Lifetime measurements in sd-shell nuclei

Nuclear Physics A147 (1970) 225--234; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout writtenpermissionfrom the publisher

LIFETIME MEASUREMENTS IN sd-SHELL NUCLEI m.

M e a n lives of S2p levels

G. VAN MIDDELKOOP and C. J. Th. GUNSING Robert J. Van de Graaff Laboratorium, Rijksuniversiteit, Utrecht Received 26 February 1970

Abstract: The 29Si(~, pT)32P reaction was used to study the y-ray decay and the lifetimes of seven bound states of 32p. A new level was found at E~ = 2216.5 -4-1.0 keV. Gamma rays were simultaneously measured in coincidence with protons detected at angles 0p = 110° and --110° or 45° and --45 °. From these Doppler-shift attenuation measurements the mean lives of the 0.51, 1.15, 1.32, 1.76, 2.18, 2.22 and 2.23 MeV levels were found to be 3000-4-850, 2704-65, 3804-80, 5104-110, 604-25, 2104-50 and 364-20 fs, respectively. A previously reported level at E~ = 1.51 MeV was not observed The data are compared with recent many-particle shell-model calculations. NUCLEAR REACTIONS 2 s , 295i(0~, lyy), E = 7.00, 9.00 and 11.00 MeV; measured Doppler shift attenuation. 3t, a2p deduced levels, T¢,7-branchings. Enriched target.

1. Introduction Extensive shell-model calculations 1, 2) were recently performed in the mass region A = 30-34. E x p e r i m e n t s involving the d e t e r m i n a t i o n of spectroscopic factors in stripping a n d p i c k - u p reactions, as well as the m e a s u r e m e n t of lifetimes, clearly d e m o n strate the success o f these calculations. However, it was also shown 2) that the lifetime calculations o f 1 + states in d o u b l y odd nuclei sometimes seriously disagree with experiment. It was therefore t h o u g h t worthwhile to measure lifetimes a n d b r a n c h i n g ratios in the d o u b l y odd nucleus 32p. States i n 32p were p o p u l a t e d with the 29Si(~, p)32p reaction. The (~, p) reaction was preferred over the (d, p) reaction, since deuterons incident o n a c a r b o n - b a c k e d target yield a high n e u t r o n b a c k g r o u n d . C a r b o n is at present the most suitable b a c k i n g material i n Doppler-shift a t t e n u a t i o n measurements, since its slowing-down properties for various ions are k n o w n experimentally. G a m m a rays were simultaneously measured in coincidence with protons, detected at two different angles. I n this way, recoiling nuclei with definite velocities a n d directions were selected. I n order to ensure that the c o n t r i b u t i o n of n u c l e a r scattering d u r i n g the slowing-down process of the nucleus is small, initial velocities between v/c = 0.7 × 10 - 2 a n d 1.0x 10 - 2 were selected. 225 May 1970

226

G. V A N M I D D E L K O O P A N D C. J. T h . G U N S I N G

2. Experimental procedure The general e x p e r i m e n t a l p r o c e d u r e is described in ref. 3), hereafter referred to as I. Some details relevant to the present e x p e r i m e n t will be given here. A l p h a - p a r t i c l e s were accelerated with the U t r e c h t 2 x 6 M V t a n d e m Van de G r a a f f accelerator to energies o f 7.00, 9.00 or 11.00 MeV. The b e a m was focussed on the target t h r o u g h a 3 m m diam. d i a p h r a g m a n d caught in a r e m o t e F a r a d a y cup b e h i n d a concrete wall. Currents o f 300 n A o f d o u b l y c h a r g e d 4He ions were obtained. x 102 10

d LU Z

z

-r u IT hi

I-

1.76.31P(2)

2.23 2.22 218

L

i

I

29 Si(a,p) 32p E~.=9.00 MeV

Q08 0

0P =45°

Ji

8

a_ 6 1.51 1.32 135 31p(1) 0:51

I-Z

~

3!P(0)

8(3 4

0

I 20O

300

400

500 CHANNEL NUMBER

F i g . 1. P r o t o n s p e c t r u m f r o m the 2 9 S i ( 0 ~ , p ) 3 2 p r e a c t i o n a t Ec~ = 9.00 M e V , 0 o = 45 °. T h e t a r g e t w a s 1 0 0 / ~ g / c m 2 295iO2 o n 230 # g / c m 2 C. A 60 # m t h i c k AI a b s o r b e r w a s used.

F o r the lifetime measurements, two 2 m m thick Si surface barrier detectors were p o s i t i o n e d at angles o f 110 ° a n d - 1 1 0 ° or 45 ° a n d - 4 5 ° with respect to the beam. The o p e n i n g angles were limited to 8.6 ° a n d 17 ° in the h o r i z o n t a l reaction plane a n d in the vertical direction, respectively. The detectors were shielded against elastically scattered c~-particles by A1 foils. The 36 cm 3 true-coaxial G e ( L i ) detector was p l a c e d a t 0~ = 90 °, at 6.5 c m f r o m the target a n d h a d a r e s o l u t i o n o f 3.5 keV F W H M at E~ = 1 MeV. Fig. 1 shows a particle s p e c t r u m o b t a i n e d at 0p = 45 °. The a b s o r b e r in front o f the d e t e c t o r is 60 p m thick. The F W H M o f the p e a k s is a b o u t 100 keV, 70 % o f which is due t ~ straggling in the A1 foil. F o r the m e a s u r e m e n t s o f b r a n c h i n g ratios a 1.5 m m thick Si surface barrier a n n u l a r detector was used at 0p = 180 °. P r o t o n s were detected between 0p = 169 ° and 175 °. The 7-ray d e t e c t o r was set at 0 r = 55 ° at a distance o f 4 cm f r o m the target. Coincidences between the y-ray c o u n t e r and the Si counters were detected with conventional timers a n d t i m e - t o - a m p l i t u d e convertors. The time gate was set 40 ns wide.

32p LEVELS MEAN LIVES

227

Various targets were used. For the lifetime measurements 100 or 240 pg/cm 2 29SIO2, enriched to 92 % in 29Si, was evaporated onto 230 pg/cm 2 thick carbon foils. The thicknesses of targets and backings were determined by measuring the energy loss of e-particles from a mixed 241Am-/g4cm source. For recoil velocities higher than vie = 0.86 x 10- 2, the targets were tilted over 45 ° to make sure that all recoils stopped in the target backing. For the measurement of branching ratios and y-ray energies, the target consisted of two self-supporting layers of about 80 pg/cm 2 29SIO2 each, at a mutual distance of 1 mm.

3. Interpretation of the Doppler-shift measurements 3.1. EXPERIMENTAL F-VALUES Peak positions in the coincident 7-ray spectra were determined from first-moment calculations. For peaks superimposed on a Compton tail of a higher-energy y-ray, this tail was first subtracted. Before and after each run the energy dispersion was determined with standard radioactNe sources. The full geometrical shift, AE~ = 2E~v/c sin 10roll sin 0~ (see also I), where 0r~c and 0~ are the angles with respect to the beam at which the nuclei recoil and the y-rays are observed, respectively, was computed including effects due to finite detector solid angles 4). Effects due to proton angular distributions and (p, 7) correlations were neglected, see also I. The F-values, defined as the measured shift divided by the full geometrical shift, determined in the present experiment are listed in table 1. 3.2. CALCULATION OF THE F-CURVES The function F(rm), defined in I, eq. (3), is computed according to Blaugrund 5), who used the stopping theory developed by Lindhard et al. 6). The slowing-down due to nuclear collisions is approximated by eq. (4) of I. The electronic part of the slowingdown process, which is dominant at ion velocities used in the present experiment, can be written 6) as :

where e and p are dimensionless quantities for energy and distance and k = 0.0793~ Z~Zz(A1 +A2)~I

(ZI + Z1) A,A2

(2)

The indices 1 and 2 refer to the ion and stopping material, respectively. Theoretically 6), ¢, = Z~, which gives ¢~ = 1.57 for 32p. Experiments by Ormrod et al. v) and Fastrup et al. 8), who measured the electronic stopping cross section for various ions in carbon as a function of ion velocity, show that ¢~(Z I) oscillates around

228

G. VAN MIDDELKOOP

A N D C . J. T h . G U N S I N G

the value Z~, and also that ~ generally depends on the ion velocity. The results of Ormrod et al. 7)indicate that 4o is independent of Z2. The quantity ~, is calculated 7) from the experimental electronic stopping cross section Se by means of the expression S~ = 1.916~,

Z1Zz

137v eV. cmZ/atom.

(3)

c

For v/c = 0.003-0.008, it is found from ref. 8) that for a2p slowing-down in carbon, ~o can be approximated by a linear expression

~ = 1.57+38.1v/c,

(4)

whereas Ormrod et al. 7) found ~e = 1.60 at v/c = 0.003, and about the same velocity dependence for v/c < 0.003. In the calculation of the F-curves, expressions (1) and (2) were used with ¢~ as given by eq. (4), for 32p ions slowing-down in C as well as in 295iO2. The F-curves for C and 295iO2 were found to yield mean lives identical to within 5 %. Therefore, the contributions to the F-curve of the target and backing material were not separately calculated. 3.3. ERRORS ASSIGNED TO TI-IE MEAN LIVES The total systematic error of 20 % in the deduced mean lives is composed of the following sources of error. (i) The, mainly systematic, experimental error in Se, thus also in ~e, was estimated 8) to be 8 %. (ii) A systematic error of 5 % is estimated in the extrapolation of ¢~, as given in eq. (4), for v/c > 0.008. (iii) The 8 % uncertainty in the density of the carbon backings (see also I). (iv) The uncertainty due to slowing-down in SiO2, of which no experimental data exist, is estimated to be 15 %. Errors due to uncertainties in the treatment of large-angle nuclear scattering were neglected since nuclear stopping contributes little. The mean lives, Zm, given in table 1 are deduced from the carbon F-curves. The errors given are the result of quadratic addition of the statistical error, which is directly related to the standard deviation in F, and the 20 % systematic error. 4. Determination of ~,-ray energies and intensities

Gamma-ray energies and intensities were measured at 0~ = 55 °, coincident with protons detected at 180 ° (sect. 2). The e-particle energy was 11.0 MeV. The energies of the v-rays were determined from a third-order polynomial fit (channel number vs. energy) to a number of accurately known v-ray energies 9) in 32p and differences between full-energy and double-escape peaks. The energies obtained, as

32p LEVELS MEAN LIVES

229

well as the calibration energies, were corrected for Doppler shifts, which were mostly unattenuated since thin self-supporting targets were used, and the initial recoil velocity was high (v/c ~ 1.3 %). For long-lived states the attenuation of the Doppler shift was taken into account. The accuracy of this procedure amounts to about 1 keV. Peak areas were computed by first subtracting the total Compton tail of higherenergy y-rays, which was estimated at the high-energy side of the peak. Upper limits were obtained in the following manner. Where peaks could be expected, the " p e a k " area was computed. In case this area was positive and its error more than half its value, the upper limit was taken equal to the area plus one standard deviation. I f the area came out negative, the upper limit was set equal to two standard deviations. The efficiency calibration of the Ge(Li) detector was obtained from a y-ray spectrum taken with a set of accurately calibrated standard radioactive sources as well as with a 5 6Co source. The estimated error in the relative intensities obtained with this calibration is 5 %.

5. Results 5.1. M E A N LIVES

A summary of the lifetime measurements in 32p is presented in table 1. The measurements on the 0.51 and 1.15 MeV levels were carried out at E~ = 7.00 MeV. The contribution of annihilation radiation due to accidental coincidences is less than 2 %. TABLE 1 S u m m a r y o f Doppler-shift m e a s u r e m e n t s /?xl(a2P) (MeV) 0.51 1.15 1.32 1.76 2.18 2.22 2.23

Ext

T a r g e t a)

(MeV)

v/c b) (~)

Full shift (keV)

0 0.08 0.51 0 0.08 0.08 0.08 0 0.08

1 2 2 1 1 1 2 2 2

0.882 0.867 0.867 1.001 1.001 0.992 0.702 0.702 0.702

2.34 4.34 2.58 6.86 6.46 8.21 8.06 8.45 8.20

0 0

1 1

1.045 1.024

7.23 11.32

F (%) 13.3 4-2.5 68 4-4 } 65 4-6 60.64-2.0 / 57.04-2.4 J 50.34-2.2 90.94-2.6 71 4-4 94.1 4-2.5

Tm (fs) 3000zk850 2704- 65

3804- 80 5104-110 604- 25 2104- 50 364- 20

Exi(31P) (MeV) 1.27 2.23

44 65

4-7 4-4

6504-220 3004- 85

a) T a r g e t 1 : 2 4 0 flg/cm 2 29SIO2 o n 230/zg/cm z C; target 2 : 1 0 0 # g / c m 2 29SIO2 o n 2 3 0 / z g / c m 2 C. T h e target was tilted over 45 ° for all m e a s u r e m e n t s with v/c ~> 0.8 %. b) Relative velocities v/c = 0.702 % c o r r e s p o n d to 0 v = 4-45 °, the others to 0p = 5:110 °. F o r the Ex = 0.51 a n d 1.15 M e V levels E~ = 7.00 MeV, for the other levels E~ = 9.00 M e V was used.

230

G. VAN MIDDELKOOP AND C. J. T h . GUNSING i

.J ILl Z

i

I

28' 29Si (~,p,y)31,32 P

e~ =110°~.[L

80

z< q.(j n.-

F

40

Ea.=9.00 MeV

60

176

30

2,23

40

20

../)

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20

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0 (J

0

I

. ~11 i i

i

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I

I

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20

l

40

I

J

20

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0

1~o

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12oo

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1740 1760 CHANNEL NUMBER

Fig. 2. Spectrum ofT-rays m e a s u r e d in coincidence with p r o t o n s (at 110 ° a n d --110 °) leading to the 1.76 a n d 2.23 M e V states in 32p a n d alp, respectively. Initial recoil velocities were v/e = 0.99 % a n d 1.02 ~o for 32p a n d atp, respectively. T h e dispersion was 1.00 channel/keV; the target consisted o f 240 fig/era 2 29SIO2 o n 230 ffg/cm 2 C.

I

80 Z Z < -r

60

hi n 'J3 I,Z

20

I

I

ep = 4 5 ° n 2.18 ~ Q 0 8

I

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I

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29Si(¢.p'y)32p ~~=_ 9 O0 M e V

u n.. 4 0

0 (J

0 8O

IJ

• e.:-W'

i

I

I

v=c91;3)O/o

I

i

/;t

{I I

'-F=(94-*3)%

~l

I

i-! F=(71t4)%

60 4O 20 I

1560

I

1580

r//

I

1600

1620

1640

" 1 -

1680 1700 CHANNEL NUMBER

Fig. 3. Spectrum o f T - r a y s m e a s u r e d in coincidence with p r o t o n s (at 45 ° a n d --45 °) leading to the 2.2 M e V triplet. T h e initial recoil velocity was v]c = 0.70 %; the dispersion was 0.98 channel/keV. T h e target consisted o f 100 # g / c m 2 29SIO2 on 230 ffg]cm 2 C.

231

32p LEVELS MEAN LIVES

A t this energy the excitation o f the second level (E, = 0.51 M e V ) was strong e n o u g h to yield an a c c u r a t e m e a s u r e m e n t o f the F-value. A l s o , thin a b s o r b e r s c o u l d be used. Consequently, the p r o t o n g r o u p feeding the Ex = 1.15 M e V level c o u l d be well separated f r o m p r o t o n s l e a d i n g to the E , = 1.32 M e V state. All o t h e r runs were p e r f o r m e d a t E , = 9.00 MeV. Fig. 2 shows p a r t o f the y-ray spectra m e a s u r e d in coincidence w i t h ' p r o t o n s p o p u l a t ing the E~ = 1.76 M e V level. P r o t o n s feeding the second excited state in 3~p ( t h r o u g h J

i

i

i

*

29Si (o',P'Y)3:zp 400

I

i

i

893

E==11.0 MeV ep =180% e v = 5 5 =

300

513

5,1 !

z z

I

200

I.)

u~ a. 1 0 0 0 U

o

°~*

0

. . . .

2~° ~ I

- -

636

r~,

~,.~=

~

2217" oJ~®=Jlo

'~ '

46o

I I

1068

]

i

l

f

i

J

2097 2 0 0 L- 1324

! 0 1

tI I 1000

221,, I 1100

I 1200

I 1300

12, 1217,a I 1400

I 1500 --

I 1600 ~

-

~'D . . . . 1700 CHANNEL NUMBER

Fig. 4. Spectrum ofT-rays coincident with protons to the Ex ~ 2.2 MeV triplet measured at 07 = 55 ° and 0p = 180°. Four channels are averaged in the regions in between peaks. The target consisted of two 80/~g/cm 2 self-supporting 295iO2foils. The measuring time was 50 h with a beam current of 200 hA.

the 28Si(~, p)31p reaction, due to 8 % 2Ssio2 in the target) have a b o u t the same energy, hence also the 31p 2.23 --+ 0 M e V t r a n s i t i o n was detected. In fig. 3 spectra o f y-rays c o i n c i d e n t with p r o t o n s to levels at Ex ~ 2.2 M e V are shown. Here, several previously u n r e p o r t e d y-rays were observed, two o f which, the 2.14 a n d 2.22 M e V 7-rays, are p r i m a r i e s f r o m a new level at E~ = 2.22 M e V (see also subsect. 5.2). T a b l e 1 includes presently m e a s u r e d m e a n lives o f the first two excited states in 31p. T h e m e a n life d e t e r m i n e d for the first excited state agrees with the weighted average o f f o r m e r results a o - 12) (760+_ 50 fs), whereas the m e a n life o f the second level is f o u n d

O. VAN MIDDELKOOP AND C. J. Th. GUNSING

232

to be somewhat lower than the average o f previously reported i 0 - 1 2 ) mean lives (410___20 fs). 5.2. GAMMA-RAY DECAY T w o y-ray spectra were simultaneously measured in coincidence with protons leading to the E~ = 1.76 MeV state and to the levels at E~ ~ 2.2 MeV. The latter spectrum is shown in fig. 4. The peaks are somewhat Doppler-broadened ( ~ 2 keV at 2 MeV), due to the solid angle o f the p r o t o n detector. 1;m (f s)

a) EXPERIMENT 2.230

36t20 21 0t50 60225

+ 1

1C~

<1

,, ol

<3

11

1.324

T

510t110

1.72 1.64

6

3* 2*

i iiol i

i

!

1

1"8 ;

c~

X=

1,149 62t3 38t3 • 811 4 =3 52:3


~

"¢rn (f s)

2.10 _/z/-.08

2;1Q3

l X-°0DA5 =

3t

b) THEORY

1+ 9" 575

7

380±80

1+ 270t65

1.14

09,

gl

!

I

13 67 20 0.513 1~l

1

1

2* 588 1" 281

O÷ 3000±850

(10781

O.le

100

|

:2

2* 49x10S 1"

2* (3.1tl,0)x105

1"

32p

0" 33x104

32p

Fig. 5. a) Excitation energies, branching ratios and lifetimes in 32p, determined experimentally. Most of the excitation energies are from ref. 9). The spins are from refs. 1o. 13), and the mean life of the first excited state from refs. 14.15). The sign convention for the mixing ratio 13) is that of ref. 2). b) Many-particle shell-model calculation 2) for ~2p. Mean lives and branchings were computed with experimental excitation energies. The decay of the first 3 + state, not given in ref. 2), was calculated with the shell-model wave functions and the program used by Glaudemaus et aL 2). Octupole transitions are not included in these calculations.

A new level at Ex = 2216.5_+ 1.0 keV was added to the 32p level scheme to explain the 2217, 2139, 1068 and 893 keV y-rays. The intensity o f the 2217 ~ 1324 keV transition (E7 = 893 keV) agrees very well with the total intensity o f y-rays deexciting the 1.32 MeV level. The peak at about 1070 keV in fig. 4 is due to 1068 and 1071 keV 7-rays, f r o m the 2217--+ 1149 and 1149 ~ 78 keV transitions, respectively. This follows f r o m the k n o w n branching o f the 1149 keV level 9). The intensity o f the 1071 keV 7-ray was calculated f r o m the intensity o f the 636 keV y-ray. The intensity remaining for the 1068 keV ~-ray equals the intensity deexciting the 1.15 MeV level, within the error.

32p LEVELS

MEAN LIVES

233

This measurement also yields E~ = 2175.3_+ 1.0 keV for the level previously reported lo) at Ex = 2177+4 keV. The branching ratios and upper limits for weak transitions are given in fig. 5a. The upper limits given for the 1.32 ~ 0.51, 1.32 ~ 1.15 and 0.51 ~ 0.08 MeV transitions were deduced from measurements at 0p = ___110 ° and 0 r = 90 °. The ?-ray branching from the E~ = 1.32 MeV level presently obtained agrees very well with the known branching 9). 6. Conclusion The results of the present work are condensed in fig. 5a. The branching ratio of the Ex = 1.15 MeV state, as well as the excitation energies are from ref. 9), except for the Ex = 2.18 and 2.22 MeV levels (see subsect. 5.2). The spins were known lo, 13), as well as the mean life of the first excited state 14,15). No evidence was found for the existence of a level 16) at E x = 1.51 MeV. The ratio R of the intensities of protons to this level and to the 1.32 MeV level was R < 0.03 and R < 0.04 at E, = 9.00 and 11.00 MeV, respectively. The 1.51 MeV level reported from (d, p) work 16) is very probably due to the 28Si(d, p2)29Si reaction. The energy of the P2 group of this common contaminant fits to within 5 keV with the proton group to the "1.51" MeV level, which is well within the experimental error of 20 keV. The doublet at Ex = 2.22 and 2.23 MeV was not resolved in published (d, p) work. The energy was reported 17) as 2223 _+4 keV, which is the average energy of the two levels. Fig. 5b shows the 32p level scheme as obtained by Glaudemans et al. 2) from MSDI shell-model calculations. In the calculation of the transition probabilities, effective g-factors and charges were used as well as experimental excitation energies. Excitation energies and spin values are generally well reproduced. Recently, Moss et al. 13) argued that from the 1, = (3) assignment 18) to the Ex = 1.32 MeV level and the lp = 3 assignment 19) to its assumed analogue in a2S, and from (~, p?) angular correlation measurements, the spin and parity of this 32p level would be J~ = (2-). From the data given in ref. 16), however, it can be shown that the spectroscopic factor for stripping leading to the E~ = 1.32 MeV level is about a factor of five smaller that for its analogue in 32S. Also, an 1 = 3 assignment to the E~ = 1.32 MeV level implies, since 9, 13) j = (2), that this is a f~ state, which is quite improbable. Therefore, one can conclude that there is little evidence yet to assign odd parity to 32p*(1.32). The calculated lifetimes and branchings reasonably agree with the observations, except for the lifetime of the second excited state, which is off by a factor of ten. This state decays entirely to the 1 + ground state. One should note, that the calculated mean life of the 1 + state at 1.15 MeV agrees perfectly with experiment. The branching ratio is not so well predicted. The best agreement between theory and experiment is observ-

234

G. VAN MIDDELKOOP AND C. J. Th. GUNSING

ed for the J = 3 state. Here, the p r e s u m a b l y faulty wave functions o f the 1 + states hardly influence the calculated lifetime and branching. T h e au t h o rs wish to t h a n k Profs. P. M. E n d t and A. M. H o o g e n b o o m for stimulating discussions a n d critical reading o f the manuscript, an d Dr. P. W. M. G l a u d e m a n s fo r p e r f o r m i n g some o f the theoretical calculations an d for his c o n t i n u o u s interest in this work. Th e help o f F. E. H. van Eijkern in the data analysis is gratefully ack n o w l ed g ed. This investigation was partly s u p p o r t e d by the j o i n t p r o g r a m o f the " S t i c h t i n g v o o r F u n d a m e n t e e l O n d e r z o e k der M a t e r i e " and the " N e d e r l a n d s e Organisatie v o o r 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) 19)

B. 14. Wildenthal et al., Phys. Lett. 27B (1968) 611 P. W. M. Glaudemans, P. M. Endt and A. E. L. Dieperink, to be published G. A. P. Engelbertink and G. van Middelkoop, Nucl. Phys. A138 (1969) 588 G. van Middelkoop and G. A. P. Engelbertink, Nucl. Phys. A138 (1969) 601 A. E. Blaugrund, Nucl. Phys. 88 (1966) 501 J. Lindhard, M. Scharff and 14. E. Schiott, Mat. Fys. Medd. Dan. Vid. Selsk. 33 (1963) No. 14 J. I-L Ormrod, J. R. MacDonald and 14. E. Duckworth, Can. J'. Phys. 43 (1965) 275 B. Fastrup, P. 14velplund and C. A. Sautter, Mat. Fys. Medd. Dan. Vid. Selsk. 35 (1966) No. 10 G. van Middelkoop, Nucl. Phys. A97 (1967) 209 P. M. Endt and C. van der Leun, Nucl. Phys. A105 (1967) 1 A. C. Wolff, M. A. Meyer and P. M. Endt, Nucl. Phys. A107 (1968) 332 W. M. Currie, L. G. Earwaker, J. Martin and A. K. Sen Gupta, Phys. Lett. 28B (1969) 480 C. E. Moss et al., Nucl. Phys. A144(1970) 577 R.. A. Mendelson and R. T. Carpenter, Phys. Rev. 165 (1968) 1214 D. M. Gordon and R. W. Kavanagh, Bull. Am. Phys. Soc. 13 (1968) 1663 T. Holtebekk, Nucl. Phys. 37 (1962) 353 D. Piraino, C. H. Paris and W. W. Buechner, Phys. Rev. 119 (1960) 732 I. B. Teplov, ZhETF (USSR) 31 (1956) 25; JETP 4 (1957) 31 A. Graue et al., Nucl. Phys. A120 (1968) 513