Angular distributions of the 2h(d, γ)4he reaction

Nuclear Physics A199 (1973) 517--529; (~) North-Holland Publishing Co., Amsterdam Not to be reproducedby photoprint or microfilmwithout written permissionfrom the publisher

A N G U L A R D I S T R I B U T I O N S OF T H E 2H(d, ?)'*He R E A C T I O N J. M. POUT1SSOU and W. DEL BIANCO t Laboratoire de Physique Nucldaire, Universitd de Montrdal, Montrdal, Quebec, Canada

Received 10 October 1972 Abstract: Angular distributions ofT-rays from the 2H(d,~')*He reaction have been measured at the deuteron energies Ea = 6.05, 8.96 and 11.67 MeV with a 12.7 cm× 15.2 cm NaI(TI) crystal enclosed in a Cerenkov anticoincidence shield. A least-square fit of the angular distributions indicates that the differential cross section is proportional to sin20 cos20 and that the process proceeds through an E2 transition of the type 1D2 --~ 1So. !

E[

I

NUCLEAR REACTIONS

2H(d,~))4He,

g :

4-12.5

Enriched gas target.

MeW;

measured o'(E, 0).

/

/

1. Introduction

The giant resonance of 4He has been the object of several experiments in recent years I). The predominant process, the (7, P) reaction has been extensively investigated over a wide range of ?-ray energies and found to proceed mainly through an electric dipole transition 2). The 4He(?, d)2H reaction and its inverse are more difficult to determine experimentally because of the small cross section (a ~ 3.2/~b at E~ = 28.9 MeV) and concurrent large backgrounds; thus relatively fewer data are available for this process. The experimental results have recently been reviewed by Skopik and Dodge 3). For ?-ray energies below 30 MeV, the 2H(d, ?)4He reaction has been measured and the cross section for the inverse process obtained by means of the principle of detailed balance. The measurements of Degr~ 4), Poutissou and Del Bianco 5, 6), and of Meyerhof et al. 7) using monoenergetic deuteron beams from Van de G r a a f accelerators and high-efficiency, good resolution ?-ray detectors are in fair agreement within the experimental errors. Skopik and Dodge 3) have determined the 4He(e, e'd)2H process and related its cross section to that of the 4He (?, d)2H reaction in the energy range E~ = 37.4 to 49.4 MeV. Their data do not overlap the lower energy ones; however, by extrapolation, the two results join. At higher ?-ray energies there still is a dearth of experimental data and inconsistencies. In fact the cross section has only been measured at the energies E~ = 220.5, 225. I, 255.3 and 265.3 MeV, and the more recent experiment of Asbury and Loeffler s) yields cross sections an order of magnitude smaller than those of Akimov et al. 9) and of Poirier and Pripstein i o). In most of the experiments the differential cross section was t Research supported by a grant from the National Research Council of Canada. 517

518

J.M. POUTISSOU AND W. DEL BIANCO

measured at one angle and the total cross section obtained by integrating over the solid angle and assuming an electric quadrupole transition. To date only one complete angular distribution measurement exists at E d = 3.68 MeV and is consistent with the above assumption 4). This article reports the experimental determination of the 2H(d, ~)4He angular distributions at the deuteron energies E a = 6.05, 8.96 and 11.67 MeV. Since 4I-Ie isa sell-conjugate nucleus, charge independence of nuclear forces prevents the occurrence of E1 transitions and requires that the strength of M1 transitions be reduced by roughly a factor of one hundred; in addition the identity of the two particles in the entrance channel restricts the number of allowed initial states. Hence in the longwavelength approximation, if one considers multipole transitions of order smaller or equal to two, E2 1D z ~ 1S o transitions are favored. Independently of the above hypothesis, if one assumes that nuclear forces are central, a more restrictive result is obtained; that is, only 1D2 ~ tSo transitions can occur and the angular distribution is proportional to sin 2 0 cos 2 0. Thus one is presented with the possibility of measuring a rare E2 photonuclear process and of testing the validity of isospin selection rules for e.m. transitions in a self-conjugate nucleus concurrently with the central force hypothesis for a 1S shell nucleus.

2. Experimental apparatus and methods The deuteron beam from the Universit6 de Montr6al tandem accelerator was used at energies E d = 6.05, 8.96 and 11.67 MeV with currents of the order of 500 nA. The beam after magnetic analysis and collimation by tantalum diaphragms was allowed through a 4 cm long gas target and came to rest under vacuum on a T a disc at approximately 50 cm from the target. The gas target consisted of a hollow aluminum cylinder with a 6.35 x 10 - 4 cm thick Ta foil at each end and was filled to a deuterium pressure of 84 cm Hg. It was enclosed in a high-vacuum chamber designed to operate at pressures lower than 5 × 10- 7 Torr and to present a small uniform absorption for ~-rays in the angular internal from 30 ° to 150 °. A special feature of the chamber was the possibility of replacing the target without affecting the vacuum (fig. 1). The capture ~-rays were detected with a 12.7 cm diameter by 15.2 cm long NaI(TI) crystal viewed by a Philips XP 1040 photomultiplier tube. The crystal was collimated and placed with its front face at 67.5 cm from the target. It was enclosed in a Cerenkov anticoincidence shield to reduce the cosmic-ray background and surrounded by a 10 cm thick lead shield and a 50 cm thick boron loaded parattin layer to minimize background radiation (fig. 2). The assembly of detector and shielding was mounted on a table 1~) of dimensions 180 cm x 180 cm, rotating through art angle of 360 °. Special care was taken to stabilize the gain of the photomultiplier tube. A voltage divider carrying a quiescent current of 12 m A and with the last stages coupled to Zener diodes was found to perform satisfactorily at counting rates as high as 7 x 104 cps.

2H(d,~,) A N G U L A R DISTRIBUTIONS

519

The anticoincidence shield has been described in a previous article 12), In this experiment an improved version was used. Its essential features are a reduction of the cosmic-ray background by a factor 40 in the y-ray energy interval from 20 to 30 MeV and its insensitivity to within 2 % to escape radiation from the NaI crystal.

',----- COLD CATHODE GAUGE

0.95 cm D COLLIMATOR

J TO FARADAYCUP

ISOLATING U ~ . . ~ FLANGE

~_~.~

"ISOLATING FLANGE TARGET CHAMBER

GAS TARGET

--VALVE CVC

-

FORE VACUUM CHAMBER

-FORE VACUUM INLET

THERMOCOUPLE GAUGE

T'''"~

TEFLON SLIDING SEAL

--SCALE

t--TO

FILLING STATION

Fig. i. Target chamber and gas target assembly.

I 12.5cm,

520

J. M. POUTISSOU AND W. DEL BIANCO

Standard electronics was employed to analyse and record the y-ray pulses and an on-line CDC-3100 computer controlled the data acquisition of the experiment. The electronics block diagram is shown in fig. 3. ADC 1 recorded the y-ray spectrum from the NaI crystal less the cosmic-ray background. Reduction of dead time in A D C I was effected by selecting pulses above a fixed threshold by means of a linear gate and a single-channel analyser (SCA). An accurate correction of the dead time of the SCA and the A D C was obtained by the counts recorded in scalers 2 and 3. The "low-low" pile-up spectrum present in the high-energy portion of the ?-ray spectrum was recorded in ADC 2. The design of the "low-low" pile-up detection circuit is similar to that described by Blatt et al. 13). We refer to that article for details on this points. The

I BEAM

l/T E,T k T OR N*2 LIQNITROGEN TRAP7 ~IB J ~ ,/TARGET

O ~ I L DIFFUSION M ~pL~ p )IFFUSION P U ~

IlL

T

GAS TARGET 2"VALVE

-

PAR-A~IN--- ----; - ;

- --: - -- -- -- - _--~- _-.

.................

FARADAY C

Fig. 2. Overall view of gas target, target chamber, andT-ray detector.

"Cerenkov" linear signal was set in coincidence with crystal pulses above E~ = 10 MeV and recorded in ADC 3. As this spectrum is broadly peaked 12), it provided a convenient means for testing the correct functioning of the anti-coincidence shield. A typical 2H(d, y)4He spectrum obtained at E a = 8.9 MeV is shown in fig. 4. The absolute y-ray yield was obtained by subtracting the empty gas target spectrum from the full gas target spectrum and by adding the number of counts above a fixed bias after correction for the "low-low" pile-up contribution and cosmic-ray background. To obtain the shape of the y-ray spectrum, 3H(p, y)4He spectra, recorded at various energies between Ep = 3 and 10 MeV, were employed and extrapolated at low energies with a straight line through the origin 1a). These spectra were also used to check the linearity and calibration in energy of the y-ray detector. The differential cross section da/dto was measured at the deuteron energies E a = 6.05, 8.96 and 11.67 MeV and at the lab angles 0L = 0 ° and 40 ° to 130° in steps of 10 °. The deuteron energies refer to the energies at the center of the gas target. The

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522

J.M. POUTISSOU AND W. DEL BIANCO

energy loss of the d e u t e r o n b e a m at the three energies a m o u n t e d to 50, 40 a n d 30 keV, respectively. The m e a s u r e m e n t s at the angles from 40 ° to 130 ° were all made in the same experimental c o n d i t i o n s thus assuring the same geometry a n d ?-ray absorption. Only at 0L = 0 ° was it necessary to modify the experimental set-up a n d the shielding of the ?-ray detector was increased to reduce the intense b a c k g r o u n d rad i a t i o n at forward angles. The charge accumulated at each angle varied from 12-24 m C a n d the N a I crystal c o u n t i n g rates ranged from 9 x 103 to 7 x 104 counts/s. T h e " I o w low" pile-up rate was kept in all r u n s less t h a n 15 ~o of the c o u n t i n g rate in the linear GAMMA-RAY I0 --3 lad z I00

20

30

i

I

•

2H(d,)') 4He

o

Z

Ed = 8.9 MeV

-r"

o • Oo

u) I.Z :D 0

o

ENERGY (MeV)

0L = 40*

i Q = 12,000/-tC

o

50

O'

I

50

90

- 70

I10

CHANNEL

NUMBER

Fig. 4. Gamma-ray spectrum from the 2H(d,7)4He reaction at 8.9 MeV incident deuteron energy. Solid symbols are the ;.'-spectrum before background subtraction. Open symbols give the empty gas target spectrum. TABLE 1

Errors in 2H(d, ~)4He differential cross section Item

Error (~o)

(i)

charge integrator calibration

3

(ii)

density ofnucleiin target 2Hz gas analysis gas target length

2 ½ ½

(iii) solid angle subtended by Na[ crystal collimator to target extrapolation of y-ray spectrum absorption in paraffin between NaI crystal and target efficiency of NaI crystal and anticoincidence shield

4 20 4 2 error = 36 Y/o

2H(d,)') A N G U L A R

DISTRIBUTIONS

523

channel and we estimate that after correction its contribution to the error in the cross section was less than 1.5 ~o. N o provision was made for correcting the pile-up of the "high-low" type 13). As this modifies the width of the y-ray peak, it should not affect the absolute value of the cross section. Other sources of error affecting the cross section are listed in table 1'. To these errors one must add the statistical error in the number of y-rays detected above a fixed bias. It varies considerably with the lab angle and in practice constitutes the only contribution to the statistical error in da/dto of table 2.

3. Experimental results The differential cross section at the energies E d = 6.05, 8.96 and 11.67 MeV is listed in table 2 as a function of the lab and c.m. angles, 0L and 0c.m., respectively. The error in the differential cross section corresponds to the statistical error in the y-ray yield. The c.m. angular distributions of table 2 were fitted with a Legendre polynomial expansion up to and including order four of the form 15) do" dto

-

1

1, 4

4r~

k

Z Akt'k(cos 0)1.

(1)

In the course of the analysis it was verified that the k-odd terms were negligible, as required by the identity of the two particles in the entrance channel; hence they were subsequently dropped and the least-square fit obtained only with k-even terms. The results are listed in table 3. For an angular distribution of the type sin 2 0 cos 2 0 the coefficients A k are A2 = 0.712 and .44 = - - 1.694 after correction for the finite diTABLE 2 Differential cross section o f the 2H(d, y ) 4 H e reaction

OL

0 ....

dtr/d,Q

Oc.m.

da/d-Q

0 ....

dtr/ dO

(deg.)

(deg.)

(nb/sr)

(deg.)

(nb/sr)

(deg.)

(nb/sr)

0 40 50 60 70 80 90 100 110 120 130

0 41.5 51.8 62 72.2 82.3 92.3 102.3 112.1 122.0 131.7

0.0 ± 0 . 3 2 1.244-0.17 1.084-0.15 0.804-0.13 0.334-0.12 0.08 4-0.12 0.04+0.10 0.13 4-0.11 0.55±0.13 0.81 4-0.14 1.12-1-0.14

0 41.8 52.2 62.4 72.6 82.8 92.8 102.7 112.6 122.4 132.1

Ed = 6.05 M e V

0.0 4-0.52 1.68+0.22 1.71 4-0.24 1.044-0.17 0.744-0.22 0.23 4-0.20 --0.02±0.18 0.36i0.20 0.864-0.21 1.304-0.15 1.664-0.14

Ea = 8.96 M e V

0 42.1 52.5 62.8 73.0 83.2 93.2 103.1 113.0 122.7 132.4

0.0 --0.65 1.56±0.19 1.64--0.16 0.734-0.13 0.51 4-0.13 0.204-0.11 0.124-0.11 0.35 4-0.12 0.894-0.12 1.08___0.14 1.61 4-0.16

Ed = 11.67 M e V

t T h e errors quoted in table 1 are larger t h a n t h o s e reported in a previous publication 5) on the y-ray yield o f t h e 2H(d,~')4He reaction at 0L = 130 °. T h e difference is partly due to a revaluation o f the errors a n d partly to difficult experimental conditions at small angles.

524

J. M. POUTISSOU AND W. DEL BIANCO

m e n s i o n s o f the d e t e c t o r a n d the lead c o l l i m a t o r 16). The errors in the A k coefficients are the external errors as defined by F e r g u s o n 17). The e x p e r i m e n t a l differential cross sections a n d the least-square-fit curves o f eq. (1) c a l c u l a t e d with the coefficients o f table 3 are p l o t t e d in figs. 5-7. The d a s h e d curves represent the sin 2 0 cos 2 0 distribut i o n after c o r r e c t i o n for the a t t e n u a t i o n coefficients 16). TABLE

3

Coefficients Ak of the expansion of the c.m. differential cross section of the 2H(d,~,)4He reaction E~ (MeV)

A2

A4

6.05 8.96 11.67

0.814±0.101 0.683!0.114 0.831 ±0.260

--1.661 ±0.148 --1.5904-0.165 --1.2874-0.372

/

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I

I

1

I

1

I

I

I

I

I

I

I

I

/ 0 °

50"

.L 1

I00 ° 0c.ro.

Fig. 5. Angular distribution of the 2H(d,7)4He reaction at 6.05 MeV deuteron energy. W i t h i n the e x p e r i m e n t a l errors it a p p e a r s well established t h a t the ,4 k coefficients c o r r e s p o n d to those o f an E2 transition. T h e a g r e e m e n t at E d = 12 M e V is n o t as g o o d as at the o t h e r two energies, however, it s h o u l d be n o t e d t h a t at 12 M e V the e x p e r i m e n t a l e r r o r in the 7-ray yield is larger. These conclusions c o n c u r with the results o f Degr6 4), S k o p i k a n d D o d g e 3), a n d M e y e r h o f et al. 7). Degr6 m e a s u r e d the a n g u l a r d i s t r i b u t i o n o f the 2H(d, y)4He r e a c t i o n with a technique similar to ours at a d e u t e r o n energy Ed = 3.68 M e V a n d o b t a i n e d for the coefficients o f eq. (1), A2 = 0 . 6 7 9 + 0 . 0 8 8 a n d A 4 = - 1 . 4 3 4 + 0 . 1 0 1 . These have to be c o m p a r e d with the values A2 = 0.712 a n d A 4 = - 1.634 for a sin 2 0 cos 2 0 distribution. M e y e r h o f et al. m e a s u r e d the differential cross section at 10 M e V at 0L = 45 °, 90 ° a n d 135 ° a n d o b t a i n e d values consistent with a sin 2 0 cos 2 0 distribution. F i n a l l y S k o p i k a n d D o d g e m e a s u r e d the differential cross section in the " v i r t u a l p h o t o n " energy interval o f

525

2H(d, 7 ) A N G U L A R D I S T R I B U T I O N S

40 + 1 MeV at six angles from 0 . . . . = 38° to 152 ° and again report an angular distribution consistent with an E2 transition. N o mention is made in their article of a least-square fit to the experimental points. "z

1.5

1.0

0.5

o°

5o*

T,oo* 0 c.,~.

Fig. 6. Angular distribution o f the 2 H ( d , 7 ) 4 H e reaction at 8.96 MeV deuteron energy. .~

i

I

I

I

I

I

I

I

I

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I

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i~

0.5

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-

0* Fig. 7. Angular

distribution

? I

of the

I I

50" 100° 0c.m. 2H(d,y)*He reaction at 11.67 McV deuteron energy.

526

J. M. P O U T I S S O U A N D W. D E L B I A N C O

The absolute value of the differential cross section also is in fair agreement with that of Degr6 4) and Meyerhof 7). For reference purposes we show in fig. 8 the excitation curve of the 2H(d, 7)4He reaction obtained in this laboratory at 0L = 130 ° and deuteron energies from 4 to 12.5 MeV. For comparison in the same figure the differential cross sections of Degr6 and Meyerhof have also been plotted. Within the experimental errors the results appear to be consistent although above E d = 7 MeV our cross section is higher than that of Meyerhof by about 30 Yo. In all cases the error I

I

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"2

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I I I l l .

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[ 0o.m.o ,32°]

5 -

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o X

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I

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5

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I

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I

I

[

I

I

I0

I

I

I

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15 Ed (MeV)

Fig. 8. Differential cross section for the 2H(d,),)4He reaction at 0 ..... = 132 °. T h e s y m b o l s have the following m e a n i n g : • present results; @ ref. 7); V ref. 4).

shown in fig. 8 is only the statistical error. However it should be noted that all the measurements are affected by a fairly large systematic error. Meyerhof reports a systematic error of the order of 30 % mainly to attribute to the uncertainty in the absolute efficiency of the ,]-ray detector. In this experiment we have estimated an error of 36 % chiefly due to the uncertainty in the shape of the response function of the crystal at low channel numbers. 4. Discussion of results

In the long-wavelength approximation and at the energies considered in this experiment the 2H(d, y)4He reaction is expected to proceed through electromagnetic transitions of order smaller or equal to two. In addition the identity of the two particles in the entrance channel restricts the initial states to total orbital angular momentum L and spin S of the same parity. Thus the allowed multipole transitions and the corresponding angular distributions, which result when these two points are considered, are those shown in table 4.

2H(d,y) ANGULAR

DISTRIBUTIONS

527

TABLE 4 Electromagnetic multipole transitions a n d c.m. a n g u l a r distributions o f the 2 H ( d , y ) * H e reaction Entrance c h a n n e l

Transition

Spins

L

d 7r

0 0 1 1 1 1 2 2 2 2

0 2 1 1 1 3 0 2 2 2

0+ 2+ 01222+ 0+ 1+ 2+

1So --~ 1So i D z --~ 1So 1Po ~ 1So sP1 -+ 1So sP2 --* ISo ~F2 --~ ISo sS2 --~ ISo 1Do -+ ISo 3D1 ~ tSo 5D2--~ ISo

forbidden E2 forbidden E1 M2 M2 E2 forbidden MI E2

A n g u l a r distribution ofT-rays

sin20 cos20 1+cos20 1+cos20 I + cos20--5 cos*0 isotropic 1+cos20 2 + 3 s i n 2 0 + 1 2 sin20

Disregarding any hypothesis on the nuclear force, one expects the transition rates to be E1 >> M1, E2 >> M2. If however the nuclear force is assumed to be central or charge independent the relative strength of the transition rates changes considerably. In the central-force approximation, one can assume the deuteron to be in a 3S state and the helium nucleus in a state 1S. In this hypothesis L and S are both good quantum numbers and one can show that the electromagnetic multipole operators operate in the ordinary space for electric transitions and in the spin-space for magnetic transitions and pure S-states. In fact, for electric transitions, the term referring to the coupling of the e.m. field to the magnetic moments of the nucleons is negligible compared to that due to the coupling to the electric charges (of the order of E / M c 2, M mass of the nucleon). For magnetic transitions of multipolarity L the operator is of the form 2o)

QLM -'~Iz° ~ V(rLyLM)(L~l gtfl~+gskSk) with/~o the Bohr nuclear magneton, ggk = 0 for neutrons and glk = 1 for protons. In the case of pure S-states the various 1k are zero and only the terms operating on the nucleons spins are to be considered. Thus in table 4, the only allowed transition is the 1D 2 --* 1S 0 transition. On the other hand charge independence of nuclear forces yields the isospin selection rules which, for a self-conjugate nucleus, require that no E1 transitions take place between states of equal isospin 21) and M1 transitions be reduced by approximately a factor one hundred 22). For light nuclei and the photon energies considered in this article, Coulomb 23) and meson effects 24), which might impair the validity of the above rules, should be small. Hence the 1D 2 ~ iS 0 transition should again be predominant and E1 and M1 transitions strongly reduced. In practice the two hypotheses are expected to be simultaneously valid. In the case

528

J.M. POUTISSOU AND W. DEL BIANCO

of a partial breakdown of both assumptions, small percentages of 3P 1 --~ 1S 0 and 5S2 ~ IS0 transitions should accompany the I D 2 ~ 1S 0 transition. The angular distribution in this instance is

at7

- A[sin 2 0 cos 2 0 + B ( 1 + c o s 2 0 ) + C ] .

(2)

do I f the 3P 1 ~ aS 0 transition predominates over the SS2 ~ ~So transition the angular distribution becomes

dtr -

A[sin 2 0 cos 2 0 + B ( 1 + c o s 2 0)].

(3)

do The analysis of sect. 3 shows that the process is mainly of the type 1D2 ~ 1So, but small contributions from other multipolarities cannot be excluded. For this reason a further least-square fit of the experimental angular distributions with the expansions (2) and (3) was attempted. The coefficients B and C, thus obtained, are listed in table 5. They are small (B, C < 2.9 %) and roughly equal to the statistical errors. Thus we conclude that in the v-ray energy range E r < 30 MeV, the 4He(y, d)2H reaction proceeds mainly through an E2 process and that the rates of other multipole transitions are only a few percent of the E2 transitions. The result is interesting because, to our knowledge, this is the only known pure E2 process in photonuclear reactions. It is worthwhile for this reason to compare the E2 cross section of the 4He(y, d)2H reaction with the E1 component of the 4He(y, p ) a H reaction. Very approximately the cross section for the quadrupole transition should be smaller than that for the dipole transition at corresponding energies by a factor of (R/~) 2 where R is the radius of the a-particle about 1.6 x 10-13 cm i) and 2n~ the wavelength of the v-ray. For a 30 MeV v-ray we obtain ( R / ~ ) 2 6 x 10 -2, whereas the ratio of the E2 and E1 cross sections 7, 25) is about 3 × 10 -3. Given the difference of the final wave functions of the two processes the agreement can be considered satisfactory. The comparison of the E2 cross sections for the 4He(y, p)3H and 4He(y, d)EH reactions has been carried out by Meyerhof et al. zs). Both cross sections show a nonTABLE5 Coefficients B and C of the c.m. angular distributions of the 2H(d,y)4He reaction Ea (MeV)

B

C

6.05

0.025 4-0.032 --0.0026 4-0.0059 0.00454-0.0350 0.0087 4-0.0080 0.07864-0.1280 0.0162~0.0136

--0.029 4-0.033

8.96 11.67

0.0044±0.0360 --0.060 ±0.123

2H(d,~,) ANGULAR DISTRIBUTIONS

529

r e s o n a n t behaviour a n d a similar energy dependence at ?-ray energies below 30 MeV. T h u s in the ?-ray energy range considered in this experiment the a s s u m p t i o n s o f central forces a n d of a direct process employed in theoretical calculations appear justified. W e are greatly indebted to P. Boucher, S. K u n d u a n d D. Benoit for their c o n t r i b u t i o n to the data acquisition a n d for their valuable assistance. We also acknowledge the aid of Mr. Touchette a n d Mr. Chenier of the electronic shop a n d of Mr. Berichon a n d the accelerator crew d u r i n g the experiment. O n e of the authors (J.M.P.) was the recipient of a n " E n t e n t e F r a n c e - Q u e b e c " scholarship.

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)

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