied by a factor of 2. It is clear that the theoretical curve fits the energy dependence of the data, including the details of the cusp which occurs at the opening of the neutron channel at E n = 2.84 MeV, to within 20 ~ and fits the data absolutely to within the factor of 2.

45Sc(p, 7)'6Ti 5.0

r

I

r

147

i

i

1

I

45Sc{p,~)46Ti

aO

E

\*

~(.

z 1.(]

,:/"

0 I-(3

0.5

/

u') 0

\'-.. - .... •

i!

0-1 I

I

1.0

1.5

I

I

I

I

I

2.0 2.5 3.0 3.5 4.0 PROTON ENERGY (MeV| Fig. 3. Comparison of predicted cross section of Woosley et al. 14) and the energy-averaged experimental cross section for the *SSc(p, 7)46Ti reaction. The full line is the cross section of ref. 14): the broken line is this cross section multiplied by a factor of 2.

3.2. T H E R M O N U C L E A R R E A C T I O N RATES

Following Fowler, Caughlan and Zimmerman ~8), the interaction rate at temperature T, for any reaction is given by

(av) ° -

(8/zt)½ r°~aE e x p ( - E / k T ) d E , M~(kT)~jo

where M is the reduced mass and E the energy of the interacting particles and the superscript zero denotes that the target nucleus is in its ground state. This expression and the present data were used to calculate ( a v ) ° for 45Sc(p, y)46Ti in the temperature r a n g e 1 0 9 - 1 0 l ° K , the temperature at which the reaction is believed to be most important in stars being 4.7 × 109 K (ref. l)). In a star, nuclei are thermally excited into excited states, and provided the population of excited states is the thermal equilibrium population, the prescription ofWoosley et al. 14) may be used to convert the laboratory interaction rate (av) ° to the stellar interaction rate (av). The stellar interaction rate, multiplied by Avagadro's number, was then fitted by an equation of the form

N A(av) ~

1

A exp [-(T/Tg)(1 + B T 9 + CT92 + OT3)],

as given by Holmes et al. 15)~where T 9 is the temperature in units of 109 K, T is given by eq. (55) of ref. 18), and A, B, C, and D are arbitrary parameters. With A = 5.65×1015, B = 1.997x10 -2, C = 9.259×10 -3, and D = - 6 . 4 8 7 × 1 0 -4 ,

148

S.B. SOLOMON A N D D. G. SARGOOD

the expression fitted the data to within 30 ~o over the temperature range 1 < T 9 < 10. These interaction rates have been reported more fully elsewhere ~9). We wish to thank Dr. Z. E. Switkowski for helpful discussions throughout this work and one of us (S.B.S.) wishes to acknowledge the support of a C o m m o n w e a l t h Post-Graduate Award.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) I1) 12) 13) 14) 15) 16) 17) 18) 19)

S. E. Woosley, W. D. Arnett and D. D. Clayton, Astrophys. J. Suppl. no. 231, 26(1973) 231 R. C. Pardo, R. G. Couch and W. D. Arnett, Astrophys. J. 191 (1974) 711 W. M. Howard, W. D. Arnen and D. D. Clayton, Astrophys. J. 165 (1971) 495 F. M. Mann, R. A. Dayras and Z. E. Switkowski, Phys. Lett. 58B (1975) 420 Z. E. Switkowski, J. C. P. Heggie and F. M. Mann, Phys. Rev. C17 (1978) 392 G. Michaud and W. A. Fowler, Astrophys. J. 173 (1972) 157 J. Dubois and S. Maripuu, Ark. Fys. 24, no. 12 (1963) 127 B. Erlandsson and K. Valli, Ark. Fys. 24, no. 3 (1962) 31 P. B. Lyons, J. W. Toevs and D. G. Sargood, Nucl. Phys. AI30 (1969) 1 E. Storm and H. I. Israel, Nucl. Data Tables A7 (1970) 565 N. A. Roughton, M. J. Fritts, R. J. Peterson, C. S. Zaidins and C. J. Hansen, Astrophys. J. 205 (1976) 302 J. R. Cameron, Phys. Rev. 90 (1953) 829 L. C. Northcliffe and R. F. Schilling, Nucl. Data Tables A7 (1970) 233 S. E. Woosley, W. A. Fowler, J. A. Holmes and B. A. Zimmerman Caltech Orange Aid Preprint 422 (1975) J. A. Holmes, S. E. Woosley, W. A. Fowler and B. A. Zimmerman, Atomic Data and Nucl. Data Tables 18 (1976) 305 G. Michaud, L. Scherk and E. Vogt, Phys. Rev. C1 (1970) 864 G. Michaud and W. A. Fowler, Phys. C2 (1970) 2041 W. A. Fowler, G. R. Caughlan and B. A. Zimmerman, Ann. Rev. Astr. and Astrophysics 5 (1967) 525 S. B. Solomon and D. G. Sargood, Astrophys. J. 223 (1978) 697