Energy levels of 28Si

Nuclear Physics A250 (1975) 235- 256; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written ix'rmistion from the publisher

E N E R G Y L E V E L S O F 2SSi M. A, MEYER, 1. VENTER and D. REITMANN ) Physics Department, Potchefstroom University, South Africa Received 15 May 1975 Al~tract: Proton energies and strengths of (p,y), (p, p,), (p, P2) and (p, at?.) resonances of the a~Al-t-p reaction were determined for Ep < 2.5 MeV. The ?'-decay of 78 resonances and 46 bound levels was established and four new bound levels were found at Ez = 9793.84-2.0, 10513.5:/:1.0, 10884.1 :l:2.0 and 11778.84-1.5 keV. The level at E, = 11.43 MeV was found to be a doublet. Lifetimes of 25 bound levels were measured by means of the Doppler-shift attenuation technique. Angular distributions were measured at 15 resonances. I

NUCLEAR REACTION 2'Al(p, 7), (P, P'7), (P, Gty), E ~ 0.3-2.5 MeV; measured a(E, EF), I~,(0), Doppler-shift attenuation. 21Si deduced levels, resonance strengths, y-ray branching ratios, r.,, ./, n, mixing ratios. Natural targets.

1. Introduction The excited states o f '8Si have recently been studied by means o f the 2"IAl(p, F)2sSi reaction by Gibson et al. t.2), Meyer et al. 3,4), Aleonard et al. s), F o r s b l o m et al. 6-8), H o l m b e r g et al. 9) and D a l m a s et al. lo, t t). In all these experiments, G e ( L i ) detectors were used and information on energies, branching ratios and lifetimes o f excited states in 28Si was obtained. T h e purpose o f the present experiment was to determine whether a better detector and higher b e a m currents could resolve some o f the previous 3,4) uncertainties. In the present experiment, (p, ~) resonances o f the 2+Al(p, ~)2ssi reaction were studied in the energy range Ep = 0.3-2.5 MeV. F o u r new b o u n d levels were observed and additional information on energies, branchings and lifetimes was obtained for the b o u n d levels in 2sSi. The spins o f a n u m b e r o f resonances were determined by means o f angular distribution measurements and Weisskopf estimates. Additional information on resonance strengths was also obtained.

2. Experimental details The experiment was performed with a p r o t o n beam o f 120-200 p A from a I. 1 MV C o c k r o f t - W a l t o n accelerator and a beam o f 30-50/~A from a 3 M V Van de G r a a f f accelerator. * Atomic Energy Board, Pretoria, South Africa. 235

236

M.A. MEYER et al.

The 3,-rays were detected in 40 and 60 cm ~ Ge(Li) detectors and the spectra were stored in 4000-channel analysers. Base line restorers and spectrum stabilisers were used when required. The efficiency curves of the Ge(Li) detectors were determined by using radioactive sources and data from resonances with known 3,-decay. The centroids and areas of peaks in the 3,-ray spectra were determined by means of a computer program. A second computer program which took account of non-linearities of the electronics and which corrected for recoil losses and Doppler shifts, was used to calculate the energies of the peaks. The targets were prepared by evaporating pure aluminium onto clean copper or tantalum backings. Tantalum backings were used for Ep > i MeV. Direct water cooling of the targets allowed beams of up to 200/~A at Ep = I MeV. 3. Experimental results 3.1. EXCITATION CURVES The 27Al(p, 3,)2sSi excitation curve for E p - - 0 . 3 - 1 . 0 M e V was measured by detecting 3,-rays with Ey > 2.6 MeV. The 27Al(p, 3,), 27AI(p, Pt), 27Al(p, P2) and 27AI(p, ut3,) excitation curves for Ep > 1.0 MeV were measured by detecting 3,-rays having E, > 2.6 MeV and E 7 = 0.84, !.01 and 1.37 MeV, respectively. The latter three energies were selected by means of narrow windows set across these energies. These three channels will also detect Compton scattered 3,-rays from the (p, 3') resonances and the (p, Pl) and (p, P2) channels will record Compton scattered ),-rays from the (p, ~t3,) reaction. The curves were measured simultaneously by means of a 12 cm × 12 cm NaI detector at 55 ° with respect to the beam and at a distance of I cm from the target. The excitation curves are shown in figs. 1 and 2. The resolution was about !.5 keV. It will be noted that a strong (p, 3,) resonance, such as the Ep = 992 keV resonance, gives rise to counts in the (p, Pt), (P, P2) and (p, ut3,) channels. The final decision whether counts observed in the (p, Pt), (P, P2) and (13, cet3,) channels were due to these reactions, followed after an analysis of the corresponding 3,-ray spectrum. The E~ = 1.37 MeV 3,-ray can also arise from the 23Na(p, 3,)24Mg reaction when 23Na is present as an impurity in the AI or the backings. The weak (p, 3,) resonance at Ep = 1439 keV, observed by Forsblom 7) and Tveter t2), was not studied in the present experiment. A weak (p, Pt) resonance was observed at Ep = 1438 keV. The doublets at Ep -- 1364, 1577, 1662 and 1723 keV (table 1) could not be resolved. Broad (p, Pt), (P, P2) and (p, cet3,) resonances were found to coincide with the narrow (p, 3,) resonances at Ep -- 1723 and 1749 keV. The large (p, Pi), (P, P2) and (p, ce13,)strengths previously attributed 4) to the Ep --- 1900 and 1911 keV resonances are now considered to arise mainly from a strong and broad (P, Pl), (P, P2) and (p, cet3,) resonance at Ep = 1907 keV which was unknown. The (p, P t ), (P, P2) and (p, ~t3,) resonances ofthe 27AI + p reactions become broad and strong above Ep = 2.3 MeV and lead to complications in the recording of),-ray spectra.

0.013 0.10 0.022 0.69 0.85 0.044 5.34-0.8 c) 2.0 1.0 1.7 2.8 0.40 2.8 2.1 9.5 0.31 3.3 3.0 31 0.52 3.8 1.0 0.45 8.9

327 406 447 505 507 612 633 655 679 731 736 742 760 767 774 885 923 937 992 1002 1025 1090 1098 1118

F~ ")

1172") 1183 ") 1199 ") 1213 ,) 1262 ") 1278 1317 ") 1328 ") 1364/5 ") 1381 *) 1388 ' ) 14384-1.0 b) 1457 1502 1520 1566 1577/8") 1588 1647 1662/3 1680 1684 1706 1723/4 r) 1749 1800 1842 1900.04-0.5 b)

(keY)

0.81 0.64 7.5 0.25 0.62 8.0 0.33 15 4.2 1.2 0.70 9.0 3.2 15 1.3 0.33

0.69 1.4 2.8 4.5 4.1 0.37 5.3 3. ! 5.9 29 23

x = ~,

4.4 0.098 1.3 65 0.37 0.80 0.88 0.45 12 1.5 330 3.9 4.3 730 390 0.50 yes

0.005

Pl

no 0.011 0.15 0.022 0.15 0.53 6.6 3.8 0.73 19 5.6 34 110 85 3.4 yes

P2

(2J + I )F,F, IF (eV) b)

t) Ref. 12).

*) Present experiment. The errors on the strengths are o f the order of 30 ~ . ' ) Ref. t~). ") Ref. *). ") Ref. 1,).

") Re/'. ~").

( ~ + l)r'~',/r ~) (eV)

G ") (keY)

0.016 0.047 no 0.026 2.3 0.12 11 4.3 49 11 62 7.3 1.3 1.7 1.4 2.8

0.12 0.84

0.15 0.092 0.020 0.026 0.15

~, 1907.4+0.5 1910.74-0.5 1969.04-0.5 2034.34-0.6 2045.3 +0.8 2049.1 4-0.8 2058.04-0.8 2073.4 4- 0.8 2101.6 4-0.8 2106.34-0.8 2127.34-0.7 2131.54-1.0 2155.24-0.7 2160.24-0.5 2171.24-0.7 2179.24-0.5 2200.24-0.5 2203.24-0.7 2303.1 4-0.8 2311.94-1.0 2329.64-1.4 2359.94-1.5 2373.8 4-1.2 2402.54-1.1 2443.24-1.0 2476.1 4-1.0 2483.44-1.0 2488.34-1.0

E, b) (keY)

TABLE I Strengths and energies of 2~AI + p resonances in the energy range £ , = 0.3-2.5 MeV

2000 no 60 320 40 47 yes no no 510 59 44 54 51 120 73 71 140 yes yes yes yes yes yes yes yes yes yes

no 4.9 5.0 1.8 9.5 no (0.3) 0.10 0.33 (0.2) 1.3 (0.2) 0.64 1.3 0.81 1.7 3.4 12 2. ! 12 0.32 (7) 34 5.1 (4) 14 7. I

(4)

Pt 510 yes 650 82 3.1 12 5.3 no no 210 19 12 6 10 61 26 57 33 yes yes yes yes yes yes yes yes yes yes

P2

Oil 7.7 no 3.3 1.2 0.49 !.7 !.0 no 3.7 7.2 1.8 I.I yes !.3 3.0 2.4 !.4 1.1 yes yes 1.0 4.8 19 8.9 12 0.66 0.84 8.1

(2J + I )P~Fp/I"' ) (eV) x ----7

",4

w rn < I'n

m Z m

(4*) (4÷), T = ! 2*,3-,4"d), T=I 2-4 2"

11870 11900 11977

12016 12072

12074

12176 12195

12217

12240

12291

12295 3* 12301 1%2 ÷ e)

12318 2(*) 12325 4, T =

12331 I % T = 12439 2" ")

295 327 406

447 505

507

612 633

655

679

731

736 742

760 767

774 885

0

48

0.2

3-

12489

937

6.3 4.6 91

75 69

89 1.0

-12475 4"*"

1

1.5

< 0.06

73 17

49

43

46

< 0.5 73

44

28 14

!.8 1.1 2.6

!.78 2+

923

I

0.5

0.5

0.1

3 + d)

2 •

2.2

< 0.2 0.1

16

< 0.5 55

< 0.5 < 0.2 <0.05

0+

2-

(5*) 3-

2(÷)

j , r ¢ ) , T r)

Ep') F_.b) (keY) (keY)

R~onances

19

2.0

3.4

77

18

0.4

26

< 0.5 15

(0.5)

25 2.8

69 75 73

1.3

0.8

4.62 4.98 4* 0 +

7.0

!.0

!.4

3.5

3.1

4.2

96 1.5

0.7

3.0 2.9

1.9 1.0

3.2

2.4

16

1.8 0.9

!.4

3.5

10

1.1

!.4

1.3

0.6

1.4

1.4

7.0

16 14 13

6.28 6.69 6.88 6.89 34. O* 34÷

3.0

0.3

9.5

1.2

2.3

0.8

1.5

0.8

7.38 2+

0.7

1.0 0.4

2.3

21

2.2

7.8

31 1.7

7.42 2*

1.4

5.6

2.7 1.0

0.7

3.1

3.6 1.9

5.1

7.80 3*

t.0

2.8 0.6

0.3

0.9

0.6

6.1

0.5

3.8

4.5 1.6

7.93 2*

G a m m a decay to E, (MeV) in =mSi (o/,)

(%)

other levels

8.59(2.2), (9.32(2.7)) 8.26(1.5), 8.59(i.7), 9.32(0.5), 9.38(I.4), 9.5o(o.7), 1o.38(5.7) 8.41(0.9), 8.59(0.9), 9.38(8.5), 1o.38(2.3) 8.59(4.0) 8.26(o.7), 8.41(i.2), 8.90(0.6), 9.32(o.3), 9.38(2.2) 8.26(i.6), 8.33(i.0), 8.41(0.8), 8.59(3.o), 8.90(0.4), 9.32(2.0), 9.38(28), 10.6o(!.1) 8.41(0.9), 8.59(0.3), 9.16(2.6), 9.48(0.3), 9.79(i.7), 10.21(o.6), 10.51(0.7) 8.33(0.6), 8.59(0.7), 9.32(9.8), 9.38(31), 9.50(0.3) 8.33(0.3), 9.32(2.0), 9.38(0.5) 8.33(4.0), 8.90(48), 9.50(19), 10.60(3.0), 10.72(8.5) 9.32(3.8) 8.41(3.0), 8.59(5.0), 9.32(5.0), 9.77(2.3) 8.33(I.5), 9.50(0.7) 8.33(0.6), 9.32(I !), 9.38(0.9), 9.50(1.1) 8.26(1.1), 8.59(0.2), 9.16(0.4), 9.32(0.3), (10.21(0.1)), 10.38(0.3) 8.41(2.4), 9.38(3.5), 10.88(0.5), 11.434(0.4)

8.41 (4.9), 8.59(3.2) 8.59(5.7), 9.42(2.3) 8.59(5.8), 9.42(2.3), 10.31(I.2)

TAIILI! 2 Gamn3a decay of aTAI(p, ?)a°Si resonances in the energy range F~ = 0.29-2.5 MeV

~r i-n ,< t-n

.>

:e

bh

12636

12644

12664

12715

12726

12742

12755

12802

12817

12855

12866

1090

1098

1118

1172

1183

1199

1213

1262

1278

1317

1328

1364 12900 (4 ÷ ) 1365 12901 2 ~ 1381 12917 2 " t ) , T =

1

I

I

I

2 +,3" d)

4+

4*

3-

( 1 - , 2 ÷)

3-,T=

2"

1",2')

4-,T=

(4-)

(3-)

12552 4 ÷ 12574 2 ¢ ) , T =

1002 1025

3 +, T =

12542

992

I

II 6.0

75

2.3

8.0

82 27

6.0

48

12

12

0.5

21

2.1

23

2.7

2.2

8.2 1.0

36

1.5

35

5.0

1.2

4.9

2.2

41

13

0.2

2.0

69

0.2

23

27

20

0.2

2.4

!.3

23

63

6.0

7.0

5.0

14

0.5

1.7

0.5

4.0

0.4

1.7

3.2

1.9

0.5

7.0

1.5

3.0

7.0

0.6

7.4

i.3

4.7

0.4

5.4

3.2

1.2

0.4 46

10 5.4

2.5

4.0 0.8

9.7

0.3

62

2.0

0.8

0.2

34

1.0

4.0

8.5

1.0

13

1.0

20

20

2.2

4.8

0.6

0.7

2.5 0.7 O.6

64 26

2.4

29

4.9

75

1.0

2.2

< 0.02

1.2

7.0

0.6

1.0

0.7

5.2

4.2

9.32(3.6), 9.38(3.4), 9.42(1.0), 9.70(I.0), 10.18(0.4), 10.92(I.0), 11.08(I.9) 8.26(2.0), 8.33(0.6), 9.32(0.3), 9.50(3.0), 10.72(1.0) 8.41(2.5), 9.16(0.5), 9.32(I.0), 9.38(I.3), 9.42(0.7), 9.79(0.2), 10.88(0.2), 10.92(0.4), 11.08(!.2) 8.54(3.0), 8.59(22), 8.94(I .4), 9.16(4.2), 9.42(14), 10.21(2.0), 10.31(3.6), 1 !.90(I.5) 8.59(1,9), 8.94(!.1), 9.32(6.2), 10.21(0.5), 10.42(0.3), 10.67(4.0) 8.33(0.9), 8.59(0.4), 9.32(0.4), 9.38(0.9), 10.38(1.1) 8.59(2.9), 8.94(I.3), 9.32(2.3), 9.38(1.4), 9.70(0.4), 10.67(4.3) 8.26(0.9), 8.59(2.9), 9.16(0.6), 9.42(!.2), 9.48(I.I), 9.79(0.3), 10.67(1.0)

8.59(0.3), 9.16(0.4), 9.42(0.9), 9.48(1.3) 8.26(3.2), 9.32(1.1), 10.38(2.3) 8.26(8.0), 8.330,.2), 8.59[~2.3), 8.90(1.0), 9.50(L.8), 9.77(!.0). 9.93(0.6), 10.21 (0.2) 8.33(5.2), 8.59(0.7), 9.32(5.6), 9.38(3.7), 9.50(0.5), 10.38(20), 11.434(0.4) 8.41(1.2), 8.94(5.5), 9.42(4.8), 9.70(31 ) 8.41(45), 8.59(14), 8.94(0.8), 9.70(1.5), 11.435(3.0) 8.26(1.3), 9.32(1.0), 9.38(6.0), 9.50(!.7), 10.60(2.7), 10.88(0.6) 8.26(0.2), 8.59(0.5), 9.32(2.3), 9.38(0.3) 8.41(1.1), 8.59(2.6), 9.16(0.6),

t,o

u1 Z I'rl CJ ,< t" ['rl < rn t--

7,

13051 2-

13096 2 " , 3 - ")

1520

1566

35-(3-), T = I 21 ÷ , 2 , 3 - ") 311.0 83 94 16 22

0.1

1.5 2.1 2.1 24

81 90 55 27

13247 13248 13272 13321 13361 13417

(2, 3)* 2*) 2, 3- °)

0.4 !.2 5.6 4.4

1723 1724 1749 1800 1842 1900

!

!.8

21

32+,T~

13173 13188 13189 13205 13209 13230

1647 1662 1663 1680 1684 1706

8.5

38

39

5.6

76

0.8

1.9

38

1588 13117 3d)

1577 13106 1578 13107 3-

13034 2+

1502

0.7

4.6

0.5

3- ' )

0.1

1388 12924 2 * d ) , T =

1457 12991

79

0*

1

1.78

2*

0

JW¢),T¢)

F.~') Et b) (keY) (keY)

Resonances

2.5 3.8

1.6

5.8

2.5

4.3

21

1.5 0.6

8.0

24

10

2.1

4.62 4.98 4* 0 ÷

0.4 5.1 3.2

i.8

7.9

2.7

13

2.9

4.7

6.2

0.7

1.3

i.8

5.0

6.28 3+ 0.2

6.69 0÷

9.0

1.8 7.9

4.7

2.7

16

6.6

9.3

0.5

5.9

8.6

21

0.5

3.1

9.5

4.8

1.0

6.88 6.89 34÷

1.1

i.6

1.8 3.6

9.0

1.2

3.4

3.0

7.38 2+

16 1.8

1.9

2.5

2.0

!.4

3.8

0.2

7.42 2*

!.6

3.4

7.1 !.9

2.3

6.2

14

1.7

1.5

8.1

0.8

7.80 3*

5.8 2.8 !.8

2.2 2.5

1.8

0.5

0.4

4.0

0.5

3.0

7.93 2÷

Gamma. decay to E, (MeV) in a*Si (*~)

TASLIg2 (continued)

9.32(8.2), 9.38(1.5) 10.38(0.6), 1 !.435(0. I ) 8.59(I.9), 9.32(21), 10.38(25) 8.59(1.8), 9.32(3.8), 10.38(26), ! 1.434(0.2), 11.435(0.6), 1i.78(3.8)

8.26(1.7), 8.41(3.2), 8.59(1.0), 9.16(3.4), 9.42(0.9), 9.48(0.5), 9.77(0.4), 10.18(0.5), 10.21(4.8), 10.67(1.2), 10.95(I.5), 11.78(0.5) 9.32(23), 9.70(19), 10.38(6.5) 8.26(I.3), 9.50(4.3), 10.51(2.3), 10.67(0.7) 9.32(2.4) 9.32(8.7), 9.77(2.2), 10.60(15) 8.59(3.8), 9.32(13), 9.38(9.2), 10.38(3.5) 8.41(0.7), 9.32(I.2), 9.70(85)

11.o8(o.4)

8.26(2.2), 8.41(I.0), 9.16(0.8), 9.32(0.7), 9.38(2.7), 9.48(I.2), 10.38(2.0), 10.88(0.3), 11.98(!.0) 8.33(0.8), 9.50(1.0), 9.77(!.0), 10.54(0.4) 8.26(5.7), 8.59(2.6), 9.32(38), 9.48(1.7), 10.38(5.4) 8.41(0.5), 8.54(4.5), 8.59(8.1), 9.32(9.3), 9.42(0.6), 10.18(8.6), 10.54(0.5), 10.90(0.5)10.92(0.7),

10.54(1.0)

8.26(I.5), 8.33(0.3), 8.59(!.1), 9.16(0.8), 10.21(0.5), 10.31(0.5). 10.67(0.4) 8.41(4.4), 8.59(7.8), 9.32(52),

other levels

~, '~

,~ m pu

• .~

13547 13557 13569 13584

13612 13616 13636 13640

13663 3")

13668 2,3,4 +*)

2034 2045 2058 2073

2102 2106 2127 2132

2155

2160

13709 2 +, 3, 4 + ") 13806 2 + ') 13814 2 +, 3 - ' )

13831 13861 13874 13902 13941 13973 13980 13984

2203 2303 2312

2330 2360 2374 2403 2443 2476 2483 2488

9.5 28 2.0 0.5

1.6 0.6

41 1.5

0.5

7.0 27

26

21 62 80 68 19 31 4.6 16

89 48 15

8.4

50 70

17

13

30 63 22 40

46 2.0 15 14

39

12 27 86 72

21 2.0 8.2

0.9 39 7.5

28

1.0

11

75

42 12

2.5 49 9.0 2.1

61

4.5

1.8 3.0

9.0 21 15 0.8 2.0

(0.3)

10

!.5

1.1 3.8 17 28 12

12

9.6

3.0

1.3

6.6 6.3

1.0

II 10

32 9.0 8.4

9.9

O.5

21

2.5

7.8

13

1.9

16

19

2.3

32

1.5

1.0

0.6

11

6.4

6.0 6.0 5.4

2.5

2.7

7.2

5.5

5.5

3.5

1.6

2.4

8.0 5.8

2.0

3.6

'+) Ref. ,2).

8.59(8.t) 8.59(20) 8.33(2.4), 8.59(18), 9.32(2.3) 8.59(I.8), 9.42(3.2), 11.78(1.0) 8.54(2.6), 8.59(2.6), 10.60(I.8)

8.41(I.!), 9.16(17), 9.42(12), 9.70(2.9), 10.31(4.5) 8.26(0.5), 8.59(3.0) 9.48(!.5), 10.38(5. ! ), 11.435(1.0) 8.26(4.5), 8.59(4.5), 9.16(9.0), 9.42(4.3), 9.48(2.8), 10.51 (2.8) 8.59(13), 8.94(7.0)

io.38(5.o), 1o.88(1.o)

8.33(2.2), 8.59(5.9), 8.90(!.0), 9.32(2.6), 9.50(5.4), 10.21(4.6) 8.59(4.7), 9.32(14), 9.38(2.3) 8.59(9.4), 10.42(7.6) 9.70(43), 10.42(3.0) 8.54(65), 8.59(!.4), 8.94(5.6), 10.42(3.5) 8.41 (3.0), 9.70(9.0), 10.42(5.0) 9.32(5.0), 9.38(5.0), 10.88(5.0) 9.38(62), 10.38(9.0) 9.32(9.7), 9.38(8.0), 10.88(2.0), 1 !.434(6.1) 8.41(2.9), 8.59(2.7), 9.16(!.2), 9.32(I .3) 8.26(2.6), 8.59(3.8), 9.16(17), 9.42(9.5), 10.31 (2.8) 10.88(2.4) 8.59(4.1), 9.32(1.0), 9.38(0.9),

i0.42(5.0), 11.78(2.5)

8.54(2.0), 8.59(3.0), 8.94(7.5),

") Ref. t+) for Ep < 1.85 MeV. Present experiment for E, > !.85 MeV. ") Calculated using O = 11585.3+0.6, from ref. ~+). c) Ref. t,) unless otherwise indicated. ") Present experiment, see subsect. 3.6. *) Present experiment, see $ubsect. 4.1.

2 , 3 , 4 + *) 2 +, 3 " ) 2, 3- *) 2 +, 3- ") 2 +') 2 +, 3- ") 2+,3-')

13707 3 - , 4 + *)

2200

2171 13679 1+,2,3 - * ) 2179 13686 2 +, 3 ' )

3-, 4 + °) 2 , 3 , 4 +* ) 1,2,3°) 1+,2,3 + 0)

2, 3- ") 2 + , 3 , 4 °) 3 - , 4 + °) 4 +, 5- 0)

13484 2 ' )

1969

1911 13427 5 + ")

m

l,J

t'i'm m

Ill ~o

_m.

242

M.A. MEYER et aL

The (p, 7) strengths were obtained from the areas under the resonance peaks and by assuming a strength of 5.3_+0.8 eV [ref. 13)] for the Ep = 633 keV resonance. Corrections due to the different decay modes of the resonances were introduced. The results are shown in table 1. Except for the Eo = 1723, 1749, 1900 and 1907 keV resonances, the (p, Pl), (P, P2) and (p, ~17) strengths were obtained from the intensity of the relevant 7-rays in the (p, 7) 7-ray spectra and the (p, 7) strength of the corresponding resonances. The (p, Pl), (P, P2) and (p, ~aT) strengths of the broad resonances at Ep = 1723, 1749, 1907 and 2312 keV were obtained from the areas of the peaks in fig. 2 and the strengths of the (p, Pl), (P, P~z) and (p, ~17) resonances at Ep = 1800 keV. The strong and broad (p, 7) resonance at Ep = 2249 keV [ref. ts)] was not observed in the present experiment. The strengths in table 1 are generally in reasonable agreement with existing results [refs. 4.1 ~, 1,t, 15.17)]. The value, S = 8.5-t-0.9 eV, obtained by Dalmas et aL 11) for the Ep = I 118 keV resonance, is in excellent agreement with the present result. Large discrepancies between the present measurements and those of Lyons et al. t 5) exist for Ep > 19(10 keV. The 7Li(p, n) threshold is) at Ep = 1880.59+0.08 keV was used as a calibration energy for the determination of proton energies above Ep = 1900 keV. Relativistic corrections were introduced and the final results are shown in table I. Large discrepancies between the present proton energies and those of Lyons et al. 15) exist for Ep > 1900 keV whereas the present measurements are in good agreement with the results obtained by Dalmas 17). 3.2. GAMMA-DECAY OF RESONANCES The 7-decay of 78 resonances of the reaction 27Al(p ' 7)28Si in the energy range Ep = 0.29-2.5 MeV is shown in table 2. The doublets at Ep = 1364, 1577, 1662 and 1723 keV could not be resolved. The present results are in excellent agreement with previous experiments, except that in almost all cases additional weak primary transitions were observed. A typical spectrum is shown in fig. 3. The resolution of the detector-amplifier system was 5 keV at E~ = 1.3 MeV and about 12 keV at Ey = 10 MeV. Transitions to the ground state were observed at the Ep = 736, 923, 1002 and 1278 keV resonances having intensities of 0.2, 0.2, 0.3 and 0.5 ~o, respectively. These M3 or E4 transitions are too strong to be attributed to these resonances. In order to determine the origin of these transitions, background spectra were recorded at Ep = 700, 910, 970 and 1290 keV. Although weak r ~ 1.78 MeV and r ~ 4.62 MeV transitions were observed, no transitions were observed at the first three energies whereas a weak r --, 0 MeV transition was observed at Ep = 1290 keV. In addition, an M3 r - * 4.62 MeV transition (intensity 1.1~o) was observed at the Ep = 774 keV resonance which was too strong. This transition presumably arises from the neighbouring Ep = 767 keV resonance which decays strongly to the E, = 4.62 MeV level. At the Ep = 1911 keV (J" = 5 +) resonance, a 3.7 ~ r -* 0 and a 2.3 ~o r --* 1.78 MeV

a'si ENERGY LEVELS

243

transition were observed which cannot be attributed to this resonance since it would lead to too strong M5 and M3 transitions, respectively. These transitions could arise from the neighbouring Ep = 1900 keV resonance which decays strongly to the ground state and first excited state. The present results for the decay of resonances with Ep > 2.1 MeV are in good agreement with those obtained by Dalmas et al. to). 3.3. ENERGIES OF BOUND LEVELS The levels at Ex = 9.48, 9.79, 9.93, 10.51, 10.54, 10.67, 10.88, 10.90, 10.92, 10.95, 11.08 and 11.78 MeV have not been observed in the previous experiments 3,4). The energies of these and other high-lying levels (table 3) were determined from 55 ° spectra. Corrections for recoil losses and Doppler shifts were introduced. Except for the TABLE3 Excitation ©nergies (in keV) of bound levels in "Si Present experiment

Re£ t,t)

7415.2+2.0 9478.5 + 2.5 9765.04-2.2 9793.84-2.0 9929.34-2.0 10514.94-2.0 10541.04-2.0 10598.25:2.0 10668.84-2.4 10884.1 -t-2.0 10901.54-2.0 10915.94-2.0 10945.4-t-2.0 11078.1 4-2.0 11434.3-t-l.0 11434.6-t- 1.5 I 1778.8 4-1.5

7418.64-1.0 a) 9480.4 4-1.5 9761.5 -t-1.4

") Ref. s).

Excited at E~ (keV)

679, 1262, 1381 9930 +7 679, 1662 10540 4-3 10594.44-2.0 ~) 10668 -t-5 937, 1172, 1262, 1502 10901 -t-3 10915.74-1.3 10945 -t-3 11077.5 -t-1.3 11432 -t-2

937, 1090, 1900, 2132 1118, 1800, 1900, 2303 1588, 1911

b) Ref. 4).

resonances at Ep = 1025 and 1588 keV (the E x = 9.93 and 10.95 MeV levels, respectively), the widths of all resonances where energies of bound levels were determined, are known ,4) and this knowledge enables one to conclude that the primary transitions at these resonances will exhibit full Doppler shifts. As far as the secondary transitions are concerned, lifetimes are only known for the E. = 7.42, 10.60 and 10.67 MeV levels. The lifetimes are short and transitions from these levels will also have full Doppler shifts. For these levels, the energies were determined from the primary and secondary transitions. Otherwise only primary transitions were used. The resonances at which the new levels at Ex = 9.79, 10.51, 10.88 and 11.78 MeV were excited, are shown in table 3. The criteria adopted for proposing a new level

1.78 4.62 4.98 6.28 6.69 6.88 6.89 7.38 7.42 7.80 7.93 8.26 8.33 8.41 8.54 8.59 8.90 8.94 9.16 9.32 9.38 9.42 9.48

E, (MeV)

2 +

( 3 - , 4 +) "' b) 3 +, T = 1 2 +, T = 1 (2 +, 3 - , 4 + ) 2+

== (-y

4* 0* 3+ 0+ 34+ 2+ 2+ 3+ 2+ 2+ 1+ 46* 3÷ 1-

J " , T')

B o u n d level

<5 <0.5 2.04-1.0 <2 854-5

<1 474-3

644-2 <4 37.5-4-1.5 944-2 <0.3 82-4-2 9 . 0 + 1.5 724-4 < 0.4

< 0.7

100 < 0.5

0 0÷

55+5 72.7 4-1.0 944-2 264-5

534-3

93.7+2.0

284-4 22±2

100 100 92.5+0.5 100 334-2 100 62.5+!.5 6-4-2 70.0-4-1.0 4.54-2.0 7O4-2

1.78 2+

<1 644-2 454-5 <2
7.520.5 <0.5 3.0~0.7 <1 <2 <2 1.04-0.4 7.84-1.3 4.0~1.0 <5 4.04-1.5

4.62 4*

TABLE 4

< 10 <5 < 3 < 0.5

< 2

5.74-1.5 17.0+1.0 <5 < 0.5

<2

<1

<0.2

4.98 0*

< 4 <5 27.3+1.0 4.04-1.0 54-2

< 0.4 <1 6.34-4-2.0

< 2

<1 <1 <3 29.0+!.0

<4

6.28 3*

< 5

< 7 <5 < i

< I

<2 < 0.2 < 3 < ! <4 < 0.3

6.69 0÷

<5 < 0.5

74±2 <2 < I

6.88 3-

234-5

364-2

6.89 4÷

G a m m a decay ( ~ ) to E, (MeV) in 2'Si

G a m m a decay o f b o u n d levels in 2ssi

< 3 8+2 (154-5)

7.38 7.42 2* 2*

8.41 4-

8.59 3*

unknown

m ,,¢ rn

.>

to

") ") =) d)

I 1.78

100

I00

1÷ , T = O - F I

I +, T = I = (_):

(4) =)

834.4 < 0.6

404-10

< 1

<4

1oo

854-4 < 0.1 < 2

1÷, T = 0-FI (2, 3) +

3( 2 ÷ , 3 , 4 *) (4 +) b) (3) ÷, T = I 3 + b)

(i, 2)-

(I, 2) + 5- ':) (2-4) d) (1-4) d)

< 2

354-10 70-1-10 100

iO0

< 5 100

60110 100 < 10 64-2

254-5 754-10 454.10 20.24-1.2

15+4 15-/-4 854-5 100

100

< 10 < 1

554-10 23.0-4-2.0 154.5

754.5

< 3 204-5 < 5

< !0

<3

<3

<1

<4

< I0

< 0.5

Ref. t4) unJess otherwise indical©d. Ref. =s). Ref. 11). Weiukopf estimates, present experiment, see subsect. 4.1.

I ! .435

11.434

11.08

10.72 10.88 10.90 10.92 10.95

9.50 9.70 9.77 9.79 9.93 10.18 10.21 10.31 10.38 10.42 10.51 10.54 10.60 10.67

<3

<4

< 2

< 0.5 21 4-5

6.04-1.0

10+2

84-4

< 0.5 344-5

20+10 and 304-10 .-*9.32

234.5 < 2 < 2 < 1 and 94-2 --* 7.93, 20-F2 ~ 9.32, 54-2 ~ 9.38

294-3 854-5

<4

<4

50±10

7+2

21.8~!.0

<2

65 30

17 30

17

15

l-o

[rn t-n c"

m r~ po O

246

M.A. MEYER et aL

were (a) the "level" must have been excited at least twice, (b) at least the stronger of its decays should have been observed at each instance and (c) the energies should agree within reasonable limits. The level at E, = !1.43 MeV was found to be a doublet as followed from the different decay modes (see subsect. 3.4.6). The resonances at which the different members of this doublet were excited, are shown in table 3. The new level at E, = 11.78 MeV is not the E, = 11.78 MeV, j x = 2 + resonance which decays to the E, = 1.78 MeV level. 3.4. GAMMA-DECAY OF BOUND LEVELS The y-decay of 46 bound levels in 2sSi is shown in table 4. These results are generally in excellent agreement with the previous 4) results obtained with a 10cm 3 Ge(Li) detector. The ),-decay of the levels at E, = 9.79, 9.93, 10.51, 10.88, 10.92, 11.08 and ! 1.78 MeV has not previously been reported. Differences with previous results will now be discussed. 3.4.1. The E x = 7.42, 7.80 and 7.93 M e V levels, in the previous experiment *), the decay of the E~ = 7.42 MeV level could not fully be accounted for. A (6_+2) ~o, 7.42 --, 1.78 MeV transition, also reported by Gibson et ai. 2), was observed at the Ep = 679, 1002, 1025, 1262 and 1381 keV resonances. This transition was not observed by Forsblom 7) at the Ep = 1381 keV resonance. A 6 ~o decay to the E, = 4.98 MeV level was observed by Gibson et al. 2) at the Ep = 679 keV resonance. Although a peak was observed at this resonance which could be interpreted as this transition, it was not observed at other resonances. Upper limits for the 7.42 ~ 4.98 MeV transition were determined at the E~ = 1002 and 1025 keV resonances and in all cases it was found that this transition, if present, must be less than 2 %. A new ( I . 0 + 0 . 4 ) % , 7.80-* 4.62MeV transition was observed at the Ep = 1025 and 1317 keV resonances. A 100 %, 7.93 ~ 0 MeV transition was reported by Gibson et al. ~) and Azuma et al. t 9) while a 79 % transition to the ground state and the remainder unknown was stated in the previous experiment 4). In agreement with existing results s.2o) transitions to the Ex = 1.78, 4.62 and 4.98 MeV levels were observed at the Ep = 992 and 1199 keV resonances. 3.4.2. The Ex = 8.26 and 8.59 M e V levels. A 100 9/0 transition from the E, = 8.26 MeV level to the E x = 1.78 MeV level was found by Gibson et al. ~) whereas an 8 % transition to the ground state and a 67 % transition to the E, = 1.78 MeV level were reported in the previous experiment 4) in agreement with Forsblom 7). The remainder was unknown. In the present experiment, additional (4.0_+ ! . 0 ) % and (17.0+ 1.0)% transitions to the Ex = 4.62 and 4.98 MeV levels respectively, were observed. A 100 ~ transition from the E, = 8.59 MeV level to the E, = 1.78 MeV level was observed by Gibson et al. t) and Forsblom 7) whereas previously 4) a 97 % transition to this level was observed. The present results also indicate that the 8.59 --. 1.78 MeV transition does not entirely account for the decay of this level and that it also decays

"ssi ENERGY LEVELS

247

to the E, = 6.28 MeV level. The 8.59 ---, 6.28 MeV transition was observed at seven resonances. 3.4.3. The E~ = 8.94 and 9.38 M e V levels. In the previous experiment 4), 53 % of the decay of the E, = 8.94 MeV level was unknown. In the present experiment, it was found that the 8.94 --, 6.89 MeV transition, observed at four resonances, fully accounted for the previously unknown decay in agreement with Gonidec et ai. 2o). A (4.05: 1.0) ~o, 9.38 -4 6.28 MeV transition which had not previously been reported, was observed at two resonances. 3.4.4. The E: = 9.42 and 9.48 M e V levels. The present branchings of the E, = 9.42 MeV level are not in agreement with the results obtained by Gibson et al. t) and Azuma et al. ! 9). A new (5_+ 2) %, 9.42 --* 6.28 MeV transition was observed at the Ep = 1278 and 2200 keV resonances. A ( 2 3 + 5 ) ~o, 9.42 ~ 6.89 MeV transition was observed at the Ep = 992, 1098, 1278 and 2200 keV resonances. This transition were also observed by Gonidec et al. 2o). The E, = 9.48 MeV level was observed by Gibson et al. 1) and Simons et al. 2,). These workers reported a 100 % transition to the ground state. The present results show an 85 % transition to the ground state and a possible decay to the E, = 7.38 MeV level. 3.4.5. The E~ = 10.21, 10.60 and 10.67 M e V levels. A 100 % 10.21 --, 1.78 MeV transition was obtained by Gibson et al. ~). Both the previous 4) and present experiments indicate that this transition does not fully account for the decay of this level. An (8_+4)%, 10.21 --- 7.42 MeV transition was observed at the E~ = 1588 keV resonance while 17 % remains unknown. Forsblom 7) has observed transitions to the E, = 0, 1.78 and 4.62 MeV levels at the same resonance. In the present experiment, the 10.21 - . 4.62 MeV transition, if present, coincided with other strong peaks in the y-ray spectrum of the Ep = 1588 keV resonance. It was previously reported 4) that the E, = 10.60 MeV level decays almost entirely to the E, = 8.41 MeV level. In the present experiment, the E, = 10.60 MeV level was excited at the Ep = 655, 742, 1172 and 1684 keV resonances and in all cases, a 10.60 --, 0 MeV transition was observed in agreement with Forsblom 7). However, the (354-15)%, 10.60 ~ 1.78 MeV transition, observed by him, was not observed in the present experiment. Instead an upper limit of 10 % was obtained for this transition. The 10.60 ~ 0 MeV transition does not account for the entire decay of this level. In contrast to the observation by Detraz z2), that the E, = 10.67 MeV level only decays to the E, = 1.78 MeV level, a number of additional branchings were observed at the Ep = 1317 and 1364 keV resonances. 3.4.6. The Ex = 11.43 M e V doublet. This level was thought 4) to decay to the E, = 6.28 and 8.59 MeV levels. In the present experiment, the E, = 1 !.43 MeV level was observed at the Ep = 937, 1090, ! 118, 1800, 1900, 2132 and 2303 keV resonances. At the Ep = 937, 1090, 1900 and 2132 keV resonances, a transition to the E, = 1.78 MeV level was observed. At the Ep = ! 118, 1800, 1900 and 2303 keV resonances, it was found that the E, = 11.43 MeV level decays to the E, = 6.28, 8.59 and

y&;, ril-

..

_-.-.

.’

.’

‘-_

,__._--.’ -.\_ *i:--’ z-. ___ -. m-x*i~ .I F-_=_‘-

----. ‘.. ,,_.,.

*

N

:.. 1.

w

5

9.

248

M.A. MEYER

et al.

9.32 MeV levels in agreement with the observations by Dalmas et al. , ! ) at the Ep = 1118 keV resonance. At this resonance, an upper limit of 2 ~ was determined for the ! i.43 --, i.78 MeV transition. These observations lead to the conclusion that the E, = 1 !.43 MeV level must be a doublet. The energies of the two levels are shown in table 3. 3.5. M E A N

LIFETIMES O F B O U N D

LEVELS

The mean lifetimes of bound levels in 2sSi were determined by means of the Doppler shift attenuation method as described in a previous 3) publication. Thick targets were used to ensure that the 28Si recoils were slowed down in the aluminium and the TABLE 5 Mean lifetimes o f bound levels in assi E, (MeV)

Doppler shift determined at F~ (keV)

Doppler shift ") attenuation F(g)

4.62 6.69 6.89 7.38 7.42

767 1172 1278 774 774 1172 1317 1199 1172 1588 774 1577 1199 1278 1577 742 1317 2045 i 588 2200 1317 1577 1172 1278 742 1577 1278 1278 2045 742 1317 742

0.674-0.01 0.374-0.02 0.734-0.04 0.924-0.04 0.744-0.02 0.76::/::0.04 0.27 4-0.01 1.004-0.02 0.784-0.04 0.924-0.06 0.15 4-0.02 0.994-0.02 0.96±0.02 0.96+0.03 0.984-0.02 0.90+0.02 0.50±0.02 0.524-0.03 0.77 +0.07 0.81-4-0.02 0.96+0.04 0.994-0.02 0.954-0.04 0.38 ± 0.03 0.944-0.02 0.934-0.02 0.904-0.06 0.884-0.06 0.854-0.04 0.994-0.01 0.85 -t-0.03 0.924-0.01

7.80 7.93 8.26 8.33 8.54 8.59

8.90 8.94 9.16

9.32 9.38 9.42 9.50 10.18 10.21 10.31 10.42 10.60 10.67 10.72

") Corrected for finite size o f detector. a) Errors shown are statistical errors.

Mean lifetime, lr,, b) (is) 39+ 2 1304-20 404- 5 84- 3 29+ 3 354- 7 250 4- 75 < 5 31 + 6 124-10 380 -4-50 < 5 6+ 2 6-t- 4 34- 3 104- 3 96+ 6 1154-10 39 4- ! 3 37+ 5 < 15 < 5 < I0 l 16 4-15 5 4- 2 10+ 3 13+ 4 164- 6 27+ 7 < 5 224- 6 84- 2

2sSi ENERGY LEVELS

249

TABLE6 Summary of asSi lifetime measurements Bound level E, (MeV) 4.62 6.69 6.89 7.38 7.42 7.80 7.93 8.26 8.33 8.54 8.59 8.90 8.94 9.16 9.32 9.38 9.42 9.50 10.18 10.21 10.31 10.42 10.60 10.67 10.72

pre~ent experiment ") 394- 2 1304-20 40+ 5 84- 3 30-t- 5 250+75 < 5 26+ 8 380+50 < 5 5+ 2 10+ 3 1004- 8 374- 5 < 5 < 10 1164-15 54- 2 104- 3 13-t- 4 16-1- 6 274- 7

Mean lifetimes, T, (fs) previous mean experiment b) lifetime c) 58+10 88+t-12 53+ 6 74- 4 244- 4 1904-30 < 6

<6 12+ 4 < 5 5+ 3 94- 3

<5

224- 6 8-t- 2

40+ 7 100+25 454- 9 8+ 2 26-4- 5 2004-35 < 5 26+ 9 380+75 < 5 5+ 2 114- 3 1004-10 37-t- 7 < 5 5+ 3 1164-23 64- 2 104- 4 134- 4 164- 6 27+ 8

ref. i,)

59=[= 6 120+30 65+10 8+ 2 36+ 4 260+50 20+10 I1+ 4 150-t-85 40+20 15+ 7 12+ 4 85+20 48+ 9 13+10 5+ 3 150+30 9i 3 15~- 7 234- 7

< 5

< 6

224- 7 8+ 2

< 6

• ) From fourth column of table 5. b) Refs. 3.4). Errors are statistical. ~) Weighted mean of columns two and three. A 15 % error was added to the internal or external error whichever was the greater. D o p p l e r shift a t t e n u a t i o n factor was corrected for the finite size of the detector. The results are shown in table 5. All the levels, except the E, = 6.89 a n d 9.32 MeV levels, were excited by p r i m a r y transitions only. The lifetimes o f the E, = 6.89 a n d 9.32 MeV levels were corrected for c o n t r i b u t i o n s o f secondary transitions to these levels. The mean lifetime o f the E, = 4.62 MeV level is the m e a n o f 20 d e t e r m i n a t i o n s at the strong Ep = 767 keV resonance which decays m a i n l y to the Ex = 4.62 MeV level. The present results are c o m p a r e d with previous m e a s u r e m e n t s 3.4) in table 6 which also includes, in c o l u m n 4, the weighted m e a n of the results o f c o l u m n s 2 and 3. The external or internal error, whichever was the larger, was used. A 15 % error was a d d e d to the statistical error in order to include possible uncertainties in the theory. T h e present lifetimes are c o m p a r e d with the recent c o m p i l a t i o n by Endt a n d Van der Leun t4) in table 6. It must be p o i n t e d out that the lifetimes shown in c o l u m n 5, also include the m e a s u r e m e n t s o f the previous experiment (see table 2 8 . l i b ,

z,

1.78 8.90 9.50 • --~ 10.60 • ~ 10.72

• ~ 1.78 • ~ 7.80 • --~ 8.26

• --,

1025

1213

1328

r ~

742

-0.06=1=0.01

--0.064-0.05

1.78

-0.O3±0.O2 0.194-0.03

-0.104-0.02 --0.074-0.07

-0.034-0.03 0.03 :t: 0.05

0.04±0.04 0.06-t-0.01 -0.164-0.14

- 0.00i0.10 --0.10±0.11 - 0 . 0 1 +0.08 0.21 +0.27 -0.16=h0.1 i

--0.03-60.07 -0.08±0.08 --0.17±0.06 --0.41 ±0.18 --0.03±0.08 --0.07±0.03 --0.13±0.01 --0.11±0.09

- 0.01 i 0 . 0 3 -0.08i0.03 0.03 ± 0.03

-0.04+0.06 -0.28±0.21

A4 ")

--0.14=t=0.01 -0.09-4-0.02 -0.06+0.02

0.144-0.03 --0.23+0.14

Aa a)

r --~ 4.62

• --~

r--~

1.78 6.69

r --~ 1.78 r -*- 4.62 r -~- 7.42

679

r~ r -~

r --~ 4.62 r --~ 8.59

Transitions

406

(keV)

TAILE 7

2, 3

I, 2

2, 3

1,2

3

2-4

Spins from angular distributions

Angular distributions coefficients and spin allocations

2 +, 3 ÷

I +. 2 +

2

52

2,3,4,5 *

Spins from Weisskopf estimates

2", 3 ÷

I ' , 2"

2

I - , 2 ~ I')

3

2.,3-,4

Spin assigned

2-4

I-, 2÷

(I *, 2)

(2*)

3 + c)

~ b) (4*)

Ref. " )

rr~ .< m

.>

~r

r -~ 1.78 r - ~ 4.62

!.78 6.88

r ~ r ~

1457

1502

1520

• --*- 1.78 • ~ 6.28

r ~ 0.02+0.06 --0.17+0.10

--0.92±0.03 --0.25+0.03

-0.09:£0.01 -0.08t0.03 0.05±0.08

-0.14±0.11 -0.29±0.08 -0.274-0.05

--0.24±0.02 0.07=£0.06

-0.294-0.04 --0.24±0.12

0.32+0.15 --0.33±0.08

-0.09±0.01 -0.08±0.06

-0.10±0.01 -0.14+0.04 -0.09+0.12

") Corrected for solid-angle attenuation,

1969

4.62 6.89

1911

~

r -*- !.78 • --* 4.62 r ---,- 6.28

1588

•

r ~ 6.89 r --* 7.80 • --* 9.32

1566

r -4-

r ~

r-, !.78 r -~ 6.28

1388

4.62 7.80

r -~ 1.78 r -* 4.62 r --~ 6.28

1381

2

5

2, 3

2, 3, 4

2, 3

2, 3

3, 4

2, 3

:~, 3

1 +, 2-4

2 ÷, 3,4, 5 ÷

3, 4 ÷

2, 3

2

2, 3

2-, 3-

2÷

2 +, 3, 4 +

b) The parity follows f r o m the known ao decay o f these resonances , s ) .

- 0 . 0 1 ±0.08 0.07±0.12

0.19±0.04 --0.02±0.04

-0.02±0.01 -0.00+0.04 0.01 ± 0 . 0 9

-0.09+0.14 -0.09±0.10 0.09i0.05

0.10±0.03 -0.04-t-0.07

-0.02+0.05 0.09±0.15

0.05+0.19 -0.03±0.10

-0.03±0.01 0.03i0.08

0.01 +0.01 -0.05+0.05 -0.00±0.14

2

5÷

3

(2-4)

( 3 - , 4 ÷)

2-

2•

3-

(2, 3) ÷

") Re£ ~4).

2 ÷, 3- b)

2

2, 3

3-

2÷

2 +, 3

m

t[n < m [..,

,<

m Z M

252

M.A. M E Y E R

et aL

ref. ~4)). The largest discrepancies exist in the case of the E, = 7.93, 8.26, 8.33 and 8.54 MeV levels although in none of these cases the differences exceed more than three times the combined error. New measurements 1l.,s) of the lifetimes of the Ez = 8.54, 8.59, 8.94 and 10.42 MeV levels are in good agreement with the present results. 3.6. A N G U L A R DISTRIBUTIONS

Angular distributions were measured at a number of resonances in order to determine the spin of the resonance states. The angular distributions were measured with a Ge(Li) detector, 7 cm from the target and at 0 °, 30 °, 60 ° and 90 ° with respect to the direction of the beam. The spectra obtained at each of these angles were stored in separate quadrants of the memory of a 4000-channel analyser. A 0 ° -~ 90 ° ~ 0 ° sequence was repeated several times and checks were made on the eccentricity and ~-ray attenuation. A least-squares analysis of the data in terms of Legendre polynomials in the expansion N(O) = B(I +A2P~+A4P4) yielded values for At and A4. The results are shown in table 7. The number of pulses observed at each angle was used as input data for a computer program which calculated the quantity

Q2 = ~ (BNt(O,)-N(O,)~2, i \ AN(Or) / normalization constant and Nt(Ol) is given by N,(O,)-- I +QeA~P,(cos 0,)+ Q4A~P,(COsOr). i i

where B is a

The quantities Q, and Q, are attenuation factors which take the finite size of the detector into account and A~ and ,q~ are the theoretical coefficients which are functions of the population parameters and mixing ratios.Where the angular distributions of two transitions from a level of unknown spin were measured, an additional term was added to the above expression. The relevant parameters in the theoretical expressions for A~ and A~ were varied in a systematic manner in order to find the minima, ~', of Q2. The spin assignment was considered unique when the corresponding Z z liesbelow the 0. l ~ limit whereas all other spins yielded values of ~2 above this limit (fig.4). The resultsand conclusions from the angular distribution measurements are shown in table 7. The ./" of the Ep = 679 keV resonance was found to be 3 + by Heyligers ~'). Positive parity was deduced from an analysis of the population parameters. This was disputed in a previous publication 5) since the ~-decay of this resonance corresponds to the "4Mg(a, ~)zsSi resonance at E, = 2634 keV which has J" -- 4 +. The present angular distributions of the r --* 1.78, r --*4.62 and r --* 7.42 M e V transitions,showed that Y = 3 and that J -- 4 does not yield a Z 2 below the 0. I ~ limit. The mixing ratios of the primary transitions which yielded unique spins are shown in table 8.

2"Si E N E R G Y LEVELS

253

lO" J=4 Y =0.557

10 ~

t Q~

10 ~ Y: -0.087

~

mits J=2 J=3

J=4.5

lor-~

Ep= 1 9 1 0 k e V [

r

I

r --

-

4.62 6.89 6.89

x

4+

4.62 90 °

60 °

30 °

0°

4+ 30 °

60 °

90 °

fOR'' ~ Fig. 4. Values o f Qa for the ~,-ray angular distributions o f the r -~ 4.62 and r -* 6.89 MeV transitions at F~ = 1911 IceV plotted as a function o f the mixing ratio o f the r -* 4.62 MeV transition with the spin o f the resonance state and the mixing ratio o f the r -+ 6.89 MeV transition as parameters. The curves are those sections t h r o u g h the Qa = f(x, y) surfaces which yielded the l o w e s t Q=I,=.

TAst~ 8 Mixing ratios o f primary transitions at resonances where unique spins were determined F~

J

Transitions

Mixing ratios " )

679

3+

r --* 1.78 r --+4.62 r --* 7.42

0.36-/-0.04 --1.704-0.18 0.004-0.03

1911

5

r --* 4.62 r ~ 6.89

1.43 -F0.11 0.00-t-0.03

1969

2

r --* 1.78 r --* 6.28

0.274-0.05 +0.60 --2.75 -1.oo

") Tim sign convention is that o f R o ~ and Brink a~).

254

M . A . MEYER ¢t al.

4. Discussion 4.1. SPINS AND PARITIES

Weisskopf estimates were used in a number of cases to restrict the spins and parities of levels. The upper limits assumed were 100 W.u. for E2, 3 W.u. for M2, 100 W.u. for E3 [ref. z~)] and 15 W.u. for M3 transitions. Weak or uncertain transitions have not been used in the following assignments. The strengths of transitions from resonance states were calculated from the strengths of the resonances and the present branching ratios. For the resonances on which angular distribution measurements were performed (table 7), Weisskopf estimates were used to restrict the spins obtained from angular distributions or to obtain information on the parity of the resonance state. Unique spin assignments, based on Weisskopf estimates could be made for the Ep = 885, 1684, 2155, 2303 and 2476 k e y resonances. The parity for the Ep = 885 keY resonance follows from the fact that this level was also observed in (c~, ~) work 2s) and must therefore have natural parity. The spins of the resonances at Ep = 1172, 1706, 2034, 2058, 2073, 2102, 2179, 2200, 2312, 2374, 2403, 2443, 2483 and 2488 keV could be limited to two possibilities (table 2). In a number of cases (table 2), the spins could be restricted to three possible values. The spin of the E, = 9.77 MeV level was limited to J = 2, 3, 4 from the strengths of the r ~ 9.77 MeV transitions at the Ep = 767 (J = 4) and 1520 (J~ = 2 - ) keY resonances. The strengths of the r -~ 9.79 MeV transitions at the Ep --- 679 ( j i = 3 +) and 1381 (J" = 2 +) keV resonances restrict the spin of this level to J = 1 - 4 . 4.2. COMPARISON WITH THEORY

The E, = 0, 1.78, 4.62 and 8.54 MeV levels are considered to be the J ! = 0 +, 2~, 4~ and 6~" members of the ground-state rotational band characteristic of an axially symmetric doubly even nucleus. It was shown by Davydov et al. 29.3o) that violation of axial symmetry in doubly even nuclei only slightly affects the rotational spectrum of an axially symmetric nucleus and that new levels with J~ = 2~, 3 +, 4 ~ ' , . . . appear. If the deviation from axial symmetry is small, then these levels lie very high. On the other hand, if the deviation from axial symmetry is increased, some of the additional levels lie much lower. Expressions for the energies and transition strengths were obtained by Davydov et al. in terms of a parameter ~, which determines the deviation of the shape of the nucleus from axial symmetry, the intrinsic quadrupole moment and an energy parameter A. It was found 3t) that this model gave an accurate account of the spins and parities of the first five levels in 24Mg and of the transition strengths between these levels. The E, = 1.78, 4.62, 7.38 and 8.54 MeV levels were considered to be the 2~', 4~, 2~ and 6 ~" rotation members of a non-axially symmetric ZSSi nucleus. The quadrupole moment of the Ex -- 1.78 MeV level is Q(2 ~') = + 0.16 __0.03 e- b [ref. 14)]. The intrinsic quadrupole moment is therefore Qo = - (0.62+0.12) e . b for ~ = 18°. This value for ~, was chosen to yield the observed spin sequence in 2sSi. The E2 strengths of a

zsSi ENERGY LEVELS

255

T^SLE 9 Energies and transition stengths in a non-axial a ' s i nucleus Initial level (MeV) exp. theor, 1.78 4.62 7.38

1.55 4.90 7.19

8.54

9.76

Transition

!.78 4.62 7.38 7.38 8.54

--*0 --* 1.78 -* 0 --* 1.78 --* 4.62

JJ --* Jt

E2 transition strengths (W.u.) exp. theor.

2t ÷ --*0 * 4t ÷ --* 2t ÷ 2, + -* 0 ÷ 2, ÷ --*2t ÷ 6t ÷ -'* 4t *

134-1 224-4 0.34-0.1 2.2q-0.6") > 34

14-t-1 20-/-! 0.9+0.1 3.6-t-0.2 23-t-2

The parameters are Qo = -(0.62-t-0.12) e • b, y = 18°, A = 318 keV. ") Assumed to be pure E2.

few transitions, calculated with these values of ? and Qo are shown in table 9. The agreement with experimental strengths is good. The energies of the levels were calculated with the above value o f y and A = 318 keV. The results are also shown in table 9 and are in reasonable agreement with the experimental values. The authors are indebted to the South African Council for Scientific and Industrial Research for financial support, to the Atomic Energy Board for the use of their accelerator and financial support and to Profs. J. H. van der Merwe and E. Friedland for the use of the Pretoria University Van de Graaff accelerator. The assistance given by Miss N. Beeton with the computer programs is greatly appreciated. The authors also wish to thank Prof. P. M. Endt and Dr. C. van der Leun for helpful suggestions during the preparation of the manuscript. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21)

E. F. Gibson, K. Battleson and D. K. McDaniels, Phys. Rev. 172 (1968) 1004 E. F. Gibson, A. Goswami, F. Huang and D. K. McDaniels, Phys. Rev. 188 (1969) 1965 M. A. Meyer and N. S. Wolmarans, Nucl. Phys. AI36 (1969) 663 M. A. Meyer, N. S. Wolmarans and D. Reitmann, Nucl. Phys. A144 (1970) 261 M. M. Aleonard et aL, Nucl. Phys. A146 (1970) 90 I. Forsblom and M. Viitasalo, Comment. Phys. Math. 38 (1970) 131 I. Forsblom, Comment. Phys. Math. 40 (1970) 65 I. Forsblom, Comment. Phys. Math. 42 (1971) 261 P. Holmberg and A. Kiuru, Comment. Phys. Math. 40 (1970) 135 J. Dalmas and D. Berlault, J. de Phys. 34 (1973) 357 J. Dalmas, F. Leccia and M. M. Aleonard, Phys. Rev. C9 (1974) 2200 A. Tveter, Nucl. Phys. A185 (1972) 433 G. A. P. Engelbertink and P. M. Endt, Nucl. Phys. 88 (1966) 12 P. M. Endt and C. van der Leun, Nucl. Phys. A214 (1973) 1 P. B. Lyons, J. W. Toevs and D. G. Sargood, Nucl. Phys. AI30 (1969) I J. P. Thibaud, Bordeaux University, private communication J. Dalmas, Compt. Rend. 27713 (1973) 237 M. L. Roush, L. A. West and J. B. Marion, Nucl. Phys. A147 (1970) 235 R. E. Axuma et aL, Can. J. Phys. 44 (1966) 3075 J. P. Gonidec, C. Miehe and G. Walter, Compt. Rend. 272B (1971) 1385 L. Simons et aL, Phys. Lett. 3 (1963) 306

256 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

M.A. MEYER. e t al. C. D,~traz, Nucl. Phys. AlSS (1972) 513 G. F. Neal and S. T. Lam, Bull. Am. Phys. Soc. 19 (1974) 74 A. Heyligers, Thesis, Utrecht University (1964) M. Bister, A. Luukko and A. Anttila, Ann. Acad. Sci. Fenn. 6 (1968) 1 H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 P. M. Endt and C. van der Leun, Atomic Data and Nucl. Data Tables 13 (1974) 67 and Nucl. Phys. A 2 ~ (1974) 27 P. J. M. Smulders and P. M. Endt, Physica 28 (1962) 1093 A. S. Davydov and G. F. Filippov, Nucl. Phys. 8 (1958) 237 A. S. Davydov and V. S. Rostovsky, Nuci. Phys. 12 (1959) 58 M. A. Meyer, J. P. L. Reinecke and D. Reitmann, Nucl. Phys. AIS5 (1972) 625