DISCUSSION

I Fast F ast

VII. DISCUSSION

-68-

-69-

(J-/ (J+ ratio for 9\,. z 90⁰ and 60⁰ plotted versus K in comparison with the (Jno / (J0 ratio obtained in this experiment. Although the ratio of (Jno / (J0 at 875 ITIev seems to be a little larger and the ratio at 750 mev seems to be a little smaller than the ratio (J-/ (J+, the data in gen- eral seeITI to agree with the assumption that both the second and third resonances are dominated by I" 1/2 state. Certainly the data rule out the possibility of having an I '" 3/ 2 state dOITIinating in this region

. no/ 0 - /

+

which would require the ratIo of (J (J as well as (J (J be equal to one.

Figure 23 shows the (JD / 2(JH ratio obtained by Bingham at various angles plotted as a function of K in cOITIparison with the ratio obtained in this experiITIent. Since only two points can be cOITIpared directly, no definite conclusion can be drawn. In general, the data agree within statistics, even though the results of this experiment show a definite tendency to be lower than tho se of BinghaITI. The figure also includes the low energy data of Tollestrup et al. (4) on the ratio D/ 2H.

The cross section for photoproduction of a neutral pion froITI the neutron as shown in Figure 21 doe s not show a third resonance.

However, the statistical accuracy is too poor and the nUITIber of data points too few to draw any definite conclusion.

Contrary to our original hope, no information on the value of angular mOITIentUITI quantUITI number is obtained from the experiITIent due to the scarcity of data points. An order of magnitude improvement on the counting rate ITIust be ITIade before enough data can be obtained in a reasonable amount of time to give information on the value of angular mOITIentum.

1.0

0.5 I-

...

o

~ 0

0::

-

- - -

0.5 _

-

-

o

-70-

, . ' no/

^{0 I _/}

^{+ '}

Companson of cr cr and cr cr

• r

no/ 0

o

cr cr This experiment

Neugebauer et aL

I

,

I

,

O cr no/ cr 0 Th15 · expen. ment

• cr-

/ cr+ ~ eug ebau e r

et al.

I I I

,

700 800 900

K (Mev)

1000

Figure Z2

I

e

^I

=

⁶⁰⁰

"IT

I

!

I 1100

- -

-

- - - - -

- -

- - - -

-

-

-

-

1.5 1.0 '"%j

.. .

OQ 0 r::

. ...

'1 ~ CD 0:: N V- 0.5

o

.1.76+ 0.60

1

Comparison of this experiment with other related experiments

t ! t ! I

no/

°

0.

o

0' 0' (9 1:::60 ) ThlS Exp. 1T no/

°

0 . • 0' 0' (9 1=90 ) Thls Exp. 1T

o

O'D / 20'H (9 1,.135°) Bingham 1T

II

D H D H -

°

• 0' /20' (9

1 :=90°) Bingham. 0' /20' (91 ;::90) Tollestrupet aL D H1T_ 1T 0' 12fT (9 1"'40°) D/ H -° ~ Toilestru¥> et al. • 0' 2fT (9 1T

1 ::;1S3 ) Tollestrup et al. 300 400 500 600 700 800 900 k (Mev)-

II

1000 1100 1200

I ooo,J

....

-72-

The present experiment suffers in the same way as that of Bingham in requiring the use of synchrotron subtraction to determine the energy of the incident photon. In order to avoid using synchrotron subtraction, one must be able to use the fast coincidence circuits as a true time-of-flight instrument. This means that unless a longer time-of-flight path can be obtained together with a correspondingly larger counter to compensate the los s in counting rate the fast coin- cidence circuits must work well with a resolution time of 2 to 3 nano- seconds independent of the large variations in pulse amplitude. For this to be feasible, one must have a photomultiplier with a rise time of 2 to 3 nanoseconds. The present phototubes have a rise time of 4 to 5 nanoseconds at best. Recently, several new tubes have been manufactured to such specifications. However, they have not been thoroughly tested.

A better way to do this experiment, at least in the forward direction of the outgoing pion, would be to use two lead glass total absorption Cerenkov counters to detect the two photons from the decayed neutral pion. The opening angle of the two lead glas s count- ers would determine the minimum momentum of the neutral pion.

The maximum momentum of the neutral pion would be determined by the maximum photon energy of the synchrotron. A large scintil- lation counter, properly placed, could be used to detect protons.

The coincidence of the two lead glas s counters and the scintillation counter would indicate the reaction y

+

p - p

+

^nO had taken place while the coincidence of the two lead glass counters alone would indi- cate the reaction y

+

n - n

+

^nO had taken place. Thus the ratio erno

/ ero

could be measured directly.

-73-

APPENDIX I - ESTIMATE OF COUNTING EFFICIENCIES FOR NEUTRONS AND NEUTRAL PIONS

In this section, the ratio of the counting efficiency for neutrons to that for protons and the ratio of the counting efficiency for neutral pions to that for charged pions are estimated.

From the derivation in Section II, we obtain the expressions for the counting rates of the four reactions.

Cno

=: A no u- p 0so P n no 11 (1 )

CO

'"

Au-0poSopP11 0

(Z)

C

'"

^{Au--p~ pP11 - (3)}

C+ + + n +

(4)

=: Au- p - P 11

Since 11 no 0 +

have been shown to be equal, we obtain from , _{11 .11} , 11

(3) and (4)

n C+

p u-

"" +"

pP C u-

and from (Z) and (3)

perimental points.

The reason that the values of pn/ pp at points 1, Z, and 3a are larger than those at points 3b, 4, and 5 is probably due to the absorp- tion of the proton by the l/ Zn lead plate. The percentage of proton

-74- Table 10

n ^{0 0} Ratio 5 of _P- and

L.L::

pp P ~

C+ n CO +

P °So

Point K 8^{1 IT"}

E-

^IT"

(mev) ^'IT

+"

_{C pp C} ⁰ +

IT" IT" p-

i 1056 60⁰ 0.42 0.64 0.27 0.56 3.5 0.82 2 876 60⁰ 0.49 0.51 0.25 0.42 3.4 0.70 3a 749 60⁰ 0.72 0.57 0.41 0.29 3. 2 0. 67 3b* 749 60⁰ 0.72 0.42 0.30 0.26 3.2 0.60

4~' 1046 90⁰ 0.42 0.44 0.19 0.52 1.8 0.39

5~~ 873 90⁰ 0.55 0.35 0.19 0.38 1.0 0.21

*No 1/2^1t lead plate in front of C5.

-75-

absorbed, calculated by using geometric cross -section, is approxi- mately 120/0. Thus pn/ pP will increase from 0.20 to 0.23 if pP decreases from 1. 00 to 0.88.

The reason that the value of p n / p p at point 3b is larger than those at points 4 and 5 is probably due to the increase of the neutron

efficiency. Figure 24 show s the neutron efficiency as a function of neutron energy (10). Curves for 24 cm and 32 cm scintillators are extrapolated from lower curves. The neutron efficiency for 32 cm scintillator increases from 180/0 for 300 mev neutrons to 25% for 95 mev neutrons. The average proton energy for point 3b is approxi- mately 150 mev. The lowest proton energy is approximately 110 mev.

Another possible reason for the variation in pn/ pp is the-.beia- tive II scanning efficiencies^l! for protons and neutrons which vary

slightly from point to point. The term 11 scanning efficiency!! is used here to denote the ratio of the number of accepted events which is used in the final results to the total number of events which is the sum of the accepted events and the rej ected events due to am- biguous identification.

The values of pO S

0 /

p

~

at points 4 and 5 are approximately 1/ 2 of the geometric efficiency for counting iTo. This is reasonable because the II scanning efficiencyll is only about 600/0 for iT o • The large value of pO SO / p

~

^{at point s 1, 2,} 3a and 3b are due to the large value s of p n / p p which come into the expres sion for pO S

0 /

^p

~

^.

.50 .40 trj

>- .. .

(J ()Q (:l s:: Cll 11

. ...

(1) u ;::; . 30 N

....

~ ~ .20

f-

.10

.L

0

\. '" ~ "---- ~ ~

I 100

Efficiency of counting neutrons for plastic scintiDator s of various thickness 32 cm 24 cm 18 cm 12 cm 6cm I 200 300 Neutron Energy (Mev)

I --.J C1'

-77- APPENDIX II

ESTIMATE OF THE PAIR PRODUCTIONS IN HYDROGEN RUNS

The following pion pair productions from hydrogen are pos- sible.

(1)

y+ + -

P-P+1T +1T

(2) y+ o 0

P-P+1T +1T (3) y+ p ... n+1T ⁰ +1T +

The second reaction, when detected, cannot be distinguished from single production of a neutral pion.

The first reaction, when detected, is clearly distinguishable from single production of a pion from hydrogen in this experiment.

Chasan et al. (12) give laboratory differential cross sections of this reaction for photons of energies from 500 to 1000 mev. Their results will be used to estimate the

(CH~..P)

/ (C+

H) ratio in hydrogen runs of

. p s

this experiment.

The third reaction, when neutron and neutral pion are detected, is also clearly di stinguishable from single pion production from hy:dro- gen in this experiment. An estimate for the ratio (Cn

H

o) / (C+) in

p s

hydrogen is obtained with the assumption that the ratio of reactions 2 and 3 is given by the isotopic spin relationship given before.

The counting rate for single production of positive pions in hydrogen can be written as

+ NW

r r

^{+ , dr2'N b(k/ E o )}

(CH)s .. EoJdnNJkCJ (9 N ) (

dn~)s

dnN k p:!:.. p N_r/ (k)E(9

1T )dk dn'

'" B CJ+ (9' N) ( dn N ) s p:!:.. p N .6. r2N (.6.k) s N

-78-

The counting rate for detecting a charged pion and a proton from pair production in hydrogen is

+p SNW

(C~)p

'"

y -

o

where y):!::"P is the efficiency of counting the particular pair production determined by the resolution of the coincidence circuits system, and S is the number of possible ways of obtaining the particular pair of final products. For the reaction y

+

p - p

+

^1T

+ +

^{1T - ,} S '" 2. For the

o

+

reaction y

+

p - n

+

^1T

+

^1T when the neutron and the neutral pion are detected S '" 1.

Assuming the angular distribution of the pions is isotropic III

the CM system for a given direction of the nucleon, then

(C-) _ SNW . .

+

_Hp-~

p

S,

_{k P}

S 1

_r2

1

_r2

N N 1T

p:!::..

PPy):!::"P (k)E (9 )dr2 dr2

NdP Ndk

1T 1T

+ +p

p- pP ^{y) -} (k) (~k)

P

+p .

where y) - (k) determmes the integration limit for dP

N, and as a function of delay T between C5 and C2 is the same as Y)

+

(k). Thus

-79-

The numerical values for (AP

N), (dO t /dO ) and (-Ak)

'IT 'IT P P

can be calculated and a-(k, eN' P

N} AP

N can be obtained from Chasan et al.

The exact calculations of the quantities mentioned above are extremely lengthy. For each experimental point, an average for (dO t / dO ) and an average for (~N) were obtained by calculating

'IT 'IT P

(dO t / dO ' ) and (P

N) re spectively for 240 different configurations,

'IT 'IT

P

16 different energies k for the incident photon, and 15 different ener- gies E for the detected pion in the laboratory system.

'IT

The re sult s of thi s calculation are shown in Table 11.

Table 11 Calculation for Pion Pair Production in Hydrogen dn' (.t.k) dn' + (p 1T P N)p (C H)

(~)p

(t.PN)p (O"t.PN}p p N Point (t.n ) (dIT:":") s 0" S (C H): 1T p (t.k) 1T N (Sr) 1T (Mev) fJ.b/Sr s N (fJ.b/Sr) (p p ) s c 1T±..P 1T±..P oN +p oN 1To N 1T 1T-1T 1T +N 1T +N 1T +N 1T+N1T +N 1T+N 1 .083 1.7 510-790 6>~ 1.8 2.40 5 3.7 0.82 2 1 .07 .003 2 .083 1.7 460-660 8 1.8 2.42 5.3 4.0 0.70 2 1 .10 .004 3 .083 1.7 420-590 7 1.8 2.45 8.2 3.3 0.60 2 1 .05.002 4 .130 4 600-900 3 1.0 3.20 2 5.3 0.39 2 1 .20 .003 5 .130 4 600-900 3 1.0 3.23 3.0 5.3 0.21 2 1 .14 .001 ~(The small value of (0" PN)p for point 1 is due to the interpolation of the data of Chasan et al. Their paper gave zero cros s section for protons with momentum above 600 mev and angle greater than c 420 . Kinematically it is possible to have protons of the above description in pion pair production.

,

co 0

,

-81- APPENDIX III

ESTIMATE OF THE PAIR PRODUCTIONS IN DEUTERIUM In this section, the corrections for the pair productions in

deuterium are estimated. The quantities to be calculated are f , f ,

+ -

fno

, and fO as defined in Section VB.

The following expression can be derived from the last equation in Appendix II by proper substitution if the effects of the internal mo- tion of the nucleons in the deuteron are ignored. The definitions of the symbols are al so given in Appendix II.

<ID'

t.P Nill (---cm-) TI (&)

TI TIP P

The first term in the parenthesis represents the contribution from

+

⁰

the reaction y

+

p -- n

+

^TI

+

^TI (S3

=

^1). The second term represents

+ -

the contribution from the reaction y

+

n - n

+

^TI

+

^TI (S 4 '" 2).

drl'

- N

4TI IT (k, eN) (~) (&)

WON s s

The first term in the parenthesis represents the contribution from

+ -

the reaction y

+

p - p

+

^TI

+

^TI (S1

=

2). The second term represents

- 0

the contribution from the reaction y

+

^{n - p}

+

^TI

+

^TI (S6:: 1).

-82-

The results of this calculation are shown in Table 5 in Section VB.

-83-