Angular distributions of four neutron groups from the 10B(d, n)11C reaction

Paris, C . H . Endt, P.M. 1954

ANGULAR

PhysicaXX 585-591

DISTRIBUTIONS OF FOUR NEUTRON F R O M T H E l°B(d, n ) l ' C R E A C T I O N

GROUPS

b y C. H. P A R I S and P. M. E N D T Physisch Laboratorium der Rijksuniversiteit, Utrecht, Nederland

Synopsis M e a s u r e m e n t s are d e s c r i b e d of t h e a n g u l a r d i s t r i b u t i o n s of the four m o s t e n e r g e t i c n e u t r o n groups f r o m t h e l°B(d, n ) l I c r e a c t i o n at a d e u t e r o n e n e r g y of 0.6 MeV. N e u t r o n s w e r e d e t e c t e d b y t h e i r recoil p r o t o n s in n u c l e a r emulsions. T h e a n g u l a r d i s t r i b u t i o n s h a v e been a n a l y z e d in t e r m s of a s t r i p p i n g c o n t r i b u t i o n and an, ass u m e d l y isotropic, c o n t r i b u t i o n f r o m c o m p o u n d n u c l e u s f o r m a t i o n . F r o m B u t l e r a n a l y s i s l# = 1 is f o u n d for t h e s t r i p p i n g c o n t r i b u t i o n of t h e n e u t r o n g r o u p l e a d i n g to t h e l I c g r o u n d state, a n d lp = 0 for t h e g r o u p leading to t h e second e x c i t e d state. This is in a g r e e m e n t w i t h p r e v i o u s results o b t a i n e d f r o m t h e m i r r o r r e a c t i o n l°B(d, p ) l l B a n d w i t h p r e d i c t i o n s f r o m t h e n u c l e a r shell model. S t r i p p i n g c o n t r i b u t i o n s of t h e o t h e r t w o n e u t r o n g r o u p s are v e r y small.

§ 1. Introduction. In a previous paper 1) angular distribution and yield measurements have been described of four proton groups from the l°B(d, p) liB reaction. It seemed interesting to supplement these measurements with an investigation of the l°B(d, n ) l l C reaction. This latter reaction leads to llC, which is the mirror nucleus of 1lB. For this reason we m a y expect that angular distributions and yields of corresponding neutron and proton groups are very nearly identical. The nucleus tiC has excited states at 1.85, 4.23 and 4.77 MeV 2)3). All these levels and the 11C ground state should be reached from the l°B(d, n)llC reaction at E d =-0.6 MeV, as the ground-state Q-value amounts to 6.472 MeV 2). Angular distribution measurements of all neutrons from the '°B(d, n)llC reaction detected b y an energy insensitive "long" counter at E d = 0.71, 1.06 and 1.43 MeV have been reported b y Burke e.a. 4). In § 2 a description will be given of the experimental procedure used for detection of neutrons b y means of the nuclear emulsion method. The results of the measurements are presented in § 3 and discussed in § 4. § 2. Experimental procedure. Neutrons were detected and their energy was measured b y means of their recoil protons in nuclear emulsions placed at 15° intervals around the target. The aluminum plate holder was very much

- - 585 - -

586

C. H. P A R I S A N D P. M. E N D T

the same as the one used for (d, p) angular distribution measurements 5) with the following alterations: a) the surface of the emulsion was put parallel to the direction of the incoming neutrons ; b) to reduce the background of neutrons resulting from bombardment of the slit system defining the deuteron beam, the slit to target distance was enlarged from 25 mm to 195 ram; c) the average distance of target to emulsions was enlarged from 60 mm to 100 m m t o reduce the uncertainty in the position of the target spot due to its finite extension and its possible eccentricity. To prevent charged particles from reaching the emulsion an aluminum shield of 1 mm thickness was mounted between target and emulsions. Of the proton recoil tracks found in the exposed and processed nuclear emulsions the following quantities were actually measured: a) the projection of the track on the surface of the emulsion; b) the "dip" of the track as measured b y its component perpendicular to the surface of the emulsion; c) the angle between the direction of the incident neutron and the direction of the projection defined under a). From elementary geometrical considerations (taking into account the shrink of the emulsion b y development) the actual range of the proton recoil can be found and the angle ~ between neutron and proton direction. The proton energy Ep can be found from the range-energy relation and finally the neutron energy from the expression: E,, = Ep/cos 2 0. These computations were much simplified b y the use of suitable nomograms, in whicli the "corrected range" (the range of protons from head-on collisions) was used as an intermediate quantity. Only proton tracks were accepted of which the dip angle was smaller than 7.5 ° (in the unprocessed emulsion), and in which the azimuth angle, defined under c), was smaller than 15°. For larger dip and azimuth angles the error in E,,, due to the errors in the measurements of the proton track parameters, rises rapidly. The target consisted of a 80 #g/cm 2 t°B layer on a 6 ~ aluminum backing. It was prepared b y electromagnetic separation b y Dr R. H. V. M. D a w t o n at the Atomic Energy Research Establishment, Harwell, England. The lib content was too low (2.5 -4- 1.5%) to interfere with the present measurements as was found from separate ~B enriched target bombardments. The same was found for ~aC b y bombarding an enriched 13C target. The contaminants ~2C a n d ~60, usually present on every target,.do not interfere because the Q-values of their (d, n) reactions are very low. The 1°B target was bombarded b y a 1 #A current of 600 keV deuterons during 20 hours. The effective deuteron energy obtained b y subtracting half the deuteron energy loss in the target amounted to 576 keV.

ANGULAR DISTRIBUTIONS OF FOUR NEUTRON GROUPS

587

§ 3. Experimental results. In Fig. 1 the energy spectrum of neutrons Jeaving the target in the forward direction (~ = 0 °) is shown, in which the "corrected range" (see § 2) is used as a measure of neutron energy. A certain amount of background was present at ranges below 100 #, and has been subtracted in Fig. 1. It is caused b y D(d, n) 3He neutrons from the slit system defining the deuteron beam, as could be certified b y bombardments of a blank aluminum target. This background is most serious in emulsions placed in the forward direction (~9 = 0 ° - - 4 5 ° ) , although these emulsions have the greatest distances to the slit system, because then the neutrons from the target and from the slit system reach the emulsion from almost the sam4 direction, which makes their recoil protons indistinguishable. • 6O 1%cd.nl"C ~d: 0.S76 M,,V. O"

u

o

(0)Ex=0 ( 1 ) Ex= 1.85 ( 2 ) Ex--{*.23 ( 3 ) Ex=/,,77

0

MaV. 0=6/*7 MeV. MeV, MeV. MeV.

~ ,-o

(ID)

(I)

J (0)

20

%. 1oo

260

--

300-

"

~6o

Ronge in ~.

500

Fig. 1. E n e r g y s p e c t r u m of n e u t r o n s e m i t t e d at ~ = 0 ° f r o m a I°B t a r g e t b o m b a r d e d b y 0.58 MeV d e u t e r o n s . T h e n u m b e r of c o u n t e d t r a c k s is p l o t t e d as a f u n c t i o n of "'the c o r r e c t e d r a n g e " of recoil p r o t o n s i.e. t h e r a n g e of p r o t o n s w i t h t h e full n e u t r o n energy. T h e n e u t r o n g r o u p m a r k e d (D), results f r o m t h e D(d, n) 3He reaction, t h e g r o u p s m a r k e d (0), (1), (2) and (3) f r o m the l°B(d, n ) l l C r e a c t i o n . The t o t a l n u m b e r of t r a c k s c o u n t e d for Fig. 1 a m o u n t e d to 416.

In emulsions placed at 0 = 60 ° and larger angles t h e recoil protons directed radially away from the target, and originating from D(d, n)3He neutrons from the slit system, have such a low energy, that they can not be mixed up with the four l°B(d, n) llC groups which were counted. Four different neutron groups can be seen in Fig. 1. The group at a range of about 100 # is due to D(d, n)3He neutrons from the target. The four other neutron groups marked (0), (1), (2) and (3) originate in the l°B(d, n)llC reaction. They correspond to transitions to the llC ground-state and to the

588

C. H. PARIS AND P. M. ENDT

three lowest excited states. Background has already been subtracted. Differential cross sections of the three most energetic l°B(d, n)11C groups are given in Figs. 2, 3 and 4. For the conversion of counted number of tracks into differential cross sections one has to take into account the escape probability of proton tracks from the emulsion 6) and the neutron proton elastic scattering cross section 7). The statistics of the neutron group leading to the 11C third excited state were too poor to allow the drawing of conclusions regarding its angular distribution. For this low-intensity and low-energy group the background correction was especially serious.

]

~ " 1

10B(d0n)11C

Ex= 0 MeV.

'

:l...~..t~._.... \

"

0°

30 °

60 °

\,

\,

90 °

120 °

150 °

[

180 °

Fig. 2. Differential cross section of the ground-state n e u t r o n group from the reaction l°B(d, n ) l l c at E a = 0.58 MeV plotted in the laboratory system. The cross section (full drawn curve) is analyzed as a sum of a stripping c o n t r i b u t i o n for lp = 1 (dotdash curve) and an isotropic compound nucleus c o n t r i b u t i o n (dashed curve).

§ 4. Discussion and conclusions. To compute stripping angular distributions for the l°B(d, n)llC reaction leading to the itC states at E x = 0, 1.85, 4.23 and 4.77 MeV one m a y safely assume that the proton angular momentum transfers lp for this reaction are the same as the neutron angular momentum transfers l, for the mirror reaction l°B(d, n)11B leading to the 'tB states at Ex = 0, 2.14, 4.46 and 5.03 MeV," i.e. respectively Ip = 1, 3, 0 and 2 1). Stripping angular distributions for these lp values were c o m p u t e d

ANGULAR

DISTRIBUTIONS OF FOUR NEUTRON

GROUPS

589

for the three most energetic neutron groups, using stripping theory in the form given b y B h a t i a e.a. s). The l°B nuclear radius was taken equal to 5.8 × 10 -la cm, the same value as was found to fit the I°B(d, p)llB angular distributions 1). The experimental differential cross sections given in Figs. 2, 3 and 4 were now analyzed into a stripping contribution and a contribution for compound nucleus formation which was assumed to be isotropic in the center of mass system 9)1). It is seen that in this way a reasonable agreement can be obtained between calculated and measured angular distributions. The

c.

10B(d.n)11G E

e)

: 1 . 8 5 MeV. X

Ed =0.576 MeV. R = 5.8x10-13om.

I =3.

P 1170

j-f" /

i

0°

30 °

60°

90 °

i

120°

,

!

150°

.

180°

Fig. 3. D i f f e r e n t i a l cross section a t E a = 0.58 MeV of t h e l°B(d, p) l l c n e u t r o n g r o u p l e a d i n g ito t h e I I c level at E x = 1.85 MeV. The s t r i p p i n g c o n t r i b u t i o n (dot-dash curve) has been d r a w n for lp = 3.

agreement is worst for the neutron group leading to the I Ic first excited state (Fig. 3), especially at the larger angles, but the discrepancy in this case might well be explained by the relatively poor statistics. In Table I are collected the total number of tracks counted for each neutron group, the total cross section, and the contributions to the total cross section from stripping and compound nucleus formation. Also the /p-value used in the calculation of the stripping part has been indicated. The stripping contributions show apparently a monotonic decrease with

590

C. H. PARIS AND P. M. ENDT

increasing /p-values, as is predicted by theory. Only group (3) shows an exception to this rule. Its stripping contribution is smaller than can be accounted for. The angular distributions and relative intensities of the neutron groups from the l°B(d, n)llC reaction agree very well with those of the proton groups from the mirror reaction I°B(d, p)llB 1). Even the inverted intensity order of groups (1) and (3) is found in both reactions. For a possible explanation of this effect see reference 1. Also the absolute values of the total cross sections

600i

10B(d.n)110

x 576 Ed=0. MeV.

E =4.23 MeV.

R= 5.8x10-13 crn.

,

I p =0.

500

400

~,1~I

30t2 I~,~XXI~

\

x

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

i

o" ' 3 ' 0 ° '

go.

i

90' ° ' - ' -120 -' °

150°

.

180°

Fig. 4. D i f f e r e n t i a l cross s e c t i o n a t E a = 0.58 M e V of t h e l°B(d, n) 11C n e u t r o n g r o u p l e a d i n g t o t h e I IC level a t E x = 4.23 MeV. T h e s t r i p p i n g c o n t r i b u t i o n ( d o t - d a s h curve), h a s b e e n d r a w n for lp = 0.

are nearly the same for the two reactions. Actually the sum of the total cross. sections of the four groups at Ed = 0.58 MeV is 2.9 times larger for the (d, p) as for the (d,n) reaction. This is outside the experimental error which is. only 10% for the (d, p) total cross section but might be up to a factor of two for the (d, n) reaction. However, a smaller cross section for the (d,n). reaction might well be explained by Coulomb repulsion, which makes it more difficult for the proton than for the neutron to enter the nucleus a f t e r deuteron break-up outside the nucleus.

A N G U L A R D I S T R I B U T I O N S OF FOUR N E U T R O N GROUPS

591

TABLE I Contributions of stripping and compound nucleus formation to the total cross section of the a°B(d, n ) n C reaction at E d = 0.58 MeV leading to the four lowest nC states Group

t'C excitation energy (MeV)

Counted number of tracks

Total cross section (nab)

Stripping cross section (mb)

lp

Compound nucleus cross section (mb)

(0) (1) (2) (3)

0 1.85 4.23 4.77

485 234 1406 463

2.0 0.8 2.2 0.7

0.7 0.2 I. 1 0.1

1 3 0 2

1.3 0.6 I. 1 0.6

Acknowledgements. This work is part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie", which was made possible by a subvention from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek". The authors are indebted to Prof. J. M. W. M i 1 a t z for his interest in this investigation. They wish to thank Miss A. M. H o o g e r d u ij n for her untiring and capable assistance in counting plates. Received 30-6-54.

REFERENCES I) 2) 3) 4) 5) 6) 7) 8) 9)

Paris, Valekx and E n d t , P h y s i c a 2 0 (1954) 573. Ajzenberg, F. and L a u r i t s e n , T., Rev. mod. Phys. ,°4 (1952) 321. Johnson, V. R., Phys. Rev. 86 (1952) 302. Burke, Risser and P h i l l i p s , Phys. Rev. 93 (1954)188. Endt, de Jong, Bogaardt en K o u d i j s , PhysicalS(1952) 399. Riehards, H . T . , Phys. Rev. 59 (1941) 796. H u g h e s, D. J., e.a. "Neutron cross sections", A.E.C. Report, A.E.C.U.-2040. Bhatia, Huang, Huby and N e w n s , Phil. Mag. 43(1952) 488. Pratt, W . W . , P h y s . Rev. 93(1954) 816.