Photoprotons from carbon

Nuclear Physics 2 6 (1961) 2 8 3 - - 2 4 9 ; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written perrni~ion from the publisher

PHOTOPROTONS

FROM CARBON

V. J. V A N I ~ U Y S E

Natuurkundig Laboratorium, Rijksuniversiteit, Gent, Belgi8 and W . C. B A R B E R

High-Energy Physics Laboratory, Stanford University, Stanford, Cali]ornia t R e c e i v e d 21 F e b r u a r y 1961 A b s t r a c t : E n e r g y a n d a n g u l a r d i s t r i b u t i o n s of p r o t o n s e j e c t e d f r o m C 11 t a r g e t s b o m b a r d e d b y t h e b e a m of t h e S t a n f o r d M a r k I I a c c e l e r a t o r h a v e b e e n m e a s u r e d b y m e a n s of a m a g n e t i c s p e c t r o m e t e r . T h e e n e r g y d i s t r i b u t i o n s , w h i c h a r e p e a k e d a t 6.0 MeV, s h o w a s t r u c t u r e t h a t c a n n o t be e x p l a i n e d b y a single r e s o n a n c e . S u p p o s i n g t h a t all t r a n s i t i o n s leave t h e r e s i d u a l n u c l e u s in t h e g r o u n d s t a t e , t h e a n a l y s i s of t h e p r o t o n d i s t r i b u t i o n s leads to a cross s e c t i o n w h i c h h a s a p e a k v a l u e of (12.7 4- 2 . 5 ) m b a n d v a l u e s of (414-9) M e V . m b a n d (77 4-18) M e V . m b w h e n i n t e g r a t e d f r o m 0 to 24 a n d 40 MeV, respectively. E x c e p t for t h e p e a k value, t h e cross s e c t i o n c u r v e is v e r y s i m i l a r to t h a t of t h e x2c(?, n) reaction. T h e a n g u l a r d i s t r i b u t i o n s of t h e (y, p) a n d (e, e ' p ) r e a c t i o n s h a v e b e e n m e a s u r e d for d i f f e r e n t p r o t o n e n e r g y g r o u p s a t a n elect r o n e n e r g y of 40 MeV. E x c e p t for a cos 0 t e r m , t h e d i s t r i b u t i o n s a r e in a g r e e m e n t w i t h t h e i n d e p e n d e n t particle p i c t u r e of t h e g i a n t r e s o n a n c e , p- to d - w a v e t r a n s i t i o n s b e i n g t h e i m p o r t a n t ones. T h e r e s u l t s are also a c o n f i r m a t i o n of t h e t h e o r y of electron i n d u c e d reactions. Yield c u r v e s as a f u n c t i o n of electron e n e r g y were m e a s u r e d u p to 40 MeV, for d i f f e r e n t p r o t o n e n e r g y g r o u p s a n d a t d i f f e r e n t angles. A n a l y s i s of t h e yield c u r v e s leads to differential cross sections as a f u n c t i o n of p h o t o n energy. T h e m a i n p r o p e r t y of t h e s e cross sections is to s u p p o r t to s o m e e x t e n t t h e a s s u m p t i o n of e x c l u s i v e l y g r o u n d s t a t e t r a n s i t i o n s .

1. I n t r o d u c t i o n The photodisintegration of C1~ in the giant-resonance region has been the subject of m a n y investigations. The review article b y De Sabbata 1) summarizes most of the work done until 1958 in the s t u d y of the principal modes of disintegration, B 11 Wp and C l l ~ n . Investigations reported since 1958 include that On photoprotons b y Penner and Leiss 3) and studies of the inverse reaction B11Wp--~ C12~? b y Gemmell et al. 8) and Gove et al. 4). Several questions remain unsettled, the main ones relating to possible fine structure in the giant resonance and to the relative magnitudes of the (y, n) and (7, p) cross sections. Our measurements used the Stanford Mark II linear electron accelerator 4) as a source of photons and a magnetic spectrometer as a proton analyzer. In all our experiments, the electron beam traversed the target so that protons were produced b y the direct interaction of the electrons as well as b y bremsstrahlung t W o r k s u p p o r t e d b y t h e Office o f N a v a l R e s e a r c h , t h e U.S. A t o m i c E n e r g y C o m m i s s i o n a n d t h e A i r Force Office of Scientific R e s e a r c h . 233

,2114

v.j.

VANHUYS E AND W. C. BARBER

from the material upstream from the target and from the target itself. By varying the material ahead of the target we were able to obtain information on both the C (y, p) B and C(e, e' p) B reactions, and to compare them. Our apparatus permitted measurements in greater detail and with greater statistical accuracy than previou s C (7, p) experiments (most of which were done with nuclear emulsions), and we believe t h e y help t o clarify or at least make more quantitative some of the questions mentioned above.

2. Apparatus The apparatus has been described in detail in a previous article s). The electrons of the Mark II were energy analysed by a two-magnet achromatic deflection system. The number of incident electrons was monitored b y a secondaryemission monitor, which was calibrated on a Faraday-cup. The energy of the electrons was variable from 10 to 44 MeV. The protons were momentum analysed and detected b y means of a magnetic double focusing spectrometer, which contained eight KI (T1) scintillation counters, located in the output focal plane. This permitted simultaneous measurement of different energy intervals. The energy resolution of the different counters varied from 2.5% in the norrowest channel to 5.5 % in the widest. The spectrometer, which was rotatable around the target, had an acceptance solid angle of a b o u t 0.01 sr. The number of detected protons Np per unit monitor response V in a specific counter can be written as

rE0 d2a(0, k, Eo)

NPv ----[AEpA~C]ntcosec 9Jo

~dEp

n(E°'k,t)dk,

(i)

where A Ep is the proton energy spread detected by the counter resulting from its finite width, /1~ the solid angle subtended by the counter, C the number of electrons required to produce unit monitor response, n t the number of target nuclei per cm 2, 9 the target angle; d~/d.QdEp is a differential cross section to produce a proton at an angle 0 and energy Ep by photons of energy k, and n(E o, k, t) is the number of photons per unit energy interval (real and virtual effective when one electron of energy E o traverses the target characterized b y t. From eq. (1), one can deduce r

f : ' daa(0,

k, Ep,

k, t)dk =

Np sin

[A_Ep/I.QC]-'. L-2 (

As explained in ref. *), b y studying protons from the photodisintegration of the deuteron, the value of the square bracket for counter 7 was found to be

AEp A~C = [9.52-4--1.4] X 109. Ep

(3)

PHOTOPROTONS

FROM

285

CARBON

The values of the product (AEp/Ep)A~ for the other counters relative to counter 7 were obtained b y measuring the same flat portion of a proton energy spectrum w i t h each counter. The targets were polystyrene sheets. Three different thicknesses were used 24.46 mg/cm 2, 7.7 mg/cm ~ and 2.39 mg/cm 2. 3. R e s u l t s

The results are illustrated b y the figs. 1 to 13. In all cases the indicated errors are standard deviations determined from counter statistics.

lit counter

2

counter

5

counter

8

I--

IX

IX W m

0

2

4

I I

6

8

10 12 E'p (MeV)

14

16

18

20

22

Fig. I. Energy distributions at 0 = 75 ° for E 0 ~ 40 MeV for three different counters. The curves are drawn arbitrarily.

236

V. J.

VANHUYSE

AND

W.

C. BARBER

The energy distributions for Omb = 750, shown in fig. 1, were taken with E o = 40 MeV and with an 0.0127 cm P b radiator in the primary beam. The

background, which turned out to be small, was measured b y removing the target and not the radiator. This was done in all the experiments where the radiator was used. The energy s p r e a d of the primary electrons A E o , was 0.02 E 0. Most of the points were obtained with the 7.7 mg/cm 2 target placed in such a w a y that the angle between the normal of the target and the line from the target to the spectrometer entrance was 15 °. For the higher energy

Jo

b

~

[,

°

b

/

I

a- x

-,

/

18

20

-

22

24

26

28

30 k (MeV)

32

34

36

38

40

Fig. 2. Cross section of Cis (7, P) a s s u m i n g 100 % of t r a n s i t i o n s leave B u in g r o u n d s t a t e a n d cross section of C12 (7, n) f r o m p h o t o n difference m e t h o d .

protons, the target was 24.46 mg/cm ~ thick, and the just mentioned angle was 20 ° . This was kept so in all the other measurements. The correction for energyloss in the target was made, assuming that all protons traversed half of the effective target. In fig. 1, the closely-spaced points are the ones where the thicker target was used. Supposing that all transitions leave the residual nucleus in the ground state, we obtained from the energy distribution for counter 7 the total cross section a(k) as a function of photon energy (fig. 2). In that case dEp = ~ d k and (2) reduces to da

Np sin 9

=

k, OVE,,

[A_E v

,

1-1

A

Cj

,

(4)

~HOTOPROTONS ~ROM C ~ P . . B O ~

237

I C 12 + e .-.-., Bl1* e'.o.p __

~>

~

colJnter

i

counter 8

~

~

'~

5

--

t~

ltil~

m n,.

tu

~i=

t

,|llill

3

~I

l= ~

=

4 MeV )

Fig. 3. E n e r g y d i s t r i b u t i o n s a t 0~b = 105 ° for E = 26 M e V for t h r e e d i f f e r e n t counters. ( T h i n C H target).

I _ _

Cf2+ e---b BlI+ e'+ p counte~" 9 = 0.055

A[p/[p

ti,~*! ½

a.

L/ II / till/

t~ uJ rn Z

3

4

qlli

\ 5

6

?

~p (MeV) Fig. 4. E n e r g y d i s t r i b u t i o n a t elab = 105 ° for E 0 = 26 MeV. T h e solid c u r v e s h o w s w h a t s h o u l d b e e x p e c t e d if t h e " b r e a k s " i n ~ (~, n) g i v e n b y K a t z a r e s u p p o s e d to b e t h e s a m e in ~ (y, p) a n d if only the ground state transitions are present.

2~8

V.

J.

VANHUYSR

AND

W;

C. B A R B E R

from which a(k)is easily found if the angular distribution /(0) is known. In determining =(k) we took for all protons ](0) = 1+0.25 c o s 0 + l . 3 5 sin 2 0. Figs. 3 and 4 show the energy distribution for E 0 = 26 MeV for four different counters under an angle 0rob = 1'05° and with the 2.39 mg/cm 2 target in place. No radiator was used. The backward angle Was chosen in order to reduce the background as m u c h as possible. No , t ~ g e t thickness corrections or recoil corrections were made. The incident electron energy spread A E 0 was 1 % of

E0.

Angular distributions were measured with a n d without the P b radiator for two different spectrometer settings. The energy spread of the primary electrons 8 ~x 10"3.1

8 -xlO :31

I e

/

y ,f

\

//"

5

5

/

3 1

21

I

_

i

C12Q{'P) 1 C12(e,e~)j counters 5,6,7

I--

[p = 4.78 ~7.30 MeV

~"p : 5.43~8 00: MeV o

.3'o

I

|

8o

9o

C12 (|'P) 1 C12(e,e'p)J counters B,9

|

,

1so

e (CENTRE-OF-MASS DEGREES) Fig. 5. A n g u l a r d i s t r i b u t i o n s for E 0 = 40 M e V of a p r o t o n e n e r g y g r o u p f r o m C II (e, e ' n ) a n d C is (~, n) reactions. T h e c u r v e s r e p r e s e n t l e a s t - s q u a r e fits to t h e d a t a . Circles: 2.86 [1-1-0.25 cos 0~-1.42 sin I e ~ 0.00 sin i 0 c o s 0] X 10 - s t cmS/MeVsr. Crosses: 2.49 [ 1 + 0 . 2 7 cos 0 + 1 . 4 0 sin t 0 + 0.04 sin I 0 cos 6] X 1 0 - " cml/MeVsr.

0

i

P

3o 60 ,so 180 @(CENTRE-OF-MASS DEGREES)

Fig. 6. A n g u l a r d i s t r i b u t i o n for E 0 = 40 MeV of a p r o t o n e n e r g y g r o u p f r o m C II {e, e' n) a n d C II (F, n) reactions. T h e c u r v e s r e p r e s e n t l e a s t s q u a r e fits to t h e d a t a . Circles: 3.12 [1-F0.24 cos 0~-1.30 sin I 0-~ 0.08 sin ~ 0 %os O] × 10 4 1 cml/MeVsr. Crosses: 2.83 [1 ~ 0 . 2 6 cos O-t- 1.20 sin I 0 - 0.04 sin I 0 cos O] × 10 - s l c m l / M e V s r .

was 2 ~/o. The number Of real photons was rather negligible in t h e case that no radiator was used, so that we were able to find the angular distributions for the (e, e' p) reaction directly and for the (7, P ) r e a c t i o n b y suitable subtraction of the numbers obtained with and without radiator. We must note, however, that a small correction, resulting from the fact that the electrons lose some energy in the radiator was not made. The weighted averages of t h e values of Y (eq. 2 ) f o r s o m e counters were used to make the plots of figs. 5, 6 and 7.

PHOTOPROTONS

FROM

CARBON

230

We used the thick 24.46 mg/cm =target in the angular distribution measurement, This made the original energy spread of the protons which are measured in one counter rather big, so that successive counters overlap. For finding the given limiting values for Ep, we took into account the energy loss in the effective target and the width of the counter. For the measurements the current in the spectrometer was slightly changed for the different angles so that protons, cort

C12(e,e,p)

J

0

I

I

~ countersl,2~3 counters 8,9 <~ counters 5,6,7 ~E counters 1,2.3

I

Ep=6.59~6.63 MeV Ep = 6.81 -- 9.09 MeV Ep = 7.'/4 --10.34 MeV Ep ~"9.40~11 .'/4 MeV _

\

30

60 90 120 6 (CENTRE-OF-MASS DEGREES)

150

Fig. 7. A n g u l a r d i s t r i b u t i o n s for E 0 = 40 lVieV of different p r o t o n (e, e ' p ) reaction. Squares: 1.5711+0.27 cos 0 + 1 . 2 7 sin s 0 + 0 . 1 2 sin I 0 cos Full circles: 1.3911+0.35 cos 0 + 1 . 2 6 sin s 0 + 0 . 1 7 sin s 0 cos Open circles: 1.03[1+0.44 cos 0 + 1 . 4 4 sin s 0 + 0 . 2 5 sin z 0 cos Crosses: 0.6311+0.40 cos 0 + 1 . 4 1 sin g 0 + 0 . 4 1 sin g 0 cos

180

energy g r o u p s f r o m the Cis 0] 0] 0] 0]

× × × ×

10 -81 10 -sl 10 -sl 10 -sl

cmS/MeV.sr. cma/MeV.sr. cmi/MeV.sr. cmm/MeV.sr.

responding to the same centre-of-mass energy, were detected at each angle. The absorption of a photon of such an energy that a ground state transition occurred was supposed. This made the value of Ep that must be used for computing Y dependent on the angle. We want to point out that the finite acceptance angle of the spectrometer introduces a small error in the angular distribution if the latter

240

V. ,.1', V A N H U Y S R A N D W . C. B A R B R R

is anisotropic. For our spectrometer, where the ratio of height t o width of the rectangular mouth was 2.5, one finds, for instance, that a real angular distribution 1 ~- 1.5 sin~0 would be measured as 1 ~- 1.49 sinS0. 6£ .xi0-31

J

j f

5~ 4£

yA,~

/

tO

/ /

f I

I

I

elab : 45" £p : ~ 7 5 ~ 7.e8 MeV

.counter 7

J

022v

I

26

24

I

28

1

30 32 34 [o (MeV)

I

36

I

38

40

42

Fig. 8. E x c i t a t i o n of a n e n e r g y g r o u p of p r o t o n s a t 45 ° a s a f u n c t i o n of p r i m a r y e l e c t r o n e n e r g y ,

"x 10-il

i

I

I

I

0ta b : 135" Ep :5.75 4 7 . 8 8 MeV counter 7

022

24

26

28

30 32 Eo (MeV)

I

34

I

36

I

38

40

Fig. 9. Excitation of an energy group of protons at 135° as a function of prhnazy electron energy.

PHOTOPROTONS

FROM

241

CARBOIq

Excitation functions were taken with the 24.46 mg/cm ~ target at two different spectrometer settings. I n each case the Pb radiator was placed in the 2.8 xlO -31 2A 2.(:

Otab = 45 °

0.~

Ep : 7.74~I0.34 MeV

O4

counters

26

28

30

32 34 [ o (MeV)

I

5,6,7.

I

36

1

38

40

42

Fig. 10. Excitation of an energy group of protons at 450 as a function of primary electron energy. ?. x10-28

J~ e

=

i' : 1e 1

4

Ola b : 45 o

i

Ep : 5.?5 - - 7.88 MeV

1 1| !1

i=i, o

a

i

i i 2

1

°

t

0

r ~'¸ I-I. "a:~,a,~_ I " r

|

I

I _T

i i

-1

-2 22

24

26

28

30 32 k (MeV)

34

I I 36

36

40

Fig. 11. Differential cross section for producing protons of a given energy group at 45 °. The 2 MeV steps histogram is derived b y a photon difference analysis of fig. 8, using the experimental points, The 1 MeV steps histogram is derived b y a photon difference analysis using the smooth curve of fig. 8.

electron beam and ZlEo/E o was 0.01. As examples, figs. 8 and 9 show the results obtained from counter 7 for e~b ---- 45 ° and 135 °, respectively, for a proton

242

V. J. V A N H U Y S E

AND

W.

C. B A R B E R

group near the maximum of the energy distribution, while fig. 10 shows the result for the weighted average of counters 5, 6 and 7 for a higher energy group 2~ -x 10-29

I

I T

I

I

glab = 135 °

Ep : 5.75~7.88 MeV

i

I

1;

0

r

I

1 -8

l

-12' 22

24

26

28

34

30 32 k (MeV)

36

38,

40

Fig. 12. Differential cross section for producing protons of a given energy group at 135 °. The histogram is derived from a photon difference analysis of fig. 9 using the experimental points. 20 xlO-29 Olab= 45 °

16

L='p = 7.74 ~ 1034 MeV

8

%1~ 4

"

I

i

0

M

22

24

26

28

30

I

1

I 32

I 34

I

I 36

38

4.0

k (MeV)

Fig. 13. Differential cross section for producing protons of a given group at 45 °. The histogram is derived from a photon difference analysis of fig. 10 using the experimental points.

at 0lab = 45°. The indicated proton energies contain all corrections except this resulting from the momentum transfer due to the absorption of the photon b y the nucleus.

PHOTOPROTONS

FROM

CARBON

243

From the excitation functions, cross sections were obtained (figs. 11-13) b y means of a photon difference analyses. The indicated errors are those resulting from the standard deviations in the excitation function. Most of the measured points in the excitation function were taken at two MeV intervals and two MeV steps were used in the analysis. In fig. 11, a one MeV step analyses is also shown. This was made from the smooth curve in fig. 8 which was drawn arbitrary through the points. As the effective photon spectrum, we took the sum of the bremsstrahlung spectrum produced in the windows and in the radiator (the number of real photons produced in the target is negligible) and the electric dipole virtual photon spectrum ~). The use of only the electric dipole virtual photon spectrum is a good approximation because not much of other types of transitions are involved. From the one-MeV-step cross section of fig. 11, we obtain da

f

d~a

dk ---- (8.7-4-1.7) × 10-~8 cm~/sr,

(5)

which leads to a total cross section of 11.24-2.2 mb if the experimental angular distribution 1+0.25 cos0+ 1.35 sin s 0 is used. The two MeV analysis leads to a total cross section of 10.6-4-2.1 rob. These values do not represent the peak cross section but an average value for the proton energy interval 5.75 to 7.88 MeV which spans the peak. The indicated errors are estimated to be 20 % (sect. 4.3). 4. D i s c u s s i o n 4.1. E N E R G Y D I S T R I B U T I O N S

The proton energy distribution taken at 40 MeV rises steeply to a peak value at 6.0 MeV. The first part of the right side of the narrow peak is steep also. Two small secondary peaks were observed with all the counters in the high energy tail: a first one at about 8.9 MeV and a second smaller bump near 13 MeV. The tail extends to 22 MeV. Since the threshold energy for C12 (~, p) is 15.95 MeV, this means t h a t groundstate transitions must be present up to the end point energy of 40 MeV. The secondary peaks must come from excited states of C12 with an energy of at least 25.5 MeV and 30 MeV, respectively. The form of the curves drawn on figs. 1 and 2 also suggest the possibility of an unresolved peak near 6.8 MeV. It should be remarked that the place of the peaks and bumps in the energy distribution is slightly dependent on the energy of the electrons producing the bremsstrahhing. There is a remarkable agreement with the energy distribution measured with a 35 MeV bremsstrahlung spectrum by Livesey s). Although the statistics are not very good, his histogram shows clearly the main peak at 6.0 MeV and smaller ones at 6.7 and 9.0 MeV. There is also an excellent agreement with the results of the s t u d y of the inverse reaction B 11 (p, ?o) Cla, using monoenergetic protons and looking for ground-

244

v.j.

VANHUYSE AND W. C. BARBER

state transition gamma rays. The yield curve measured b y Gemmell et ~. s) shows the peak cross section at a proton energy at 7.2 l~IeV which corresponds to 7.2 MeV × (1~) ~ ---- 6.05 MeV in our experiment. They do not go high enough in proton energy to be able to see the other peaks. Gore, Batchelor and Litherland 4, 9), who did the same experiment, found their main peak at 7.1 MeV, and a smaller one at 10.5 MeV. In the (p, 7) case these energies correspond to 5.97 MeV and 8.82 MeV, respectively. Furthermore the form of their yield curve suggests the possibility of an unresolved peak at about 8.3 MeV, which is in agreement with our unresolved peak of 6.8 MeV. The energy distribution at E 0 ---- 26 MeV (fig. 3) was taken in order to look for fine structure in the energy region from 4 to 7 MeV. Such fine structure is present in the result of the Pennsylvania group 10). They used a polyethylene target that was slightly thinner than ours (2 mg/cm 2) and E o ---- 25 MeV. Their statistics are rather poor. As is clear from figs. 3 and 4, we did not find resolved peaks, b u t alternating plateaus and rising portions, indicating that the energy distribution cannot be explained b y a single resonance. The small dip at about 5 MeV corresponds with the dip found b y Cohen et ~. lO). The dip at about 5.8 MeV found b y them is not visible on our results. The yield curve for Bll [P, 7) C19 groundstate gamma rays given b y Gemmell, Morton and Titterton s) shows similarity with our results. Although their resolution is good, t h e y find only very small peaks at 21.4 and 22.1 MeV excitation of the C12 nucleus, b u t the curve is otherwise smooth. Their first peak should correspond to about 4.9 MeV in fig. 3. The agreement is rather good. Their second one is not visible in our results. Neither are these results compatible with the data of Katz n), for the "breaks" in the C1~ (7, n) yield curve if one expects to find the corresponding peaks in C12 (7, P). This is well illustrated b y fig. 4. The solid curve shows what should be expected if one starts from Katz' breaks and values of the cross section of the corresponding resonances which are given in table 1, except for low energies. TABLE 1 Breaks in t h e C II (7, n) C 11 yield curve Break energy E i(Mev)

oJ~,a d E ( M e V . rob)

Break energy Et(NIeV)

19.57 19.76 19.92 20.13 20.29 20.62

0.064 0.057 0.11 0.19 0.26 0.56

20.90 21.08 21.22 21.58 22.02 22.88

oi~n d E (MeV. rob) 0.60 0.69 0.87 2.7 2.5 3.8

After subtraction of the threshold energy from the break energy, recoil corrections were made. Neglecting the width of the levels wittr respect to the energy-

PHOTOPROTONS FROM CARBON

245

loss in the target, the latter defines the width of the rectangles of fig. 4, whose surface is proportional to the product of ~ n and the number of virtual photons per energy interval at the corresponding photon energy. This gives the result one should obtain with an apparatus with infinite energy resolution. The complete experimental energy resolution curve for counter 9, given in ref. s), was used to find the solid curve. The agreement with the measured points is not good at all except for the place of the 5 MeV dip. It m a y be possible that more breaks are found in the Cla (~, n) yield curve since Katz' publication. If however, the break experiments are consistent, the early ones should give the same gross distribution as later ones, which discover still finer structure. Thus, we think it is not sure that more breaks will explain the discrepancy. The penetrability of a proton through the Coulomb and angular momentum barriers, being larger than the penetrability of a neutron through the angular momentum barrier alone (for the same k), the width of the proton level will be larger. It is however questionable whether the difference will be sufficient in order to give an explanation for the disagreement with the experiment. 4.2. A N G U L A R D I S T R I B U T I O N S

The experimental angular distributions (figs. 5, 6 and 7) are approximately the same whether the reaction is induced b y electrons or b y real bremsstrahlung. The multiple scattering of electrons in the radiator produces a root-mean-square spread of about 4 ° in the angle of incidence of the bremsstrahlung. The scattering of the electrons in the directly induced reaction results in an angular distribution for the products which is somewhat more isotropic than would be produced b y a beam of photons. Bosco and Fubini 1~) have calculated this effect for the case of electric-dipole transitions. Their result can be extended to show that if the reaction induced b y photons has the angular distribution da~ _ ¢¢+/5 sin a0, dQs

(6)

it will appear as

dcxe-- C Ion+

E/E°

[(Eo/E) +--C~-E0)]2- 2

~+ {1-- [(Eo/E(~)(EIE°) I] ) + (E/Eo)]2-- 2JJ t5 sin z 0], (7)

when induced b y electrons *. In eqs. (6) and (7), 2 = In [2EoE/m(Eo--E)] , where E 0 and E are the initial and final electron energies, respectively, m is the electron rest energy, C a constant, the subscript N refers to the nuclear particle detected in the experiment and terms of order rolE have been neglected in comparison with unity. If we represent the electron-induced angular distribution b y dae/dQ N = a + b sin 2 0, (8) t We are indebted to W. R. Dodge for p o i n t i n g o u t a sign error in eq. (6) of Bosco a n d F u b i n i ' s p a p e r a n d for i n t e g r a t i n g their result over final electron angels so t h a t it corresponds to t h e condition oI o u r experiment.

246

v.J.

VANHUYSE AND W. C. BARBER

we find for the case of the carbon giant resonance, with E 0 = 40 MeV and E = 17 MeV, b 0.943 (r/x) a = 1+0.038 (fl/a)" (9) This smearing of the electron-induced angular distribution toward isotropy is about the same as the smearing of the bremsstraMung-induced distribution b y multiple scattering of electrons in the radiator, and thus it is to be expected that the experimental angular distributions are the same. The angular distributions derived from our experiment are in good agreement with those observed b y Penner and Leiss 3) for the Clz (7, p) reaction, and b y Gore et al 9) for the B 11 (p, 70) reaction. This is shown b y table 2 where the TABLE 2 Comparison of angular distributions observed in C(e, e' p), C(~, p) and B 11 (p, F0) reactions Experiment

Excitation energy (MeV)

Co

C1

Cs

Average of data given b y crosses on figs. 5 and 6 after correction Penner and Leiss a) C(~, p) Gore et al. *) B 11 (p, ~0)

22 to 23 22.1 22.5

0.144-0.02 0.094-0.02 0.124-0.03

--0.504-0.03 --0.564-0.04 --0.694-0.05

Full circles on fig. 7, after correction Penner a n d Leiss a) Gore et al. *)

25 25.3 25.5

0.264-0.04 0.274-0.04 0.294-0.06

--0.494-0.06

--0.59t0.06 --0.574-0.09

angular distributions are expressed in a series of Legendre polynomials [(0) = ~,zC~P, (cos 0). In representing our results in table 2, we have corrected the electron-induced angular distributions given b y figs. 5, 6 and 7 for the small amount of smearing caused b y experimental angular resolution and for the electron effect given b y eq. (9). The agreement between the angular distributions observed in the C(y, p) reaction and those derived, from observations on the C(e, e'p) reaction is a, confirmation of the theory of electron-induced nuclear reactions. The similarity of the angular distributions in the B 11 (p, 70) and the C (~, p) reactions is a confirmation of detailed balancing. The cos 0 term in the angular distribution can result only from mixing of final states of different parity. The results (figs. 5, 6 and 7 and table 2) show that the amount of mixing increases as the excitation energy is increased. Except for the cos 0 term, the angular distribution is in good agreement with the independent particle picture of the giant resonance. In carbon, p- to d-wave transitions are the important ones in producing the resonance. In this case the angular distribtttion predicted 13) in the L - S coupling limit, 1 + 1 . 5 sin 2 0, is in best agreement with the experiments.

P.OTOPRO~O~S

4.3. A B S O L U T E

FROM C * R . O ~ '

347

CROSS SECTION

The cross section (fig. 2), which is based on our measured energy and angular distributions together with the assumption t h a t all protons are the result of transitions leaving the residual nucleus in the ground state, has a peak value of (12.7+2.5) mb and values of 414-9 MeV • mb and 77+18 MeV • mb when integrated to 24 and 40 MeV, respectively. We have assigned a possible 20 % standard error to the results based on estimated errors of 15 % in determining the constants of the spectrometer and detectors (eq. (2)) and uncertainties of about 5 % in our knowledge of the effective photon spectrum and in our extrapolation of the angular distributions. The assumption of exclusively ground state transitions is supported to some extent by the excitation-function analysis, which showed that protons in the energy group from 5.8 to 7.9 MeV are produced with an average cross section of about 11 mb, a result in good agreement with fig. 2. The presence of transitions to excited final states would tend to make our estimate of the integrated cross sections too low. Our results are in fair agreement with that of Penner and Leiss *), who found 8.1 + 2 . 4 mb for the peak cross section leading to ground state transitions only, under the assumption that the full width at half-maximum of the giant resonance is 3.6 MeV. They found that the contribution of transitions to excited final states of B n to the cross section in the neighbourhood of the giant resonance maximum was only of the order of 10 %. An early determination of the C(y, p) cross section from a bremsstrahlung yield curve b y Halpern and Mann 1,) gave a very narrow resonance (1.7 MeV) with a maximum value of 4n(dagoo/d.(2) equal to (34+8) rob, and an integrated value ]*24 MeV d a 9 o °

4~Jo

~-~ X d E = 63 MeV- mb.

A later measurement from the same laboratory Io) determined the proton energy distribution at 90 ° and gave about 18 mb for the peak cross section and 56 MeV • mb for the cross section integrated to 24 MeV if the angular distributions were isotropic. The latter workers remarked that the earlier determination contained an over-correction for absorption of protons in the target which accounted for the discrepancy in the integrated cross sections. If the latter measurements are corrected for an angular distribution of the form 1 + 1.5 sin*0, the results, r' 24

apeak---- 14.7 mb and Jo

MeV

a d E = 46 MeV • mb,

are in agreement with ours. The only s t u d y of the inverse reaction yielding an absolute cross section was t h a t of Gemmell et al. 3). This gave a value of (2.7+0.5) × 10-*3cm * for the peak cross section for the B n (p, Y0) reaction leading to the ground state

248

V. J . V A N H U Y S E AND W. C. B A ~ E R

of C1~. If this value, which was derived from 90 ° measurements under the assumption of an isotropic angular distribution, is combined with the principle of detailed balancing, a result (294-5) mb is obtained for the peak value of the C12 (7, P) B n ground state reaction. After correction for the angular distribution, this value becomes (244-4) mb, which is still considerably higher than any of the recent C(7, p) experiments. (The apparent agreement with the early experiment 14) is illusory because the narrow width observed in that case was not observed in the Blimp, 7o) experiment.) This disagreement between measurements of the reaction and its inverse cannot be reconciled b y consideration of other than ground state transitions. Gemmell et al. 8) were able to resolve the ground-state 7-ray from all others, and hence their experiment should be the exact inverse of that of Penner and Leiss 3). Our result and that of Cohen eta/. lo) included the possibility of transitions leaving excited states of B n, but these can cause only an increase in yield of protons and hence a further discrepancy with the inverse-reaction result. In view of the good agreement between the reaction and its inverse shown b y the energy and angular distributions, it is disconcerting that the absolute cross sections do not agree. The determination of absolute cross sections is, however, subject to experimental errors which are difficult to evaluate, and we feel that more experiments are required to resolve this important problem. The energy at the peak of the cross section curve of fig. 2, can be situated at (22.54-0.2) MeV, which is in excellent agreement with the result of Gemmell et al. 8), who found (22.55-4-0.1) MeV. On fig. 2 we have also plotted the C12(7, n)C n cross section obtained b y Barber, George and Reagan 15), using a photon difference analysis of a yield curve. It is remarkable that there is good agreement between the two cross sections (as one should expect from charge symmetry of nuclear forces, C1~ being a self conjugate nucleus), as far as the place of the peak and the high energy tail is concerned. The large difference in amplitude at the left part of the diagram can partly be explained b y the difference in threshold energy which is 15.95 MeV for (7, P) and 18.72 MeV for (7, n). This causes a difference in penetrability of the potential barriers. As is seen from the angular distribution the ejected protons are d-protons. The same holds for the neutrons which have also an angular distribution that is compatible with 1+ 1.5 sin 2 0 (ref. le)). For a given k and supposing ground state transitions in both cases, the energy of the protons will be 2.77 MeV larger than the energy of the neutrons, and the penetrability of the Coulomb barrier plus the angular m o m e n t u m barrier for Ep = k - - 1 5 . 9 5 MeV will be larger than the penetrability of the angular momentum barrier alone for E n -----k--18.72 MeV. In addition to the barrier effect there is a possible large effect due to the isobaric spin mixing. Radicati ~) and Gell-Mann and Telegdi is) have shown that for any radiation the selection rule AT = 0, 4-1 holds; however electric

PHOTOPROTONS FROM

CARBON

249

dipole transitions between states of the same isobaric spin are forbidden (except for very small contributions from higher order terms in the E 1 operator). This means that for C12 the dipole state is a T = 1 state. Coulomb interactions will relax partially the selection rules and small amounts of the T = 0 state can be admixed to the T ~- 1 state. Barker and Mann 19) have pointed out that such an admixture of about 1 % is sufficient to have a(7, p) ~- 2a(7, n) for C12. This includes already a factor 1.3 due to the difference in barrier penetrability. We should like to thank W. R. Dodge for aiding us in the operation of the equipment and in the analysis of the experimental results. One of us (VJV) wishes to acknowledge the support of the Belgian Interurdversity Institute for Nuclear Science which made his stay at Stanford possible, and to thank Professor W. K. H. Panofsky for his hospitality in making the facilities of the High-Energy Physics Laboratory available to him. References 1 V. De Sabbata, Nuovo Cim. 11 (1959) 225 2 S. Penner and J. E. Leiss, Phys. Rev. 114 (1959) 1101 3 D. S. Gemmell, A. H. Morton and E. W. Titterton, Nuclear Physics 10 (1959) 33 4 H. E, Cove, A. E. Litherland and R. Batchelor, Phys. Rev. Lett. 3 (1959) 177 5 R. F. Post and N. S. Shiren, Rev. Sci. Instr. 26 (1955) 205 6 W. C. Barber and V. J. Vanhuyse, Nuclear Physics l b (1960) 381 7 R. H. Dalitz and D. R. Yennie, Phys. Rev. 105 (1957) 1598 8 S. L. Livesey, Ca. J. Phys. 35 (1957) 987 9 H. E. Gove, private communication to W. C. Barber 10 L. Cohen, A. K. Mann, B. J. Barton, K. Reibel, W. E. Stepheus and E. J. Winhold, Phys. Rev. 104 (1956) 108 11 L. Katz, Washington Photonuclear Conf. (May 1958) 12 B. Bosco and S. Fubini, Nuovo Cim. 9 (1958) 350 13 A. K. Mann, W. E. Stephens and D. H. Wilkinson, Phys. Rev. 97 (1955) 1184 14 J. H~dpern and A. K. Mann, Phys. Rev. 83 (1951) 370 15 W. C. Barber, W. D. George and D. D. Reagan, Phys. Rev. 98 (1955) 73 16 V. E m m a , C. Milone and A. Rubbino, Phys. Rev. 118 (1960) 1297 17 L. A. Radicati, Phys. Rev. 87 (1952) 521 18 M. Gell-Mann and V. L. Telegdi, Phys. Rev. 91 (1953) 169 19 F. C. Barker and A. K. Mann, Phil. Mag. 5 (1957) 2