The reaction 30Si(α, γ)34S

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Nuclear Physics 72 (1965) 113-121; ( ~ North-Holland Publishin9 Co.. Amsterdam

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THE R E A C T I O N

3°Si('t,

?)34S

W. R. M c M U R R A Y and 1. J. VAN HEERDEN Southern Universities Nuclear Institute, Faure. South Africa and G. WlECHERS Department of Physics, University of Cape To wn, Cape Town, South Africa Received 17 May 1965 Abstract: The radiative capture alpha particle reaction in z°Si has been studied in the energy range from 3.25 to 4.25 MeV. Thirty-six resonances corresponding to excited states in 3'S were observed and for sixteen of these which decay appreciably by ground state transitions, the spins and parities have been uniquely determined by angular distribution measurements. The main modes of decay have been obtained from gamma spectra and the partial resonance strengths of these levels evaluated. The average values of the deduced radiative widths in Weisskopf units agree with measurements of El and E2 transitions in other nuclei.

El

N U C L E A R REACTIONS a°Si(ct, ~,), E -- 3.25--4.25 MeV; measured a(E; 0), I s a4S, deduced levels, J, :'t, l'y. Enriched target.

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1. Introduction It is well known that radiative alpha capture provides a useful tool for the spectroscopic investigation of nuclei ~). In this paper results are presented of a study of the reaction 3°Si(~, 7)34S in the energy range from 3.25 to 4.25 MeV. The energy range from 2.10 to 3.25 MeV has been investigated by van der Leun and Wiechers 2). At lower energies, alpha capture is inhibited by the Coulomb barrier. At higher energies than 4.25 MeV there is evidence to suggest that the competing 3°Si(~, n)33S reaction is beginning to dominate the 3°Si(~, 7)34S reaction. 2. Apparatus The measurements were carried out using alpha particle beams from the 5.5 MeV Van de Graaff accelerator of the Southern Universities Nuclear Institute. The accelerated beam is deflected through a 90 '> vertical analysing magnet before being directed onto the target by means of a seven port horizontal switching magnet. Immediately before hitting the target, the beam passes through the aperture of a liquid nitrogen cooled cold finger, 25 cm long, limiting carbon deposit on the target. This is situated over a vacuum pumping assembly isolated by another liquid nitrogen cooled vapour trap. 113

114

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Nuclear magnetic resonance ( N M R ) in the magnetic field of the 90: allalysing magnet is used to measure the beam energy. The N M R system has been calibrated by observing various (p, n) threshold rcactions covering the energy range of the accclcrator. For alpha beams, the calibration (based on proton energies) is corrected for the difference in particle masses. The target was firmly supported inside the end of a cylindrical can cut away at the end to an angle of 45 '~ to facilitate angular distribution measurements and air-cooled by a jet of compressed air. The enriched 3°Si targets, 15 to 25/~g,"cm 2 thick, cvaporated onto tantalum or copper backings, were obtained from AERH, Harwell, England. The g a m m a rays were detectcd in a 12.5 cm diam. by 10cm long NaI(TI) crystal shielded by lead and supported on a trolley on an arm pivoted exactly under the point of the target bombarded by the alpha beam. The beam current was typically 2 I~A focussed thlough a 0.5 cm aperture. The g a m m a intensity was monitored against the output count of a current integrator measuring the charge collected on the insulated target can. The gamma spectra were measured with a 512-channel pulse-hcight analyser. 3. Yield Curve

The yield curve was measured with the front face of the NaI(TI) crystal placed at a distance D = 2.3 cm from the target at an angle 0 = 45 ° with respect to the alpha beam. Three discriminator channels were used, one adjusted to observe ground state transitions, and two others to observe transitions to the tirst and second excited states in 34S at 2.13 and 3.30 MeV respectively. Fig. 1 shows the observed yield curves, the lower one giving ground state transitions only ('io), and the upper one the combined transitions ('/0+7~) to the ground state and 2.13 MeV level of 34S. The discriminator channel set to observe transitions to the 3.30 MeV level of 34S does show a few additional resonances, but in the energy range reported here these are very weak compared to those shown in fig. 1. The thirty-six observed resonances are listed in table 1 together with the excitation energies of the corresponding 34S levels, which have been calculated using a reaction Q value 3) of 7.917 MeV. The assignment ot" these resonances to the 3°Si(~, ~')345 reaction follows from the spectra which all show ),-transitions to the ground and excitcd states of 34S. Some confusion with the resonances in the reaction 2sSi(~, )')32S is possible, as the energies of the cmitted 7-rays are not much smaller than in the 3°Si(~, y)34S reaction. A separate study of the radiative capture alpha reaction in 2sSi using natural silicon targets, however, has shown that the partial resonant strengths of ground state transitions in 32S arc too small to bc measurable in the 1'0 yield curve obtained with enriched 3°Si targets. No isotopic analysis of these targets was available, but the considerable enrichment factor could be gauged from the relative strengths of known resonant states in 32S and 34S observed with natural Si and enriched 3°Si targets respectively.

80Si('~, y):~4S REACTION

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The energy calibration of the alpha particle beam is confirmed by the fact that resonance 1 found at E, = 3.250 MeV in the present work, was excited at E, = 3.249 MeV in the earlier work of van der Leun and Wiechers 2). Resonance 1 is included so as to provide a link between the present measurements and the earlier work. TABLE I R e s o n a n c e s in the s°Si(cq ?)34S reaction Resonance number

E~t(lab) (MeV)

34S* (MeV)

Resonance number

E~(lab) (MeV)

3'S* (MeV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

3.250 3.313 3.338 3.368 3.392 3.408 3.480 3.503 3.515 3.540 3.586 3.609 3.647 3.674 3.690 3.706 3.736 3.751

10.784 10.840 10.862 10.888 10.909 10.924 10.987 1.007 1.018 1.040 1.081 1.101 1.134 1.158 1.172 1.186 1.213 1.226

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

3.795 3.814 3.843 3.853 3.894 3.908 3.918 3.940 3.948 3.961 3.993 4.007 4.024 4.043 4.058 4.106 4.160 4.220

1.265 1.282 1.307 1.316 1.352 1.365 1.373 1.393 11.400 11.411 11.440 11.452 11.467 11.484 11.497 11.539 11.614 11.640

All values -t-5 keV.

4. Angular Distributions Measurement of the angular distribution of the ~-radiation produced in ground state transitions following a reaction with spins 0 (l = J ) J ( l = J ) 0 provides a simple means of establishing the value of J ~ for the resonant state concerned. The theoretical angular distributions have the form 4) W(O) oc sin20

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W(O) ~ sin220 for J " = 2 +.

The measured angular distributions for those resonances which have an appreciable decay to the ground state are shown in figs. 2 and 3. The measurements were performed with the face of the N a l crystal at distances of between 2.5 and 20 cm from the target. The solid lines in each figure are the theoretical distributions for the assigned spin values, incorporating the computed effect of the large solid angle subtended by the detector. In most cases the fit to the experimental data is very good, resulting in unique assignments of spin and parity to the corresponding levels in 34S.

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3°Si(~, ],,)3"~S REACTION

119

Table 2 lists those resonances for which angular distributions have been measured. Gamma ray spectra were obtained during the measurements in order to establish the main modes of decay of the 34S levels. Columns 4 to 7 show the 7o, "~'~and 72 transitions, and transitions to higher levels, denoted as 7. where these could be clearly distinguished. The numbers in these columns indicate the intensities relative to that of the ground state transition. Since the spectra were taken during the angular distribution measurements (at 0 = 0 '~, 30 °, 45 ~, 60 ° and 90") the intensities are fairly well averaged over the angular range. TABLE 2 Spins a n d parities, main m o d e s o f decay a n d resonance strengths o f g r o u n d state transitions in ~S Resonance number

E~ (MeV)

J~

1 9 11 13 14 17 18 21 22 23 24 25 28 32 34 36

3.250 3.515 3.586 3.647 3.674 3.736 3.751 3.843 3.853 3.894 3.908 3.918 3.961 4.043 4.106 4.220

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3 1.7 0.2 2.6 1.7 0.2 2.8 0.08 2.2 1.4 1.5 0.1 4.4 0.6 1.0 2.3

Resonances 17 and 24 have comparatively weak Yo transitions. Although a correction has been applied to the data for the background of sum coincidences following 71 and 72 transitions, it will be desirable to confirm the J" assignments with angular correlation measurements. 5. Resonance Strengths The strengths of the resonances, for which a spin assignment is possible, have been listed in column 8 of table 2. The relative strengths of ground state transitions were calculated from the heights of the peaks in the yo-resonance curve shown in fig. I. This procedure is allowed since the resonance strengths are of the order of eV, whereas the width of the resonance peaks is several keV, and thus purely instrumental. The heights, after correction for counter efficiency, dE/dx, variation in ~-particle wavelength, and for the fact that the yield curve was taken at 0 = 45 °, are proportional to (2J+I)F.~oFJF. The relative resonance strengths can be converted to absolute strengths using the known strength s) of the 2.904 MeV 2sSi(~, 7)32S resonance:

w.R. McMURRAYet al.

120

(2J+ 1)F~Fr/F = 0.7 eV. It was f o u n d that the strength o f the 3.250 M e V 3°Si(~, ~,) 34S resonance is 13 times that o f the 2.904 M e V 2aSi(~, V)32S resonance 2). Since the v-ray s p e c t r u m reveals that the level at E~ = 3.250 M e V has a p r o b a b i l i t y o f a b o u t 0.8 for decay to the g r o u n d state we p u t the p a r t i a l strength o f this level for decay to the g r o u n d state at 7.2 eV. The last c o l u m n o f table 2 gives the g a m m a width F r for decay only to the g r o u n d a n d first two excited states. Here we have a s s u m e d that F~ << F~. TAat~ 3 Radiative widths in a4S

Ea

E,t

(MeV)

(MeV)

Partial width l'~(eV)

IMi 2 × 103

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3.250 3.515 3.647 3.674 3.751 3.853 3.894 3.961 4.043 4.106 4.220

10.78 11.02 11.13 11.16 11.23 11.32 11.35 11.41 11.49 11.54 11.64

2.4 1.3 2.1 0.7 0.4 1.0 0.3 3.6 0.3 0.3 1.6

2.3 1.2 1.8 0.6 0.4 0.8 0.3 2.9 0.2 0.2 1.2

E2

3.586 3.736 3.843 3.908 3.918

11.08 11.21 11.31 11.37 11.38

0.1 0.04 0.04 0.02 0.03

90 35 35 20 25

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It is interesting to evaluate the radiative width in W e i s s k o p f units I MI 2 = F~,/l'~w, where Frw is the extreme single particle width given by F~w(EI) = 0.08 A~E~ eV for E l transitions, and by Fvw(E2 ) = 6.3 × 10-8A ~ E~ eV for E2 transitions. Here we have used a nuclear radius ro A~ with r o = 1.278 fm. This value o f r o was f o u n d f r o m a calculation o f the C o u l o m b energy o f nuclei in the 2s½ ld~ shell 6). T a b l e 3 shows the radiative widths of), o transitions in 34S, where the m o d e o f decay is k n o w n . The average o f IMI 2 for the eleven E l transitions f o u n d is 1.1 × 10 -3 which is the same as f o u n d 2) for the range E~ = 2 . 1 0 - 3 . 2 5 MeV in 3°Si(~, ~)34S. The average o f [MI 2 for the five E2 transitions in 34S is 4 x 10 -2. This is a b o u t a factor 5 smaller than the average value for five E2 transitions to the g r o u n d state in -~4Mg r e p o r t e d by Smulders 7) a n d a b o u t a factor 7 smaller than the average value d e d u c e d by van d e r Leun 8). 6. Discussion A feature o f the spectra taken at the resonances at E~ = 3.918, 4.093, 4.106 a n d 4.220 M e V a n d at higher energies not included in this report, is the presence o f ~,-rays

8eSi(~, 7)a(S REACTION

121

of energy up to about 7 MeV. These are about an order of magnitude more intense than the 3'0 transition and show sharp total absorption peaks and resonance effects as if corresponding to transitions to the group of levels in 34S at excitations between 4 and 5 MeV. It is well known that the gamma radiation resulting from the 13C(:t, n)160 reaction produces a high energy 7 background, hence the care to avoid any build-up of carbon deposits on the targets. It is also known that the 3°Si(ct, n)335 reaction becomes energetically possible at E~ = 3.971 MeV. The response of the NaI(TI) crystal to fast neutrons was therefore investigated in order to determine the origin of the approximately 7 MeV "/-rays observed in the 3°Si(~, ),) studies at higher alpha energies. It has been found that detection of low-energy neutrons by the NaI(TI) crystal is primarily due to capture-gamma reactions in Na and I which result in the emission of about 7 MeV 7-rays. High-energy neutrons must be detected primarily by inelastic neutron scattering events, giving rise to the structureless spectra observed in the 13C(ct' n) reaction. The emission of low-energy neutrons by the 3°Si(~, n)33S reaction, not far above threshold, must thus give rise to a sharply defined 2:-spectrum cutting off around 7 MeV as has been observed in the present work. It has also been observed by the authors that the ~H channel becomes more prominent at higher energies (though with less structure) and there is often little or no measurable ~o transition in 34S. It is concluded that this is a result of increasing competition from the 3°Si(~, n)33S reaction. This has been confirmed in a separate study of this reaction to be reported in a later paper.

References 1) C. van der Leun, Proc. Lawrence Symposium on The Structure of Low-Medium Mass Nuclei (Kansas, 1964) 2) C. van der Leun and G. Wiechers, Nuclear Physics 52 (1964) 104 3) F. Everling, L. A. Kocnig, J. H. E. Mattauch and A. H. Wapstra, 1960 nuclear data tables, Part 1, (U.S. Government Printing Office, Washington 25. D.C., 1961) 4) L. C. Biedenharn, in Nuclear spectroscopy, Part B, ed. by F. Ajzenberg-Selove (Academic Press, New York, 1960) chapt. V.C. 5) P. J. M. Smulders, Physica 30 (1964) 1197 6) P. W. M. Glaudemans, G. Wiechcrs and P..1. Brussaard, Nuclear Physics 56 (1964) 529 7) P. J. M. Smulders, Physica 31 (1965) 973 8) C. van dcr Leun, Compt. Rend. Cong. hat. de Physique Nucl6aire, Vol. II, ed. by P. Gugenberger (Paris, 1964) p. 382