Charge symmetry in the mirror reactions Li6(d, p)Li7 and Li6(d, n)Be7

Nuclear Physics 41 (1963) 58---67; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

CHARGE SYMMETRY IN THE MIRROR REACTIONS Li6(d, p)Li 7 AND Li6(d,n)Be 7 M. B I R K , G. G O L D R I N G ,

P. H I L L M A N

a n d R. M O R E H t

Department of Nuclear Physics, The Weizmann Institute of Science, Rehovoth, Israel tt Received 26 September 1962 Abstract: A c o m p a r a t i v e s t u d y o f the Li6(d, p ) L F a n d Li6(d, n)Be 7 reactions h a s been m a d e in order to serve as a critical test o f the principle o f charge s y m m e t r y in nuclear reactions. T h e g r o u n d a n d first excited states o f Li T a n d Be T are believed to be p u r e isobaric spin doublets. T h e need h a s been eliminated for substantial C o u l o m b a n d p h a s e space corrections, since the ratios o f t h e g r o u n d to first excited state cross-sections are c o m p a r e d . T h e observed equality o f t h e n e u t r o n a n d p r o t o n results over t h e b o m b a r d i n g energy range 0.4-3.2 M e V m a y be taken as a striking a n d m o d e l i n d e p e n d e n t confirmation o f the principle o f charge s y m m e t r y . A n interesting a n o m a l y in the a n g u l a r distribution results was observed which does n o t seem explainable in ordinary distorted wave stripping theory.

1. Introduction The concept of charge independence plays a fundamental role in the theoretical investigation and analysis of nuclear reactions and it is therefore somewhat disconcerting that there is only very scant direct experimental proof that nuclear reactions are indeed charge independent. In fact the comparison of cross-sections for mirror reactions, the equality of which is the most direct consequence of the restrictive statement of charge symmetry, has yielded some surprisingly large discrepancies in a few cases 1). Although these can all be explained in terms of "reasonable" mixing of different T values in the compound nucleus, they cannot be considered a critical test of the principle. In the present experiment we have chosen a case in which the T admixtures are expected to be small. It is believed that the ground and first excited state of the mirror nuclei Li 7 and Be7 are pure isobaric spin doublets. Their formation cross-sections in the reactions Li6(d, p)Li 7 and LiP(d, n)Be 7 should therefore, apart from Coulomb and phase space effects, be equal. D. H. Wilkinson 2) measured the cross-sections for these reactions leading to the first excited states of Li 7 and Be T, and they were indeed found to be equal within 15~o throughout the deuteron energy range of 0.2-1.8 MeV. However, the corrections he had to apply for Coulomb and phase space effects were substantial and in the case of Coulomb effects these corrections are strongly model dependent, in fact of opposite sign for the compound nucleus and t N o w at Israel A t o m i c Energy Laboratories. tt W o l k s u p p o r t e d in part by a g r a n t f r o m Indian H e a d Mills Inc., N e w York. 58

CHARGESYMMETRY

59

direct interaction models. Since the exact mechanism of the reaction is very difficult to establish the results are hard to interpret. In the present experiment we have almost entirely cancelled out Coulomb corrections, as well as phase space effects, by comparing the branching ratios to the ground and first excited states in the same pair of reactions. That is, we have measured the ratio of the (d, p) cross-section to the ground state of Li 7 to that to the first excited state of Li 7 and the same ratio for the (d, n) reaction to Be 7. These ratios should be equal if the principle of charge symmetry is valid, and, we believe, only if this principle is valid, aside from the possibility of accidental equality, which we hope to have avoided by carrying out the measurements over a wide range of bombarding energies covering a wide variation in the reaction mechanism. It is unfortunately not equally clear that by using the chosen ratios we have not made our measurement a test of charge symmetry for the relevant nuclear states only, for which it is already very well established, and perhaps not specifically for the nuclear reactions. Li6 + a

~

Q=3.380&tel/ n n~ ,/2-

--~/~-

807 3/Li 7

Fig. 1. The energy level diagram defining the various reactions observed in this experiment. The energy level diagram is shown in fig. 1. The ratios in question are p/p* and n/n* where p, p*, n and n* are defined in fig. 1. Wilkinson carried out his experiment on p*/n* by measuring the relative yield of the 431 keV and 478 keV gamma rays, but his inability to separate them led to an appreciable experimental error. The rapidly rising contribution of gamma rays from other reactions also led to his abandonment of attempts to go above 1.8 MeV bombarding energy. In our case we have measured both proton and both neutron groups directly and covered the bombarding energy range of 0.4-3.2 MeV.

2. Experimental Procedure The deuteron beam was provided by our 3 MeV Van de Graaff accelerator. Below 0.8 MeV the focussing properties of the accelerator are poor so that in order to work

M. BIRK et aL

60

down to 0.4 MeV, D~ molecules were accelerated. The target consisted of a layer of Li 6 about 100 ~ g - c m - z thick covered with a v e r y thin layer of evaporated gold to protect the target from oxidation and sputtering. The beam was focused onto a spot about 2 mm in diameter. For the proton runs, the high counting rates enabled us to run with beams of 20-40 m/~A; no target damage was observable. For neutrons, I

I

1

I

I

I

I

LiSCd, p) Li T 2000

--

LtS(d,p) LiX~

--

1500

:::) o o

tO00

CS~(c D) C I"~

500

o

--

/

}

,.. . . . . . . .

....j

I

I

t

I

120

150

f&O

210 CHANNEL

Fig. 2. A portion of the observed proton spectrum for

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

t

I

I

2~;0

270

300

Ea =

2.3 MeV and 0 = 40°.

however, beams of 5-10/~A were required, resulting sometimes in appreciable (up to 50 ~o) loss of lithium during the runs. However, by repeating certain measurements frequently we were able to normalize all runs and obtain angular distributions with small error. Although the ratios discussed above are of total cross-sections, it was more convenient as well as more informative to measure the angular distribution in each case.

CHARGE

61

SYMM~TKY

F o r the p r o t o n runs an R C A 20 m m 2 solid state d e t e c t o r c o l l i m a t e d to 5 m m 2 was used. It was placed j u s t outside thin M y l a r w i n d o w s o f the 5 c m d i a m e t e r scattering c h a m b e r for the p u r p o s e o f c o u n t i n g p r o t o n s . T h e o u t p u t o f the d e t e c t o r was amplified in a charge sensitive amplifier a n d displayed on a m u l t i - c h a n n e l analyser. A typical s p e c t r u m is shown in fig. 2. As m a y be seen the p e a k s in question are clearly s e p a r a t e d f r o m each o t h e r a n d f r o m b a c k g r o u n d reactions so t h a t their areas c o u l d be easily measured.

+I

I

I

I

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(a)

000

~o 36o~_

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o

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00 0

0 0

o0

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0 0

0

° 0

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X X°XxXXXXx X

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0 °

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x x XXXxxxxxxxxx Xx Xx~x~xmm~1

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(b)

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-

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l

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I o•

f

+.

+

180

190 CHANNEL

200

o

__f..1 210

/

.'" +' "-I E'80

Fig. 3(a). The observed spectrum of proton recoils from the polyetheiyne radiator at Ed = 2.28 MeV

and 0 = 25°. The circles are the measurements with radiator and the crosses without radiator. The arrows point to two small peaks which are attributed to the reaction Si'*(n, ct)Mg26. Fig. 3(b). The difference between the two spectra shown in fig. 3 (a) together with fitted congruent curves. A smoothly rising background is assumed to exist under the peaks as shown by the straight line. This background is attributed to scattered neutrons. F o r the p u r p o s e o f detecting n e u t r o n s a n o t h e r solid state d e t e c t o r o f 7 m m 2 a r e a was placed s o m e 2 c m f r o m the scattering c h a m b e r a n d a 4 m m d i a m e t e r r a d i a t o r o f 3 m g - c m - z thickness polyethelyne i n t e r p o s e d at the wall o f the scattering c h a m b e r . T h o s e p r o t o n s recoiling f r o m the r a d i a t o r in the n e a r l y f o r w a r d direction s h o u l d be detected a n d should faithfully reproduce, with s o m e loss o f r e s o l u t i o n due to g e o m e t r i c a l factors, the incident neutron spectrum, after c o r r e c t i n g for the energy v a r i a t i o n o f the n-p scattering cross-section. A substantial p o r t i o n o f the counts in the detector, however, d i d n o t c o m e f r o m the r a d i a t o r a n d a m e a s u r e m e n t without r a d i a t o r was always m a d e o f this b a c k g r o u n d . Fig. 3(a) shows t h e m e a s u r e m e n t s in a

62

M.

BIRK

e t al.

typical case with and without radiator and fig. 3(b) displays a subtracted result together with fitted curves. The arrows in fig. 3(a) point to two small peaks appearing in the radiator-out measurement. These peaks were attributed to the reaction Si29(n, ~)Mg 26 occurring [

t

(d,n)

1200

-

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1~00

1200

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150"

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90 ° ~ 30 ° 0c e c~. e C.ut Fig. 4. T h e a n g u l a r distributions in t h e centre-of-mass system with visually fitted curves. T h e dots are for the g r o u n d state a n d t h e crosses for t h e first excited state. T h e ordinates o f the n e u t r o n g r a p h s have in each case been adjusted in s u c h a way as to m a k e the weighted areas o f t h e n e u t r o n curves equal to t h o s e o f the c o r r e s p o n d i n g p r o t o n curves for the g r o u n d state. T h e 2.0 M e V n e u t r o n results are those o f Cranberg, J a q u o t a n d Liskien s). T h e n e u t r o n errors are difficult to assess a n d those s h o w n on the 2.9 M e V g r a p h are representative.

SYMMETRY

CHARGE

63

in the silicon of the counter itself. The existence o f this reaction showed promise o f making silicon solid state detectors into useful neutron detectors, and extensive further

i --i- f ~ I-/~/. (d,n)

Ed = 2 . 0 M e V

I

I

J

I

I •

| 4

£d = 2.28 MeV

5OO

30O

i_

°

ii 2

°

_

200

/U~-~-x'~-( x/

I

100

r.n

Z 0

(d,p) Ed =2.OMeV

fK/'~ /

\

15000

15000

. ~ ~-i~".~.. 10000

z I0000 0

50OO

5000

I t80 °

150 °

120 °

90 °

60 °

30 °

0o

180"

150 °

I

I

I

120 °

90°

60 °

i 30 =

ecj,a

e c.u.

Fig. 4. measurements were made on this and similar reactions. The results will be published elsewhere. In the present experiment these reactions were used only to establish the eleanness o f the neutron spectra, that is to say, the non-existence o f appreciable contributions to the neutron spectra from reactions in contaminant material.

Ce

64

a m g e t al.

M.

3. Results Fig. 4 shows the complete set o f neutron and proton results. The 2.0 MeV neutron results are taken from ref. a). From these angular distributions the total cross-sections F

t

I -

~ ---

E

/('~, ') (d,n) £d =I 1,77 M,eVI

I

l

"']

io/._...~

/

I

~00

~

--

W

~

o

60O

6OO

4OO 4OO

200

.J

1 200

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o

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15000

--

I0000

5000

L~""'I .......... i 150° 120°

leo n

I

I

I

[ --

9 0 '=

60*

30*

O*

I

Oc.~.

180"

150='

I

120"

1.....

90*

]

I

60"

30*

eC.M

Fig. 4. were calculated by integrating these curves appropriately weighted for solid angle factors. In order to facilitate the comparison o f the neutron and proton results in fig. 4 the ordinates o f the neutron graphs have in each case been adjusted in such a way as to make the weighted areas o f the neutron curves equal to those of the correspond-

0*

65

C]UmGE SYMMETRY

ing proton curves. This was done for the ground state, but is in fact, as will be seen, also very nearly valid for the excited state. t

I

I

I

I

I

25O

(d ,n) J

Ed =056 MeV

//

i

/

f

/

1 200

/,: /

/

/

/

i_ / , t i

I I

:

i

i

I

I

/ /

~ 150 ,~

8OO

£d = 0.97 MeV

/

II

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• ;

( 6OO

I00

/

j

z

/

//

/

/ ,o /

/

)400

200 /

×

/

/

50

I

~

~x

~x ~

o u

(d ,p)

~

f5000

15000

£d = 1.0 MeV

t /

"

~000

10000

_

/~/i/l~ ----~ I------I~j

5000

5000

t

I

180 °

150 °

I

i

]

120°

90 •

60 =

I

30 o

I

0o

180 °

150°

I

i

I

I

120°

90 °

60 °

30o

~Cu. Fig.

4.

Fig. 5. shows the final results for p/p* and n/n*. Also displayed are results of an experiment by Cranberg, Jaquot and Liskien carried out at HarweU 3). The errors

0o

M. BXRK et al.

66

shown for our results are total estimated probable errors and come in the proton case largely from the angular incompleteness of the data and in the neutron case from the incomplete separation of the two groups. 5.0

I

t

I

t

I

I

x p/p°

on~n. • tVh,, (Gr~ber9 ~ olJ ,/,.0

~/plr 3.O

20

1.0

o

I

I

I

I

I

I

0.5

1.0

1.5

2.0

2.5

3.0

3.5

[..V]

Fig. 5. T h e final results for the g r o u n d to excited state ratios as defined in fig. 1. Also s h o w n are s o m e results o f Cranberg, J a q u o t a n d Liskien a).

By making use of the well-known values of the forward scattering (n, p) crosssection, it was possible from the present results to obtain values for the protonneutron ratios in the ground and excited states, that is to say, of pin and p*/n* as defined in fig. 1. TABLE 1 P r o t o n to n e u t r o n total cross-section ratios for the g r o u n d a n d excited states Ea (MeV)

p/n

p*/n*

0.56 0.97 1.38 1.77 2.28 2.58 2.9

1.005:0.25 0.785:0.2 1.23-t-0.2 1.3520.35 1.205:0.25 1.15+0.25 0.9320.15

1.05-t-0.25 0.835:0.2 1.255:0.2 1.4521-0.35 1.212:t:0.25 1.21 5:0.25 1.00:t:0.15

The proton-neutron ratio results without any corrections for Coulomb and phase space effects are shown in table I. The errors are again total estimated errors and come

CHARGE SY~a~TRY

67

largely from uncertainties about the equality of the target thickness in the two measure ments. The values ofp*/n* in the region 0.56-1.77 MeV agree with those of Wilkinson for these energies within the limits of error. 4. Discussion The equality of the neutron and proton results in fig. 5 over a wide range of energies may be taken as a striking and model independent confirmation of the principle of charge symmetry. This is especially so in view of the rapid charge in branching ratio and angular distribution below 2 MeV, which seems to indicate that the reaction mechanism changes radically over this energy region. Further confirmation of charge symmetry may be drawn from the fact that even the corresponding neutron and proton angular distributions are very similar over most of the energy range, as well as from the equality of the corresponding neutron and proton total cross-sections. The results, incidentally, also indicate that the deuteron retains its T = 0 character until after its role in the reaction is over. An examination of the angular distribution reveals an interesting feature which persists for both neutron and protons at all energies down to about 1.4 MeV. This is the close correspondence at forward angles of the ground and excited state distributions and their rapid divergence beyond 90 °. There is a strong indication that this feature persists 4) even up to 8 MeV. Butler fits have been made to the peaks at forward angles and are in all cases clearly l = 1, but the fits of course do not exhibit the large backward cross-section experimentally observed. Distorted wave analysis, which can predict quite large backward cross-sections, is unable to explain the divergence between the ground and excited state distributions in view of the l equality. The explanation apparently must lie in an alternative interpretation of the mechanism of the reaction such as in terms of heavy particle stripping s) or compound nucleus formation 3). References 1) 2) 3) 4) 5)

E. S. Shire and R. D. Edge, Phil. Mag. 46 (1955) 640 D. H. Wilkinson, Phil. Mag. 2 (1957) 83 L. Cranberg, A. Jaquot and H. Liskien, Nuclear Physics, to be published J. R. Holt and T. N. Marsham, Proc. Phys. Soc. 66 (1953) 1032 D. Robson, private communication