Direct proton capture on 32S

Nuclear Physics A539 (1992) 97-111 North-Holland

NUCLEAR PHYSICS A

Direct proton capture on 32 S C. Iliadis, U. Giesen, J. Gärres and M. Wiescher

Department ofPhysics, University of Notre Dame, College ofScience, Notre Dame, IN 46556 USA

S.M. Graff

Los Alamos National Laboratory, Los Alamos, NM 87545, USA

R.E. Azuma

McLennan Physical Laboratories, University of Toronto, Toronto, Ontario MSS ]A7, Canada

C.A. Barnes

W.K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, CA 91125, USA Received 23 October 1991 Abstract: The 32S(p, y)33C1 reaction has been measured in the proton-energy range EP = 0.4-2.0 MeV. Non-resonant y-transitions were observed to the final states in 33C1 at E,, = 0, 811 and 2846 keV. The corresponding spectroscopic factors have been extracted from fits to the exciiati ;M. functions and are compared to values from stripping data as well as theoretical model calculations . The astrophysical aspects of the 32S(p, Y)33Cl reaction are also discussed.

l . Introduction

Non-resonant radiative proton capture has been studied '-s) on several target nuclei in the mass range A--<40 . It has been demonstrated that the experimental data can be analysed in terms of an extra-nuclear direct-capture (DC) process with simple potentials for the targeF-projectile interaction . The observed total cross sections yield, when compared with these model calculations, the spectroscopic factors for the final states . In a continuing study of direct-capture reactions, the radiative proton capture on 32S has been investigated . Although the reaction 32 S(p, y)33C1 (Q = 2.277 MeV) had been studied previously'), no investigation of the non-resonant cross section has yet been reported . Sizeable spectroscopic factors for the low-lying energy levels in 33C1 have been reported 7) from single-particle stripping reactions, therefore DC -y-ray transitions to all these states (fig. 1) are expected with cross sections of 0.01-0 .1 Rb at Ep =1 .5 MeV. In the energy range of the present experiment, Ep = 0.4-2 .0 MeV, the search for direct-capture transitions to the ground and first excited state is complicated by the 0375-9474/92/$05 .00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

C. plia is et ai. / Direct proton capture

98

4-qq4113 4117

3-0-5,710 :3,51

0.5

32 S

+P

33c

I

Y)33CI . The vertical Fig. 1. Level diagram of "Cl and proton energies of resonances in the reaction 32S(p, arrows indicate the Gamow windows for the given temperatures (in 10' K) .

resence of a broad resonance') at Ep =1898 keV (J' = 2!-) with a total width of F =: 10 keV and a resonance cross section of O'R =16 ~,b. The expected interference e ects between the resonant and the direct capture process should be most prominent on the tails of the resonance where the interfering amplitudes are of the same order. Further, the reaction 32S( p, Y)33CI may be of importance for nuclear astrophysics . 8) For high stellar temperatures in hydrogen-burning environments the rp-process involving rapid capture of protons on seed nuclei can lead to the production of heavy elements up to and beyond the iron group. The actual reaction path, a sequence of proton capture and P-decay processes, is determined by the nuclear reactions involved . Reaction flow studies 9 ) indicate that for T9 < 0.5 the dominant reaction sequence will lead to the production of "P via 28si(p' 7 )29KP, Y )IOS(p+ I,)30p( p' Y )31S(p+ I,)31p .

The further reaction path depends on the (p, y)/(p, a) reaction branching at 31p

C. Iliadis et al. / Direct proton capture

99

[ref. 10)]. If the 3' P(p, y)32S reaction dominates, the stellar rate of the subsequent proton capture on 32S will be important. We therefore present an updated stellar reaction rate for 32S(p, y)33C1 . The experimental equipment and set-up is described :n sect. ?, followed by the discussion of the experimental procedures and results in sect. 3. A comparison of the results with corresponding information from stripping data as well as theoreticalmodel calculations and a discussion of the astrophysical aspects is given in sect . 4. Throughout this work, Ep is the proton bombarding energy and ER the resonance energy. Both energies are given in the laboratory system unless stated otherwise . 2. Experimental equipment and set-up The measurements were carried out at the 3 MV Pelletron tandem accelerator at the Kellogg Radiation Laboratory of the California Institute of Technology . An RF source, installed in the terminal of the tandem, provided proton b'-ams of up to 65 p,A in the energy range Ep = 0.4-2.0 MeV. The energy resolution of ® E = 2 keV was measured using the known, narrow 27Al(p, Y)2". Si resonance at ER= 991 .88 t 0.04 keV [ref. 7)]. The proton energy was calibrated with this resonance and the known 32 S(p, Y) 33C1 resonance at ER =1757.2+0.9 keV [ref. 6)] to t l keV. The target was produced by implanting 32S ions into a 0.5 mm thick Ta-backing with an incident dose of 120 RA - h, using the SNICS source at the University of Notre Dame. The implantation energy was 80 keV which gave a well-defined target thickness of -5 keV at Ep =1760 keV bombarding energy. Fig. 2 shows a typical yield curve for this target, obtained for the resonance at ER =1588 keV. The target stoichiometry was determined by measuring the thick-target yield curve of the well-known 32S(p, y )33C1 resonance at ER =1757 keV [ref. 6)]. A ratio of sulfur to tantalum of 1 .0 t 0.2 was found using the stopping-power tables of Andersen and Ziegler "). The targets were directly water cooled and found to be very stable under proton bombardment . No noticeable deterioration was observed after an accumulated charge of 10 C. The proton beam passed through a set of horizontal and vertical slits and was directed onto the target which was mounted at 45° with respect to the beam direction. The beam was scanned over an effective area of _ 1 cm2 by magnetic steerers to illuminate the target uniformly. A liquid-nitrogen-cooled copper tube was placed between the slits and the target to minimize carbon deposition on the target. Target and chamber formed a Faraday cup for charge integration and a negative voltage (--300 V) was applied to the Cu tube to suppress secondary electron emission from the target. The y-radiation was observed by a 35% Ge-detector with an energy resolution of 2.0 keV at E,, =1 .3 MeV. The detector was placed at 55° with respect to the beam direction at a front-face-to-target distance of d =1 .8 cm and was shielded by 5 cm of lead to reduce contributions from room background. During the measurement

100

C lliadis et al. / Direct proton capture

1565

1590

I

1595

1600

Proton energy ( keV )

y)33C1, measured at 9 = 55° for the transition Fig. 2. Yield curve of the E R = 1588 keV resonance in 3`S( p, from the first excited state at Ex = 811 keV in 33CL The data points shown are not corrected for the absolute y-ray efficiency of the Ge detector. The solid line through the data points is to guide the eye only.

of the angular distributions, the detector was placed at 0°, 55° and 90° at a distance of .3 cm from the target. The y-ray efficiencies of the detector were determined from the known branching ratios and resonance strength of the 27Al(p, y)28Si resonance at ER = 992 keV [refs . 12, ")]. The energy calibration of the detector was obtained 'from background lines as well as from the known 7) y-ray energies of transitions in the residual nucleus 33Cl . The energies of the latter transitions were corrected for Doppler shifts when appropriate . . Experimental results an

analysis

3.1 . NARROW RESONANCES

Five narrow resonances have been observed at proton energies of ER = 422, 588, 1588, 1748 and 1757 keV (see table 1). The resonance energies are in very good agreement with previous results 6) . On-resonance y-spectra were measured with the Ge-detector at 55° and with k harge accumulations of -0.01-1 .0 C. In addition, y-spectra have been measured at energies just below the resonances to correct the resonance yield for possible non-resonant contributions . This is of special importance for the weak primary transitions . The resulting y-branching ratios are shown in

C. Iliadis et al. / Direct proton capture TABLE 1 Energies and strengths for 32S(p, ER (keV) present')

1899 ± 2 b)

ref. 6)

present -"f) 3 .5x10 (3 .7±0.8) x 10 -5

2 (2, 2) 5+ 2 32

421.8±0.6 579.8 :k 0.6 587.9±0 .5 720.7±0 .6 1587 .8±1 .1 1748 .4±1 .0 1757 .2±0 .9 9) 1879 .7±1 .1 1893 .8±1 .1 1898 ± 2

1589±1 1749± 1

wy (eV) `)

refs. 6.') 3+

589±1

Cl resonances

JIff

ref. 6)

77 .3 ± 0.8 e) 424±2

Y)33

101

(1 .3±0 .3) x 10-'

1+ 2 5+ 2 3+

2 52 (-!+, 1, 5+)

(2 .7±0 .6) x 10-2 (4.5 ± 0.9) x 10-2

22

(i -5, i+) 32

(8 .9±4 .0) x 10-2 b)

(4.5±2 .0) x 10 -5 (4 .0±0.5) x 10 -2 (1 .0±0.1) x 10 -' (0 .7±0.3) x 10 -4 (2 .6±0.3) x 10 -2 (4 .5 ± 1.0) x 10 -2 (1 .9±0.2) x 10 -' d) (9 .5±4.0) x 10 -3 (33 :L 1.0) x 10 -2 (9 .5±3.5) x 10 -2

From location of midpoint of front edge of thick-target yield curve. b) From least squares fit of yield curve (see sect . 3.2); for the total width a value of I' _ (10±3) keV has been deduced [I'=(14±4) keV from ref. 6)]. `) With wy equal to wy = (2JR + 1)Tp r.,/2T. d) Used as a reference for the calculation of the target stoichiometry. e) Calculated from Ex =12351 .8±0 .3) keV and Q = (2276.9±0.7) keV f_ref. 71] . f) Calculated with eq . (8) and C2S=0.064 (see sect . 4.2 .) . s) Used for the beam energy calibration (see sect. 2) . a)

TABLE 2 Gamma-ray branching ratios (in %) of 32S(p, ER (keV) : E,,; (keV) : Exf

(keV)

J,

0 811 1986 2352 2685 2839 2846

3+ 2 1+ 2 5+ 2 3+ 2

2975 a)

2,2) 5+ 2 3-

2

J-:

422 2685 5 7 (2, 2)

588 2846

34±6

45=3 55±4

66± 11

32

1588 3816 5+ 2

161=3 b) 2.0±0.7 24±4 40±7 18±2

y)33C1

resonances a) e)

1748 3972

1757 3980

1898 4117

26±6 39±8 15±3 9±3

88±13

26±8 74± 10

3+

2

11 ±3

52

5.0 :t 0 .8 23 :t 0.5 4.7

±0.8 d)

z

All energies in keV. b) Corrected') for P4(cos 0) component (see sect . 3.1 .) . `) Not analysed due to strong background contribution. d) Energetically not resolved from transition to state at E,, ---- 2839 keV. e) Branchings from least squares fit of yield curve (see sect . 3.2 .) .

32

C. ilia Ls et aL / Direct proton capture

10 2

6) re in good overall agreement with the previous results . The y- ray ang lar distributions of the J 2 resonances at ER = 588 and 1748 keV will be afar ined by Qcos 0) Legendre polynomial terms which are zero for the chosen acct r angle. For the resonances at ER =1588 keV (J' = 5-2 ') and 1757 keV (J' = 5-) 2 t e assured angular distributionS 6 ) indicate only small P4(cos 0) components except for the ground-state transition of the ER =1588 keV resonance (a4 =0 .49+ 0.05). Taking the large opening angle of the Cie-detector into account. we have estimated that in all other cases explicitly neglecting possible P4(cos 0) terms for the 32S( p, Y)33CI resonances would introduce a systematic error of at most 6% in the branching ratios. he strength cry of a resonance in a (p, y) reaction is defined by: t

X

2J+1 (2jp +1)(2j,+o

r ,

with JJp and j, as spin of the resonance, the projectile and the target nucleus, respectively ; F is the total width ofthe resonance level and Fp , r, are the correspondartial widths . The resonance strength is related to the thick-target yield YR of ance bv2E,ff where AR is the proton wavelength at the resonance energy, A, (A p ) the mass of the target (projectile) in a. .u. and E,fF the effective stopping power of the TaS target c 0 Eet, = Es +

(NTJ

) 6 Ta -)

with NTa/ Ns =1 .0 :± 0.2 .

The stopping power values for Es and ETa have been obtained from ref. ") . The resulting resonance strengths are listed in table 1 . The quoted errors include the uncertainty of the effective stopping power ( :±:18%), the relative -y-ray efficiency (6%) and the charge measurement (±10%) . The results of Aleonard et A 6) are also hoed for comparison and agree well with our values . 3 .2 . CONT

UTIONS FROM DC AND THE BROAD RESONANCE AT ER!'__1898keV

amma-ray spectra were obtained in the energy range Ep =1 .38-1 .93 MeV with t e Ge- etector at 55'. Fig. 3 shows parts of spectra which were taken at four ifferent proton energies outside the regions of the narrow resonances . The y-peaks w ish correspond in energy to the transition to the first excited state in 33 0.1 at E, = 811 keV are indicated. In total, primary y-transitions to three different final states in 33CI were observed . The resulting excitation functions (fig. 4) show clear evidence for non-resonant contributions to the total reaction cross section . The yield curves for the transitions to the states at Ex = 0 and 811 keV in 330.1 are dominated

C Iliadit et al. / Direct proton capture

103

3000 2000

1000 U)

'c

0 0 b-

W .0

500 500

E

=1 C

100

2000

1000 3.02

3.0

3.26

3 .38

-r-energy (MeV)

3 .50

Mg. 3. Selected parts of y-ray spectra (0 = 55') for the reaction 32S( O' Y)33CI taken at four differen! proton energies . The shift in energy for the /-peak which corresponds to the primary transition to the first excited state at E,, = 811 keV in 33CI is indicated .

at higher energies by the broad resonance at ER =1898 keV (F =10 keV). Data points of the yield curves on top of this broad resonance are not shown in fig. 4 and have been excluded from the analysis due to the influence of the narrow resonance at ER =189- 4 keV which has a primary y-decay similar to the ER =1898 k(--V resonance. The contribution of the weak and narrow resonance at ER =1880 keV was subtracted from the measured yield by analysis of its strong primary decay to the state at E,, =1986 keV. The excitation function for the transition to the unbound state at E,, = 2846 keV also is shown in hg. 4. No contribution from the broad

i04

C d~:adis et al, / Direct proton capture __ 32~

0 0

I 0f3

(p,r ~33c1

e = ~5°

R/DC --~ 0

v C

R/DC -~ 811 0 10 '3

v v . . v 1400 1600 1800 2000 Bombarding Energy Ep Ae ( keV ) Fig, 4. Fxciiation functions of the prignary transitions to the states at EX = 0, 811 and 2846 keV in ~'S(p, y)33C1 . The solid lines represent the best fits to the data (see text) and the dotted lines show the contributions from the direct capture and the broad resonance at ER =1898 keV, respectively. Data points on top of the broad resonance are not shown and were omitte~ from the analysis due to the influence of the ~R = 1894 keV resonance . Further, for reasons of clearness not all datapoints are shown on the low and high energy tails of the broad resonance .

=1898 keV resonance is observed. The reported 6) (1 .0 t 0.5)% branch of the = 1898 keV resonance to the state at EX = 2846 keV is probably entirely caused y this lion-resonant y-yield. The relation between the cross section ~( E ) and the observed yield Y( EP) is given by the integral over the target thickness ~ : R R

Q( E ) dE . (3) E~_~ ~(E) T e di erential cross section including possible interference effects was calculated fro the expression : Y(EP) =

d~~_

(EP~

®-55°)= 1 ~r

En

~~ (2 - S~k)~P )~ti(~P )

~k( ® =55°)

cos (+~~ - ~Gk) ~

(4)

In order to extract the resonance parameters of the broad resonance at E R =1898 keV

C. lliadis et al. / Direct proton capture

105

and the strengths of the direct capture transitions, eq. (4) was incorporated in eq. (3) in a least-squares fit to the data. The indices i, k refer to the resonance at ER =1898 keV and the DC components for different incoming partial waves, and Sik denotes the Kronecker symbol. The resonances were described by Breit-Wigner expressions, which included the energy dependencies of Tp , T,, and T and the Thomas shift of the level energy "). The y- angular distributions W(O) and the phase shifts 4Gi of the resonance are given in re .'5 ). Cross sections for the direct capture were calculated following the formalism described by Rolfs 2) using a Woods-Saxon potential with a radius of R = 1 .25 A,'/3 fm and a diffuseness of a = 0.65 fm [refs. 16 °")] . The actual DC cross section is given by: 0, . = C 2 SO' oc (theory) DC , (5) where C2 denotes the isospin Clebsch-Gordan coefficient (C 2 =1 for T = 2 states). The spectroscopic factor S for the final state was used as a fitting parameter in the analysis of the data. The ground state (J' = 2+, If = 2) can be populated by p- and f-w-.ve capture, the first excited state (J~ = 2 + , If = 0) by s-wave capture only and the transition to the state at E,t = 2846 keV (J'T = 2 - ,1f=1) can proceed via s- and d-wave capture. Phase shifts qii for the direct capture and angular distributions Wi (®) for individual transitions as well as for the interferences between different incoming partial waves or with resonances are given by ref. 2 ). The state at EX = 2846 keV is proton-unbound by -600 keV. Therefore the cross section O'DC (theory) has been calculated for various excitation energies below the proton threshold at Q = 2276 .9 ::1: 0.7 keV [ref. 7)] assuming a bound-state formalism and has then been extrapolated to the correct excitation energy . In addition to the excitation function, angular distributions have been measured on the tails of the broad ER =1898 keV resonance at Ep =1875 and 1916 keV and far below that resonance at Ep =1623 keV using the angles 0°, 55° and 90°. These data were fitted to Legendre polynomials : (6) W(O) =E a k Pk (cos 8) . k

Since the spins and parities involved in the resonant and direct capture are known, it follows from the expressions in refs. 2,'5), that only a P2(cos 0) term will determine the angular distributions. The resulting measured a2 -coefficients are shown in fig. 5 as a function of the proton energy. Moreover, to resolve ambiguities in the choice of the sign of the interference terms, a2-coefficients were calculated from the parameters of the fits to the excitation functions and compared with the experimental coefficients. The solid lines in fig. 5 represent the a2 -coefficients calculated from the best fits and are in good agreement with the me :isured angular distributions. The results of the final fits to the excitation functions are shown in fig. 4 as solid lines. Also shown are the individual contributions of the direct capture and the

C. Madis et al. / Direct proton capture

10

I

I

2

R / DC

I

OF -I

-2 2

r

1 11, N

I

f I

R/DC -~ 811

0

J

-1

CI

2-

DC --~ 2846

1 .4

1 .8 1 .6 2 .0 LAB Boanbarding Energy E P (MeV) Fig. 5. a 2 -coefficients for the proton capture to the states at E, = 0, 811 and 2846 keV in 32S( p, Y )33CI . The solid lines represent the values calculated from the parameters ofthe best fit to the excitation functions .

resonance as dotted lines. The resulting parameters for the ER =1898 keV resonance are listed in tables I and 2 and are in good agreement with the previous results 6) . The measured spectroscopic factors are given in table 3 together with results from single-particle stripping reactions and theoretical-model calculations . It should be mentioned that, despite large errors for the resonance parameters due to the fact that data points on top of the resonance yield curve have been neglected, our spectroscopic factors are rather insensitive to these variations. The uncertainty of the spectroscopic factors include the errors of the individual fits, the number of target nuclei ( :E15%) and the realtive efficiency ( :±6%) . Not included are errors introduced by the choice of the potential parameters. We have estimated that a 10% change in the nuclear radius R and the diffuseness parameter a results in a 25% and 10% change in the theoretical direct-capture cross section, respectively . iscussio 4.1 . SPECTROSCOPIC FACTORS

From a comparison of the observed and predicted DC cross sections to the final states in 33CI, the corresponding spectroscopic factors C'S' have been deduced

C. Riadis et al. / Direct proton capture

10 7

TABLE 3

Single-particle spectroscopic factors for the final states in E,,(keV)

J7T

nt

0 811 1986 2352 2685 2839 2846

3+

Id3 / 2 2s 1 / 2 Id5/2 Id3/ 2 1f,/2 e)

2 2 s+ 2

3+ 2

(2, i) s+ 2 32

C2S

a`

Ids/2

2P3/2

33C1

present b)

stripping `)

theory d)

0.84±0.21 0 .28 t 0.05 0.26 0.66 3.8 0.47 .77 0 .13 :t0

0.73 0.24

0.70 0.24 0 0.05

0.064 0.65 0.71

0.025

a) Orbit of the captured proton; n is the number of nodes in the wave function including the origin. b) Woods-Saxon potential assumed with radius R =1.25 .41 ~3 fm and diffuseness a = 0.65 fm (see sect. 3.2.). The quoted uncertainties include an error of 16% from the number of target nuclei and the relative efficiency. `) Average value from (3He, d) [refs. 16" 18.20)] and (d, n) [refs. 1',19)] stripping reactions. d) Average value from intermediate-coupling vibrational 24) and shell 23) model calculations. e) Spin and parity .i' = ;- of the analog level in 33S [ref.')] was adopted .

(table 3). The direct-capture process is treated as an extra-nuclear channel process which involves only the well-known electromagnetic interaction and is therefore not very sensitive to the shape of the nuclear potential 2). The radius 1Z and the difuseness a of the Woods-Saxon potential are the only parameters in the theoretical calculation of the reaction cross section. For the ground and first excited state, the reported values from single-particle stripping reactions show large variations and center around the values from theoretical-model predictions, which are in excellent agreement with our results. Our spectroscopic factor for the F,,, = 2846 keV unbound state also agrees with the average value from transfer reactions . In additian, table 3 contains upper limits of spectroscopic factors for unobserved primary transitions obtained from the present experiment which are not in conflict with the values from the literature . Therefore, we conclude that in the case of non-resonant proton capture on 32 S the simple directcapture description, although sensitive to the values of the parameters involved, is capable of reproducing the experimental cross sections with the appropriate energy dependencies and angular distributions. 4.2. ASTROPHYSICAL ASPECTS

The stellar reaction rate NA (o v) of 32 S(p, Y) 33 C1 can have contributions from narrow resonances and the direct-capture process into the low-lying states in 3 ; Cl.

108

C Riadis et al. /

rect proton capture

he reaction rate (in units of reactions s' mol - 'cm') for isolated narrow resona ces is given by the expression 2 ') NA(av) = 1 .54 X

I W I (I& p -312

(wyj exp (-11 .605 E;j T9) ,

(7)

where the reduced mass Na, is in a.m.u. and the strengths (wy) j and c.m. energies Ej of the resonances are in MeV. For temperatures of greatest interest here ( T9 < 2), all experimentally known resonances with E, -,- 2577 keV were considered . The broad ER =1898 keV resonance (F - 10 keV) also has been included in the sum of eq. (7) and treated as a narrow resonance since the relation`' ) F< ER is still applicable . The Ej and (may); values for resonances measured in the present experiment were for taken from table 1 . The corresponding values the other resonances were adopted from ref. A esonant contributions from the threshold state at E, = 2352 keV (J' = 2="), which corresponds to a resonance energy of E R = 77 keV, will also effect the reaction rates. Since for a low-lying resonance we have Fp << F, == F, the strength is determined by ojy == (oFp with Fp = 3

h2

uR

C'S

ere, the quantity R denotes the nuclear-channel radius, A the reduced mass and I the penetrability at the resonance energy Ej for the orbital angular momentum I of the resonance . ne single-particle spectroscopic factor C2S for this level is known from Qe, d) and (d, n) ~refs. " . ' y )] stripping reactions and an average value of C2 S = 0.064 was adopted for the present calculations (see table 3) . The obtained resonance strength is liste0 in table 1 . The resulting reaction rates due to all the resonances with known or estimated strengths are listed in table 4 as a function of stellar temperature . It should be noted that primary transitions of several resonances considered lead to unbound states which might decay successively through the proton channel rather than by yy-cascades to the ground state of ;;Cl. The total contribution to NA (crv) of resonances with branchings to unbound states has been estimated to be less than 1% and therefore no correction was made . Or the calculation of the non-resonant reaction rates, the DC cross section for transitions to the ground and first excited state were calculated using the spectroscopic factors of table 3 . The effect of transitions to the states at E,, =1986 and 2352 keV has been estimated to be less than 2% and was therefore neglected . The cross sections were converted into astrophysical S-factors, defined by

n

S( E) = a(

)E exp (2 iTq),

the Sommerfeld parameter . The total S-factor for proton energies below Ec' =1 .0 MeV can be parametrized using the polynomial P

with

S(E) = S(o) + SI«» E = 0. 106 - 1 .94 x 1()-2 E

C. Iliadis et al. / Direct proton capture

109

TABLE 4

Stellar reaction rates NA(o v) of 32S(p, T9 (109 K) 0.05 0.08 0.1 0.14 0.2 0.3 0.5 0.8 1 .0 2.0 a)

b) `) sect. d)

y)33C1

in units of (cm3/mol . s)

,v) NA(o ER , 422 keV a)

ER = 77 keV b)

DC `)

total d)

3.16 x 10-39 4.51 x 10-24 4.59 x 10-'9 2.17 x 10-13 4.80 x 10-9 5.29 x 10-5 1 .47 x 10-' 1.01x10' 3.76 x 10' 3.60 x 102

1.39 x 10- " 4.70 x 10- ' S 2.96 x 10-14 2.15 x 10-13 8.13 x 10-13 1.89 x 10-12 2.80 x 10-12 2.66x10-'2 2.36 x 10-12 1 .29 x 10-12

5.21 x 10-22 1 .38 x 10-" 1 .01 x 10-1S 3.56 x 10-13 8.81 x 10-" 2.10x 10-' 7.26 x 10-6 6.23x10-4 3.85 x 10-3

1.39 x 10-" 4.71 x 10- 'S 3.06 x 10-14 7.88 X 10-13 4.88 x 10-9 5.29 x 10-5 1 .47 x 10-' 1 .01 x10' 3.76 x 10' 3.60 x 102

Based on all experimental known resonances with ER =422-2577 keV. Estimated contribution of resonance at E R = 77 keV (see table 1). Contribution of direct capture into ground and first excitec' state of 33C1 (see 4.2.). Sum of columns 2, 3 and 4.

with S the S-factor in MeV - b and E the c.m. energy in MeV. The non-resonant reaction rate NA(ov) was calculated using the relations 21) NA(o'v) = 4.34 x 1Ogr2(,u,Z)- ' exp ( - T)Seff(E0) with Z =16 and using T=

(10)

4.25(Z2lu I T9)1/3 ,

Se ff(EO) = S(0)[1 + E0=

,

+S/(0)[E0+36kT ]

122(Z 2 UT9) 1/3

(keV) .

The resulting DC reaction rates are summarized in table 4. Column 5 of table 4 lists the total reaction rates which are displayed in fig. 6a together with the individual contributions discussed above. It can be seen that the threshold resonance at Ep = 77 keV dominates the rates below T9 = 0.1 . The C process contributes substantially in the narrow temperature window of T9 = 0.12-0.16 with a maximum contribution of 45% to the total reaction rates at T9 = 0.14 (see table 4) . The resonances with E R :-:- 422 keV dominate for temperatures T9 > 0.17. Our stellar reaction rates are compared in fig. 6b with the .user-Feshbac calculations of Woosley et gal. 25 ). In the temperature range of T9 = 0.1-0.5 which is important for the rp-process our rates are smaller by four orders of magnitude. The disagreement of our reaction rates with the results of ref. 25 ) is expected, because the statistical theory of nuclear reactions is not applicable to the low level-density in the compound nucleus "Cl for excitation energies below EX = 4 eV. Further,

11 0

C Iliadis et aL /

irect proton capture

0.1

Stellar

temperature

T,

1 .0

Fig. 6. (a) Total reaction rate (solid line) and individual contributions (dashed lines) for the reaction 712S( p, y)_13CI ; (b) Ratio of the present rate to the reaction rate of Woosley et A (WFHZ 75 [ref. 21)]) .

it s 0 Id be noted that the stellar rates for the reaction ;2 S( P, y) 33 CI given by Wallace a oosley ') are based on incorrect resonance parameters and should be disregar ed "). I conclusion, although the resonance strengths of the previous work ') remain essentially unchanged by the present results, the stellar reaction rates of 32S(p, Y)33ci ow based on more precise input data by inclusion of the non-resonant contritio is work was supported by the US National Science Foundation grants PHY8803035 (Notre Dame), PHY88-17296 (Caltesh) and by the Natural Sciences and Engineering Research Council of Canada . fare ces 1) C. Rolfs and R .E . Azuma, Nucl . Phys. A227 (1974) 291 2) C. Rolfs, Nucl. Phys. A217 (1973) 29 3) H.P. Trautvetter and C. Rolfs, Nucl. Phys. A242 (1975) 519

C. Iliadis et al. / Direct proton capture

11 1

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