Excited levels of 28Si investigated by inelastic scattering of 185 MeV protons

Nuclear Physics A101 (1967) 481--494; ~ ) North-Holland Publishing Co., Amsterdam

1.E.I: 2.L

Not to be reproduced by photoprint or microfilmwithout writtenpermissionfrom the publisher

E X C I T E D L E V E L S O F 28Si I N V E S T I G A T E D BY I N E L A S T I C S C A T T E R I N G O F 185 M e V P R O T O N S o. SUNDBERG, A. JOHANSSON, G. TIBELL, S. DAHLGREN, D. HASSELGREN, B. H(}ISTAD, A. INGEMARSSON and P.-U. RENBERG The Gustaf 14"erner Institute, University of Uppsala, Uppsala, Sweden Received 29 May 1967 Abstract: Energy spectra of protons scattered from a silicon target of natural isotopic composition have been recorded in the angular range of 4° to 40°(lab system). The incident energy was 185 MeV, and the energy range of scattered protons corresponded to a region of excitation energies for 28Sifrom 0 to 25 MeV. The full width at half maximum of resolved peaks in the spectra was 380 keY. The differential cross sections measured are presented in graphs giving the angular distributions for the resolved peaks. A qualitative discussion of the excited states which correspond to the observed peaks is presented and is based mainly on the shapes of the angular distributions. Comparisons are made with relevant results from similar experiments. E [

I

NUCLEAR REACTIONS 2sSi(p, p'), E 185 MeV; measured cr(Ev,, 0). 2~Sideduced levels, 1. Natural target.

I

1. Introduction The usefulness of inelastic scattering of 185 MeV p r o t o n s as a tool for investigations of nuclear structure in the 2 s - l d shell has been d e m o n s t r a t e d in a recent publication 1) from this institute, in which 24Mg a n d 27AI were studied. As a c o n t i n u a t i o n of the investigation of the 2 s - l d shell nuclei, we have now measured the differential cross section as a f u n c t i o n of scattering angle a n d excitation energy for p r o t o n s scattered from a silicon target (natural isotopic composition). A large n u m b e r of peaks was observed in the energy spectra of scattered protons. D u e to good energy resolution (380 keV F W H M for the target used), it was possible to deduce the essential characteristics of m a n y of the states excited in the scattering process. The discussion has been limited to the extraction of transition multipolarities from the shapes of the a n g u l a r distributions. It should be kept in m i n d , however, that using, for instance, the distorted-wave i m p u l s e - a p p r o x i m a t i o n , the present results (particularly the magnitude of the cross sections) could be used to test details of nuclear wave functions. Thus, a full analysis of the results would give m u c h m o r e insight into nuclear structure t h a n is available from spin a n d parity assignments. The i n f o r m a t i o n available o n the level structure of 28Si has been presented by E n d t a n d v a n der Leun 2). M o r e recently the literature has been reviewed by C h e n a n d 481 September 1967

482

o. SUNDBERGet al.

Hurley 3). Results concerning the parities of certain levels in 28Si have been reported in ref. ¢). In a few cases, this experiment has led to assignments of probable quantum numbers. In particular, we have observed angular distributions that probably result from scattering to states with high spins ( > 5), and at small scattering angles our results indicate that we mainly excite levels with quantum numbers J~ = 1 +, T - - 1 and J~ = 0 +, T = 0. At high excitation energies, i.e. 10-15 MeV, it has been possible to separate about ten peaks and also to deduce their essential behaviour as a function of scattering angle. We also present some evidence for a level in 2ssi, which was only recently reported for the first time. These measurements make possible a comparison between the results for 185 MeV proton scattering from 2VA1 and 28Si which is interesting in terms of the excited-core model, as first discussed by Lawson and Uretsky 5) and de-Shalit 6). Several other experiments have recently been undertaken which test this model, e.g. proton scattering 7,8) at 17.5 MeV and 155 MeV, deuteron scattering 9)at 12.8 MeV and alpha scattering 1o) at 28.5 MeV. The agreement between experimental results and the predictions of the model is in many cases remarkable. 2. Experimental arrangement and evaluation of results

The experimental equipment as well as the methods to obtain the final results have been described previously a, a 1). The details particular to the present experiment were the following: solid angle for 0 < 10 ° 0.58 • 10-3 sr 0 > 10 ° target thickness

1.17.10 -a sr, 0.221 g/cm 2.

We also had to take into account the scattering from several isotopes in the target (92.2 % 28Si, 4.7 % 29Si and 3.1% 3°Si). Judging from the fact that most of the peaks observed in the energy spectra had the same width as the elastic peak (0.38 MeV F W H M ) and that they could be related to well-known energy levels of 28Si, it is not probable that the other isotopes present in the target made any contributions to the scattering cross section. However, very small differential cross sections ( < 0.1 rob/st) must be treated with caution due to the possibility of contributions from 29Si and 3°Si. If the cross section exceeds 0.2 mb/sr, however, it is rather unlikely that 29Si and a osi contribute essentially to the scattering. If they did, the corresponding cross section would be unexpectedly high. 3. Results and discussion

Excitation energies, maximum cross sections and suggested spin-parity assignments related to resolved peaks in the energy spectra are presented in table 1. A comparison with other relevant experiments is made in table 2.

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(P,

483

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TABLE 1

Summary

of results

for YSi Published

This experiment

Maximum cross section

Excitation energy (MeV)

(mbisr)

1.77 f0.03 4.62+0.03 4.96hO.05 6.66kO.15 6.87hO.03

12.5 0.79 0.80,0.34,0.22 0.15 3.1

Type of distribution

Suggested JX

&,(MeV)

data corresponding observed peaks Parity

J= %b)

“)

to

“)

&,(deg) 13.6 23.6 4, 13.7,34 4 18.8

2f 4+

E2 E4 EO (PO) E3

(& I-, 3-

7.40f0.08

0.49

18

7.9850.12 8.28 &O. 15

0.28 0.23

13.0 23.0

(E4)

(4+)

8.89kO.10

0.24

17.5

E3

l-, 3-,T=O

9.53 iO.08 9.66+0.08 10.19*0.05 10.65f0.10 10.93*0.12 11.40 $0.05 11.47+0.10 12.25hO.12 12.67+0.10 13.09&0.10 14.00~0.10 14.20&0.08

0.56 0.41 1.02 0.93 0.15 2.11 0.35 0.43 0.48 0.5 1.3 0.66

4 28.5 17.0 4

E5 E3 Ml

5l-, 3-,T=O (I+, T=l)

“) Refs. 2,23).

1.7721_0.005 4.614+0.006 4.975 iO.006 6.69 6.87810.003 6.88710.004 7.382iO.008 7.415iO.008 7.932*0.008 8.26OCO.008 8.328 10.008 8.90210.010 8.94110.010 9.491*0.010 9.700i0.010 10.180~0.020 10.71 io.02 10.91 -Lo.02 11.40 10.02

2+

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b, Refs. % *2).

d) Ref. la).

“) Ref. 4).

“) Ref. 24)

TABLE 2

Comparison

with other

experiments

This experiment

Ref. lb).

Ref. 8) ______.-

Excitation energy (MeV) 1.77kO.03 4.62kO.03 4.96hO.05 6.8710.03 9.66hO.08 10.19+0.05 “) The angular

Type of distribution (mbisr) 12.5 1-0.4 0.79 +0.03 0.80+0.08 0.34io.03 0.22kO.02 3.1 10.1 0.41+0.03 1.02&0.05 distribution

E2 E4

Excitation energy (MeV) 1.77*0.15 4.550.1

(mbisr)

Type of distribution

16’2 1.1 io.l

E2 (E4)

shows

14.7&0.7 0.64kO.06 0.31$0.05

EO E3 ES E3

du lab i-1dSJ max (mbisr)

6.8 9.8

-co.1 $0.2

only one maximum.

8.910.9 1.510.3

E3 E3

3.8

*0.3

“)

I

1 13.09 1225

14.00

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Fig. ]. Energy spectrum at 4 ° (lab system) f o r 185 M e V protons scattered f r o m a target o f natural silicon. T h e e r r o r s s h o w n a r e statistical. I

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486

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Figs. 1-3 show energy spectra recorded at 4 °, 17°5 and 32°5, respectively. For clarity only every third point (approximately) is shown. In fig. 4, the elastic cross section for scattering from 2~Si is shown. The shape of the angular distribution agrees well with that previously 1) obtained for 27A1, but the cross sections are somewhat smaller. The angular distributions for most of the resolved peaks can be seen in figs. 5-13. Absolute cross sections were obtained by comparison with the well-known peak at 4.43 MeV in 12C as was done in ref. 1). The overall uncertainty in the cross-section scale is believed to be about 10 ~ .

tO 3 ~

• 2~5i~ elastic .scattering

10 2

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!

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t o

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Fig. 4. Angular distribution for elastically scattered protons. 3.1. T H E P E A K S A T 1.77, 4.62 A N D 4.96 MeV

The angular distributions for the first three peaks observed are shown in figs. 5 and 6. The corresponding excited states in 28Si at 1.772, 4.614 and 4.975 MeV have spin-parity assignments 2 +, 4 + and 0 ÷, respectively 2). The angular distributions obtained are characteristic of the transitions involved. A comparison with the distributions for 24Mg shows excellent agreement in shape and peak position of the three pairs (see table 3). The excited-core model implies that the five, low-lying, excited states of 27A1 are closely related to the 1.77 MeV (2 +) level of 28Si. It is of interest to compare the maximum cross section for the 28Si level with the sum of the maximum cross sections obtained previously 1) for inelastic scattering to the five 27A1 levels. For the former we get 12.5 mb/sr and for the latter 10.7 mb/sr with relative errors in both cases of about 3.5 ~ . Thus the equality predicted by the model is almost fulfilled. It should be re-

28Si(p, p')

487

marked that the angular distributions in the two cases are not completely identical; the one obtained for 28Si decreases more rapidly for scattering angles larger than 20 °. The partition of cross section among the five 27A1 levels was already demonstrated to agree very well with the predictions of the excited-core model. Some doubt has been cast, however, on the validity of the model by Lawergren in this study 12) of r

q-

I

r

---

t5 I. 77

tO.03 MeV

10

E

I

I0

~

_

20

_

i _ _

30

40 0°lob

Fig. 5. Angular distribution for the peak at 1.77 MeV. I

I

i

I

I

~ 4.62+O.03Mev } 4.96+-O.05Meg

0.7

E

0.5

0.3

0.1 I

0

I0

20

30

40

Oiob

Fig. 6. Angular distributions for the peaks at 4.62 and 4.96 MeV.

spectroscopic factors obtained in an experiment on the 27Mg(d, n)26A1 reaction. On the other hand, the statement 13) that the spin of the level at 3.000 MeV is 5, instead of the previously assumed 9 seems incorrect 14). This would have meant that the level of spin ~ was not yet identified. Finally, an appreciable cross section for the 2 + level of 27A1 at 2.976 MeV would also tend to invalidate this model.

488

o. SUNDBERGet al.

F o r the peak at 4.62_+0.03 MeV, which certainly corresponds to the k n o w n z) level at 4.614_+0.006 MeV, we obtained a m a x i m u m cross section of 0.79 mb/sr and an angular distribution typical of an E4 transition. The cross section for the peak found at 4.96-+0.05 MeV has an angular dependence which very m u c h resembles previously-observed distributions for 0 + levels in 12C [ref. 11)] and ZgMg [ref. 1)]. TABLE 3 Comparison of the angular distributions for three pairs of levels of 24Mg and 28Si J~

State (MeV)

2+

24Mg 2sSi ~4Mg 2sSi

4+ 0+

Peak angle Width of (deg) distribution (deg)

1.37 1.77

13.5 13.6

10.5 10.0

6.01 4.62

25.0 23.6

19.5 15.6

~Mg 6.44 28Si 4.96

4, 14.0 and 32 4, 13.7 and 34

max. d,Q (mb/sr) 25 12.5 1.4 0.79 1.1, 0.41 and 0.11 0.8, 0.34 and 0.22

3.2. THE PEAKS AT 6.66, 6.87 AND 7.40 MeV Before discussing these peaks, it might be mentioned that we have observed a peak at 5.35 MeV with a cross section never exceeding 0.1 mb/sr. Since the cross section is so small and no state is k n o w n in 28Si at this excitation energy, the peak is probably caused by scattering from one or b o t h of the other isotopes (29Si and 3°Si) present in the target. F o r both o f the latter, there are several states at about 5.3 MeV excitation 2). A state listed 2) at 6.272 MeV with spin-parity 3 + is not seen in the present experiment. It has so-called unnatural parity and is therefore expected to be weakly excited. In this respect, it is analogous to the 3 + state o f 24Mg at 5.224 MeV, which was observed with a very small cross section in inelastic p r o t o n scattering 1). A t a scattering angle of 4 °, a peak at 6.66+0.15 MeV, which cannot be identified with listed levels 2), is observed. It has a rather small cross section (0.15 mb/sr), and therefore the possibility o f contributions f r o m the other isotopes in the target cannot definitely be excluded. A forward-peaked angular distribution indicates a 0 ÷ state (if we consider the peak as belonging to 28Si). The alternative would be a 1 +, T = 1 state but the excitation energy is so low that only T = 0 states should occur. Our conclusions are supported by a recent report in which Levesque e t al. 16) present evidence for a state in 28Si at 6.69 MeV with spin-parity 0 ÷. The peak at 6.87_+0.03 MeV is seen from fig. 7 to give a m a x i m u m cross section o f 3.1 mb/sr at a scattering angle o f 18°.8. The width of the forward dipped angular distribution is a b o u t 15 °. It is k n o w n that the electric dipole transition from a 1-, T = 0 state to a 0 +, T = 0 state is forbidden. This has a direct analogy in the inelastic scattering of high-energy protons; the angular distribution for protons exciting a 1-,

28si(p, p')

489

T = 0 state is very similar to that for an E3 transition t. Using only rather approximate empirical methods, we should not expect to be able to distinguish between the angular distributions for the excitation of 1- and 3- states (T = 0). It should, however, be pointed out that in 28Si as well as in 24Mg we have found angular distribu_

_

[

r

F

T

7

T

E

I

I

l

I

10

20

30

40

e%b

Fig. 7. A n g u l a r distribution for the peak at 6.87 MeV. I

I

I

I

0.7

• E

?.40+-0.08 Met; } %98tO.f2 1'4eV 0.5

0,3

0.1

0

L

J

I

tO

20

30

40

o

0 lob

Fig. 8. A n g u l a r distributions for the peaks at 7.40, 7.98 a n d 8.28 MeV.

tions of the E3 type with rather different widths (see for instance, the 6.87 and 10.19 MeV peaks in 28Si and the peaks 1) at 7.60 and 8.38 MeV in 24Mg). This may suggest that we do, in fact, observe different angular distributions for 1 - and 3- excitations. It t W e are grateful to Dr. T o r b j 0 r n Erikson for pointing this fact out to us. T h e discussion in ref. 1) on the 7.60 a n d 8.38 M e V levels o f 24Mg should be modified to take this into account.

490

o. SUNDBERGe t a / .

appears that the possibility of two different spins has been overlooked in other work on inelastic scattering. The known 23) states at 6.878 and 6.887 MeV might both contribute to the 6.87 MeV peak. The spin-parity assignments of these two levels have been discussed in a number of publications 17-23) after the appearance of ref. 2). For some time it was thought that one of the levels had spin-parity 2-, but recent work 2o) on proton capture in 27A1 and studies 23) of the 25Mg(~, ny) reaction favours a 3- assignment and excludes the spin 1 possibility that has to be taken into account in our experiment as discussed above. Studies of proton scattering 8, 15) at 155 MeV and of alpha scattering 21) at 28.5 MeV also support the 3- assignment. The other level around 6.9 MeV probably 22) has spin-parity 4 +. As our angular distribution for the 6.87 MeV peak is of the broad E3 type, we might excite also this state. An upper limit of 0.8 mb/sr can be set for the maximum differential cross section of a possible E4 part of the angular distribution. The angular distribution for the peak at 7.40_+0.08 MeV is shown in fig. 8. 3.3. THE PEAKS AT 7.98, 8.28 AND 8.89 MeV

With increasing excitation energy, the spectra become more and more complex. The peaks can show "intrinsic widths", and in many cases the cross sections are rather small. As in the case of magnesium and aluminium 1), a smooth background starting at approximately 8 MeV was drawn under the peaks. The identification with known levels is, however, still possible in some cases in spite of the high level density in 2aSi.

0.5

13.09 -~0.I0 MeV

E bc~

0. I - -

0

--I

10

I

L

I

20

30

40

o

e lob

Fig. 9. Angular distributions for the peaks at 8.89 and 13.09 MeV.

In the energy region 7.5-9 MeV, three peaks have been observed with small maximum cross sections at 7.98+0.12 MeV, 8.28+0.15 MeV (fig. 8) and at 8.89+0.10 MeV (fig. 9). Suggestions concerning quantum numbers can be found in table 1. 3.4. PEAKS AT EXCITATION ENERGIES LARGER THAN 9 MeV

3.4.1. Forward-peaked angular distributions. In table l, 12 peaks with excitation

~8Si(p,p')

491

energies larger than 9 MeV are listed. Six of these have measurable cross sections in the forward direction. Of the peaks at 9.53+0.08 MeV (fig. 10), 12.25+0.12 MeV I

T

I

T

I

0.7L 9.53+-0.00 MeV

F

9.66 tO.O~ MeV

0.5~ E 0.3

0.1 1

I

I

I

10

20

30

40

e'to b

Fig. 10. Angular distributions for the peaks at 9.53 and 9.66 MeV. i

1

2.0

T

I

10.19 +-0.05 MeV 10.65t0.10 MeV ~t 11.40"-0.05 MeV

1.5 E

1.0

0.5

£

0

10

1. . . . . . . . . .

20

I

30

--

I

40

o

8lc 5

Fig. 11. Angular distributions for the peaks at 10.19, 10.65 and 11.40 MeV.

(fig. 12) and 13.09-t-0.10 MeV (fig. 9), the first can be identified with the state listed 2) at 9.491 MeV. The two remaining peaks have been observed in work on inelastic elec-

492

o.

SUNDBERG

et al.

tron scattering by Liesem 24), who reports a peak at 12.32 MeV and shows an energy spectrum with a peak at 13 MeV. A possible contributor to the peak at 12.35 MeV is the state at 12.326 MeV, 1 +. Two M1 distributions (AT = 1) have been observed, namely for the peaks at 10.65+_0.10 MeV and 11.40+0.05 MeV (fig. 11). The former has an intrinsic width of 0.45 MeV and thus several states might contribute to this peak. However, the major I

o. 5

I

~..T

L

{ 12.25 CO. 12 M e V

,%

.

-

.

MeV

o+

,

0

I

I

I

I0

20

30

o

e lab

Fig. 12. Angular distributions for the peaks at 12.25 and 12.67 MeV. I

I

I

I

~5 { 14.00 ~0.10 HeY

~14.20 *-0.08 t4eV

E

l.O

0.5

,

0

I0

20

I

1

30

40

O* lab

Fig. 13. Angular distributions for the peaks at 14.00 and 14.20 MeV.

part of the cross section evidently comes from scattering to a level at 10.71 +0.02 MeV with quantum numbers 1 ÷, T = 1, also seen in a study of (p, 7) resonances 25). The latter corresponds to the peak observed at 11.6 MeV in 180 ° electron scattering [ref. 26)]. The experiment performed by Liesem z4) gives an excitation energy of 11.42 +0.02 MeV in good agreement with our value. Analogous cases of agreement between electron-scattering results and forward-

28Si(p,p')

493

peaked angular distributions in proton scattering were previously 1) observed in 24Mg and 27A1. It is interesting to note that there is no such correspondence 26) for the broad peak seen at 14.00__+0.10 MeV. Also, the distribution for the peak at 14.00 MeV (fig. 13) is not typical of an M1 transition but instead resembles the ones observed for a transition 0 + --* 0 +. 3.4.2. Forward-dipped angular distributions. The peak at 9.66_+0.08 MeV (fig. 10) can be identified with the state listed 2) at 9.700 MeV. The distribution with its maxim u m at 28°.5 is characteristic of an E5 transition thus confirming a recent suggestion by Nordhagen 27) that this state has J~ = 5-. A peak seen at 10.19+0.05 MeV (fig. 11) has a rather large maximum cross section at 17°.0 and shows an E3 distribution of the narrow type. For the corresponding level 2) in 28Si ' at 10.180 MeV, there are no suggestions in the literature concerning the quantum numbers. The remaining four peaks cannot be identified with known levels except perhaps the one at 10.93_+0.12 MeV. It has a maximum differential cross section of about 0.15 mb/sr, and thus scattering from 29Si and 3°Si might contribute. Liesem 24) observes a peak at 10.90_+0.06 MeV and connects it with the level 2) at 10.91 MeV. A peak seen at 12.67+0.10 MeV (fig. 12) has its maximum at 13°.5, and the two broad peaks at 11.47_+0.10 MeV and 14.20_+0.08 MeV (fig. 13) have maxima around 30 °. As seen from the energy spectra there was some structure also between 14 MeV and 19.5 MeV excitation energy. In this region very broad peaks were observed at 15.0, 16.6, 17.8 and 18.7 MeV. The authors wish to thank Professor The Svedberg, the head of the institute, for his kind interest in this work. We are very grateful to Professor G. W. Crawford who provided us with the target used in this experiment. Conversations with Dr. R. Nordhagen on the level structure o f / s S i have been very stimulating. We also wish to thank Drs. A. Willis and C. van der Leun for communicating unpublished results. Financial support has been given by the Swedish Atomic Research Council.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)

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