A study of the 23Na(p, γ)24Mg reaction and the excited states of 24Mg

I zc I

Nuclear

Physics

A185 (1972) 625-643;

Not to be reproduced

by photoprint

@

North-~o~lond

or microfilm without written

Publishing

Co., Amsterdam

permission

from the pubhsher

A STUDY OF THE 23Na(p, y)24Mg REACTION AND THE EXCITED

STATES

M. A. MEYER, 3. P. L. REINECKE Ph_vsics L)epartment,

Potchefstroom

OF *‘Mg

and D. REtTMANN 5 Sol&z AfLico

Unicersitv,

Received 3 January 1972 Abstract: Proton energies and strengths of (p, ~j), (p, p,) and (p, cc,) resonances of the Z3Na-tp reaction were determined for ED = l-2 MeV. The :)-decay of 25 resonances in the energy range Ep = 0.3-2.0 MeV was studied by means of a 40 cm3 Ge(Li) detector. The Q-value of the *3Na(p,Y)Z4Mg reaction was found to be Q x 11691.2f I .l keV. The energies and branching ratios of 32 bound levels and the lifetimes of I8 bound levels were determined. The 2,-ray transition strengths have been calculated and compared with various models.

E

NUCLEAR REACTION Z3Na(p,y), E = 0.3-1.9 MeV; measured n(E, I$), Q, Ey, Iy, Doppler-shift attenuation. *‘Mg deduced levels, resonance strengths, y-ray branching ratios. T1. J. n. Natural targets. Ge(Li) detector.

1. Introduction

Information on bound levels of nuclei can be obtained from a study of the y-decay of (p, y) resonances. Since only a small number of bound Ievels are excited at each resonance, it is necessary to study the decay of a large number in order to obtain information on as many bound levels as possible. Unambiguous interpretation of spectra requires the proton energies of the resonances, the Q-value of the reaction and the energies of the bound levels to an accuracy of the order of 1 keV. The 24Mg nucleus was studied in this experiment by means of the 23Na(p, y)24Mg reaction. Since the proton resonance energies above Ep = 1.5 MeV for this reaction were not accurately known, it was decided to measure the excitation curve in the range Ep = 0.98 - 2.08 MeV and to determine the (p, y), (p, pl) and (p, LX,)resonance strengths in this range. The energies and y-decay of the resonances as well as the energies, branching ratios and mean lifetimes of a number of bound levels were determined. These results are compared with theoretical predictions of various models. 2. Experimental

details

This experiment was performed with proton beams from a 1.1 MV CockcroftWalton accelerator and a 3 MV Van de Graaff accelerator. The average beam current + Atomic Energy Board, Pretoria, South Africa. 625

626

M. A. MEYER ei al.

below E, = 1 MeV was approximately 100 PA and about 25 PA in the energy range Ep = 1-2 MeV. The proton beams were deflected through 90” by means of analyzing magnets and the magnetic field was measured by means of NMR fluxmeters.

20

15 Fig. 1. Excitation curve for the reaction 25Na+p

E&M&)

in the energy range EP = 1-2 MeV.

Clean copper target backings were used for E,, < 1 MeV and tantalum backings were used for EP = 1-2 MeV. The backings were cleaned by electron bombardment. The targets were water cooled and the target material was pure Na2W04.

23Na(p, y)24Mg

REACTION

627

TABLE 1 Energies and strengths of Z3Na+p

resonances for 4

= 0.95-2.08

S = (2J+ I)r,rJr(eV)

E. (keV) present experiment

refs. 2. 3,

987.5*0.4 1008.810.4 1010.7~0.5 1020.53,-0.5 1086.210.6 1092.2f0.7 1164.0&0.5 1174.410.5 1204.8hO.5 1210.4f0.5 1255.1*0.5 1282.7ztO.7 1318.0+0.5 1326.9hO.5 1331.1 hO.5 1362.2kO.5 139X210.6 1416.4hO.5 1457.2kO.6 1532.1&0.7 1557.2hO.8 1645.1&0.7 1652.2 h 1.0 1725.5 10.6 1735.2kO.8 1747.6hO.8 1802.3f0.8 1807.9h1.2 1831.010.8 1837.5+0.8 1860.3+0.8 1868.7kO.8 1930.7&0.8 1977.5 * 1.o 2024.9 5 1.1 2071.7hO.9

987.OkO.6 1007.9*0.9 1010.0*0.7 1020.4*0.5 1085.9+0.5 1091.0*0.5 1163.3hl.2 1173.8kO.5 1204.1 kl.1 1210.0+1.4 1254.Oyhl.O 1283.611.9 1318.310.6 1327.5 +0.8 1331.4kO.8 1362.5*0.6 1394.4+1.5 1416.810.6 1458.OhO.7

MeV

ref. J)

1’

x = y

x = Pl

x=c(,

tkeV) 987.4810.10 1008.77&0.10 1010.52kO.5 1019.96kO.5

1174.4110.25

1282.79kO.5 1318.13+0.15

1395.75f0.10 1416.85*0.07 1457.3OkO.5

1558.2 1645.2 1653.1 1718.6 1737.3 1748.6 1802.3 1805.1 1832.4 1839.0

1

< 1.5 (i.8) 1.110.6 4.8*1.0 < 1.5 6.7hl.O 0.9f0.6 2.910.7 0.2 +o. 1 < 1.5 0.3 10.2 6.3fl.O 1.7hO.7 3.450.7 < 1.5 0.3 *0.2 1.7 10.7 < 1.5 7.8*1.0 1.7*0.7

0.640.4

(0.2) 12

3 10 2 0.7 0.9 8 46 1.5

17 34 7

(0.1) (0.2) 11

1.6+0.7 4.110.7

2

< 1.5 3.2hO.7

3

(8)

68 7 15 35 14 5 31 24 1100 45 520 660 82 130 54 1700 44

(35) 1.9 28 160

80 74 5 6 150

3 15 57 4 13

(550) 590 2300

10 23

550 260 55 380

360

19 1700 830

3 21

6 69

>. 1870.2 1933.3 1979.4 2026.8 2075.2

6.951.0 8.0&1.0 0.9*1.0 7.8% 1.0

33 1600

Strengths of weak and unresolved resonances were not determined. Strengths in brackets are rough estimates. The error on the strenghs is of the order of 30 %.

The y-rays were detected in 40 cm3 Ge(Li) in 4000-channel analyzers. The resolution 5 keV at 1 MeV and 12 keV at 10 MeV. The computer calculated the positions of the spectra.

detectors and the spectra were recorded of the detector-amplifier system was spectra were read out on paper tape. A areas under the peaks in the y-ray

M. A. MEYER

6’8

et d.

3. Experimental results 3. EXCITATION

CURVE

measured (P, r), (P, ~~1 and (P, @1) excitation curves were simultaneously with thin targets and a 10 cm x IO cm Nal detector at a distance of 5 cm from the target and at 55” with respect to the beam. The (p, y) excitation curve (fig. I) was obtained by detecting only y-rays for which El, > 2.6 MeV. The (p, pl) and (p, aI) excitation curves (fig. I) were obtained with windows set across the Ey = 0.44 and 1.63 MeV y-rays from the above reactions. The energies of the resonances were determined by using the Ep = 991.88+0.04 keV resonance of the 27Al(p, y)‘%i reaction and the 7Li(p, n) threshold at E,, = 1880.59+0.08 keV as calibration energies ‘) and applying a relativistic correction on the energies calculated from Eb = kf2where f is the frequency. The present results for E,, are shown in table 1 which also includes values for E,, as summarized by Endt and Van der Leun ‘), results obtained by Stelson and Preston “) and by Mourad et al. “1. The present results for the resonance energies below fZ,, = 1.5 MeV are in excellent agreement with previous measurements. The widths of the resonances shown in table 1 were derived from the measured and instrumental widths by means of curves calculated by Bruynesteyn 60). The instrumental width, which was found to be 1S keV, did not change significantly between E,, = 1.0 and 1.8 MeV, These widths are in reasonable agreement with the values given by Endt and Van der Leun ‘) and with precision measurements by Mourad et ai. “). The results for the (p, y) resonance strengths, which are shown in table 1, were derived from the areas under the resonances and from assuming the value ‘) S = 1.05 t_ 0.16 eV for the resonance at Ep = 512 keV. Corrections resulting from the differences in the y-decay of the resonances were introduced. The errors on the strengths are of the order of 30 “/,. The present results are in excellent agreement with the measurements by Baxter et al. “f for the Ep = 988, 1021, 1174 and 1318 keV resonances and generally in reasonable agreement with the values given by Endt and Van der Leun ‘). The (p, pl) and (p, x1) strengths of the E,, = 1416 keV resonance were derived from the (p, y) strength of this resonance and the intensities of the E, = 0.44 and 1.63 MeV y-rays in the spectrum. The values obtained were 54 eV and 15 eV, respectively. The remaining (p, pI) and (p, aI) strengths in table 1 were derived from these values and the areas under the corresponding peaks of the (p, pi) and (p, al) excitation curves. The results obtained by Nordhagen and Steen ‘) are generally in poor agreement with the present results. The

3.2. GAMMA-DECAY

OF RESONANCES

The y-decay of 18 resonances below &., = 1.5 MeV of the 23Na(p, y)24Mg reaction was studied by Nordhagen and Steen 7), Flack et al. *), Prosser et al. “) and by

I.,*-+?27"

4

L 12-P, 31’

___._ _.__--.-Ep' 1395 kc"

co ILII

spec:rxTl

2‘

Nalmi Mg

21

-I__

121'

L2S-e0

---~---

Fig. 2. A y-ray spectrum of the 23Na(p, y)24Mg reaction at E,,= 1395keV. Every fifth channel is plotted between peaks whereas all channels are plotted in the peaks.

137/l~ I:137

r-r--

..-__l_-

12669

12527

872

1021

4

12404

744

12637

12399

739

12658 12659

12339

677

988

12258

592

1009 1011

If

12182

512

2-z

3-

2+

3f

3+,

2-

I’+’

2+

11987

309

s

Jn “)

_-

(keV)

(keV)

-___-

J&9

Resonances .-_

E,“)

-~-.

T=

i-=1”)

T=10)

T

~---__

lb)

0.4

C 0.3

42

1.9

< 0.3

cco.1

I.0

5.0

0.8

0”

0

10

19

1.5

h.4

2.1

14

II

27

71

28

1.37 2+

--..- ^_ _^-. ---

--4.12 4+

< 1

6

76

< 0.4

0.9

2.5

2.2

0.5

< 0.4

for E,, < 1.9 MeV

67

37

0.5

15

63

39

45

45

3

6.6

1.2

17

21

II

9.1 < 0.3

12

14

1.3

7

1‘9

12

13

4.0

1.4

7.5

3.8

3.9

3.5

2

6.9

2.6

2.7

-10.06(0.7),

9.00

g.OO(2.3).

9.00

9.515(g), 8.36(1.5), 8X6(15), (OX), 10.73(0.4)

8.86(10), 10.73(2)

9.46(0.7)

9.83

10.06(6)

8.438(3.1), 8.65(.5.4), 8.86 (2.8), 9.83(1.1), 10.06(2.5), 10.73(0.8)

8.36&O), 8.438(2.6). 8.65 (12), 8.86U.6). 9.00(2.8), 9.83(1.5)

9.515

10.66

9.97(0.5),

8.86(4.0),

9.00(1.9), 9.46(1.1), (7.2), 10.06(i.5)

(0.5)

8.65(1.1),

(2.0)9.83(1.0), 10.06(1.5)

8.438(2.5),

8.6.5(3.4), 9.97(1.0), 10.26 (3.6), 10.73(1.4)11.21(1.5)

(0.6), 9.28(0.9), 10.73(0.4)

y-decay (in 7;) to E,(MeV) in *&Mg __.__~___~__ ._...____^____. .,_ _____ ._.. _.._ 7.55 7.62 7.75 7.81 other levels 5.24 6.01 6.43 7.35 3+ 4+ o+ 2+ I31+ “) (St) E.(%) --_____ ---46 8.1 1.5 5.1 8.438(2.9), 8.86(5.0),

4.24 2’

resonances

TABLE 2 of Z3Na(p, y)Z4Mg

< 0.3

Gamma-decay

;

? $j

3

?

rr;

12920

12954

12962

13028

13048

13087

13344

13365

13445

13473

1318

1327

1395

1416

1457

1726

1748

1831

1860

3 4+)“)

2) ‘)

3-

4f

3+

(2, 3, 4) ‘)

(1,21e)

3- “)

(l+,

1 ‘)

2+ ‘)

1+

(1+:2:3-y)

(2+

2+

1+,

T=

I ‘)

6

8

5

<2

11

6

0.3

0.2

< 0.1

< 0.3

t2

66 39

4

48

6

3.0

6

0.5

1.7

73

89

7

72

10

10

10

26

3.0

<3 8

11

19

93

<2

< 0.4

15

< 7

36



8

56

49

<2

9

12

0.5

24

3

1

21

<6

i

5 21

55

< II

1

30

1.0

49

15

< 0.3

29

12

29

2

1

2

33

3

1.5

3

I

I

7

errors in the branchings > 10 ‘A is of the order of 5 %. The errors in branchings Table 1 and ref. *). Calculated from the proton energies in table I, ref. ‘) and Q = 11691.2 keV. Ref. *) unless otherwise indicated. See table 4. Present experiment, see subsect. 4. I. ‘) Ref. II). ‘) Ref. 12). “) Refs. lz*r3).

12894

1255

1283

The “) “) ‘) d, “)

12845

12851

1210

1174

1205

12806

12816

1164

12

< 2 ‘A is of the order

2

11

23

of 50 ‘A.

(5)

8.65(4),

9.28(7)

8.65(1.8),

10.02(0.5),

9.28(8)

10.58

8.438(10),

10.58(65) (11.39(31))

8.437(36), 9.00(l), 9.30(10) 9.46(7), 10.66(7), 11.52(0.7)

8.36(20),

(1.5)

9.46(2),

8.437(1.5), 8.65(2), 9.00 (3.8), 9.30(1.5), 9.46(2.0), 10.36(0.5)

10.06(3)

9.30(l)

8.36(17),

8.65(3)

8.438(3.5), 8.65(6.5), 8.86 (2.5), 9.83(1.5), 10.36(l)

Lz 09

; “,

2 &

632

M. A. MEYER et

al.

Glaudemans and Endt lo) by means of NaI detectors. These results have been summarized by Endt and Van der Leun “). Recently Baxter et al. “) have studied the decay of the resonances at E, = 512, 988, 1021, 1174, 1318 and 1416 keV by means of a 40 cm3 Ge(Li) detector. In the present experiment, the y-decay of 25 resonances of this reaction was studied by means of 40 cm3 Ge(Li) detectors. The weakest resonances were not investigated. The y-ray spectra were recorded with the detector at 55” with respect to the proton beam. The total charge collected on the targets varied between 3.2 and 0.2 C depending on the strength of the resonance. A typical y-ray spectrum is shown in fig. 2. The energies of the y-rays were determined by means of a computer programme which corrected for recoil losses and Doppler shifts. In all cases, the primary and secondary transitions were observed. Transitions to the E, = 8437 and 8438 keV levels could be identified by the different decay modes of these levels. The results are shown in table 2. The y-decay of the resonances at E,., = 1011, 1210, 1327, 1726, 1748, 1831 and 1860 keV is reported here for the first time. The results for the resonances below EP = 750 keV are in good agreement with NaI results by Glaudemans and Endt lo) and the Ge(Li) results by Baxter et al. “) except for additional weak transitions observed in the present experiment. Weak ground state transitions were observed at the E, = 988,1205 and 1283 keV resonances. However, a simple calculation showed that the strong and broad resonarces at Ep = 872, 1174 and 1318 keV which decay to the ground state, give rise to fictitious ground state transitions which have intensities of the order of the observed transitions at the resonances Ep = 988, 1205 and 1283 keV. 3.3. ENERGIES OF BOUND LEVELS

The energies of bound levels were determined with the detector at 90” with respect to the proton beam to eliminate Doppler shifts. Corrections for recoil losses were applied in order to determine the energies of the levels. The energies of the E, = 1.37 and 4.12 MeV levels were accurately determined by Murray et al. 14) (table 3). In the present experiment, the excitation energies of the E, = 4.24 and 5.24 MeV levels were accurately determined at the E, = 677 keV resonance by using a 208Tl radioactive source and transitions from the E, = 1.37 and 4.12 MeV levels as calibration energies. This yielded the results shown in table 3. The Q-value of the 23Na(p, y)24Mg reaction was determined at the E,,= 676.7 kO.4 and 872.4kO.6 keV resonances. In both cases, transitions from the fust four excited states in 24Mg and the E,,= 6129.310.3 keV y-ray from the 19F(p, cry) reaction were used as calibration energies. The orientation of the target was such that a shift of the centre of gravity of the 6.13 MeV y-ray peak due to I60 recoils which escape into the vacuum of the target holder was eliminated r “). This yielded accurate energies for the r -+ 7.35,7.35 * 1.37, r + 7.62 and 7.62 --f 1.37 MeV transitions in the case of the E, = 677 keV resonance. In the case of the Ep = 872 keV resonance, accurate

23Na(p, y)24Mg

REACTION

633

energies for the r --f 7.75, 7.75 + 1.37, r --f 6.43 and 6.43 + 1.37 MeV transitions were obtained. These results and the accurate values for the proton energies of the resonances yielded four values for Q. The mean value, Q = 11691.2+1.1 keV, is in excellent agreement with the value, Q = 11691.55 1.5 keV, from the 1971 mass table ’ “). TABLE 3 Excitation energies of 24Mg levels in keV Present experiment

Ref. I’)

Ref. 14)

1368.5710.04 4122.66&0.13 4238.7kO.4 5235.4f0.4 6010.3&0.4 6431.8+0.6 7341.9&0.7 7551 *3 7615.211.5 7747.011.0 7811.6ztl.O X357.7&0.6 8437.112.5 8437.7zt1.5 8653.8ki.0 8863.5 + 1.0 9002.1 f 1.O 9282.5 k2.0 9300.0&0.9 9455.8ztO.7 9515.3kl.2 9827.3 12.5 9967 &3 10024 &3 10059.0+1.0 10355 f4 10578.4+1.5 10660.3&1.0 10731.4*1.5 11206 14 11390 &4 11520 *4

4237.4kl.4 5232.712.0 6009.812.0

5236.0 10.4 “) 6440

Ref. Is)

4122 (datum) 4232f 8 5236.5f 0.5 ‘) 6005& 8

120 “) 7350+ 8 756lflO 7620f10 7746ilO 7808&10 s357*10 8439&10

Ref. IQ)

1368.5hO.7 4121.8h1.2 4237.2+1.3 S235.3*1.6 6002.9&1.6 6430 5-25 d, 7559 7617 7750

15 13 13

8363 8442

13 13

8655 8870

i3 &3

9826 (9959

i4 i6)

(10734

i4)

8435.4&1.5 8654&10 8864&10 9004112 9282f12

9516.Ok2.8

9456i12 95171t12 9826-12 9960+15 10025115 10055*15 10353 120 10577 120 10661120 10723120 112231tlO “) 11380&25 11511&25

Only the levels which were excited in this experiment are shown. “) Ref. 56). b, Ref. 21). ‘) Ref. 12). d, Ref. 2*). ‘) Ref. 20).

The energies of other levels shown in table 3 were determined at various resonances by using the present Q-value and proton energies to calculate the excitation energies

M. A. MEYER

634

et al.

TABLE 4

Gamma-decay Bound level in Z4Mg (ZeV)

1.37 4.12 4.24 5.24 6.01 6.43 7.35 7.55 7.62 7.75 7.81 8.36 8.437 8.438 8.65 8.86 9.00 9.28 9.30 9.46 9.515 9.83 9.97 10.02 10.06 10.36 10.58 10.66 10.73 11.21 11.39 11.52

Only “) b, “) d, ‘) r) ‘) “) r)

Jr =)

y-decay (in %) to E, (MeV) in zsMg

T

2’ 4+ 2f 3+ 4” 02+ 13(5+) l+b !) 34’ 12+ 2- ‘) 2f 2f ‘) (2f, 3,4) d) 3+ d) 4+ T=l 1+ ‘) If 8) T= 1”) (1, 2)- “) 2+

1+ (1, 2;+, 12+

of bound levels in 24Mg

T = 1 “)

T=l’) T= 1’)

0

1.37

0+

2+

100 < 0.5 77f2 <8 <2 < 16 62&5 45*10 24&5 25&S <6

80&10 <5 <2 50&10 <5

< 10

100 23 &2 99.0+0.5 93f3 80&10 38&5 35110 58&5 75*5 <5 48*5 69&5 (20) 69zt5 8955 < 20 85&5 55*10 90*15

4.24 2+


l.OkO.5

23&5 < 10 <5 i4 i 30 15+5 45+10

(83x5) < 10

60&15 < 15 < 20

<5 85*10 90&20 (100) < 10

4.12 4+

100

(50)

(50)

< 40

90flO 75115 100

< 20

713 20+10 <2 < 40 i9 < 14 i 13

18+z5 11&5 < 20 < 10 .< 5 -: 20 < 15 < 20

30

(20) (70)

the levels which were excited in this experiment are included. Ref. 2, unless otherwise indicated. Refs. 13*23). Refs. 23*36). Present experiment, see subsect. 4.1. Refs. r3sz6). Ref 2’). Refs. r3**‘). Ref. 13). Refs. r*.13).

i6 59’3 17t5 -< 10 < 10 < 15

25+15

8.437 4+

unknown

20 13 22+5 655

29

-< 5

13 50

10 40*15 15 10

30+15

(10)

6.01 4’

il <7 t3 < 10

i 10

70&15 i

5.24 3+

23Na(p, y)24Mg REACTiON

635

of the resonances and by using transitions from the resonance levels to accurately known levels and the decay of these levels as calibration energies. 3.4. GAMMA-DECAY

OF BOUND

The y-decay of 32 bound

LEVELS

levels as derived from a study of 25 resonances

is shown

in table 4. The results are generally in good agreement with the summary given by Endt and Van der Leun “). The y-decay of the E, = 7.8 1, 8.36,9.28, 9.30, 9.46, 10.58, 11.39 and 11.52 MeV levels has not previously been reported. The y-decay of a number of levels requires further discussion. 3.4.1. The E, = 5.24 MeV level. In addition to the known strong 5.24 + 1.37 MeV transition, a weak 5.24 + 4.24 MeV transition was observed at the Ep = 309, 592, 677, 739 and 1395 keV resonances. 3.4.2. T&e E, = 6.01 MeV level. The formerly uncertain transition to the E, = 4.24 MeV level has been confirmed at the E, = 988 keV resonance where the E, = 6.01 MeV level was strongly excited. 3.4.3. The E, = 7.55 MeV Eevei. This level was weakly (a 1 %) excited at the E,, = 309 and 1021 keV resonances. The 18 % transition to the E, = 4.24 MeV IeveI given in ref. ‘“) is within the present upper limit for this transition. 3.4.4. Tlze E, = 7.81 MeV level. The certain 7.81 + 5.24 MeV transition and the uncertain 7.81 -+ 4.12 and 7.81 + 6.01 MeV transitions observed by Ollerhead et al. 23) are confirmed by the present results. 3.4.5. The E, = 8.65 MeV level. The 6 %, 8.65 + 6.43 MeV transition observed by Ollerhead ef al. 23) could not b e confirmed in this experiment as this transition coincided with other peaks in the spectrum. The upper limit of 5 y0 on a possible 8.65 -+ 0 MeV transition is not in agreement with the 15 9,; branch reported by Glaudemans and Endt lo). 3.4.6. The E, = 8.86 MeV level. The strong transition to the first excited state lo) was confirmed. In addition, an 8.86 -+ 4.24 MeV transition, also observed by Ollerhead et al. 23), was observed at the Eb = 592 and 1021 keV resonances. 3.4.7. Tile E, = 9.00 MeV level. This level was weakly excited and only the transition to the ground state was observed. The other transitions observed by Ollerhead er al. ‘“) are within the present upper limits. 3.4.8. The E, = 9.52 MeV doublet. At the E, = 739 and 1009 keV resonances, a level at E, = 9515 keV was excited which decays to the E, = 4.12 and 8.437 MeV levels. These transitions were also observed by Ollerhead et al. 23). The J” = 6’ member of the doublet at E, = 9.52 MeV was not excited in this experiment. 3.4.9. The E, = 10.02 MeV leuel. This level was weakly excited at the E, = 1416 keV resonance only and a transition to the ground state was observed instead of to the first excited state as suggested by Glaudemans and Endt lo). They have excited this level at the E,, = 592 keV resonance. The present experiment has shown that this level is not excited at the E, = 592 keV resonance. Instead, the E, = 10.06 MeV level was excited.

M. A. MEYER

636

et al.

3.4.10. The E, = 10.06 MeV level. The y-decay of this level is not in agreement with the decay suggested by Glaudemans and Endt ’ “). In this experiment the E, = 10.06 MeV level was weakly excited at a number of resonances and the indications are that this level decays to the E, = 1.3’7 MeV level only, in agreement with Lawergren et al. ‘“). TABLE 5

Summaryof Z (MeV)

mean lifetime measurements of excited states in “Mg

Lifetime determined at E, (keV)

1.37 4.12

4.24

5.24

6.01 6.43 7.35 7.62 7.75 8.437 8.438 8.65 8.86 9.28 9.30 9.46 10.06 10.66

1318 677 677 “) 988 988 “) 1416 677 677 “) 872 677 617 “) 988 988 872 677 1395 872 1726 812 872 872 1457 1726 1126 872 1726

rm Y (fs) 0.04~0.01 0.62&0.03 0.7710.06 0.80&0.06 0.85 +0.05 0.77+0.03 0.52~0.02 0.6410.05 0.5210.03 0.43 10.03 0.6010.05 0.56*0.06 0.58 kO.06 0.47 +0.03 0.9010.02 0.02*0.02 0.86 +0.03 0.87 kO.04 0.97f0.03 0.84kO.03 0.94*0*03 0.98 +0.04 0.90~0.04 0.98 10.04 0.99 +0.03 1.02ztO.04

1400*400 34*5 33+10 1717 26IfilO 23+3 5ort.5 60&12 5517 71 _irs 6851-.12 501-12 46&12 66+8 7+2 > 1400 1114 13*.5 <5 1315 513 t6 10&4 t6 <5 <5

Lifetime ‘) adopted (fs) 14OOI_t450 2515

53+9

65+11

46&14 66113 712 > 1400 1114 1315 <5 13;5 5f3 <6 10&4 t6 <5 <5

Target material

was Na2W04 unless otherwise indicated. “) Target material was NaCI. “) Errors are statistical. ‘) A 15 % error is included in order to allow for possible errors in the theory.

3.4.11. The E, = 10.66 MeV

level.

A level at E, = 10.66 MeV was excited at the

E, = 677 and 1726 keV resonances. This level was also observed by Glaudemans and Endt lo) at the Ep = 677 and 743 keV resonances. The present results show that the E, = 10.66 MeV level decays mainly to the first excited state in agreement with Glaudemans and Endt lo). This level is not the E, = 10.68 MeV, J" = Of level observed in the 2oNe(cc, y)24Mg reaction 25) at E, = 1640 keV. The E, = 10.66

MeV level was excited at the ED = 677 keV (J” = 3+) resonance. An M3, Y-+ 10.66 MeV transition at this resonance would be too strong.

=Na(p; y)=Mg

3.412.

The E, = 10.73 MeV

level. This

637

REACTION

level was also

studied

by Lawergren

et al. 24) w h o h ave observed 40 %, 48 % and 12 % transitions to the E, = 0, 1.37 and 4.24 MeV levels, respectively. This level was weakly excited at a number of resonances and only the decays to the E, = 1.37 and 4.24 MeV levels were observed. 3.4.13. The E, = 11.21 MeV level. This level was weakly excited at the Ep = 512 keV resonance and only a decay to the first excited state was observed. Branchings of 17 % and 83 y0 to the ground and first excited states were observed by Lawergren et al. ‘4). 3.5. MEAN LIFETIMES OF BOUND LEVELS

The Doppler-shift attenuation method was used to determine the lifetimes of bound levels in 24Mg. Thick Na,WO, and NaCl targets, covered with a thin layer

of gold to slow down the deterioration of the targets, were used. Care was taken to ensure that the ions were stopped in the target material and not partly in the backing. The material of the target backings was copper or tantalum. Resonances were selected where the levels studied were almost entirely excited by primary transitions. The Doppler-shift attenuation factor, F, which is the ratio of the observed to the maximum shift was found by measuring the positions of the y-ray peaks at 0” and 140” with respect to the beam. The mean lifetimes were derived from the observed Doppler-shift attenuation and calculations based on Blaugrund’s work **). Corrections to the expression used by Blaugrund for the electronic stopping cross section, as observed by Ormrod et al. 29), were introduced. The present results are shown in table 5. Possible errors in the theory of the stopping of ions in matter were allowed

for by adding a 15 % error to the experimental error. A large number of measurements on the lifetime of the E;. = 1.37 MeV level exist. These results have been summarized by Herrmann and Kalus 30). The weighted mean of the values obtained by means of resonance fluorescence scattering, the selfabsorption resonance fluorescence method and the Coulomb excitation results is 7ln = 129Oi 110 fs. Recent resonant scattering measurements by Swann 57) yielded T = 19202 150 fs and recoil distance lifetime measurements by Alexander and Bell ‘*) yielded 21 lot_ 160 fs for the lifetime of the E, = 1.37 MeV level. It will be noted that the mean lifetimes of the E, = 4.12, 4.24 and 6.43 MeV levels are significantly smaller than the existing results. However, the lifetimes of the Ex = 4.12, 4.24 and 5.24 MeV levels were measured at various resonances (table 5) and in different target materials and consistent results were obtained. 4. Discussion 4.1. SPINS AND PARITIES

A number of spin and parity assignments in this section are based on Weisskopf estimates of y-ray transition strengths. Spins and/or parities can be rejected if transition strengths exceed certain upper limits. Too low upper limits might erroneously

638

M. A. MEYER et al.

exclude certain J” assignments. It was therefore considered that relatively large upper limits would yield more reliable assignments. The following upper limits were assumed : E2 30 W.U., M2 10 W.U., E3

25 W.U.,

M3

15 W.U.

In the majority of cases, spin or parity assignments other than those adopted, yielded transition strengths which were at least twice the above upper limits. 4.1.1. The E, = 9.30 MeV level. This level decays strongly to levels with J” = 2+ and 4’. A Weisskopf estimate excluded J” = 1’. A J” = 2- would lead to a strength of 65 W.U. for an M2, 9.30 3 4.12 MeV transition. Consequently J” = 2+, 3, 4. Hird et al. 36) have suggested that the E, = 9.28 MeV level is probably a doublet and that both members have natural parity. Recent measurements 61) have shown that there is even a triplet at 9.30 MeV. 4.1.2. The E, = 9.46 MeV level. This level was excited at resonances having J” = 3 and 4+ and it decays to a J” = 2’ level. Consequently, J = 2,3,4 and since it has unnatural parity 36), J” = 2-, 3+, 4-. A Weisskopf estimate eliminated J” = 4- since this would lead to an M2 strength of more than 23 W.U. for the 9.46 + 1.37 MeV transition. The value of J” = 2- can be rejected since this would lead to an M2, r -+ 9.46 MeV strength of 1300 W.U. at the E,, = 1416 keV resonance. Hence J”(9.46) = 3+. 4.1.3. The E, = 12.85 MeV (E, = 1205 keV) level. A possible value of J” = 2was suggested by Baumann et al. 38) from the elastic scattering of protons by 23Na. The parity assignment is based on the absence of ground state cc-particle decay. However the y-decay of this resonance is such that a J” = 2- assignment would lead to an M2, r + 4.12 MeV transition of 24 W.U.; J = 1 can be excluded since this would lead to too strong E3 or M3, r + 4.12 MeV transitions. Similarly, Weisskopf estimates of the r + 4.24 MeV transition exclude J” = 4- and 5. Hence J” = 2+, 3,4+. 4.1.4. The E, = 12.85 MeV (E, = 1210 keV) level. The J” = (3+) assignment by Baumann et al. 38) is not in agreement with the y-decay of this resonance. This assignment would lead to an M3, r + 0 transition of 240 W.U. The y-decay of this resonance and Weisskopf estimates leave J” = I+, 2, 3- as possibilities. 4.1.5. The E, = 12.92 MeV (E, = 1283 keV) level. Baumann et al. 38) and Stelson 39) have found J” = l- and Nordhagen and Steen ‘) have found J” = 2’. This level decays to the E, = 4.12 MeV level with a 15 % transition. A Weisskopf estimate excludes J” = l-. Therefore, J” = 2+ was assigned to this level. 4.1.6. The E, = 12.96 MeV (E, = 1327 keV) level. The y-decay of this level and Weisskopf estimates limit the possibilities to J” = l+, 2. 4.1.7. The E, = 13.34, 13.37, 13.45 and 13.47 MeV (E, = 1726, 1748, 1831 and 1860 keV) levels. The y-decay and Weisskopf estimates at these resonances restrict

23Na(p, y)24Mg REACTION

the spins to the values shown in table 2 and indicate is probably a doublet. 4.2. ISOSPIN

The isospin

QUANTUM

quantum

639

that the Ep = 1748 keV resonance

NUMBERS

T, included in Van der Leun 2), Lawergren et al. 12) and Tang 10.06, 10.73, 10.82 (not excited in this experiment) to the ground state and first five excited states in 10.58 and 10.66 MeV levels, therefore have T = levels correspond to 2oNe(cc, y)24Mg reso nances

tables 2 and 4 are from Endt and et al. 13). The E, = 9.515, 9.97, and 11.21 MeV levels correspond 24Na. The E, = 9.83, 10.02,10.36, 0. The E, = 11.39 and 11.52 MeV and should therefore have T = 0. Using published data on the 23Na(p, y)24Mg reaction, Lawergren et al. “) suggested that the E, = 12.34, 12.53, 12.67 and 12.82 MeV levels could be analogues of the E, = 2.98, 3.41, 3.37 and 3.58 MeV levels, respectively, in 24Na. By comparing the spectroscopic factors and Z-values obtained in (d, p) and (d, n) reactions on 23Na, Tang et al. 13) concluded that T = 1 assignments to the E, = 12.53 and 12.67 MeV levels are highly probable. The y-decay of the resonances at E, = 677 and 739 keV, both having J” = 3+ is almost identical. The same applies to the J” = l+ resonances at Ep = 872 and 1174 keV. Other examples of very similar decays were observed at the J” = 55, EP = 1089 and 1094 keV resonances of the 37Cl(p, y)38Ar reaction 40). These resonances decay with strong Ml, J + J transitions. It is known that they are the split analogue of the first excited state in 38C1 The similarity of the decay of the E,, = 677 and 739 keV resonances of the 23Na(p, y)24Mg reaction suggests that they are the split analogue of a level at E, = 2.98 MeV in 24Na and a level at E, = 2.88 MeV in 24A1. Similarly it is possible that the E,, = 872 and 1174 keV resonances are the split analogue of a level at E, = 3.41 MeV in 24Na. The Ml, J -+ J rule for the decay of analogue states is not well illustrated m the 24Mg nucleus presumably because of the scarcity of low-lying J” = l+, 2- and 3+ levels. The T = 1 level at E, = 9.52 MeV has only J -+ J decays.

4.3. TRANSITION

numbers,

STRENGTHS

The transition strengths based on the branching ratios in table 4 and the lifetimes in table 5 are shown in table 7. The strengths of the isospin-forbidden dipole transitions are in agreement with the average values 41) El,

AT = 0,

/Ml2 = 2x 1O-4 W.U.,

Ml, AT = 0,

lM12 = 9x 1O-3 W.U.

for nuclei in the mass region A = 20-40.

640

M. A. MEYER

et al.

TABLE 6 Summary of 24Mg lifetime measurements Bound state in 24Mg & (MeV) 1.37 4.12 4.24 5.24 6.01 6.43 7.35 7.62 7.75 8.437 8.438 8.65 8.86 9.28 9.30 9.46 10.06 10.66

Mean lifetime (fs) present experiment

ref. I*)

14003L450 25*5 53&P 65flI 46f14 66113 7&2 > 1400 11+4 1345 <5 13&S 5f3 <6 10$,4 ~6 <5 <5

1700&800 7O,t25 105f20 95125 50&25

2718

-

ref. 31)

ref. 32)

14401220 51*30 101*35 79155 71145 241&230

ref. 33)

ref. 59)

2070+340

1650&150”) 169&34 185133 173f46 124&20

120&30 130-+70 b) 200140 270+60 < 100 2100+400 < 100

1 lo+26

‘)

The lifetimes shown in this table are all based on Doppler-shift *) Ref. 34). b, Ref. 3s). ‘) Ref. 6).

measurements.

TABLE 7 Strengths of y-ray transitions in a4Mg Jr + Jr, LIT

1.37 4.12 4.24 4.24 5.24 5.24 6.01 6.01 6.43 6.43 7.35 7.62 8.437

-+ -+ -+ -+ -+ -+ -+ -+ -+ -+ --f + --f

0 1.37 0 1.37 1.37 4.24 1.37 4.24 1.37 4.24 0 0 1.37

8.438 --f 0 9.28 -+ 4.12 10.66 -+ 1.37

2f 4+ 2+ 2f 3+ 3+ 4+ 4+ Of o+ 2f 34+

-+ o+, 0 +2+,0 -to+,0 + 2+, 0 +2+,0 +2+,0 +2+,0 +2+,0 +2+,0 -+2+,0 -to+,0 -i-o+,0 -+ 2+, 0

Mixing ratio

23&9 “) co “)

I- -to,0 2+ -+ 4+, 0 0’ -+ 2+, 0

“) Ref. 42) “1 Ref. 43). ‘) Pure transitions were assumed.

FY (mev) 1400 25 53 53 65 65 46 46 66 66 7 > 1400 13 cc 5 <6 i5

Strengths (in W.U.) jM!2 Bl(

0.47% 0.15 26 h5 10 f2 2.9 & 0.6 10 $12 O.lO& 0.05 ‘) 13 14 1.0 + 0.5 8.0 i. 1.9 2.0 4 1.1 58 &17 < 0.11 35 114 > 106 i 11 > 110

~2

x 104)

29 49 2.0 4.4 3.4 30 1.8 17 0.7 12 0.8

E3

+9 *9 kO.3 & 0.9 10.6 &16 “) j, 0.6 1.9 * 0.2 ri:6 f 0.2

>3 > 0.9 > 0.5

104)

0.12* 48

< 5.6 0.6 & 0.2

Ml(x

0.05

&25=)

641

23Na(p, y)ZSMg REACTION

5. Comparison with theories 5.1. SYMMETRIC

ROTATOR

It is generally believed that the E, = 0, 1.37, 4.24 and 8.12 MeV levels are the O+, 2+, 4+ and 6+ members of the ground state (K” = Of) rotational band. The TABLE

Ratio of reduced y-ray transition Transition Kf + Kr O-0 2+2 2-+0 2+0 2-+0

Comparison

strengths

8

within and between the K" = O+ and Kn = 2+ bands

Theoretical

Ratio B(E2,4.12 B(E2, 1.37 6.01 B(E2, B(E2, 5.24 4.24 B(E2, B(E2, 4.24 B(E2, 5.24 B(E2,4.24 6.01 B(E2, B(E2, 5.24

of experimental

--f + -+ + ++ + + + +

Experimental

1.37) 0)

1.43

1.7kO.6

4.24) 4.24)

0.48

0.6+0.4

1.37) 0)

1.43

2.2+0.6

1.37) 1.37)

1.25

0.8&0.2

1.37) 1.37)

0.33

0.5*0.2

TABLE 9 B(E2) with theoretical predictions f0.14 b, y = 21.5”

Transition

by Davydov et al. 48*49) Q, = 0.84

E(E2)(W.u.) theor.

1.37 -+ 4.12 + 4.24 -+ 4.24 -+ 5.24 + 5.24 + 6.01 -+ 6.01 +

0 1.37 0 1.37 1.37 4.24 1.37 4.24

29 49 2.0 4.4 3.4 30 1.8 17

&9 *9 f 0.3 i 0.9 + 0.6 &16 & 0.6 *9

32 ill 47 &I6 2.2 + 0.7 16 +5 4.0 *1.3 57 +19 0.18&- 0.06 16 &5

E2 transition strengths within this band may be calculated from the quadrupole moment of the E, = 1.37 MeV level which was measured by Bamberger et al. 44) and H&usser et al. 45). Th e weighted mean of their results is -0.24JrO.04 b. The intrinsic quadrupole moment of the K = 0 band is therefore Q, = g (- 0.24f0.04) b = -0.84f0.14 b. With this value for Q,, the symmetric rotator model predicts the following E2 transition strengths within the ground state rotational band 1.37 + 0 MeV,

34111

4.12 + 1.37 MeV,

49+ 16 W.U.

W.U.,

M. A. MEYER ef at.

642

These values are in good agreement with the strengths shown in table 7. The Ex = 4.24, 5.24, 6.01 and 7.81 MeV levels are believed to be the 2+, 3’, 4+, 5+ members of a K” = 2’ rotational band based on the E, = 4.24 MeV level 26*31*46). The theoretical and experimental ratios of the reduced y-ray transition strengths within and between the K = 0 and 1y = 2 bands are shown in table 8. 5.2. ASYMMETRIC

ROTATOR

Calculations by Bar Touv and Kelson 47) indicate that the 24Mg nucleus is not an axially symmetric deformed nucleus. One can identify the E, = 1.37, 4.12, 4.24 and 5.24 MeV levels with the J” = 2:, 4:, 2: and 3* levels, respectively, of the asymmetric rotator model developed by Davydov and others 48$“). The energies of the E;,= 1.37 and 4.24 MeV levels were used to determine the value of the asymmetry parameter y. This yielded 22” which, however, did not yield the correct spin sequence. A slight reduction to y = 21.5” yielded the spin sequence observed in 24Mg. The transition strengths shown in table 9 were obtained with y = 21.5” and the value Q0 = -0.84kO.14 b (subsect. 5.1). 5.3. SHELL-MODEL

CALCULATIONS

Shell-model calculations on the 24Mg nucleus were carried out by various authors 50-55). Th ese authors all predict the first few excited states of the ik: = 0 and K = 2 rotational bands. However, in many cases the energy of the band head of the K = 2 rotational band is too low. The branching ratios were calculated by Elliot and Harvey “) and by Wathne and Engeland 52). The E2 branching ratios are in many cases different from the experimental values. The authors are indebted to the Atomic Energy Board and the Council for Scientific and Industrial Research for financial support. The authors wish to thank Prof. P. M. Endt and Dr. C. van der Leun for helpful criticism of the manuscript. References 1) M. L. Roush, L. A. West and J. B. Marion, Nucl. Phys. Al.47 (1970) 235 2) P. M. Endt and C. van der Leun, NucI. Phys. A105 (1967)1 3) P. H. Stelson and W. M. Preston, Phys. Rev. 95 (1954) 974 4) W. G. Mourad, K. E. Nielsen and M. Petrilak, Nucl. Phys. A102 (1967) 406 5) G. A. P. Engelbertink and P. M. Endt, Nucl. Phys. 88 (1966) 12 6) A. M. Baxter, K. J. Cassell and A. J. Kuehner, Can. J. Phys. 47 (1969) 2319 7) R. Nordhagen and H. B. Steen, Physica Norvegica 1 (1964) 239 8) F. C. Flack, J. G. Rutherglen and P. 3. Grant, Proc. Phys. Sot. 67A (1964) 973 9) F. W. Prosser, W. P. Unruh, B. H. Wifdenthal and R. W. Krone, Phys. Rev. 125 (1962) 594 10) P. W. M. Glaudemans and P. M. Endt, Nucl. Phys. 30 (1962) 30 11) A. M. Baxter, C. Mabey, B. W. J. Gillespie and J. A. Kuehner, Can. J. Phys. 47 (1969) 2327 12) B. T. Lawergren, A. T. G. Ferguson and G. C. Morrison, Nucl. Phys. A108 (1968)325 13) S. M. Tang, B. D. Sowerby and D. M. Sheppard, Nucl. Phys. Al25 (1969) 289 14) G. Murry, R. L. Graham and J. S. Geiger, Nucl. Phys. 63 (1965) 353 15) M. A. Meyer and N. S. Wolmarans, Nucl. Phys. Al36 (1969) 663

23Na(p, 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 55) 56) 57) 58) 59) 60) 61)

y)24Mg

REACTION

643

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