Angular correlation studies of electromagnetic transitions following the 16O(τ, α)15O reaction

Nuclear Phyzfcs Al’72 (1971) 113-126;

j-q

@ North-Ho&d

Pubffsfting Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

ANGULAR CORRElLATION STUDIES OF ELECTROMAGNETIC TRANSITIONS FOLLOWING THE “60(r, cc)‘% REACTION R. AVIDA, M. B. GOLDBERG, De~rtment

Y. HGRGWITZ,

K.-H. SPEIDEL t and Y. WOLFSON

of Nuclear Pkysics, Weizmams Institute of Science, Re~ovot~ Israel Received 13 April 1971

AWract: A particfe-gamma angular correlation coincidence teclmique enabling Be measurement of 0” coincidences was used to study Ieveis in I50 at 5.24 MeV (J” = a+), 6.18 MeV (p = 6-1, 6.79 MeV (.rfl = #+) and 6.86 MeV (J* = t+). The multipole mixing ratios of the de-excitation y-rays were determined as the following: x(5.24 -+ 0) = +0.08&0.08 an E3/M2 mixture; x(6.86 + 5.24) = +0.04f0.03, an EZ/Ml mixture; x(6.79 -+ 0) = -0.02&0.02, an MZ/El mixture and x(6.18 + 0) = -0.121 rtO.008 an E2jMl mixture. The latter value is to be compared witb x((E2jMI) = $0.13&0.02 for the mirror 6.323 MeV transition in lSN indicating Ix(“O)I d l~f’~N)j contrary to previous findings (10). The results obtained, together with those ~or~spon~~ to mirror transitions in 15N are compared with recent IPM and core polarization theoretical investi~tions. E

1. Iutroductiou The mirror nuclei 15N and IsO have been the subject of sustained interest because both lack a single nucleon to complete their 1p shells. Theoretical predictions regarding these nuclei are, therefore, expected to be in reasonable agreement with experiment. Kurath I), Halbert and French *), Inglis ‘), and Lane “) have shown that the properties (especially level schemes, El and Ml widths) of the low-lying states of these mass-15 nuclei can be reasonably interpreted in terms of the independentparticle model. In particular, the properties of the $- levels at 6.18 MeV in ’ sO and the mirror state at 6.323 MeV in ‘“N (which have been shown “) to be predominantly p+ hole states relative to the 160 core) have been expected to provide a sensitive test of the purity of the single-hole wave functions ’ - “). A problematic situation developed, however, from a comparison of the EZ/Ml mixing ratios of these mirror transitions when an experiment lo) indicated that the E2 matrix element was larger in ’ “0 than in “N. This result is extremely difficult to explain in terms of the independent particle model, in which the “0 transition is a pi 1 + pi 1 neutron hole jump. Various attempts have been made to account theoretically for a larger E2 matrix * On leave from the Institut fiir Strahlen und Kernphysik, Bonn University Bonn, Germany. 113

114

R. AVIDA

et al.

element while retaining simple independent-particle model wave functions. In ref. “) it is shown that a weak coupling treatment cannot yield the effective charge parameters required to describe the t- to J- mixing ratios. Poletti et al. ‘I) have applied the IPM with collective E2 enhancement for seven mixed E2/Ml transitions in the lp shell. Agreement is excellent for all transitions except the 6.18 -+ 0 neutron hole jump in “0 (see table 7 of ref. “)). Shukla and Brown “) have investigated the effects of residual interactions on the wave functions of the various states in 15N and “0 by mixing in multi-particle, multi-hole deformed configurations. The effective charge for the E2 transitions was calculated by taking into account the contribution of the 2’ states of the I60 core. The calculation again failed to yield Ix(~~O)/ > /x(15N)I. The experimental values obtained in ref. lo) are x(’ “0) = -0.17 +O.Ol t and x(’ 5N) = +O. 13 kO.02. A recent inelastic electron scattering experiment 12) has measured directly the ground state radiative widths Ti(Ml) and rf(E2) for the 15N level with the result jx(E2/Ml)l = 0.13-&0.03 in excellent agreement with that of ref. lo). The experimental situation in “0, is however, not so clear cut. An earlier measurement by Povh and Hebbard 13) yielded x(’ 50) = 0.12 20.03 while it is difficult to reconcile the recent work of Horowitz et al. 14) with ~(~~0) < -0.10. In view of these discrepancies a careful measurement of the 6.18 --* 0 mixing ratio was considered desirable. In the present paper we report an investigation of the electromagnetic properties. of the +- state at 6.18 MeV as well as those of the positive parity states of “0 at 5.24 MeV (s’), 6.79 MeV (3’) and 6.86 MeV (3’). In sect. 2 the experimental procedure is outlined. In sect. 3 the experimental results are presented while their significance is discussed and tentatively related to the properties of the I60 core in sect. 4. 2. Experimental

procedure

In the present work the ’ 60(r, CX)’ 5O reaction was used to populate the ’ 5O states. The y-ray transitions were investigated in coincidence with back-scattered or-particles using the particle-gamma angular correlation geometry (method II) proposed by Litherland and Ferguson ’ “). Self-supporting, thin (approximately 20-40 pg/cm2) SiO targets were bombarded by a doubly charged 3He beam supplied by the Heinemann Laboratory Tandem Van de Graaff accelerator, at energies around 10 MeV. The 150 mm2 active area, 100 pm depletion layer annular counter was placed 4.2 cm from the target, thus. accepting particles scattered into lab. angles between 170” and 174”. The finite solid angle correction for the detector in this geometry is estimated * “) as a I .5 Y0correction to the coefficient of P,(cos 0) and 4 y0 to that of P4(cos 0). It was necessary to operate the detector at bias voltages _, ‘-z20 V to keep the tail of the proton continuum t In the present work treatment of ref. Is).

all x-values

are quoted

and presented

in keeping

with the phase

consistent

‘6O(t, cc)‘50

115

well below the alpha peaks of interest. The particle spectrum was digitally stabilized. Coincident y-ray spectra were accumulated in 256 channel subgroups of two 4096 channel analysers using a conventional fast-slow coincidence arrangement (x 10 ns resolving time). The current pulses from the last dynode of the photomultipliers were gated by the coincidence (gate length x 300 ns) and only then integrated. The rate dependence of the system was checked with a strong 137Cs source close to the crystals thus generating gamma singles rates up to 1.5 x lo5 s -’ in each tube. The coincidence losses at the highest counting rates did not exceed 4 %, which is consistent with that expected for current pulse widths of x 300 ns. In the measurements reported here the gamma singles rates never exceeded 4 x lo4 s-l, even at 8, = O”, close to the beam stop. Provision was made for routing of gamma rays (into different memory subsections) according to digitally defined energy windows on the particle spectrum. The respective random coincidences were separately stored, but never exceeded 1 % of the true coincidence rate. In order to cover the full angular range a system was developed which allowed the 12.5 cm x 12.5 cm NaI(T1) scintillators (the front faces of which were covered by 3 mm lead and 1 mm tin discs) to be placed at 0” to the beam direction (see fig. 1). This entails clean beam stopping relatively close to the particle detector (approxi-

1 - NoI

5ClNTlLLATOR5

%- BEAM GTOP (PLATINUM)

3-

TAUGETCUAMBER

4-

TARGET MOUNT(T”NOSTEN)

5- SCREENINO

CASING

FOIL (PLATINUM)

6- TAROET POSITION I-

COUNTER-TARGET

S-RING

COUNTER

9- PL’MPINO lO-COLLIMATOR II-BEAM

A%EMBLY SENSITIVE

FRAME SURFACE

HOLES SHAFT

COLLIMATORS

(TANTALUM)

Fig. 1. Experimental

set-up illustrating facility for 13~= 0” measurement.

116

R. AVIDA et al.

mately 20 cm distant in our case). To this end, the beam was collimated down to 1.6 mm and directed through a 3 mm hole in a tungsten target mounting assembly designed so as to minimize the particle rate off the platinum beam stop and yet maintain relatively small 90” y-absorption (Z 4 % for 6oCo). The elongated shape of the beam stop also tends to minimize the 0” absorption (1.5 % for 6oCo). To illustrate the advantage of this geometry consider a typical dist~bution ~(~) cc 1 -t-O.5P,(cos 8). When the beam is stopped far away from the target, one is usually limited to observation angles or 2 25”. It follows that in our geometry the maximum observable anisotropy is increased by about 35 o/o; moreover, the sensitivity to small amounts of P4 is greatly increased. The compromise involved in measuring at 0” is a continuous particle background (coming predominantly from the target holder) which somewhat limits the maximum peak to background achievable, rendering it also rather sensitive to the beam optics. Therefore, all our measurements included the simultaneous recording of y-rays coincident with the high and low backgrounds flanking each particle peak. This coincidence rate was found to be very low throughout (i.e. of the order of the random coincidence rate) so that our geometry entailed essentially just a correction to the normalization of each individual run (made by subtracting the flat background from the particle normaIiza~on). All the corrections discussed above were applied to the analysis of the angular distributions, as well as those due to the motion of the radiating source (y-rays selected by the coincidence are emitted by “0 nuclei recoiling at o/c FX2.7 % along the beam direction). The data, obtained by summing the full-energy peaks (plus first and second escapes where applicable) was computer fitted to a Legendre polynomial expansion of the form W(0) = 1 l-A,BqYP,(cos e)+A,B~~P,(cos q, where BiY represent the products of the geometrical corrections for both detectors.

3. Results 3.1. PRELIMINARY

MEASUREMENTS

The 3’ state in “C at 1.99 MeV was populated via the “C(Z, a)‘% reaction for which the y angular distribution is isotropic. The results, shown in fig. 2, are in excellent agreement with absorption and centering measurements carried out with a 6oCo point source. Another measurement was performed on a known and strongly anisotropic angular correlation, namely the Of -+ 2+ + Of, “C(a, q y)l'C reaction. The results are shown in fig. 3. The excellent fit to the data allowed the experimental determination of the scintillator finite size corrections. These were found to be in excellent agreement with values from tables compiled by Rutledge ’ ‘).

117 I

I

I

I

I

I

I

1/2+

199

I 1/e-

0

“C

I 0

350’

I 15

I 30

I 45

I 60

I 75

I 90

OY Fig. 2. Measured angular correlation of the isotropic transition in “C.

O-

IO-

O-

to-

Fig. 3. Measured angular correlation of the 4.43 MeV - 0 transition in %. The state was populated via the %(a, a’)‘*C reaction. The excellent fit to the data allowed the experimental determination of the scintillator finite size corrections.

R. AVIDA et al.

118 3.2. THE 6.18 MeV, $- LEVEL

An excitation curve for the 160(~, ti3)150 reaction yielded differential cross-section maxima at approximately 8.8 MeV, 9.6 MeV and 10.8 MeV. The presence of a small contaminant peak, however, ruled out the first energy so the experiment ed at 3He bombarding energies of 9.55 MeV and 10.84 MeV. Si O+ i

PARTICLE

Er =10.84

a

L

2

I:...

IO4

:.“”

;’

2

s

,03

/cm2

-I

-172”

target

(‘0)

o

aIzl 0) IS

”

: ,,

,. ,.,. ./. ,,..‘.

r.r’“o,

I

a.l’o)

,..‘.

I

-i

”

adso)

Protons

0

8,

I

i:

/

SPECTRUM

MeV,

2Opg

z

,

I

I

was perform-

a,c’“o) I ‘Y.,

19

1 .....

2

_...., ‘,. .

1

I

0

50

I

I

I

I

100

150

200

250

CHANNEL

NUMBER

Fig. 4. Particle spectrum as obtained with an 100 pm annular surface-barrier counter at 180” to the incident 3He beam using the reaction 160(z, CC)‘~Oat a bombarding energy of 10.84 MeV. The peaks labelled 160, lzC are due to elastically scattered t-particles and the ones labelled Q(‘%), CL,(“C) to alpha particles from W(t, cc)“C. The other labelled peaks correspond to states in “0; the group to the 6.18 MeV state is a3 (“0). The detector was operated at bias voltages I 20 V to keep the tail of the proton continuum well below the cc-peaks of interest.

A good particle spectrum obtained in the geometry described in sect. 2 is illustrated in fig. 4. Gamma-ray spectra were recorded at four and five angles at the former and latter energies respectively. Least-squares fits to the angular distribution data at the higher bombarding energy are shown in fig. 5. No evidence for a non-zero A, was found. The results at both beam energies, analysed in accord with the phase consistent treatment of angular correlations of Rose and Brink Is), are presented in table 1. We obtain for the average of the two runs A, = -0.278 50.017, corresponding to a mixing ratio x(E2/Ml) = -0.121 f0.008 or +2.35*0.06. Referring to sect. 1 we

119

‘SO@, ct)%

see that this result is in excellent agreement with the work of Povh et al. 13) but is about 5 standard deviations removed from the more recent work of Lopes et ai. lo) who obtained x(E2/Ml) = -0.17$0.01. Gorodetzky et al. 19) report x(E2/Ml) = -O.lS;g:g$ which, because of the large errors, overlaps with all measurements.

45c

4oc

350

300

250

I

I

I

1

I

I

I

0

15

30

45

60

75

90

Fig.5. Measured angular correlation of the 6.18 MeV-0 transition shown corresponds to x = -0.128.

at EI = 10.84 MeV. The fit

3.3. THE 6.79 MeV (a+), 6.86 MeV (a’+) AND 5.24 MeV (&+) LEVELS

A level diagram for ’ 5O is shown in fig. 6. The energies, spins and branching ratios have been taken from the compilation of Warburton et al. 20) as well as the recent work of Gill et al. 21). The 6.79 MeV leve1 decays virtually 100 % to ground while the 6.86 MeV level decays predominantly to the 5.24 MeV level. The decay of the 6.79 MeV level to either member of the pos~~ve-parity doublet at 5.2 MeV has been shown to be less than 6 % whereas the 6.86 MeV to ground branch is lms than 10 %. Since the 6.79 MeV and 6.86 MeV particle peaks were not resolvable our results were analysed assuming that both the 6.86 MeV and 6.79 MeV decay modes are 100 y/, pure. The coincident y-ray spectrum (fig. 7) shows y-rays from the 6.79 MeV to

1”)

0.55

ra (R2) (eV x 10’) I50

2.4

r,(Ml) (eV) I50 ‘50

BEOllb,

-0.24 0.79 -0.19 0.40 -0.17 0.25 -0.17~0.01 “) -0.12f0.008 d,

150

x

-0.02~0.04 +0.04*0.03

1.18

To (E2) (eV x 102) lSN

3.7 3.4f0.7

l’o(M1) (eV) ‘“N

‘)

decay of the #-, 6 MeV levels in ’ 5O and lsN from ref. ‘)

TABLE 2

+0.41 f0,04 +0.29f0.03

A4

(present) exp .

‘)

&O.Oll ztO.08) kO.02 *0.06) f0.03 +0.08

+0.25 +0.23 +0.22 +0.13*0.02

-0.128 (or +2.39 -0.02 (or + 1.79 +0.04 +0.08

-0.115f0.011 (or +2.30 f0.07)

x

“) il is the location of the unperturbed #- state used as a free parameter in the calculation of the deformed wave functions ‘). b, The parameter fi0,, gives the equivalent effective charge due to deformed state admixture 5). d, Present work. ‘) Ref. l’). ‘) Ref. lo).

9.0 10.0 11.0 experimental

WeV)

Electromagnetic

The second solution quoted is always the unphysical one.

E2/M1 E3/M2

4fJ-f 8’ f’ + t-

6.86 + 5.24 5.24 -+ 0

9.55 9.55

M2/El

%’ + a-

-0.48 kO.02

-0.29f0.02

‘&

6.79 + 0

E2/Ml

Multipolarities

9.55

4- *g-

Jf + Jl

-0.27f0.02

6.18 -+ 0

Transition (MeV)

10.80

9.55

“He energy (MeV)

TABLE 1

Coefficients of Legendre polynomial fits and extracted mixing ratios

0.37 0.18 0.11

-0.04f0.03 +0.13f0.05

-0.10f0.02

x[ref. *‘)I

160(t, a)‘“0

121

ground state decay and the 6.86 MeV + 5.24 MeV + 0 cascade. The 1.99 MeV y-ray is due to the inclusion in the energy window of the particle group leading to the first excited state of “C from the contaminant reaction 12C(t, a)l’C. This, E(MeV)

J”

6.66

5/2’

6.79

-

3/2’

-

5/2+ 1/2+

2< 5 x IO-‘hc

6.16 -

5.245.1 9-

E3/M2

E2/MI

T = 3.2 x IO- I2 set

M2KI

_l_Ll_

l/2’

Fig. 6. Level and &cay scheme for 150 taken from the compilation as the work of Gill et al. 21).

CHANNEL

of Warburton et al. 20) as well

NUMBER

Fig. 7. Gamma-ray spectrum observed in coincidence with the 6.79 MeV and 6.86 MeV a-particle groups. The 1.99 MeV y-ray is due to the inclusion of the particle group leading to the 1.99 MeV state of “C in the energy window.

I

450-

W2;

6.66

400 IS 0

350-

300 -

2501 2oc -

30

90

@Y Fig. 8. Measured angular correlation of the 6.79 MeV-0 transition extracted from the spectrum in coincidence with the unresolved 6.79 MeV and 6.86 MeV levels. The fit shown corresponds to X = -0.02. T

I

I

I

6.66 6.79

750

5.24

650

600

0

30

60

so

eY Fig. 9. Measured angular correlation of the 6.86 MeV-5.24 MeV transition. The full line represents the theoretical fit to the points for a mixing ratio x = +0.04.

160@, a)150

123

however, did not affect the analysis since we observed that the intensity of this y-ray was constant throughout the experiment, thus not altering the overall normalization. The y-ray spectra were decomposed using line shapes determined by radioactive sources (E, 6 2.7 MeV) as well as the coincident 6.18 MeV (’ ‘0) and 4.43 MeV (‘“C) peaks, which are very clean. At 10.8 MeV 3He energy the excitation of the 6.79 MeV and 6.86 MeV levels was too weak to permit the extraction of angular correlation coefficients. The measured distributions are shown in figs. 8-10 and the results tabulated in table 1. Our results for the 6.86 -+ 5.24 MeV -+ 0 cascade are in essential agreement with the work of Gill et al. *l); however, for the 6.79 MeV --+0 transition our value lies 4 standard deviations away from that of the previous work +. It was not possible to derive the mixing ratio of the 3’ --t +- transition by observing y-rays coincident with the c1i,2 p article group, as the correlation was essentially isotropic, indicating that at our bombarding energies the excitation of the 4’ state dominates. 4. Discussion Prior to the present work a number of theoretical investigations which attempted to explain the experimental result that for the +- states lx(i50)l > l~(~‘N)l were carried out. Although it was proved possible to increase somewhat the electric quadrupole matrix elements in both mass-15 nuclei by adding in collective contributions, the theoretical calculations have unanimously yielded l~(~~O)l < l~(i~N)l. In the most trivial shell-model description the E2 transition amplitude in “0 is only due to the fact that the centers of mass and charge do not coincide. The “0 amplitude is therefore due to an effective charge e/A and is much smaller than the 1‘N amplitude due to a proton hole. From this point of departure the theoretical problem is twofold -to calculate the contributions to the effective charge from the non-spherical components of the 160 core as well as to elicit a mechanism which will result, hopefully, in a considerably increased effective charge in i ‘0 relative to ’ 'N. Rose et al. ‘* “) interpreted th e smaller x(’ ‘N) as resulting from destructive interference between the collective and single-hole amplitudes in “N (the latter amplitude is absent in IsO). Both Rose et al. ‘) and Brown et al. “) have since shown, however, that the collective and single-hole amplitudes are additive. The latter authors point t In the cases where there is disagreement between the present work and other particle? angular correlation studies the anisotropies measured in the present work are larger. This corresponds to a smaller 1x1for both the 6.18 + 0 and the 6.79 + 0 transitions. Among factors which could contribute to a reduction in anisotropy attention should be drawn to recent investigations in this laboratory “) in which it is shown that the intermediate nuclear state is not always strongly aligned by light particles emerging at angles close to 180”. This phenomenon is associated with high partial wave effects. In principle, therefore, an experimental determination of the population parameters for the intermediate state is called for and this in turn can only be achieved by a simultaneous measurement on a pure multipole branch de-exciting the level in question. For the transitions considered above, no such branch is available.

124

R. AVIDA et al.

out that there are still some effects which could enhance the effective charge in 1‘0 compared to “N These are, first, a greater intrinsic quadrupole moment for the collective state of’ 15O giving rise to a collective E2 amplitude in I50 roughly double that in r5N and second, the effect that in r 5O the T = 0 and T = 1 effective

650

600

550 :

I

I

I

0

30

60

,I 90

Fig. 10. Measured angular correlation of the 5.24 MeV-0 transition with the 6.86 MeV-5.24 transition unobserved. The full line represents the theoretical fit to the points for an initial spin of +‘, x = +0.04 for the #+‘+)+ transition and x = +0.08 for the lower transition.

charges are additive while in “N they are of opp osite sign. Some of the results of their calculations are shown in table 2. Although in the case of 15O (in the notation of ref. “)) 1 = 11 MeV gives excellent agreement, the mixing ratio in 15N comes out greatly exaggerated. Moreover the trend of x as I increases suggests that this calculation in its present form cannot yield Ix(’ 50)1 > Ix(15N)I for physically reasonable values of 2. The sources of uncertainty were suggested “) to be most probably due to approximations in the calculation of the Ml amplitude, namely, neglect of the contributions of the 160 core to the Ml collective amplitude as well as the omission of an Ml effective charge. Recent electron scattering studies by Beer et al. 12) have measured directly the radiative widths in 15N and yield f(M1, 15N) = 3.4kO.7 eV. It follows from

125

the present results that the theoretical E2 collective amplitude has been seriously overestimated in both nuclei. A more careful appraisal of this work would be possible if the location and intensity of the upper pi ’ and pi ’ strengths could be accurately determined. The IPM calculations of Poletti et al. ’ “) with collective enhancements for E2 rates calculated via the effective charge approximation with B = 0.5 yield good results for all Ip shell transitions except in “0 for which they obtain x(EZ~Ml) = -0.048. In a more detailed calculation where the effects of higher (Nilsson) shells are included explicitly, albeit approximately, both A, (the isoscalar component) and 3.i (the isovector component) are enhanced by factors E, = 1 +/?,-I-/3,, El = I+ & - /?, respectively. The procedure is to include small admixtures of states from two oscillator levels higher in the single particle orbitals yielding x( “0) = -0.048 (E. -El) and x(15N) = f0.041(E,+El). Assuming r~ = -4 and keeping the AN = 2 admixture the same as for rest of lp shell yields E,, = 2.2 and E, = 0.2, or l~(“~O)l c lx(“N)/ * 0.1 in fairly good agreement with the combination of experimental results x(lSN) = f0.13 (ref. I”)) and ~(~~0) = -0.12 (present work). On the other hand the experimental result x(’ “0) = -0.17 would require .E, < 0 or /?, > I+&, If E, > El and E, > 1 the mixing ratios increase accordingly and approach the same value. It is questionable, however, whether the degree of deformation q < -4 necessary to obtain even x(’ 50, 15N) = (-0.12, +0.13) is reasonable. The experimental situation for two of the remaining three transitions in “0 and the mirror transitions in “N remains confused. For the first )’ states the rather large values of x(E3/M2) = +0,13 f0.05 [ref. 2i) ] -0.16 & 0.02 [ref. ““) J + for the ground state transitions were tentatively interpreted as due to a large component of these states being each a p:, hole coupled to the 3- state of i60. This 3- state has a strongly enhanced E3 decay to the ground state and can in fact be regarded as an octupole vibration. Indeed excitation of “N by inelastic a-particle scattering 23) shows the )’ state at 7.15 MeV to be excited in a manner similar to the 3- state. Recently, however, Siefken et al, 24) in a y-y angular correlation experiment obtained x(15N) = -t-0.02+0.02 in disagreement with the work of ref. ‘“)_ Our own result ~(“0) = f0.08 to.08 is not sticiently accurate to lend weight in either direction. The M2/El mixing ratios for the 6.79 MeV and 7.30 MeV transitions in “‘0 ’ 5N have been previously measured to be -0.10+0.02 [ref. ““)I and -0.07&0.02 [ref. 22)] respectively, indicating exceptionally high El retardation in a non-zelfconjugate nucleus. Our own results ~(~~0) = -0.02f0.02 and the results of Siefken et al. ““) who obtain x(l 5N) = -0.05 f0.03 suggest a smaller degree of El retardation. In the calculations of Brown et al. ‘) the wave functions obtained by admixing Ip-2h and 3p-4h states did not even crudely reproduce the experimental t In ref. 22) x(15N, E3/M2) = -+-0.16&0.02 is reported, using the phase convention of Rose and Brink “). This erroneous positive phase is in error and is corrected in a later publication “1 where the authors quote x(~~N, E3/M2) = -0~16~0.02.

126

R. AVIDA et al.

El transition determination

probabilities

for the positive

parity

states. Obviously

an experimental

of the widths of these states would be highly desirable.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25)

D. Kurath et al., Phys. Rev. 101 (1956) 216; 106 (1957) 975; Nucl. Phys. 73 (1965) 1 E. C. Halbert and J. B. French, Phys. Rev. 105 (1957) 1563 D. R. Inglis, Rev. Mod. Phys. 25 (1963) 390 A. M. Lane, Rev. Mod. Phys. 32 (1960) 519 A. P. Shukla and G. E. Brown, Nucl. Phys. All2 (1968) 296 E. K. Warburton, P. D. Parker and P. F. Donovan, Phys. Lett. 19 (1965) 397 H. J. Rose and J. S. Lopes, Phys. Lett. 18 (1965) 130 H. J. Rose, J. S. Lopes and W. Greiner, Phys. Lett. 19 (1966) 686 H. J. Rose and J. S. Lopes, Phys. Lett. 22 (1966) 601 J. S. Lopes, 0. Hlusser, H. J. Rose, A. R. Poletti and M. F. Thomas, Nucl. Phys. 76 (1966) 223 A. R. Poletti, E. K. Warburton and D. Kurath, Phys. Rev. 155 (1967) 1096 G. A. Beer, P. Brix, H.-G. Clerc and B. Laube, Phys. Lett. 26B (1968) 506 B. Povh and D. F. Hebbard, Phys. Rev. 115 (1959) 608 Y. S. Horowitz, D. B. McConnell, J. Ssengabi and N. Keller, Nucl. Phys. A151 (1970) 161 A. E. Litherland and A. J. Ferguson, Can. J. Phys. 39 (1961) 788 H. Frauenfelder and R. M. Steffen, in Alpha-, beta- and gamma-ray spectroscopy, ed. K. Siegbahn (North-Holland, Amsterdam, 1965) p. 1192 A. R. Rutledge, Atomic Energy of Canada Ltd. Report CRP-851 (1959) H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 S. Gorodetzky, R. M. Freeman, A. Gallman and F. Haas, Phys. Rev. 149 (1966) 801 E. K. Warburton, J. W. Olness and D. E. Alburger, Phys. Rev. 140 (1965) B1202 R. D. Gill, J. S. Lopes, B. C. Robertson, R. A. I. Bell and H. J. Rose, Nucl. Phys. A106 (1968) 678 0. Hlusser, R. D. Gill, J. S. Lopes and H. J. Rose, Nucl. Phys. 84 (1966) 683 A. Bussiere et al., Phys. Lett. 16 (1965) 296 H. E. Siefken, P. M. Cockburn and R. W. Krone, Nucl. Phys. Al28 (1969) 162 Z. Berant et al., Nucl. Phys., to be published