Lifetime measurements in sd-shell nuclei

I

I.E.4

]

Nuclear Physics AI38 (1969) 588--630; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprlnt or microfilm without written permission from the publisher

L I F E T I M E M E A S U R E M E N T S IN sd-SHELL NUCLEI

(I). Mean lives of aSAr levels G. A. P. E N G E L B E R T I N K t a n d G. V A N M I D D E L K O O P

Robert J. Van de Graaff'Laboratorium, Rijksuniversiteit, Utrecht Received 12 September 1969 Abstract: T h e 4t K(.p, ~7) a n d 35CI(~, p•) reactions were used to populate levels in 3SAr. T h e m e a n lives o f the lowest six excited states in aSAr were m e a s u r e d with the Doppler shift a t t e n u a t i o n m e t h o d . G a m m a rays were detected at 90 °, in coincidence with particles obselved at angles 0 = 10W a n d -- 100 ° or 110" a n d -- 110 °. T h e aSAr* ions slowed d o w n in thick c a r b o n backings, the stopping power o f which is k n o w n experimentally. M e a n lives o f t , , = 540--65, 7000--4000, 75:t:30, 4 6 & 1 8 , 751500--330 a n d 2 5 - - 2 5 fs were f o u n d for the levels at Ez = 2.17, 3.38, 3.81, 3.94, 4.48 a n d 4.57, respectively. T h e relatively fast decay o f the second excited state indicates that positive parity states in 3SAr are only well described if ( d s ) - 4 ( f p ) a shell-model configurations are taken into account.

E

N U C L E A R R E A C T I O N S '*~K(p, ~ty), E =- 4.47 MeV; 35C1(~t, p~.,), E ~ 7.61 McV: m e a s u r e d D o p p l e r shift attenuation. 3SAr levels deduced T½. Enriched 4~K target, natural CI target.

1. Introduction Lifetimes of states in ~SAr are reported in refs. ~. z), while the lifetime of the first excited state is also given in refs. s, ,~). In the Doppler shift attenuation measurements ( D S A M ) of ref. t) the 3 8 m r states were populated in the 3 7 C 1 ( p , 7)SaAr reaction and the Ar ions, with a starting velocity o f v / c ~ 0.2 "/~, slowed down in the target material BaCI2. Due to the lack of experimental int\)rmation about the slowing down of heavy ions with low velocity in such a material, ol" which thc properties after oval:oration may even be different fi'om what is cxpected, the interpretation of the experimentally measured shifts depends on the stopping theory used. So far, no correct treatment s. 6) has been given of the large-angle nuclear scattering, which is dominant for iotas at low velocities in heavy stopping media. Recently, Currie et al. 7) performed a scrics of measurements of the lifetime of the lirst excited state of 3 ° S i . In these measurements the Si ions, with starting velocity v/c ~. 0.9 c'~, were slowed down in six different matcrlals. In spite of the fact that the slowing-down theory is expected to be much bctter at this relatively high velocity, where the electronic stopping is dominant, the results for different materials were only consistent to within a factor or" 1.5. In the DSAM measurements p,'esented in this paper, 3BAr* ions with an initial ÷ Present address: B r o o k h a v e n National Laboratory, Upton, L.I., N.Y. 11973. 588

3~Ar LEVELS

589

velocity of v/c "~ 0.8 % were slowed down in carbon, the stopping power of which is known experimentally a, 9). Again, the nuclear scattering is of minor importance, since the electronic stopping dominates. The (p, cry) and (ct, pv) reactions were used to populate aSAr levels. G a m m a rays were simultaneously detected in coincidence with particles observed at two different angles. The details are given in the next paragraph. This coincident version of the D S A M has a number of advantages compared with simpler non-coincidence techniques. (i) The level of interest has no other indirect, eventually unknown, feedings (e.g. fl-decay). (ii) As the cones of the directions of recoiling nuclei are narrow the influence of the angular distribution of these nuclei is negligible. (iii) G a m m a - r a y spectra coincident with particles detected in either counter do not have electronic shifts with respect to each other, which makes long runs possible. (iv) The initial velocity of the ions can b= made as high as the accelerator voltage and counting rate permit. Both the experimentally known slowing down of 3aAr ions in carbon and the improved technique enables one to measure the lifetimes of the lowest 3aAr states more reliably than in previous experiments. It was also thought worthwhile to measure the lifetimes of the 3.38 and 4.48 MeV levels, for which so far only lower limits were given [refs. 2,2)]. Especially the lifetime of the 3.38 MeV level (J~ = 0 +) is of interest as in shell-model calculations involving the I d,r, 2s~ and l d,~ sub-shells to) its decay to the first excited state (J~ = 2 +) is forbidden, such that the transition probability is a direct measure of possible (ds) -4 (fp)2 admixtures. 2. Experimental procedure 2.1. E X P E R I M E N T A L A R R A N G E M E N T

In the 35Cl(~t, PT) reaction doubly charged helium ions were accelerated with the Utrecht 2 x 6 MV tandem Van de Graaff accelerator to an energy of 7.61 MeV. Currents up to 500 nA were obtained on the target. In the 41K(p, cry) reaction at Ep =4.47 MeV the proton current was limited to 600 nA in order to keep pile-up in the or-particle detector sufficiently low. The beam was focussed by a magnetic quadrupole doublet lens through two Ta diaphragms of 3 and 5 m m diam., respectively, positioned at 4 cm before the target. The position of the 1 x 2 m m 2 beam spot was stable to within 0.5 mm. The beam was caught in a remote Faraday cup behind a 0.5 m thick concrete wall. Focussing was such that the ratio of total current to diaphragm current was about 300. A chamber of 12 cm diam. housed the target and particle detectors. The two silicon surface barrier detectors (Philips) were located at angles Oo.v. either 100 ° and - 1 0 0 ° or 110 ° and - I l0 ° at 33 m m from the target. Rectangular 5 x 10 m m 2 collimators in front of the dctectors limited the opening angle to 8.6 ° in the horizontal reaction plane and to 17.2 ° in the vertical direction. The 36 cm a, true coaxial, Ge(Li)),-ray detector (Philips), placed at 0 r = 90 ° at a distance of 6.5 cm, subtended a half-angle of 14°; see fig. 1.

590

G.A.P.

ENGELBERTINK

AND G. VAN MIDDELKOOP

I Ooo

_y/

./

-':'7- ~ 14"

...~_~_~ . . . . . . .

: .

.

.

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TRUE

.

COAXIAL

36crn

43"

Sil

5ram --"

("B.. G e ( L I )\'~.'~

* ................

--

SI

3

~'

2 FULL

SHIFT=

2Ey

~" S m O r e ¢ s J n S ¥

DIAF RAGMS ~ 3mm

I BEAM

'lcrn '

Fig. 1. Experimental arrangement used in the coincident DSAM.

If the recoiling ions and the 7-rays make angles 0 .... - 0 ~ ¢ and O~ with the beam direction, respectively, a 7-ray with energy E~ will show a maximum shift AE~ with AE./ _ v {cos ( 0 v - 0 , , c ) - c o s (0~+0,~¢)} = 2 v sin 0,e¢ sin 0,.

Ev

c

(1)

c

Here v denotes the starting velocity of the 38Ar ions in the laboratory system and the bar indicates the mean over the solid angles of the particle and ?-ray detectors. Independently of v sin 0 .... AE~, reaches a maximum for 0y = 90 °, while vsin 0,~¢ is largest if the particle detectors are also placed at 90 °. Particle detection at 90 ° is impossible for the target position given in fig. I. As another target orientation would introduce asymmetries, 0o.p. was chosen to be 100 ~ or 1 l0 °. Backward angles for the particle detectors are preferred above forward angles, since the first ones yield a higher velocity for the recoiling ions. The full shift A E / E y is of the order of 4.5 keV/MeV for the 3sCI(~, PT) and 11 keV/MeV for the *tK(p, cq,) reaction, with v/c ~ 0.8 for both reactions (sec table 1). In the analysis it is assumed that the angular distribution of the outgoing particles is isotropic over the small solid angle of the particle detector (half-angle 4.3°). For the two reactions mentioned above, the variation in vsin 0~e~and v over this opening angle is at most 3 ''//oand 1.5 ol;, respectively. Gamma-ray angular correlation cffects are difficult to estimate in this geometry. If the gamma-ray detector is assumed to bc at an angle where the derivative o f a hypothetical angular correlation W ( O ) = 1 + 0.5 P2(cos 0) reaches a maximum, the correction on the full shift, due to the detector opening angles, would be 2 ',"o. For an isotropic correlation the correction would be about 1.2 ,o~,. Since these corrections are small, they are neglected. 2.2. TARGETS AND BACKINGS

The target material BaCl2 (natural) a n d 4 1 K 2 S O 4 (enriched in 41K to 99~/o)was evaporated onto 180-220 /ig/cm 2 carbon backings. During the evaporation special

38Ar LEVELS

591

care was taken to prevent a deposit at the back of the carbon foil. In all experiments, the thickness of the carbon foil was at least 15 ~o larger than the range 8, 9,11) of the 3SAr ions. A crystallographic investigation of the carbon foils, obtained from Yssum, Israel, showed that the structure was amorphous, in agreement with the findings of Fastrup et el. 8, 9) who used foils from the same company for their stopping power measurements. To improve the heat conduction, the foils were backed with an Au layer of about 200/lg/cm 2. The thickness of the BaC12 and 4 ' K 2 SO4 targets varied between 40 and 200 #g/cm 2. For the measurement of very short lifetimes also a target of 740/~g/cm 2 BaCI 2 on 290/~g/cm z Au was used (see table 1). The thickness of the foils and targets was determined by measuring the energy loss of g-particles from a mixed 241Am and 244Cm source. 2.3. D E T E C T O R S A N D E L E C T R O N I C S

[n the (ct, py) measurements the protons were detected in 2 mm thick silicon surface barrier detectors. A 8.1 mg/cm z thick AI foil in front of each detector stopped the elastically scattered aHe projectiles and other heavy particles. The spectrum deterioration caused by proton straggling in this foil was of no consequence in these experiments. A typical proton spectrum is shown in fig. 2. The resolution of about 90 keV is adequate since the ),-rays are generally well resolved by the Ge(Li) detector. The or-particles in the (p, cry) experiment were detected in silicon surface barrier detectors with a depletion depth of 0.2 mm. The Ge(Li) detector had a resolution of 3.3 keV F W H M for 1.33 MeV y-rays.

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II

300

CHANNEL

NUMBER

Fig. 2. Proton spectrum produced by bombardment of BaClz with 7.61 MeV '*He ions. The protons traversed a 8.1 mg/crn z aluminium absorber.

592

G. A. P. ENGELBERTINK AND G. VAN MIDDELKOOP J

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Fig. 3. The 2.17 MeV ;,-ray photo-peaks, detected at 90 ~, coincident with the =~ groups observed at 100" and --100 ° in the 41K(p, =7)38Ar reaction at Ep = 4.46? MeV.

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CHANNEL Fig. 4. The 1.21 and 2.17 MeV ;,-ray p h o t o - p e a k s , detected at 90% coincident with the p= groups observed at 110 ~ and --110 ° in the asCI(~, py)38Ar reaction at E~ =: 7.61 MeV.

3BAr LEVELS

593

Coincidences were determined with leading-edge timers and time-to-amplitude converters. The time spectra, for a particular particle group and all 3'-ray energies, showed a F W H M of 15 ns, but were asymmetric, largely due to the collection properties of the Ge(Li) counter. To avoid selective acceptance of pulses from certain parts of the Ge(Li) detector, which could lead to systematic errors in the shift measurements, a time gate of 50 ns was used. This time gate is sufficiently narrow to suppress false coincidences (see the region beyond the highest energy photo-peak in figs. 3-5). Chance coincidences would mix the direct ~vith the coincident y-ray spectrum and thus cause a smaller shift. In the Ge(Li) detector amplification chain a Tennelec TC 130 preamplifier and a Nuclear Enterprises main amplifier provided stable operation. I

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C H AN N EL Fig. 5. The 3.94 MeV y-ray photo-peak, detected at 90 °, coincident with the p,, groups observed at 110 ° and --1 l0 ° in the asCl(~, lyy)3aAr reaction at E a = 7.61 MeV.

Data were accumulated in a 4096-channel Laben analyser, in such a way that the two coincidence spectra, analysed with one 2048-channel ADC, were routed each to a 2048-memory subgroup. This simultaneous measurement of both y-ray spectra prevents systematic errors due to electronic drifts. The drifts which will only broaden the peaks were small, see fig. 4. A typical run lasted 24 h. No gain or zero stabilization was used. The target room was temperature controlled. In the (p, ~ty) measurement a conventional pile-up suppression system 12) was used. 2.4. A N A L Y S I S O F T H E S P E C T R A

Peak positions P were found from first moment calculations, P = (~..~=,,N~cl)/ Z~=oc~, where N i and c~ are the channel number and its contents, respectively, and

594

G . A . P . ENGELBERIINK AND G. VAN MIDDELKOOP

a and b indices such that the summation is over the peaks only. In all cases a constant background determined at the high-energy side of the peak was first subtracted. For the highest energy peak of the spectrum the background was always negligible as can be seen from figs. 3-5, but in some cases the peak under consideration was superimposed on the C o m p t o n tail of a higher-energy peak. The dispersion was measured with 6°Co and s s y sources before and after a measurement. In some cases the dispersion could also be determined directly from the coincident spectra. The measured F-values, defined as the measured shift divided by the full shift 2E~ are given in table 1.

v/c sin 0rec sin 0r,

3. Interpretation of the measured F-values 3.1. S T O P P I N G

POWER

AND

NUCLEAR

SCA"I"FER1NG

In the DSAM version used here, the initial direction of the recoiling nucleus is defined by the particle detector. The Doppler-shifted energy of a y-ray emitted at an angle 0 relative to the recoil direction is E=

Eo(l+

v-(O---)F(z)c°sO) ' c

if v(O)/c << 1 ; Eo is the unshifted y-ray energy, cleus at the time t of y-ray emission and F(z) = (o(0)~) -1

fo v(t)

v(t) cos

(2)

is the velocity of the recoiling nu-

dp(t)e-t/* dt,

(3)

where cos q~(t) denotes an ensemble average over the nuclei which are scattered at the angle ~b(t) relative to their initial direction. The stopping of heavy ions has been treated by Lindhard et al. 13) who considered both electronic stopping and stopping due to nuclear collisions. The latter process leads to large-angle scattering which has been treated in this context by Blaugrund 14). In this framework we will discuss the stopping power used in the analysis. In the dimensionless quantities [notation of ref. 13)] the stopping power can be separated into an electronic and a nuclear part: (de/dp) = (d~/dp)e + (de/dp).. As the initial velocity is about v/c = 0.8 ~o, the stopping process takes place both in the target material and in the backing, while the electronic term is dominating. For the nuclear energy loss function (de/dp). the following expression was used 1): dP n = - - c l o g

+ ~-

(4)

with c = 0.200, c~ = 1.215, a = 70.0, b = 0.00200 and /~ = 0.815. In the range 2 × 1 0 - 3 ~ g ~ 10 this function fits the theoretical curve given by Lindhard to within 2 ~ . For this part of the stopping power there is no experimental information. How-

38Ar LEVELS

595

ever, for high recoil velocities and slowing down in light materials, e.g. carbon, the contribution from this term is small. For 3SAt ions with v/c < ~ T Z ~ = 5.0 % the electronic loss function (de/dp)~ can be written as 8)

with k=0.0793~,

z t ZI(At +A2) ~ , ~ ~ ~, ( Z I + Z 2 ) AI A2

(6)

where indices 1 and 2 refer to the ion and stopping material, respectively. Theoretically one estimates ~, = Z], which gives ~, = 1.62 for Zt = 18. However, from the experimental work of Ormrod et al. 15) it appears that the electronic stopping cross section shows oscillations around ~c = Z~. The difference depends on Z1 and is independent of Z2. For Z t = 18 (and v/c = 0.3%) Ormrod gives the value A r ions in c a r b o n

Z~16:1'62

~e

2.0-

18-

%J, 0.2

100 ~

o14

o16

o'8

,io

Fig. 6. The velocity dependence o f ~:c for 3aAr ions in carbon as extracted from the experimental data given in ref. a). The theoretical estimate 13) for ~:, is ~:, ~ Z t t = 1.62.

~, = 2.15, an increase of almost 30 % over the theoretical estimate. The work of Ormrod was extended by Fastrup et al. a.9) who measured the slowing-down of several nuclei in carbon at different velocities. They showed that for Ar ions in carbon ~ decreases with increasing velocity, which means that the "shell effect" is less important at higher velocities. From their data the graph in fig. 6 is extracted. The line through the data points has the form ~ = 2 . 3 7 - 61.0 v . c

(7)

For the exponent p, for which the theoretical estimate is p = 0.5, they obtained the experimental values p = 0.423 for v/c > 0.28 9/o and p = 0.550 for v/c < 0.28 9/o. For the slowing-down of Ar ions in BaCl2 and K2SO4, for which no experimental

596

G . A . P . ENGELBERTINK AND G. VAN M[DDIELKOOP

information is available, the value p = 0.5 is used, while ~c is taken again as given in eq. 7, since the results of Ormrod et al. i s) show that ~-c is independent of Z2. In fig. 7 the results are shown for v(tjl/~'(O)and cos 4)(0 for 38Ar ions in carbon and BaCIz, calculated from the stopping powers mentioned above. For the calculation of cos q~(t) the formulae given in ref. ~4) are used. Tile large-angle scattering is seen to be relatively small for the slowing-down m carbon. f

1

--

i

. . . . . .

1132keV 3BAr ions in BaCI 2 (--.--)and C[

f

) _v = 0 . 8 Olo

1.0

c

"~ 0.5

\.. ":,.\

v~

....

x-~,.~.

".

\.\

"%\: \.

"\

.... , (3

o

o12

0.'4

x.

t(ps)

d6

0.'8

1.o

Fig. 7. Results for v(t)/v(O) a n d cos ~(t) for aSAr ions with v(0)/c = 0.8 % in c a r b o n a nd BaCI2, calculated with the s t o p p i n g powers given in sect. 3. The large-angle s c a t t e r i n g is seen to be relatively small for the s l o w i n g d o w n in c a rbon.

To minimize the influence on the final result of the nuclear stopping power and the experimentally unknown stopping power of the target material, one generally prefers high values for v/c and thin targets. On the other hand the yield must be sufficient to make coincidence experiments possible. In the next section is will be shown that the influence of the targets used is rather small, except of course for very short lifetimes. 3.2. I N F L U E N C E O F T H E F I N I T E T A R G E T T H I C K N E S S

The 3BAr ions produced in a thin layer i of the target ~ill reach the backing after a time Ti. The FI(T) holding for these ions can be written as Fi(z) = F,i(r) + Fzi(T),

(8)

3$Ar LEVELS

597

with

F . ( z ) = (v(O)z)-'

,,JO

F2i(T ) = (/)(0)~) -1

v(t) cos dp(t)e -'/" dr,

(9)

V(t) COS d?(t)e -'/" dr,

(10)

Tt

where different stopping powers are used for Fxi(z)(target) and F2i(z) (backing). With the target divided in N layers, the quantities r l ( z ) = 1/N~,Ni=IF~,(z), F2(~) = I/NZ~=IF2i(T) and r(z) = rl(x)+Fz(z) are formed. If Fo(z) and Fb(z ) are the F-curves for target and backing material, respectively, then the curve F(z) lies between the curves Fo(z) and Fb(Z). For a given target-backing combination, F(z) approaches Fa(z) for short lifetimes and Fb(Z) for long lifetimes. The quantity q = F2(z)/(F, (z)+ F2(z))is introduced to indicate which fraction of the F-curve for a certain value ofz is due to the backing. For thin targets and long lifetimes q approaches unity. In the aScl(~, p~,) reaction the yield is assumed to be constant throughout the target. Since Fa(z) and Fb(z) did not differ much, N = 5 was chosen, which is quite sufficient. The curve F(z) was used to convert the measured F-values into mean lives. In the '*tK(p, :iV) reaction, which has a strong resonance structure at the energy used, the aaAr ions are assumed to be formed in the middle of the thin (45 #g/cm 2) target. The influence of this assumption on the lifetime is small since the curves F,(z) and Fb(T) are not much different. 3.3. E R R O R S A S S I G N E D TO T H E M E A N LIVES

The errors assigned to the mean lives given in table 1 are the result of a quadratic addition of the following independent errors. (i) The statistical error in the measured F-value. (ii) A relative error of 0.3(1 - q ) . An error of 30 % is attributed to the stopping power of the target material v, ~3), which is reduced by a factor 1 - q , see subsect. 3.2. (iii) A relative error of 0.08 q due to the 8 % uncertainty in the density of the carbon foils. For amorphous carbon (see subsect. 2.2) the specific weight varies, depending on the manufacturer, between 1.8 and 2.1. In the analysis the specific weight is taken as 1.954-0.15. This 8 % error, which will also cause an 8 % error in the mean life, is reduced by the factor q. In view of the factors mentioned above the smallest obtainable error in ~m is of the order of 10 %. 4. Results

A summary of the Doppler-shift data is given in table 1. The full shift is more than twice as large for the 4tK(p, ~V) reaction as for the 35C1(~, p~t) reaction. Since v/c is about the same, the difference is due to the different 0 .... which reflects the different

598

G . A . P . ENGELBERI'INK AND G. VAN MIDDELKOOP TABLE 1 S u m m a r y o f m e a s u r e d Doppler shifts a)

E~ (3~Ar) (MeV) 2.17 3.38 3.81 3.94 4.48 4.57

Transition (MeV)

2.17 -~- 0 t 3.38 --~ 2.17 / 3.38 ~ 2.17 3.81 -~- 2.17 3.94 ~ 0 4.48 -~- 3.81 4.57 ~ 2.17

Target Backing 0o.p. BaCI2 C (degrees) (,ug/cm 2) (,ug/cm 2) ~) 100 200 40 740 95 740

180 190 220 200 ~) 195 ~)

100 100 110 I00 110 110 110

100 r

c

Full shift

F

AE.JE./

(';(,)

rm h) (fs)

q ~)

(keV/MeV) 0.670 0.756 0.791 0.750 0.781 0.770 0.769

11.29 4.86 4.58 4.60 4.26 3.93 3.87

43.2-.:1.7 5404- 65 5.4-;-2.3 ~ 4 . 3 ± 2 . 3 / 7000"_4000 89.5 k3.5 75~ 30 91.9-:2.0 46-18 25 =:5 "S1500:!: 330 96 _-_4 2 5 - - 25

0.7 0.8 0.6 0.7 0.0 0.8 0.0

a) T h e p o p u l a t i n g reaction was in all cases 35C1(~, p)~SAr at E:~ = 7.61 MeV, except for the 2.17 MeV level. T h i s state was populated in the 4~K(p, ~)3SAr reaction at Ep --- 4.467 MeV. In this case the target was 4 5 / t g / c m 2 4~K2SO 4 on a 180 p g / c m 2 c a r b o n backing. b) T h e error includes 8 % uncertainty in the specific weight o f the carbon foils a n d a 30 % error in the stopping p o w e r o f the target material (see subsect. 3.3). ¢) T h e backing was 2 9 0 / t g / c m 2 Au. a) See subsect. 3.2 for definition.

directions ot the ~-particles. For the (p, c~),) experiment 0~¢ was 58 ~, whereas for the (~, pv) measurements it was about 18 °. For a large recoil angle the F-value can be measured with higher accuracy, but the interpretation is influenced by the deficiencies in our knowledge of the stopping power. The 45 pg/cm 2 41K2SO 4 target used, had an effective thickness of 84 pg/cm 2 for the 3SAr ions. Measurcments on the higher-lying 3SAt states were not performed with the (p, ~y) reaction as pile-up, largely due to protons elastically scattered by the thick carbon backing, deteriorated the ~-particle spectrum. Some examples of the measurements are ~hown in figs. 3-5. In the measurement on the 4.48 MeV level, the discriminator window also contained the proton group feeding the 4.59 MeV level. The 4.59 McV level decays ~) mainly (90 i~) to the 4.48 MeV state with a 0.11 MeV 7-ray and also (10 ~o) to the 3.81 MeV level. A:~ the mean life of the 4.59 MeV level ~)is > 0.5 ps, the partial feeding of the 4.48 MeV level via the 0. I 1 MeV ~/-ray is delayed. Therefore, the mcan life of the 4.48 MeV level is shorter than the value which corresponds to the measured F-value. As the 0.11 McV 7-ray is not recorded, the intensity from the delayed feeding has to be estimated from the intensity of the 0.78 MeV }.--ray. I,s weakness indicates that the mean life of the 4.48 MeV level is close to the upper limit of 1.5 ps. Preliminary measurementb on the 3.94 and 4.57 McV levels indicated that both mean lives were shorter than 50 fs. As for such short lifetimes, the ;,'-ray emission takes place almost exclusively during the slowing-down in the target, the final measurement: were performed with a very thick target on an Au backing. The contribution of the Au backing to the F-value is less than 1 °.o~.

3"qAr LEVELS

599

5. Discussion Table 2 summarizes the lifetime measurements in 3BAr. It is seen that the present results are in agreement with those given in refs. 2 - , ) . However, a comparison can only be made for the 2.17 and 3.81 MeV levels. For the 2.17 and 3.94 MeV levels the present work disagrees with the (p, ~) D S A M results of reL 1). The difference for the 3.94 MeV level amounts to 6 0 + 4 0 Is, if the errors in ref. 1) are enlarged to include stopping power uncertainties (30 %). The more serious disagreement for the first excited state is not understood. It may be that large-angle scattering, playing an important role in the previous (p, ~,) measurements, especially for long lifetimes, causes the discrepancy. TABLE 2

Summary and comparison of 3SAr measurements E. (MeV)

2.17

present work 540+

65

3.38 7000=1=4000 3.81 75+ 30 3.94 46+ 18 4.48 -~1500.__ 330 4.57 25?_: 25 4.59 4.88 5.51 5.66 6.21 6.60

a)

b)

> 1000

__~ 500 llOi90 105,35 ~-" 600 48--18 ~ 500 39--18 ~'-_- 300 64-.*-25 90,40 254-10

704-20 __~ 1000 "<-350000 150-t-80

~m (fs) ¢)

d)

600+140

4504-110

adopted value 530=i=

60

7000,4000 72+ 20 58-- 19 13005: 400 40=1= 15 500 < 3= ~_ 350000 c) 4 5 , 18 ~ 300 64fi: 25 90=t= 40 2 5 , l0

°) Ref. ,). In this ref. errors due to uncertainties in the stopping theory are not included. Therefore an error of 30 % has been added quadratically to the errors listed there. b) Ref. 2). ¢) Ref. a). d) Ref. 4). This result is announced in ref. 2) as 590-70 fs. Q) A theoretical estimate of 110000 fs is given in ref. 16). For the mean lives of the negative parity states at 3.81 and 4.48 MeV, see the discussion in ref. t 6 ) . The J~ = 0 ÷ level at 3.38 MeV decays 1) only to the j r = 2 ÷ first excited state with a pure E2 transition of 6 +__3 W.u., which corresponds to the mean life of 7 4-4 ps. Shell-model calculations to), for A = 35-39 nuclei, which take into account the positive parity Ida, 2s~ and l d , shells, do not generate this low-lying j r ___ 0 ÷ level. It has therefore been assumed that this level predominantly has a configuration with two particles in negative parity shells. Calculations ~7, 18) indicate a (d.~)a(f~) z configuration. The 2.17 MeV level is rather well described 10. ~6) without invoking (f~)2 components. If the above descriptions are correct, the 3.38 ~ 2.17 MeV transition would be forbidden. The strong transition between these two low-lying positive-parity

600

G.A.P.

ENGLLBERTINK AND G. VAN M I D D E L K O O P

states indicates again t6) that ( s d ) - 4 ( f p ) 2 configurations have to be taken into account. It the wave function of the 3.38 MeV level is assumed 17) to ]lave the pure c o n f i g u r a t i o n [(d~)oo(f.})ox4 2 ]s= o, T = ~ then due to the single-particle character of the E2 operator, the transition rate to the 2.17 MeV level is determined by the (f.~)2 comp o n e n t in the wave function of this level. A c o m p o n e n t [(d.,})2o(fk)ol4 2 ]s= z. r = , with a m p l i t u d e A gives for the E2 transition B(E2) -- 1.32 A2(e/eo) 2 W.u. For an effective charge e -- 1.5eo, the m a x i m u m transition rate is only 3 W.u.. This indicates that, unless both levels have pure (d2l)4(f~.) 2 configurations, the wave function of the 3.38 MeV level is also mixed with s-d configurations. It follows from the discussion above that the lifetimes of the positive-parity states at 2.17, 3.38, 3.94 a n d 4.57 MeV have to be discussed in a model, more elaborate than that used in previous calculations 10, 16). The a u t h o r s are indebted to Professors A. M. H o o g e n b o o m and P. M. E n d t for s t i m u l a t i n g discussions. Tile cooperation with Drs. P. W. M. G l a u d e m a n s a n d H. D. G r a b e r a n d the assistance of W. J. J. M. lllem is appreciated. This investigation was partly supportcd by the j o i n t p r o g r a m of the " S t i c h t i n g voor F u n d a m e n t e e l Onderzoek der Materie" a n d t h e " N e d e r l a n d s e Organisatie voor Z u i v e r Wetenschappelijk O n d e r z o e k " .

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

o. A. P. Engelbertink, H. Lindcman and M. J. N. Jacobs, Nucl. Phys. AI07 (1968) 305 K.P. Lieb, H. R0pke, H. Grawe, H. J. Brundiers and O. Klepper, Nucl. Phys. AI08 (1968) 233 D. Evers, dissertation (1968) Hamburg H. Grawe and K. P. Lieb, Nucl. Phys. AI27 (1969) 13 R. E. Pixley and W. Benenson, Nucl. Phys. A9! (1967) 177 H. E. Schiott, private communication W. M. Currie, L. G. Earwaker and J. Martin, Nucl. Phys. A135 (1969) 325 B. Fastrup, P. Hvelplund and C. A. Sautter, Mat. Fys. Medd. Dan. Vid. Selsk. 35, No. 10 (1966) P. Hvelplund and B. Fastrup, Phys. Rev. 165 (1968) 408 B. H. Wildenthal and E. Newman, Nucl. Phys. All8 (1968) 347 D. Powers, W. K. Chu and P. D. Bourland, Phys. Rev. 165 (1968) 376 B. Bognjakovi~.,J. A. van Best and J. Bouwmeestcr, Nucl. Phys. A94 (1967) 625 J. Lindhard, M. Scharff and H. E. Schiott, Mat. Fys. Medd. Dan. Vid. Selsk. 33, No. 14 (1963) A. E. Blaugrund, Nucl. Phys. 88 (1966) 501 J. H. Ormrod, J. R. MacDonald and H. E. Duckworth, Can. J. Phys. 43 (1965) 275 G. A. P. Engelbertink and P. W. M. Glaudemans, Nucl. Phys. A123 (1969) 225 F. C. Ern~, Nucl. Phys. 84 (1966) 91 L. B. Hubbard and H. P. Jolly, Phys. Rcv. 178 (1969) 1783