Photoalpha reactions below 21.5 MeV with 14N and 16O

2.I

[

Nuclear Physics 54 (1964) 625----640; (~) North-Holland Publishing Co., Amsterdam

I

Not to be reproduced by photoprint or microfilm without written permission from the publisher

PHOTOALPHA REACTIONS BELOW 21.5 MeV WITH 14N AND t60 M. E L A I N E TOMS

U. S. Naval Research Laboratory, Washington, D.C. Received 20 January 1964 Abstract: Cross-section measurements integrated to 21.5 MeV have been made for the l~N(y, ~)t°B reaction (59 everits), the t60(7, ~)mC reaction (48 events) and the tee(7, 4~) reaction (53 events), with the assumption that ~°B and x~C were left in their ground states. The values for the singlealpha events are 0.74-t-0.11 M e V . mb for 14N and 0.055 +0.008 MeV • m b for 1cO. The value for the four-alpha events is 0.124-t-0.017 MeV • mb. Partial cross-sections for the distinct modes of 1cO breakup into two aBe nuclei both in the ground state, and via the 7.7 MeV state of ~2C, are 0.015-4-0.006 M e V . mb and 0.0534-0.011 M e V . mb, respectively. The distribution in angle between the alpha and the photon direction for the t e e 0 , , ~)12C reaction (12C assumed to be in its ground state) gives an E2/EI intensity ratio of 0.3 while for the 7.7 MeV state the ratio is 0.2. The smallness of the cross-section for the photodisintegration of xaO yielding an alpha or four alphas, being 0.184-0.02 MeV • mb, agrees with the strongly inhibiting effects of A T = =El for E1 absorption and for no change in T for alpha decay. E[

N U C L E A R R E A C T I O N N1'(7' c0' F"e --~ 21"5 MeV; measured (7(E)" Ole(7, ~), (7, 4a), E v <; 21.5 MeV; measured a(E, E~), F, o~(0).

]

1. Introduction

Photoalpha reactions with light-element constituents of nuclear emulsions have been studied by various groups of investigators. Nabholtz et al. 1) used gamma rays from the 7Li(p, 3') reaction to obtain a distribution in energy of alpha particles produced singly. Goward and Wilkins 2) used bremsstrahlung of various energies to study the 12C(?, 300 and 160(~,, 4a) reactions. MiUar and Cameron a) investigated photoalpha reactions with light elements in emulsions irradiated by aluminium filtered 24 MeV and 27 MeV bremsstrahlung. Livesey and Smith 4) reported results for the ~2C(?, 3~) and ~60(~, 4a) reactions produced in emulsions exposed to bremsstrahlung of maximum energies between 26 arid 32 MeV. Erdrs et al. ~) measured the cross-section for a single alpha particle from 160 by using 31 MeV bremsstrahlung. Stoll 6) reported further on that work and on the investigation of the 14N(~,, ~)I°B reaction. Dawson and Livesey 7) studied the ~60(?, 4~) reaction by using emulsions exposed to bremsstrahlung from a 70 MeV synchrotron. In order to investigate carefully the ~2C(y, 3c0 reaction 8), all photoalpha reactions with nuclear emulsion constituents were considered. Tracks produced by alphas from the heavy elements, silver and bromine, have no recoil tracks associated with them and could be distinguished visually from other photoalpha reactions. Measurements of events consisting of a single alpha track with a recoil track and events showing four alpha tracks give information concerning photoalpha reactions with nitrogen and oxygen. 625

626

M.E. TOMS 2. Experiment

The results concerning the X2C(7, 3ct) events observed in volumes o f Ilford E. 1 nuclear emulsions exposed to 21.5 MeV bremsstrahlung filtered by 86.2 cm of graphite or by 41.9 cm o f aluminium have been reported B). In the same volumes o f emulsion 110 recoil events and 53 events from the l~O(y, 4=) reaction were observed• As a recoil event might be produced by the photodisintegration o f a 160, X+N or 13C nucleus, calculations were made for each event in the centre-of-mass (c.m.) system of each o f the three possible target nuclei. Since the breakup o f 160 into four alphas 2

I x\

>=

_

,+* . . . . ;. . . *. . . .

;",, C

,,

•

~

~-a5

........

",*** +÷ ,~** +,,

~---"

it. ~'

•

.

~-

+;;.r- C,-- . . . . . . . . . . . . . 2 . b,r

"I.-" ".%.°

° I

x,4

\\

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".

i

u

t~

' INDENTIFICATION CHAR" ',FOR THE REACTIONS + 160 (7, a) IZC

/

-2~-

-~-

L

• =4N (7,a) lOB • 13C (7,e)

9Be

el

f

-,

-o5 o 0.5 I E r ( a } - E r (R) FOR 108 IONS (MeV)

2

Fig. 1. Identification chart for alpha-plus-recoil events. Events are plotted by the difference in energy for recoil based on the alpha energy F_=(¢) and based on its range Er(R) for Z°Bions versus the difference for ztC ions. may proceed directly, via an excited state of 12C or via two aBe nuclei, calculations were made in the c.m. system o f the 160 nucleus which included all possible breakup modes. The appendix gives details o f the calculations for the recoil events and the four-alpha events. In order to calculate quantities in the c.m. system of a target nucleus, the effects of photon m o m e n t u m need to be removed. Convenient units for m o m e n t u m are (atomic m a s s . MeV) +. The photon m o m e n t u m P7 was considered to be E~,/(mc2) + = 0.0328 E r and the m o m e n t u m o f an alpha or a recoil nucleus P , to be (2M, E,) ½ where M , is the mass in atomic mass units and the energy E, is in MeV. Goward and

PHOTOALPHA REACTIONS

627

Wilkins 2) used other self-consistent values; namely, Pn = ()linE,) ½ and Pr = Er[(2mc2)~ = 0.0232 E~. The difference in these factors enters into the size of the units of momentum imbalance Ap. For the recoil events the three possible reactions t60(~, ~)12C, I*N(v, ~)l°B and 13C(y, ~)9Be have binding energies for the alpha of 7.148 MeV, 11.615 MeV and10.654 MeV, respectively 9). For each reaction a value for the photon energy E r was given by: Er = (1 + f ) E , + E b, where f i s the ratio of the mass of the alpha to the mass of the recoil nucleus, E~ is the energy of the alpha obtained from its range and E b is the binding energy. It was necessary to assume that the recoil nucleus was in its ground state. The validity o f this assumption will be discussed later. On the basis of the alpha energy three possible recoil energies Er(c¢) were obtained. A plot of these values versus the measured range o f the recoil nuclei showed that 48 events should be classified as due to the 160(~, ~)12C reaction, 59 to the I*N(~, c~)t °B reaction and three to the i3C(~,, ~)9Be reaction. This method of distinguishing the three reactions was similar to that used by Millar and Cameron 3). These data yielded range-energy relationships for t°B and t2C ions which were nearly the same as those found by Millar and Cameron. For each event values of the energy of the recoil nucleus based on its range E~(R) were obtained for l°B and 12C. The events are plotted in fig. 1 by the difference E~(~x)-E~(R)for a oB against the difference for 12C. The separation of the events on the basis of which energy difference was nearer the zero line for either residual nucleus is shown. Three events do not fit the patterns for X°B or 12C but are consistent with being due to the 13C(?, ~)gBe reaction.

3. The 14N(~,, ~)t°B and t60(~, at)t2C Reactions The 14N(~,, ~)x oB reaction has been studied in nuclear emulsions primarily to distinguish it from the 160(?, ~)12C reaction. Millar and Cameron 3) distinguished 40 events of the I~N type from the 160 type. Since the residual nucleus lOB has several photon-emitting states in the excitation energy region from 0.7 to 7.6 MeV, the assumption that it is left in its ground state may be very poor. The photon energy Er was obtained using this assumption and in order to obtain cross-section values spectral intensities corresponding to E~ were used. In fig. 2 the cross-section data for the 59 events from the I*N(?, ~)I°B reaction are plotted against E~-E* where E* is the unknown (but assumed to be zero) excitation of ~°B. The cross-section data are shown as a curve rather than as a histogram as the same moving weighted averaging was applied to the data that was used for the 12C(~,, 3~) data s). Typical uncertainty values are shown. The bulk of these data can be attributed to X*N excitation of at least between 16 and 19 MeV. This is a region of excitation for which data are not available from investigations from other reactions 9). The value of the cross-section integrated to 19.2 MeV was found to be 0.55+0.08 M e V . mb and is in agreement with the value up to 19 MeV estimated from Stoll's 6) measurement to be 0.43 MeV • mb.

628

M.E.

TOMS

For excitation with 21.5 M e V bremsstrahlung the assumption that the residual nucleus f r o m the 160(7 , ~)lZC reaction is left in its ground state m a y be rather g o o d

o5I

14N (),=)lO B

0.4

0.3 .,o E b 0.2

O,t

1

15

I 16

17 tSE y - E * (MeV}

19

20

21

Fig. 2. The cross-section for the :4N(y, a)l°B reaction versus Er--E* where Ey is the photon energy if E* equals zero and E* is the ~°B excitation energy. 0.03 I te 0 (7a)'Zc

t

0.02:t - E b 0.0~

I0

II

12

t5

14 15 16 E y - E * (MeV)

17

18

19

20

21

Fig. 3. The cross-section for the x60(7, ~)t=C reaction versus ET--E*where E~ is the photon energy if E* equals zero and E* can be either zero or 4.43 MeV, the ~C excitation energy. as the only g a m m a - e m i t t i n g state available is the one at 4.43 MeV. T o calculate crosssection values for the 48 events f r o m the 160(~, ~)12C reaction this assumption w a s

PHOTOALPHA REACTIONS

629

used. These values are shown plotted as a curve in fig. 3 versus E r - E* where the 12C excitation E* was assumed to be zero but could be 4.43 MeV. MiUar and Cameron 3) show relative cross-section data from events produced by 24 MeV and 27 MeV bremsstrahlung and give an absolute value for their peak near 17 MeV of 26/tb. The statistical uncertainties of the two measurements bring the values at that energy into agreemeat. However, these values are smaller by about an order of magnitude than the value 195_+80/~b given by Nabholtz et al. ~) at 17.6 MeV produced by photons from the 7Li(p, ~) reaction. Their value was obtained by measuring all single alpha tracks in the emulsion including tracks formed by alphas from the heavy elements, subtracting the contribution from Br (indicated as a curve peaked near 10.5 MeV alpha energy) and estimating the numbers of ~60 events from a peak near 8 MeV of alpha energy. Without separation of the single alphas from alphas accompanied by a recoil nucleus the identification of reactions contributing to the alpha energy distribution is subject to considerable error. The cross-section data of Millar and Cameron are given in energy intervals of one MeV so that agreement of their data with this investigation at one energy does not necessarily indicate agreement for the integrated cross-section. For the region up to 19.5 MeV the estimate from their data gives a value of 0.104 MeV" mb while these data give 0.048_+0.007 MeV" mb. Up to 14.5 MeV the two values of the integrated cross-section are equal, being 0.028 MeV. rob, so that between 14.5 and 19.5 MeV their data give a value three times that given by data from this investigation. Most of their data (,-~~) came from the 27 MeV exposure and the difference in available energy over the 21.5 MeV exposures may increase the number of E r - E * values between 14.5 and 19.5 MeV by more participation of the 4.43 MeV and 7.7 MeV states of 12C. The breakup of the 7.7 MeV state into three alpha particles produces tracks which lie close together and can be mistaken for a recoil track. Erd6s et aL 5) report values of the crosssection for the 160(~, ct)l 2C reaction by E ~ - E * from data obtained by using 31 MeV bremsstrahlung. The integral of their values up to 19.5 MeV is estimated to be 1.15 MeV. mb or about ten times the value obtained by Millar and Cameron. Even though more photon-emitting states of 12C become available with higher energy, one would not expect an increase of 4 MeV in bremsstrahlung energy to make such a large difference in cross-section values. The small values of the cross-section for the 1600, , ~)12C reaction found in this investigation in the region up to 21.5 MeV are in agreement with the strongly inhibiting nature of the isobaric spin selection rule of A T = ___1 for E1 photon absorption and the companion inhibiting of the decay by alpha emission of T = 1, J = 1- states, excited by E1 absorption, when only T = 0 states are available in the residual nucleus. From the ~2C(~, 3c~)results s) it was found that such reactions are not totally forbidden. If one assumes that ~2C is left in its ground state for the 48 observed 160 events, the angular intensity 1(0) = N(O) cosec 0 versus the angle 0 may be interpreted as showing mixed El and E2 interactions where 0 is the angle between the alpha particle and the photon direction. Goward and Wilkins 1o) give the expression for these in-

630

~. E. TO~tS

teractions involving initial and final states of the nuclei being both J = 0 + as I ( 0 ) = (1 + 2 k cos r/cos O + k 2 cos 2 0) sin 2 0,

where r/is an arbitrary phase angle and the E2/E1 intensity ratio is 0.2 k 2. The plot of I(O) values for these events by 30 ° intervals of 0 is shown as the points in fig. 4 with uncertainties indicated. The curve shown is for 1(0) = 14.6(1 + 1.5 cos 2 0) sin 2 0. As there is no definite indication of asymmetry around 90 ° the phase angle was chosen to be 90 ° and with k 2 = 1.5 the E2/E1 intensity ratio is 0.3, that is E1 interactions have an intensity of about three times that for E2 interactions.

0.10(..

iSo ( y.a ) '= C I (0) = 14.60 * t.5 cos=8)sin=8 E2/EI = 0.3

'60 ( y, 4(=}

20 00Sl-

15

"+tO[

b

r

0"04i -

0

'

--

!

L

45 0

90 DEGREES

I;35

180

Fig. 4. The intensity distribution/(0) = N(O) cosec 0 in 30 ° intervals o f 0, w h e r e O is t h e angle between t h e a l p h a a n d t h e p h o t o n direction. T h e curve 1 ( 0 ) = 1 4 . 6 ( 1 + 1 . 5 cos ~ 0) sin * 0 is b a s e d o n t h e a s s u m p t i o n t h a t 1=C is left in its g r o u n d state. A ratio o f t h e intensities o f p h o t o n interactions E2/E1 = 0.3 is indicated f r o m the fit o f the curve.

/

~

160 EXCITATION (MeV) Fig. 5. The cross-section for the xeO(7, 4¢) reaction versus aeO excitation energy.

4. The 160( 7, 4=) Reaction The photon energy E~ which produced a t60(~,, 4~) reaction can be obtained unambiguously from the sum of the energies of the four alphas plus the binding energy, E b = 14.429 MeV 9). The excitation energy E~ of the 160 nucleus differs only slightly from Ey as the calculations in the centre-of-mass system (indicated by primes) have

PHOTOALPHA REACTIONS

631

little effect on energy values, more effect on momentum values and the most effect in the determination of angles. (See the appendix for details of calculations.) The crosssection data for this reaction are plotted as a curve in fig. 5 versus 160 excitation energy with typical uncertainties indicated. The value of the cross-section integrated to 21.5 MeV is 0.124+0.017 MeV" rob. All of this cross-section lies below the first major peak found by other investigators at 22.5 MeV. Estimates of the cross-section from the data of Millar and Cameron 3) integrated to 21.5 MeV and to 26.5 MeV are 0.082 MeV. mb and 0.44 MeV" rob, respectively, while the values from the data of Goward and Wilkins 2) are 0.07 MeV. mb and 0.92 MeV" rob. Dawson and Livesey 7) give their value up to 26.5 MeV as 1.3 MeV" mb. The 160(y, 4g) reaction can have various modes of breakup: besides direct quadripartition, it may proceed through an excited state of 12C with or without an 8Be nucleus being involved or it may proceed via two 8Be nuclei which may be in their ground state or in an excited state. It is also conceivable that 160 might have a threebody breakup involving two alpha particles and an SBe nucleus. When the breakup process includes an SBe nucleus in its ground state, it is generally observable by the characteristic small v formed by the two alphas as it breaks up. When two 8Be nuclei both in their ground state comprise the mode of decay, a double v-formation is observable. Most investigators have attempted to determine possible modes of breakup for events which showed an SBe in its ground state to be involved, by calculating possible 12C excited states or the excitation of a second 8Be nucleus. Millar and Cameron 3) concluded that such events which they observed were most likely due to tripartition of 160. Goward and Wilkins 2) found evidence of the 9.63 MeV state of 12C to be involved in the breakup for some events. Livesey and Smith 4) found 12C excitations of 9.6 MeV and 11.3 MeV to be consistent with their data. Dawson and Livesey 7) found excitations of 9.6 MeV and 10.8 MeV for the intermediate 12C nucleus. All of these investigators found the 8Be ground state to participate strongly below 25 MeV photon energy. For this investigation, calculations of all possible modes of breakup in the c.m. systems of 160 and of possible intermediate nuclei made it unnecessary to depend on visual observation to determine whether an SBe nucleus in its ground state was involved in the breakup process. It was found at these excitations of 21.5 MeV or less, that all the events had a probable mode of breakup that involved a ground-state SBe nucleus. By considering the height of the Coulomb barrier for an alpha particle from 160 in the c.m. system as being about 2.2 MeV, probability categories for an alpha to be the first alpha were established as > 2.2 MeV-high, 1.65 to 2.2 MeV-good, 1.1 to 1.64MeV-fairand < 1.1 MeV-poor. Likewise for 160 to break up into two SBe nuclei in the c.m. system the Coulomb barrier was considered to be 1.0 MeV and probability categories for this process were > 1.0 MeV-high, 0.75 to 1.0 MeV-good, 0.50 to 0.74 MeV-fair and < 0.5 MeV-poor. On the basis of these probabilities various possible modes of breakup for each event were given numerical weights and the most probable mode or more probable modes were determined. Seven events (probability sum = 6.0)

PHOTOALPHA

633

REACTIONS

could be determined for these events, the angle ~ between that alpha and the photon direction was obtained. The angular intensity I(~) = N(~) cosec ~ is shown plotted in 30 ° intervals of ~/, in fig. 6 as the points with uncertainties indicated. ' Since the 7.7 MeV level of 12C has J = 0 +, the same formula for mixed E2 and E1 interactions (see sect. 3 above) could be applied. The curve shown is for I(~) = 7.4(1 - 1.732 cos + c o s 2 ~) sin 2 Ip. The phase angle ~/was chosen to be 150° and as k equals unity the E2/E1 intensity ratio is 0.2 and is similar to that found for the 160(y, ~)~2C reaction. The third group of ~60(?, 4~) events includes the remaining 24 "other" events each of which had more than one probable mode of breakup. The sums o f probability weights for breakup via two aBe nuclei have been plotted in fig. 7 versus aBe exciPROBABILITY FOR - ~ E t 6 0 ()t,Q} ~2C*(>7.7 MeV) VENTS) Z= 15.5

3.0

m 2.0

m a. m

--L_

F

8.1

I

1

I

9.0 9.9 12 C EXCITATION

10.8

(MeV)

Fig. 8. Sums of probabilities for 24 "other" events of breakup via 1~C excited states versus 12C excitation energy.

tation energy in 0.3 MeV intervals. (The sums were divided by two as both of the 8Be excitation energies were counted.) The graph seems to indicate that some events may have been formed by a two aBe breakup with one nucleus in the ground state and the other in the 2.9 MeV excited state. The sum of the weights is 8.7 so that perhaps as many as one-third of these events were thus formed. The probability weights, for the same events, for breakup via a 12C intermediate nucleus were summed and are shown in fig. 8 plotted against 12C excitation energy jn 0.3 MeV intervals. The sum of these values is~:l5.3 and indicates that a majority of the "other" events were probably formed by breakup of 12C excited higher than 7.7 MeV. Indication of the participation of the 9.6 MeV state of 12C is quite strong. These results do not eliminate the possibility that a fe~y events could have been formed by tripartition of 160 into two alphas and an 8Be nucleus or by direct quadripartition of 160.

634

M.s.

TOMS

In order to verify the selection of events into these three groups, the relative energy d' = 1.33 E'~/E~ was computed for each alpha, where E" is the alpha energy and E~ is the sum of the four alpha energies. The use of relative alpha energies facilitates comparison of events produced by various excitations irt order to observe patterns characteristic of breakup modes. The number of values, four for each event, are shown in fig. 9 plotted against relative energy. The results for the two groups whose breakup

>~ ~)

,ii o.o

VIA TWO 8Be IN GROUND STATE (7 EVENTS)

o.,

o.,

o.,

,.o

=SO (y,4=) VIA IZc Z7MeV STATE (22 EVENTS) 20

=,t5

>~

o. I0 o

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D

0.1

J

0.2

~

0.3

I 0.4

I 0.5

1 0.6

0.7

0.8

0.9

1.0

leO (y, 4a)

20-

OTHER BREAKUP (24EVENTS)

c OD

O.I

0.2

0.5 0.4 0.5 ALPHA RELATIVE

0.6

0.7

0.8

, 0.9

V

1.0

ENERGY

F i g . 9. Alpha relative energies (four values for each event) for the three groups: via two 8Be nuclei in their ground states (above), via the x2C 7.7 MeV state (middle) and via "other" modes (lowest), where shaded areas indicate via 1=C excitation of 9 . 6 4 - 0 . 4 M e V .

mode is definite, are as would be expected; a clustering of low 8 values for the two8Be ground-state mode and for the 7.7 MeV 12C excitation mode, one high ~ value and three low d ~values for each event. The lowest histogram of fig. 9 shows the plot of 8 values for the "other" events with the shaded areas indicating values associated with 12C excitation of 9.65:0.4 MeV. Partial cross-section curves for the three groups are shown in fig. 10 where the upper two curves are for the two definite breakup modes. The lowest curve shows small

PHOTOALPHA

0.020"03IIsO ()"eBe)

O.~L II ~ ~ 1 16.5 17.0 17,5

635

abe

'~ ' ~ 2 ,

I

18.0 18.5 19.0 19.5 20.0 20.5 210 21.5

.ob 005 I..sa o.02!L-~-Is° ()"'°~c* ( 77 MeV) ~

o o o ~ 006

REACTIONS

~~/

~

' Tf

2'°~o~-~5

- ,So ( 7, 4= )

T

OTHER

i

0.05-

g

,

b 003

-

[

0.02

ooV

\ 160 EXCITATIONENERGY(MeV)

Fig. ]0. Partial cross-sections for the three ~'oups: via two 8Be nuclei in their ground states (above), via the 1=C 7.7 MeV state (middle) and via "other" modes (lowest).

0.05

'60 (7, a) 12C ANDIZC* (7.7MeV)

0.04 - 0.03 -b 0.02 0.01

--

0.009...... _L_ ~0

II

12

13

14 15 16 17 18 160 EXCITATION (MeV)

19

20

Fig. l 1. T h e cross section for leO( F, ~t)~C and 1~C*(7.7 MeV).

21

' M. ~. T O M S

636

participation below 19.5 MeV but between 19.5 MeV and 21.5 MeV the cross-section for these "other" events accounts for 59 % of the total. This percentage indicates the tendency for modes involving higher excitations of 12C and 8Be to participate strongly when sufficient energy is available. This tendency is seen also in fig. 11 where the cross-section for the 12C 7.7 MeV mode has been combined with the cross-section for the 160(V, ~)12C reaction (fig. 3) to give a total cross-section for photoalphas from 160 leaving 12C in an excitation up through 7.7 MeV, Up to 16.3 MeV the integrated cross-section is 0.035 MeV. mb and is due entirely to the 160(~, ~)12C reaction. Between 16.3 MeV and 21.5 MeV, where there is suttieient energy for 12C to •

. :.:.

O.10r 160 ( T , O ) 12C A N D I 6 0 ( y , 4 = )

0.0~

OO~

b

0.01

9.0

I0.0

I1.0

12.0

13.0 14.0 15.0 160 EXCITATION

16.0 1 7 . 0 (MeV)

18.0

1 9 . 0 20.0

21.0

Fig. 12. The cross-sectionfor the photodisintegratton • of leO yielding an alpha particle of four alpha particles. (Combination of figs. 3 and 5). break up, the integrated cross-section is 0.072 MeV • mb of which 73 ~ is due to the 160(y, ~)12C*(7.7 MeV)reaction. The fact that the 12C 7.7 MeV mode of breakup contributes practically the same amount to the cross-section integrated to 21.5 MeV as does the 160 (~, ~) 12C reaction confirms the validity of the magnitude of the latter cross-section. The total cross-section for the photodisintegration of 160 yielding an alpha particle or four alpha particles is shown in fig. 12 which is the combined cross-section data of the 160(~, ~)12C reaction ('fig. 3) and the 160 (y, 4~) reaction (fig. 5). The value of the cross-section integrated to 21.5 MeV is 0.18 + 0.02 MeV • rob. The magnitude of the

PHOTOALPHA REACTIONS

637

peak at 20.5 MeV is 0.075 mb which is one-fourth the magnitude found by Goward and Wilkins 2) for the first major peak at 22.5 MeV.

5. Conclusions The cross-section measurements for the 14N(7, ~)I°B reaction have the inherent uncertainties associated with the possibility that 1oB is not left in its ground state. In the energy region of study the magnitude of the cross-section is about four times that for the 160(7, ~)12C and 160(7, 4~) reactions combined. Below an excitation of 16.3 MeV the 160(7, ~)12C reaction is dominant as insufficient energy remains for 12C to be disintegrated. The 160(7, 4~) reaction can proceed through two 8Be nuclei in their ground states. A large proportion of events attributed to breakup via the 7.7 MeV state of 12C was observed. With excitation energies above 19.5 MeV higher 12C excitation may be involved (especially the 9.6 MeV state) and breakup via two SBe nuclei, one in the ground state and one in the 2.9 MeV state, becomes possible.

Appendix A.1. MEASUREMENTS AND INPUT DATA The components of length in emulsion coordinates Lx, Ly andL, with respect to the centre of the event for the alpha track and the recoil track or for the four alpha tracks together with the depth factor d were the values which comprised the input data for the computer programmes. The value d was obtained for each event in order to compensate for possible changes in the processed emulsion thickness. In addition to containing the shrinkage factor for the emulsions, the value d included the fine focus calibration of the microscope. The reticule calibration factor k was a constant so that the length coordinates in micrometers were kLx, kLy and dLz. A.2. COMPUTATIONS FOR ONE-ALPHA-PLUS-RECOILEVENTS The lengths L~ and L r for the alpha track and the recoil track and their direction cosines 2,/~, v)~ and 2, #, V)r were calculated. The energy of the alpha E~ was obtained from L~ by using the range-energy relationship. The components of alpha momentum Px~, Py~ and P,, were obtained from P, = (8E~)½ with Px~ = 2~P~, Py~ = /~P~ and Pz~ = v~P~. The three possible reactions 160(7 , ~)12C, 14N(7, ~)l°B and 13C(7, ~)gBe have binding energies for an alpha of 7.148 MeV, 11.615 MeV and 10.654 MeV, respectively 9). A value for photon energy Er was calculated for each possible reaction with E r = (1 +f)E~+E b

(A.1)

wherefis the ratio of the mass of the alpha to the mass of the recoil ion and E b is the appropriate binding energy. This assumes that the recoil nucleus was left in its ground state. The photon momentum Pr = Er/(rnc2) ~ = 0.0328 Er and its components were

638

M.E. Torts

obtained. For both emulsion plates P ~ = Pr cos 67.5 ° and Pyr = zero; for plate a Pzr = P~ sin 67.5 ° and for plate b Pz7 = - P ~ sin 67.5 ° in emulsion coordinates. The components of alpha momentum in the c.m. system of the target nucleus are:

p " = Px~-qP~r, v;= = P,=, P~: = P::-qP:7' where q is the ratio of the mass of the alpha to the mass of the target nucleus for each case.

Alpha energy values in the c.m. system differ slightly for the three cases, E" values being obtained from the three momentum values P" by E~' = ~p,2 where p,2 = p,2 a- p,2 4_p,2 Excitation values E i for the target nuclei were obtained from eq. (A.1) where E" is used instead of E~. New direction cosine values for the alpha 2'_ = , ,+ , , ,+ Pj,:/(8E;) and v: = P~:/(8E~) for each case were used to compute the angle between the alpha and the photon direction from cos Cx. 2.3 = 2'=x,2, 3 2~+v'=1.2. 3v~ for the three possible target nuclei, where ;tr and vr are the direction cosines of the photon direction in emulsion coordinates. The energy of the recoil nucleus based on the alpha energy is given by: E'(o 0 = f E ; w h e r e f i s the ratio of the mass of the alpha to the mass of the recoil nucleus. The energy given to the recoil by the momentum of the photon is sufficiently small that it can be neglected, hence E~(~) = E,(~). In order to calculate the amount of momentum imbalance Ap, momentum components for each possible recoil nucleus were obtained by multiplying the direction cosines for the recoil by the value [2m, E,(00] ~ where m, is the mass (in atomic mass units) of the recoil and E,(o~) is the corresponding energy based on the alpha energy. The value of Ap is given by

ap = [(ZP=) ~ + (ZP~) ~ + (Zp=)2]+, where

ZPx = P~=+P::-P:~, A.3. COMPUTATION

FOR

THE

ZP, = Py=+Py: and ZP: = P,=+P:,-P:r. x 6 0 ( y , 4o0 R E A C T I O N

A.3.1. For the events as a whole. The length L,,b.c,d of each alpha track (subscripts a, b, c, and d refer to the observed tracks) were computed and the energy for each alpha was obtained by using the range energy relationship. The momentum Pa, b, c.d in (atomic mass • MeV) + units was found for each alpha from P~ = (8E~) + and the momentum components for track a are given by Pxa = kLx, PdL~, Py~ = kLyaPJLa and P~a = dL=~P,/L~ and likewise for tracks b, c and d. The photon energy E r is the sum of the alpha energies Ea- plus the binding energy 14.429 MeV 9). The photon mo-

PHOTOALPELA REACTIONS

639

mentum P~ = 0.0328 E~ was obtained and its components in the same manner as for the recoil events. The effects of photon momentum were removed by subtracting from each component of alpha momentum ¼ the appropriate component of photon momentum. The quantities in the e.m. system of 160 are indicated by primes and quantities in the c.m. system of an intermediate nucleus by double primes. For each alpha its energy Eat,b,c,d was obtained from £" = ~p,2 where p,Z = -p'24"p'24-P'2x~--y~ --z~ and the amount of momentum imbalance Ap is given by Ap = [(I;P~) 2 + (ZP~) 2 + (ZP~)2] ½,

where the sums are over the four alphas. The excitation energy of the ~ O nucleus E~ equals E~ plus the binding energy. Direction cosines in the c.m. system were obtained for each alpha from 2' = P~,/ (8E') ½, #' = P~/(SE') + and v' = P~/(8E') ~. The cosine of the angle between an alpha and the photon direction is given by the sum of the products of the direction cosines and, for alpha a, can be written cos ~ka = 2; 2~ + v" v~ where 2~ and vy are the direction cosines of the photon direction in emulsion coordinates. A.3.2. For breakup via an excited 12C nucleus. The possible 12C excitation energy values E* are given by E* = E~ - ~ E ; +7.28 MeV, where the subscript one refers to the alpha chosen as the first alpha to leave 160, (Each of the four alphas was taken in turn as a possible first alpha.) and 7.28 MeV is the binding energy of an alpha in 12C. The kinetic energy of the three alphas in the c.m. system of 12C is given by ~r

/7p 4ig,, ~t"T - - 3 ~'1 •

Each of the three other alphas was then considered as the second alpha (first from the 12C nucleus). Components of momentum in the 12C c.m. system for alpha 2 are rr

D~

1Dr

P2 (x, y, z) = -2(~ y, z) --~-1 ix, y, z), from which P;' was obtained and E;' was computed and the possible SBe excitation energy E34 is given by E3,, = E ~ ' - I.5 E~'. A.3.3. For breakup via two SBe nuclei. Let the subscripts 12, 13 and 14 refer to the three ways of taking alphas by pairs to investigate possible two SBe breakup. The momentum components for one of the SBe nuclei are P:,,:.,: ,,, = P'a + P~
and likewise for Py<,:. ,~. ,,~ and P:.:. ,:, ,,>. From these components P12. la 14 were obtained and the kinetic energy of either SBe nucleus of each pair is 1

E 1 2 , 13p 14. -~- ~

p2

12,13j14.

M. E. TOMS

T h e possible SBe excitation energies of the first pair are:

Ex12 = E ~ + E ~ - E 1 2

and Ex3, = E~-I-E~-E12

and likewise for Ex13 and Ex24 and for Ex,, and Ex23.

References I) H. Nabholtz, P. Stolland H. Wiiffier,Helv. Phys. Acta 25 (1952) 701 2) F. K. Gowaxd and J. J. Wilkins, Proc. Phys. Soc. 63A (1950) 1171, 64A (1951) 94 and 65A (1952) 671 3) C. H. Millar and A. G. W. Cameron, Can. J. Phys. 31 (1953) 723 4) D. L. Livescy and C. L. Smith, Proc. Phys. Soc. 66A (1953) 689 5) P. Erd6s, J. Schmouker and P. Stoll,Helv. Phys. Acta 27 (1954) 186 6) P. Stoll,Helv. Phys. Acta 27 (1954) 395 7) W. K. Dawson and D. L. Livesey, Can. J. Phys. 34 (1956) 241 8) M. E. Toms, Nuclear Physics 50 (1964) 561 9) F. Ajzenbcrg-Selove and T. LRuritscn, Nuclear Physics 11 (1959) I 10) F. K. Goward and J'.J. Wilkins, Proc. Roy. Soc. A228 (1955) 376