Mean lives of excited states in 28Al

Nuclear Physics A283 (1977) 12-22;(~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

M E A N L I V E S O F E X C I T E D S T A T E S I N :'SAl F. A. EL-AKADt, S. BACKE, T. HOLTEBEKK, F. INGEBRETSEN and J. REKSTAD Institute of Physics, University of Oslo, Norway Received 20 October 1976 (Revised 1 February 1977) Abstract: The mean lives of excited states in 2SAl formed in the 27Al(d, p) reaction have been determined from the measured Doppler shift of ~,-rays emitted in coincidence with the protons. The multipole order and maximum admixture of higher order ?'-radiation are determined. In several cases the result leads to a definite assignment or strongly favoured assumptions for the spin value of the excited state. A total of 28 levels below 5.45 MeV excitation energy have been studied. Previously mean lives have been reported for twelve of these levels. The experimental results indicate that several closely spaced doublets may be explained as a s~ neutron coupled to states in 27A1. E [

I

NUCLEAR REACTIONS 27Al(d, p),), E = 2.4 MeV; measured o'(Ep, E.),), Doppler shift attenuation. 2SAI levels deduced Tt, J, n, T.

1. I n t r o d u c t i o n

T h e p r o p e r t i e s o f low-lying states in nuclei close to the stability line in the 2 s - l d shell have been the subject o f a large a m o u n t o f theoretical a n d e x p e r i m e n t a l investig a t i o n s t). T h e a t t e n t i o n has hitherto m a i n l y been p a i d to the d o u b l y even a n d the o d d - A nuclei. B o t h m a c r o s c o p i c " c o l l e c t i v e " m o d e l s 2) a n d m o r e detailed ( a n d e l a b o r a t e ) m i c r o s c o p i c m o d e l s 3) have been a p p l i e d to these nuclei, a n d despite the challenging p r o b l e m s t h a t remain, m a n y p r o p e r t i e s m u s t be characterized as understood. T h e s i t u a t i o n a p p e a r s m o r e c o m p l i c a t e d for d o u b l y o d d nuclei. T h e y are all c h a r a c t e r i z e d by a high level density even at low excitation energies. T h e b u l k o f the e x p e r i m e n t a l i n f o r m a t i o n comes f r o m transfer r e a c t i o n studies. These reactions will in general give i n f o r m a t i o n o n the energy a n d the p a r i t y o f the final states. I n a d dition, t h e m e a s u r e d c a p t u r e d particle reduced widths can establish likely limitations o f the spins. H o w e v e r , the level spins, t h e m e a n lives a n d the r a d i o a c t i v e decay m o d e s are quite decisive when the theories are to be c o n f r o n t e d with the e x p e r i m e n t a l data. It is therefore i m p o r t a n t also t o u n d e r t a k e ),-decay studies o f these nuclei. T h e m e a n lives o f b o u n d states that decay t h r o u g h E l , M I a n d E2 transitions in this m a s s region, lie in the range ps-fs, a n d they can therefore often be m e a s u r e d with Present address: The Faculty of Science, University of Alexandria, Egypt. 12

M E A N LIVES IN 2SAl

13

PI DETECTOR

~ T 2

4 BEAM ~

~

"%"

P'2DETECTOR DETECTOR I Fig. 1. Sketch of the detectors and target arrangement together with the recoil directions of tile reaction products.

1

I

I

"G U') re"

LU Z _J

LIJ Z Z "1"

20 ns hi Q. V} I--" Z 0 0

I 100

I 200 t (ns)

I 300

Fig. 2. A typical time spectrum from coincidences between protons and 7-rays.

14

F . A . E L - A K A D e t aL

the Doppler shift attenuation method (DSAM). The aim of the present work was to determine lifetimes of levels in 2SAl. The levels below 5.45 MeV" have been studied. 2. Experimental method A 2.4 MeV deuteron beam from the University of Oslo Van de Graaff accelerator was used to populate excited states in 2SAl through the 27Al(d, p) reaction. The targets were made of 45 pg/cm 2 metallic AI, evaporated onto 400 /tg/cm 2 gold backings.

a) 604033--*- 3465

3 4 6 5 ~ g.s.

60-

[

40-

t

1/3 z

0

//~

I

3706"* g.s.

!1

-,,,

ta Ik

/.9o~;~ g.s.

='.-'= /

.

I

I//,

80-

O

60-

40-

20O

I i

I

550

600

,

~

'

~J

t ''

I

I

, ~ ~I ~ ~i ,e

,k ' ff

s

I

~

I

1

,l. . . . I /'

3400 3450 3500 3650 3700 3750 ENERGY ( keV )

t

I

/,900 4950

Fig. 3. Details from the T-ray spectrum coincident with protons recorded in detectors PI (fig. 3a) and P2 (fig. 3b). The different sections correspond to different proton gates.

The experimental arrangement, shown schematically in fig. 1, is described in detail in a previous paper 4). It consists of two targets in tandem, both hit by the same beam. Protons from the reaction are recorded by one detector for each target, both in coincidence with a 10 cm 3 planar Ge(Li) detector. The detector geometry is care-

MEAN LIVES IN 2SAI

15

fully chosen to select ~-rays emitted either in the forward or in the backward direction relative to the recoiling nuclei. Furthermore, the targets are positioned so that the recoil directions are close to parallel with the target surface. This scheme has the advantage that instabilities in the ~-ray spectrometer during long runs have no effect on the observed centroid shifts. The coincident pulse heights from the detectors and the time delay between them were digitized and stored event by event on magnetic tapes by means of a PDP-7 and a NORD-1 computer coupled together on the occasion of this experiment. The data were later sorted to get true coincident spectra. A time resolution of about 20 ns ( F W H M ) was obtained. A typical time spectrum is shown in fig. 2. The ratio between random and true coincidence was of the order of 20 ~o for all runs. The proton resolution was about 80 keV. The energy spread was mainly due to a 9 mg/cm 2 AI absorber in front of the detectors that stopped the elastic scattered deuterons. However, with the aid of existing information on the decay scheme, the resolution was sufficient to ensure direct feeding of the levels studied. The peak resolution in the 7-ray spectrometer was 2.5 keV ( F W H M ) for the 1.33 MeV 6°Co line. Details from coincident 7-ray spectra are shown in fig. 3. 3. Extraction of lifetimes The nuclear mean lives, T, were determined from the centroid shift between peaks of ~-rays accumulated simultaneously in the forward and backward directions relative to the recoiling nuclei. The method of analysis follows closely the prescription given by Blaugrund 5). Experimentally determined attenuation factors F = AEr[ AEmax were compared with theoretical values of F as a function of r. The slowing down process of the recoiling nuclei was treated within the model of Lindhard et aL 6). As an approximative description of the nuclear stopping power, the formulae given by Blaugrund s) and by Engelbertink et aL 7) were used in the same way as in ref. 4). A main contribution to the uncertainty if mean lives are measured by the DSAM, comes from the 20 ~ error conventionally associated with Lindhard's formula for the electronic stopping power 6):

In accordance with the experimental results of Ormrod et aL s), the Lindhard figure for the constant k has been reduced 20 ~ and a corresponding uncertainty is set to 10 ~ in the total stopping power. 4. Experimental results The experimental results are listed in table 1 together with results from previous measurements. Only mean lives measured by the DSAM are entered into the table.

F . A . EL-AKAD et aL

16

TABLE 1 Mean lives for states in 2aAI from this work compared with values from previous DSAM measurements El (keV) 1014 1373 1620 1623 2138 2202 2272 2485 2582 2656 2987 3296 3347 3465 3591 3669 3706 3876 3900 3936 4033 4243 4598 4691 4766 4905 5135 5443

Er (keV)

F (%)

T (fs)

T prey. known ") (fs)

0

74-t- 5

190-t- 30

130=I= 20

31 31 31 0 0 31 31 0 1620 0 1014 1623 31 0 0 0 31 0 31 0 1014 1623 31 3465 31 0 0 31 0 31 0 0 31

76=t= 4 574- 7 914- 8 724- 4 884- 7 874- 4 814-10 894- 4 814- 6 384- 4 874- 5 854-12 754- 5 75-4- 9 834- 2 814- 4 674- 8 594- 5 544- 4 85-4- 5 604- 7 524- 5 101+ 8 614- 4 874- 8 62 4-17 894- 4 884- 4 854- 6 91 4- 4 874- 2 91 4- 2 924- 3

37046042004804-

90 50 40 20

3004- 60 1804- 40 704- 20 <15

120=t= 70 604- 20 110+ 40 6004-100 704- 30 904- 80 1404- 30 1404- 50 9 0 + 12 100-6 20 1904- 60 2704- 30

354- 10 154- 8 1004- 30 5504-100 304- 12

< 7 0 b)

804- 20 2704- 40 <60 2204- 30 604- 30 230:t: 120 504- 13

944- 20 b)

504- 13 564- 9 404- 10 30-t- 10

• ) Mean lives from ref. 9). b) Mean lives from ref. ~°L Other values according to ref. *).

T h e l i m i t s o f e r r o r , AF, a r e e s t i m a t e d s t a n d a r d e r r o r s i n F, b a s e d o n t h e s t a t i s t i c a l u n c e r t a i n t y i n t h e d e t e r m i n a t i o n o f t h e c e n t r o i d s h i f t a n d t h e v a r i a t i o n i n AE,~, d u e t o t h e finite s o l i d a n g l e o f t h e d e t e c t o r s . T h e u n c e r t a i n t y i n d e d u c e d m e a n lives i n cludes also the mentioned

u n c e r t a i n t y i n s t o p p i n g p o w e r . T h e meaxt lives a r e g i v e n

w i t h s y m m e t r i c a l e r r o r s , i.e. z = ½(~+ + T _ ) , w h e r e 3± a r e t h e v a l u e s o b t a i n e d f r o m

F± = F+__AF, a n d A F is t h e w e i g h t e d e r r o r i n F f o r a g i v e n level. I n c a s e s w h e r e

MEAN LIVES IN aSAl

17

F + A F > 1 the listed upper limits of • corresponds to F - 2 A F , and for F - A F < 0, the listed lower limit of z corresponds to F+2AF. The mean lives for the two lowest states are from previous measurements ~) known to be too long to be obtained by the DSAM. Mean lives for the third to the twelfth excited state have previously been measured by Maher et aL 9). Furthermore, the mean life of the 4033 keV level and a limit for the mean life of the 3465 keV level have been measured by Freeman et aLlo). For most levels our results are consistent with theirs. There is, however, a disagreement in the results obtained for the 1620-1623 keV doublet. We fred the longest mean life, 200 fs, for the 1623 keV level and 60 fs for the 1620 keV level, whereas Maher et aL quote about the same values, but with opposite level assignments. The 1623 keV level, which is the one that is strongest populated in our experiment, decays mainly to the ground state, with a weak ( < 15 Yo) branch to the first excited state l). The mean life of the 1623 keV level is therefore well determined from the ground-state transition. The 1620 keV level decays mainly (92 Yo) to the first excited state, with 6 Yo to the ground state. The large F-value for the 1620--31 keV transition verifies that the contribution from the 1623-31 keV level, if any, is very small. 5. Discussion In the present investigation several new mean lives of states in 2aAl have been determined. Based on these mean lives and on energies, branching ratios and mixing ratios adopted from previous works 1, 9, 12), the transition strengths for El, MI, E2 and M2 transitions were calculated. Mixing ratios corresponding to transition rates above the acceptance limits ~z) were not included in the discussion. Since the parities of the levels are known, it was found convenient to present information on the even and odd parity levels separately. 5.1. EVEN PARITY LEVELS

tn addition to already measured mean fives 9, x0), the mean lives of seven more levels of positive parity have been determined in the present work. These levels are populated with lo = 0 and 2 in the (d, p) stripping reaction a), which leads to spins 2, 3 and 0--5, respectively. In general the measured mean lives support the spin assignments suggested previously. For two levels the new data lead to more restricted spin possibilities. The 2987 Ice Vlevel. The mean life of this level is 90 5- 80 fs. Thus the transition to the 1623 keV level with spin 2 + has to be of M1 type (190 W.u. E2 strength), and the spin is restricted to 1+-3 + . After this work was completed we became acquainted with the results of Boerma et al. 21), who find 3 + ( 1 +, 2 - , 4 - ) for this state. The assignment should then be 3 + or less probably 1 +. The 3900 keVIevel. This level decays by (504-20) ~ branches to the 1014 keV level and the 1623 keV level. The observed mean life, 2704-40 fs, corresponds to typical

18

F . A . E L - A K A D et aL

E2 or slow M 1 transitions. The spin is thus restricted to I - 4 with 1 or 4 as the most probable assignments since no I, = 0 component is seen in the stripping cross section. Boerma et al. find 3 + (1 +) for this state. The 4243 k e V level This level decays by a (25+ 10) ~ branch to the ground state and a (75+ 10)~o branch to the 31 keV level. The measured mean life of 6 0 + 3 0 fs is in favour of the spin assignment 2 + or 3 + suggested previously 1) and 2 + in ref. 2x). The 4598 k e V level. The decay of this level goes by (50+20) ~o branches to the ground state and the 1623 level. Also for this level the mean life of 2304-120 fs supports the previous 13) 2 +, 3 + spin assignment. Spin doublets. Attempts have been made to describe even parity states of 28A1 in terms of the Nilsson model with rotational motion t 4 - t 7), and in terms of more or less complex variants of the shell model a, 9, ta). These attempts have so far had only moderate success.

In this discussion no new quantitative model description will be presented, but some interesting systematic behaviour in the experimental data will be discussed qualitatively. In the stripping reaction used in the present study, one expects to populate most strongly states consisting of a proton hole in the d~ shell coupled to a neutron positioned in either the s~ or d~ shell-model states. The s~ doublet is clearly identified as the 3 +, 2 "~ ground-state doublet. Of the d~ multiplet, the 3 + state at 1.01 MeV" and the probable 4 + state 2t) at 2.27 MeV (fractionated with the 2.66 MeV level) are also clearly identified from stripping data 1). These three states carry almost the total In = 2 stripping strength, whereas the I, = 2 strength for the d = 0, 1 and 2 members of the d~ multiplet is spread over several levels. Another class of states may be constructed by a neutron in the s~. state coupled to various excited states in 27A1" In a weak coupling model states of this kind should constitute narrow doublets with spin differences of one unit. Members of the same doublet are expected to have similar decay schemes and transition probabilities, and will have small reduced widths in transfer reactions. In fig. 4 the level scheme for even parity states in 27Al and 2SAI are shown together. An attempt has also been made to identify the states in 27A1 with corresponding doublets in 2SAl. Although it is not possible to propose a one-to-one level-doublet correspondence, the numbers of states and doublets with corresponding spins match surprisingly well. Also the measured transition probabilities seem to agree with the interpretation in terms of doublets. Corresponding to the two (or three) ~ states in 27A1, two or three ~+½ doublets in 2aAl are indicated. The large 1. = 2 stripping strengths to the members of the two lowest doublets show that they contain a considerable admixture of the (d~)-t(d~)l configuration. Obviously a one-to-one correspondence between 27A1 and 2aA! doublets is in this case not present.

MEAN LIVES IN 2SAl

(~)~ 4812

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4580 4510 " - - , /

4409. 3956

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(z3J

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- 4115 / 3936

.39oo

J 3706 .3669

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(%)

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3o,,

.,, 3/2

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5/2

2211

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3/2

% lOlg

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~, 2656 25,2

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2,, I"

/ 1623 '- /620

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.

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1373

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,, lOt4

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,44

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.

31o

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Fig. 4. Comparison of even parity states in Z~Al (left) and 2SAl (right). For 2SA! possible energy doublets with spin difference o f 1 are indicated. Levels with uncertain assignments are shown in brackets.

The { + {- doublets are probably the easiest to identify since they must appear as I, -- 0 states in stripping. Corresponding to the four (or five) { states, one also see four doublets with this characteristic. Corresponding to the only ~.r+ state, one finds with nearly the same excitation energy the assumed 4+-5 + doublet. Here one notices the considerable I, = 2 reduced width for the J = 4 state. It has nearly the same stripping strength as the other 4 + state which is situated 300 keV lower. These two levels together contain the total Io = 2 strength for the I(d~)-l(d~)[4 configuration. Also regarded as doublet members, one expects corresponding splitting of the 4 + state. The spin difference of one unit is fairly well established for eight of the eleven doublets (including the lowest 0 ÷ and 1 ÷ state) shown in fig. 4, and there are eight levels below 5 MeV excitation in z 7AI that may correspond to these doublets. With the

F . A . EL-AKAD et al.

20

r e c e n t a s s i g n m e n t o f 0 + to t h e 3.01 M e V level 21), this a n d t h e 1 +, 3.11 M e V level m a y be c o n s i d e r e d as a p o s s i b l e ½+½ d o u b l e t b u i l t o n t h e ½+ state at 3.67 M e V in 27A1. F o r t h e t h r e e levels in 27A1 w i t h J = ~ at 2.21 M e V , J = ~ o r x2 at 3.96 M e V , a n d J = -~ a t 4.58 M e V t h e r e a r e t h r e e p o s s i b l e c o r r e s p o n d i n g d o u b l e t s o f spins za-, ~- o r ~ + ~ , w h e r e a s n o c a n d i d a t e s f o r a d o u b l e t c o r r e s p o n d i n g to t h e ~ is f o u n d .

state at 4.51

5.2. THE 28A1 ODD PARITY LEVELS I n t h e e x c i t a t i o n e n e r g y r a n g e 3.46 to 5.44 M e V the m e a n lives o f n i n e o d d p a r i t y levels w e r e m e a s u r e d . M o s t o f t h e s e levels a r e o b s e r v e d in t h e (d, p ) r e a c t i o n w i t h TABLE 2 Transition strengths and spin of odd parity states in 28A1

E,

Et

(keV)

(keY)

Branch ") (%)

(E ! ) × 10- 4

3465

0 2272 0 31 1014 0 1620 2272 3465 0 31 0 31 1373 1623 2138 0 1014 0 31 0 31 1373 2138

93 7 56 14 27 82 18 50 50 64 36 11 70 7 1.5 10 95 5 89 11 3 62 3 32

3 5 i.3 0.3 1.7 1.8 2 3 0.4 c) 1.3 0.7 0.2 i .4 0.4 0.1 1.2 1.5 0.2 1.7 0.2 0.07 1.4 0.2 3

3591

3876 4033 4691 4766

4905 5135 5443

Fr/F,, b )

jj prev. known d)

present assign.

4 (2)

4 (2)

3 (1)

3

2 (4)

2

5 (3, I)

5 (3)

I--4

2, 3

2, 4

2

2, 4

2, 4

3 (1)

3

0-2

2 (1)

") Values for levels below 4.5 MeV are from ref. 1). For the higher levels the entries are averages from refs. 11,19). b) Calculated for pure El transition. The present mean lives excluded an M2 character for all transitions except for 5443--0 keV. c) M1 strength. d) Spin assignments from refs. I.z1). Other values according to ref. 1).

M E A N LIVES IN 2reAl

21

In = 1 transfer and therefore 1 - < J~ < 4 - . The only exception is the 4033 keV level where there is strong evidence for a pure 14 = 3 transfer 1). The results for these levels are summarized in table 2. The levels at 3465, 4691, 5135 and 5443 keV have been assigned even parity from the (3He, p) reaction data 13). The strong population of these levels in the (n, y) capture reaction if, t g) suggest, however, negative parity assignments in accordance with the (d, p) stripping results. The 3465, 3591 and 4033 ke V levels. These three levels are strongly populated with an I, = 3 transfer ~) in (d, p) stripping. The transfer strength ( 2 J + 1)go, indicates J > 2 for the two lower levels and J > 4 for the highest level. The 4033 keV level, where no noticeable In = I component is seen, is also the only known odd parity state which is not reported fed directly after thermal neutron capture. These facts indicate a spin value of 5 or 6. In the decay process the 3465 keV level and the 4033 keV level are linked together with a transition that according to the strength has to be MI. The most likely spin assignments are therefore 4 - for the 3465 keV level and 5 - for the 4033 keV level as suggested by ref. to). This is also in agreement with the requirement of El for the transitions from these two levels to the assumed 4 ÷, 2272 keV state and for the 3465 keV-g.s, transition. However, taking into account that the spin o f the 2272 keV level is not fully established, and also that a 1, = 1 component according to ref. 20) is seen in (d, p) stripping to the 4033 keV level, the possibility of 3- for the 3465 level and 4 - for the 4033 keV level still exists. The 3591 keV level decays with a strength that requires an E1 transition to the 31 keV 2 + state, and to the gound state and the 1014 keV state, both with J : = 3 ÷. The possible spin values are accordingly limited to 2 or 3. The large reduced width for/° -- 3, (d, p) stripping, ( 2 J + 1)Sn > 5 [ref. ~)], makes J = 3 the most probable assignment. The 3876, 4691, 4766, 4905 and5135 keVlevels, all formed by a mixture of In = 1 and In = 3 capture in (d, p) reactions and also strongly fed after thermal neutron capture, decay mainly to even parity states with transition rates that exclude pure M2 transitions. The known spin of the final states leads to an unambiguous assignment o f J = 2 for the 3876 and 4766 keV states. For the remaining levels two or more possible spin values remain (see table 2). The 5443 keV level has not been reported studied in the (d, p) reaction, but is seen in the (3He, p) reaction t3) with L = 1 transfer, and it is the highest level that is strongly populated in the (n, ~) capture reaction. The parity therefore seems well established. It decays to the 31 and 2138 keV 2 + states and to the 1373 keV 1 ÷ state with rates excluding a pure M2 transition. The branch to the 3 ÷ ground state, although below the limits for acceptable M2 strength, is also most likely an E1 transition. The spin assignment is accordingly 2 - , or less probably 1-.

22

F . A . EL-AKAD et aL

References 1) P. M. Endt and C. van der Leun, Nucl. Phys. A214 (1973) 1 2) B. R. Mottelson and S. G. Nilsson, Mat. Fys. Skr. Dan. Vid. Selsk. 1 (1959) no. 8 3) J. F. A. van Hienen, P. W. M. Glaudemans and J. van Lidth de Jende, Nucl. Phys. A225 (1974) 119 4) T. Hoitebekk, P. Stromme and S. Tryti, Nucl. Phys. A142 (1970) 251 5) A. E. Blaugrund, Nucl. Phys. 88 (1966) 501 6) J. Lindhard, U. Scharff and H. E. Schiott, Mat. Fys. Medd. Dan. Vid. Selsk. 33 (1963) no. 14 7) G. A. P. Engelbertink, H. Lindeman and M. J. N. Jacobs, Nucl. Phys. AI07 (1968) 305 8) J. H. Ormrod, J. R. MacDonald and H. E. Duckworth, Can. J. Phys. 43 (1965) 275 9) J. V. Maher, G. B. Beard, G. H. Wedeberg, E. Sprenkel-Segel, A. Yousef, B. H. Wildenthal and R. E. Segel, Phys. Rev. C5 (1972) 1322 10) R. M. Freeman, F. Haas, A. R. Achari and R. Modjtahed-Zadeh, Phys. Rev. C I I (1975) 1948 11) A. F. M. Ishag, A. H. Colenbrander and T. J. Kennett, Can. J. Phys. 50 (1972) 2845 12) P. M. Endt and C. van der Lcun, Atomic Data and Nucl. Data Tables 13 (1974) 13) R. R. Betts, H. T. Fortune and D. J. Pullen, Phys. Rev. C9 (1974) 589 14) R. Sheline, Nucl. Phys. 2 (1958) 382 15) R. J. Ascuitto, P. A. Bell and J. P. Davidsson, Phys. Rev. 176 (1968) 1323 16) B. Lawergren and J. Beya, Phys. Rev. C6 (1972) 2082 17) L. G. Mann and S. D. Bloom, Phys. Rev. 139B (1965) 540 18) M. J. A. Voigt and B. H. Wildenthai, Nucl. Phys. A206 (1973) 305 19) R. Hardell, S. O. Idetj~lrn and H. Ahlgren, Nucl. Phys. A126 (1969) 392 20) S. Chen, J. Rapaport, H. Enge and W. W. Buechner, Nucl. Phys. A!97 (1972) 97 21) D. O. Boerma, W. Grilebler, V. K6nig, P. A. Schmelzbach and R. Risler, Nucl. Phys. A7.70 (1976) 15