An investigation of the C12 + He3 reactions at bombarding energies between 1.8 and 5.4 MeV

~ I

l NuclearPhysics51 2.C

(1964) 481--517; (~)

North-HollandPublishingCo., Amsterdam

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

AN INVESTIGATION OF T H E C t 2 + H e 3 REACTIONS AT BOMBARDING ENERGIES BETWEEN 1.8 A N D 5.4 MeV HSIN-MIN K U A N , T. W. BONNER t and J. R. RISSER Rice University,Houston, Texas tt Received 9 September 1963 Abstract: The differential cross sections at several angles and s o m e angular distributions o f the following o u t g o i n g radiations induced by He a in C x~ targets from 1.8 to 5.4 MeV were measured; elastic He 8, p r o t o n groups cerresponding to the f o r m a t i o n o f the N 14 ground state and excited states at 2.311, 3.945, 4.91, 5.10, 5.69, 5.83, 6.23, 6.44 and 7.03 MeV (p0 to p6; Ps, P9 and p , ) , the 6.44 McV gamma ray (Te.~,) f o l l o w i n g the pe group, and the u groups corresponding to the formation o f the C ~1 ground state and the first excited state at 2,00 MeV. Proton groups to N 1. states at 6.05 and 6.70 MeV (p~ andp]0) were not observed. B o t h the P9 and the corresponding Fe., show a strong isolated resonance at 2.990±0.010 MeV w i t h / ' ~ b = 125± 10 keV. Analyses at this resonance o n the elastic He a, P9, 76.,~, Pz and no data, assuming pure compound nucleus f o r m a t i o n as the reaction mechanism, yielded J~ = j+ for the corresponding state in O:5*at 14.46 MeV and even parity for the 6.44 MeV state o f the residual nucleus N it. Indications o f resonances at 2.45±0.04, 2.75q-0.04, 3.28+0.04, 3.604-0.04, 4.20=t=0.01, 4.374-0.04, 4.6-t-0.1 and 5.04-0.1 MeV, corresponding to the states in O x5 at 14.03, 14.27, 14.69, 14.95, 15.43, 15.57.

15.75 and 16.07 MeV were also observed.

1. Introduction There have been a number of investigations of the reactions induced by He 3 in C 12 targets. Bromley et aL 1) investigated the C12(He 3, p ) N 14 reactions for proton groups to the ground and first two excited states of N 14, the C12(He a, no)O 1¢ reaction and the C12(He 3, ~o)C 11 total cross section for He 3 bombarding energies from 1 to 3 MeV. Johnston et al. 2) extended the proton measurements in greater detail for the same proton groups to 5 MeV. Towle and Macefield 3) and Din, Kuan and Bonner 4) investigated the C12(He 3, no)O 14 reaction to He 3 energies of about 5 MeV. The work described in this paper consisted primarily of an extension of the excitation-function and angular distribution data to include reaction products not previously investigated and of an attempt to synthesize the information on all the reaction products for He 3 energies up to 5 MeV. Data are included on proton groups to the N 14 ground state and excited states at 2.311, 3.945, 4.91, 5.10, 5.69, 5.83, 6.23, 6.44 and 7.03 MeV (Po to P6, Pa, P9 and P11), on alpha groups to the C 11 ground state and the first excited state, and on the 6.44 MeV gamma ray (~6.a4) following the P9 group. The elastic cross section was taken at a number of angles in the 3 MeV region and at t Deceased. tt W o r k supported in part by the U. S. A t o m i c Energy C o m m i s s i o n . 481

482

HSIN-MIN KUAN et

al.

90 ° and 165 ° from 1.8 to 5.4 MeV. At higher energies, Hinds and Middleton 5) have reported the excitation functions at 10 ° from 5.7 to 10.23 M e V and angular distributions at 5.98, 8.83, 9.37 and 10.14 MeV of the P0 to P6, ~o, cq and do groups. 15.91

12.

I1"

10"

.6.5 . . . . 6.1

5

~= 9-

15.62

.JaQ. oj

NI3

5 . o

.=

7.40 c

3

•

5/2 + (1/2 + ]

%

=,.Sz tLI

12

4.5 ~-~ 7

-- ,,~

13.79 13.7 (> 5/2) 1/2)

7.03

4,32

(2) o

6.44 3 (-) 6.23 I (+) 6.05 .~" 5.83 5 G') 5.69. --II-~

0 3+ 0 • "~ 0 0

5,10 4.91

2 I-) 0 (0-) 0

3.95

I ~" 0

13.22 (3+1

2.0

C~Z+He3 99.4%

"x~ Io.21~/z

C II i2.31

0+ I

I.+ 0

7,291 NI4-=- p

NI4

Fig. 1. Energy level diagram appropriate for discussing the Ct2+ He a reactions. Levels are from ref. 6). The J" values marked on the side of each nucleus are parameters obtained from the present work. The reaction mechanisms in the C 12 + H e 3 reactions have not been clearly established, and the question of direct interaction versus c o m p o u n d nucleus formation is o f considerable interest. For many o f these reactions, while direct interaction is possibly indicated above 4 MeV, the c o m p o u n d nucleus mechanism appears to contribute appreciably below 4 MeV. In the course o f the present investigation it was discovered that a strong isolated resonance occurred at 2.99 M e V in C x2(He3, pg)N 14.

C12@He a REACTIONS

483

(6.44 MeV state), for the P9 group and the corresponding ?6.44, with indications of a resonance for other outgoing particles also 1,-4). An analysis in terms of compound nucleus dispersion theory was successfully applied in the 3 MeV energy region to the elastic He 3, Pg, ?6.44, Px and n o cross sections. From the experimental point of view, a detailed study of the He 3 induced reactions on C 12 has its own importance. The high cross section of many of these reactions makes correction for the carbon deposits on the target a difficult task in the case of some He a induced reactions on other targets, so that measurements of the He 3 induced reactions on C~2"can be of importance for the study of other He a induced reactions. An energy level diagram appropriate for describing the reactions discussed in the present work is shown in fig. 1. Upon bombarding C 12 by He 3, the outgoing channels consist of proton groups to the various states of N 14, alpha groups to the ground and the first excited states of C H, neutrons to O 14, and the gamma rays following the decay of the residual nuclei. The levels shown here are from the recent compilations 6).

2. Experimental Methods The Rice University 5.5 MeV van de Graaff accelerator was used for the present experiment. The energy of the singly charged He a+ ions was determined using the 90 ° analysing magnet. The field strength of the magnet was determined by a protonmoment magnetometer. At the beginning of each experiment, an energy calibration was made by measuring the Cla(p, n)N la threshold 7), taken to be 3.235 MeV. In the measurements of the various outgoing radiations, the different kinds of experimental apparatus were used according to the nature of the radiations. The methods used in the identifications and measurements of these various radiations are described in some detail in the following subsections. 2.1. CHARGED PARTICLE MEASUREMENTS 2.1.1. Scattering chamber. All the charged particle measurements were carried out by using the small scattering chamber first constructed by Kashy et al. 8), designed for use with self-supporting targets. Two detectors with associated slit systems were mounted in the movable half of the chamber at 75 ° to the axis of rotation and 90 ° apart in azimuth. Data could thus be taken simultaneously at two angles spaced approximately 90 ° apart, covering the laboratory angular range 15° to 165 °. The solid angles used throughout all the measurements were 4.06 x 10 -4 sr, which gave reasonable counting rates and adequate resolution to see all the particle groups. The H e 3 beam collected in the Faraday cup after passing through the 15-30/~g/cm 2 targets consisted principally of doubly charged He 3 + + ions. Corrections for the charge state of the beam (estimated 9) as 3 ~o at 2 MeV and less than 1 ~o at 5 MeV) were not made in calculating the absolute cross sections, but the errors ( ~ l0 ~o) indicated for the experimental data take this effect into account.

484

I-ISIbI-MIN KUAN e l

al.

2.1.2. Targets. The method of preparation of foil targets was the same as described by Kashy et al. ~o). The thicknesses of the targets varied from 15 to 30 pg/cm 2. The determination of target thickness and reaction cross sections were based on the comparison with the known differential cross section 11) for the scattering of protons by C 12 at an incident proton energy of 3.0 MeV and laboratory angle of 165 °. Since the carbon foil targets were extremely thin, the cracking of carbohydrates from the vacuum system on to the foils resulted in a sizable increase in the target thickness. At the end o f each extended run on an excitation curve or angular distribution, a correction for this effect was obtained by taking a number of widely spaced check points of the target thickness. During all of the experiments, the beam was kept off the target between data points. 2.1.3. Detectors. For He a on C m, there are many outgoing particles having energies distributed over a spectrum from a few hundred keV to nearly I0 MeV. In order to observe all of these groups, a high resolution and high stopping power detector was needed. Two RCA diffused-junction detectors and one Ortee solid state detector were used in the present measurements. They all had good resolution and high stopping power. Typical spectra obtained from two of these detectors are shown in figs. 2(a) and 2(b). 2.1.4. Multi-channel analysers. As there were many closely situated and very narrow peaks on the particle spectra, a multi-channel analyser with large numbers of channels was required. A T M C 400-channel analyser or a Nuclear Data 2-dimensional analyser in the 511-channel mode were used in many of the experiments. 2.1.5. Identification of the various outgoing radiations. For He a on C 12 the possible reactions involving charged particles as outgoing radiations in the present bombarding energy regions are C12q_He a _-, 0 ls -~ He3-{-C 12 p o + N 14 (ground state) -~ P l + N 1 4 * ( 2-31 MeV state) --* P2+N14*(3.95 MeV state) p3+N14*(4.91 MeV state) -~ p4+N14*(5.10 MeV state) Ps +N14"( 5.69 MeV state) --* P6 + N14"( 5.83 MeV state) -~ Pa + N 1 4 " ( 6.23 MeV state) -'* P9 +N14"( 6.44 MeV state) Pll +N14"(7-03 MeV state) --* ~o + C11 (ground state) -~ cq+Cl1"(2.00 MeV state)

Q value (MeV) 4.779 2.467 0.834 -0.130 -0.320 -0.910 - 1.050 - 1.450 - 1.660 -2.250 1.860 -0.140

The subscripted numbers were assigned to the outgoing particles for convenience. The proton groups to the tentatively assigned states 6) of N 14 at E, = 6.05 MeV (P7)

Pz

"400

(all

E(He~) = 4 . 2 0 MeV 8(Lob)= 4 6 . 9 °

P4

ao P9

P3

DETECTOR A WITH AI

200

P,

40

Po

120

80

160

Pz

(c)

E(He3) = 4.20

MeV

30O

8(Lob) = 46.9`= 200

p~

p~

DETECTOR B WITH AI

P3

oo AA •~ 600

%,/

',~oO-

"

,

40

v Ot°

80

120

I

(b) P4

400

%

Pl

He3

160

E(He3)=4.88

MeV

O(Lob) = 146.6 `=

Pz

I

DETECTOR

B

!00

Po Pl

40

160

120

80 He~

P, (a)

E(He3)=4.88

MeV

e(Lab) = 146.6 = DETECTOR A

80

160

CHANNEL

240

320

NUMBER

Fig. 2. C h a r g e d particle energy spectra. Detector A was an Ortec solid state detector which h a d a very thin gold c o a t i n g on the face. Detector B was an R C A diffused-junction detector which had a thicker layer o f coating on the face. Spectra(a) a n d (b) s h o w the relative positions o f p r o t o n groups a n d the d o u b l y c h a r g e d He 8 a n d c¢ groups f r o m the two detectors taken u n d e r the s a m e experimental conditions. Spectra (c) a n d (d) were taken u n d e r a n o t h e r similar experimental condition except that a 10/~m Ai sheet was in front o f detector A a n d a 13/~m AI sheet was in front o f detector B. Spectra (e) a n d (d) s h o w that the elastic He a particles were stopped by the AI sheets. T h e linearity o f the de-

486

HSIN-MINKUANet aL

and Ex = 6.70 MeV (Pl 0) were not observable in all the present experiments. The Q values given here were from the known energy level diagrams 4). To identify all the outgoing particles unambiguously, a kinematical calculation to predict the expected laboratory energies of these particles at chosen laboratory angles and bombarding energies was made and was used to compare with the spectra obtained under the same conditions. The identification of the various particle groups is shown in the spectra of fig. 2. 2.1.6. Methods of taking data. Since the variation of laboratory energies of the outgoing He 3 and alpha particles are different from those of protons, there are always regions where the overlapping of the doubly charged He 3 and ~ particles and protons can occur. In order to obtain a complete measurement in these overlapping regions, two detectors having different thicknesses of stopping material on the detector surfaces were used to make two successive measurements at the same angle and energy. From the fact that doubly charged particles lose more energy than protons o f nearly the same energy when passing through a stopping material, the alpha and He a groups will shift more than proton groups adjacent to them in a spectrum. A comparison of the spectra obtained from different detectors with different thicknesses of stopping material on the face allows a full identification of the groups. The relative positions of the particle groups in the spectra of figs. 2(a) and 2(b) illustrate this effect. The fact that two detectors could be used at the same time greatly simplified the experiment. For data at forward angles thin aluminium foils were used to stop the elastic He 3 groups. Typical spectra taken in this way are shown in figs. 2(c) and 2(d). 2.2. GAMMA-RAY MEASUREMENTS Upon bombarding C 12 target by He 3 beam, one can see the various gamma rays from the decay of the residual nuclei N 14 and C ~1. However, the present investigation was mainly for the 6.44 MeV gamma rays from the reaction C12(He a, pgy6.44)N 14. (6.44 MeV state) because this gamma ray showed a pronounced resonance at 2.99 MeV. It was hoped that from the study of the behaviour of this gamma ray one could obtain some properties of the nuclear states. The experimental details are described in the following subsections. The two targets used were made by cracking methane (CH4) gas on to a tungsten and a tantalum blank. Their thicknesses were about 20 and 60 #g/em z, respectively. 2.2.1. Experimental arrangement. A 2.54 c m x 2 . 5 4 cm NaI(TI) scintillator was used for angular distribution measurements, and a 5.08 cm × 5.08 em NaI(T1) for the excitation curves. Mu-metal shields were used on the photomultipliers to reduce gain variations. A schematic diagram of the experimental arrangement is shown in fig, 3. The positioning of the 2.54 cm x 2.54 cm NaI(T1) detector is shown as it was for the angular distribution measurements with the larger crystal in position as a monitor. For the excitation-curve measurements, another target holder was used, the target was put at 0 ° to the beam direction, and the 5.08 cm x 5.08 cm NaI(T1) detector was placed about 1 cm from the target.

C1="~-Fie8 REACTIONS

487

The pulse from the output of the single-channel pulse-height analyser of the Hammer amplifier-analyser was used to gate the 256-channel analyser. The data for the angular distributions were taken from the print-out of the spectrum from the 256channel analyser, and the coincidence from the single-channel analyser in integral mode was used to prevent the 256-channel analyser from processing low energy pulses. The excitation curve data were taken with the single-channel analyser in /L METAL

TARGET

~2.Sx2.5crn

I THIN STEEL TUBE ' }

I~ "

25.7 eros" rL1

[ ~ 5 . 1 x s . 1 c m NaI

I I DELAY

I

I

P.H. ANALYZER I

|

I

I

F

" L ANALYZER I

MODE Fig. 3. Schematic d i a g r a m o f the apparatus for measuring the gamma-ray excitation curves and angular distributions. GAMMA-RAY ENERGY (MeV) 3 4 5 6 ~l

o 2.62 MeV

1600

xX

o.

7

i

i

i

• 2.99

x

x 3.46

i

,

'

~

ie

e:'~l4 MeV

800 -400 60

• ( 2.99)- (2.62) • (2.99)--(3.46) 80

~ f

\~

[

~¢,d '~

I00 120 140 160 CHANNEL NUMBER

/

180

Fig. 4. Gamma-ray spectra from C z2-F H e s reactions t a k e n b e l o w the 2.99 M e V resonance (2.62 MeV), on the resonance (2.99 M e V ) and above the resonance (3.46 M c V ) with a 5.1 c m × 5 . ] cm N a ! c r y s t a l T h e differences in the spectra t a k e n o n the resonance a n d o f f the resonance s h o w clearly the c o n t r i b u t i o n o f the 6.44 M e V gamma ray to the resonance.

rISIN-MrN KUAN e t al.

488

differential mode, and the coincidence was used in setting the upper and lower biases by inspection of the spectrum shown by the 256-channel analyser to be in the window of the single-channel analyser. 2.2.2. Measurements of the excitation curve of the 6.44 MeV gamma-ray. The fact that it was the 6.44 MeV gamma ray which contributes the strong resonance at 2.99 MeV is shown clearly from a comparison of spectra taken below, on, and above the resonance, at 2.62, 2.99, 3.46 MeV as shown in fig. 4. The spectra obtained by subtracting the spectra away from resonance from the spectrum on the resonance show clearly the 6.44 MeV g a m m a rays. The gamma-ray energy scale in fig. 4 was from the 4.43 MeV gamma-ray source of PuBe. GAMMA-RAY ENERGY (MeV) I 320Q ..=1 W Z Z -r" ¢'~ 1600

LU Q..

80

' ' " " "'"''" " " " " '140 i'""'"i" CHANNEL

200

NUMBER

Fig. 5. Gamma-ray spectra at 30° and 90° from the measurement of the angular distribution at the 2.99 MeV resonance with a 2.5 cm × 2.5 cm NaI crystal. The difference between the spectrum at 30° and at 90° is also shown. For each excitation curve measurement, the window could be set very accurately using the 256-channel analyser in coincidence with the single-channel analyser. Then, the excitation curve could be obtained from the readings of the scaler on the output of the single-channel analyser. The spectrum for each data point was checked to watch for possible gain shift. There was no gain shift in the excitation curve measurements. The window setting for the 6.44 MeV g a m m a ray excitation-curve measurement included the first escape peak and the photo peak, as shown in fig. 4. 2.2.3. Measurements of the 6.44 MeV gamma-ray angular distribution. To show that the angular distribution measured on the 2.99 MeV resonance was really from the 6.44 MeV g a m m a rays, the spectra obtained at 0 = 30 ° and 90 ° are shown in fig. 5. The spectrum obtained by subtracting the 90 ° spectrum from the 30 ° one shows clearly that the 6.44 MeV gamma ray is the cause of the difference in the yield be-

C12-]- He s R E A C T I O N S

489

tween 90 ° and 30 °. Only the extreme upper portion of the spectrum was used for the data points of the angular distribution. In actually taking data, the single-channel scaler reading and the multi-channel spectrum were both recorded for each data point. As there were still small gain shifts and the single-channel scaler data were not good enough for analysis, the final data were obtained from the analysis of the spectrum taken at each angle. All the spectra were plotted out. The shift of gain could easily be observed from the shifts of peak positions of the many peaks in the spectrum. Then the area of the spectrum above the second escape peak of the 6.44 MeV gamma rays was taken (see fig. 5). The measurements were repeated four times with two different targets. There was good agreement between the data of the four runs. Corrections for the attenuation loss from the target backing and the wall of the target chamber, as well as corrections for a carbon build-up, were applied to the final data. The maximum build-up correction was about 9 ~o for the last data point compared with the first data point. The maximum attenuation loss was about 10 ~o at the backward angle.

3. Experimental Results The results are described in some detail in the following subsections according to the nature of radiations. Most of the data have been repeated 2 to 6 times with good agreement. Typical estimated errors for the final data obtained after averaging are shown in the figures. 3.1. THE CI~(He 8, Hea)C TM REACTION

The elastic scattering results are presented in fig. 6. The curves in the figure are from theoretical calculations. They will be discussed later. Since the original interest was in the 3 MeV region, measurements in this energy region were made at angles: 0c.m. = 84.5 °, 90.0 °, 122.3 °, 154.5 ° and 164.5 °. However, at two angles, 0o.m. = 90.0 ° and 164.5 °, the measurements were extended from 1.8 to 5.4 MeV. Measurements at c.m. angle 114.5 ° near 4.2 MeV region were also taken (not shown in the figure). Besides the pronounced resonance structure in the 3 MeV region which appeared in all the measured angles, the indication of resonance structure from 4.5 to 5.2 MeV and in the 4.2 MeV region can also be seen from data taken at 0c.m. = 164.5 ° and 114.5 °. In general, one would not expect the resonances in the elastic scattering of He a from C 12 to be very strong because there are many open channels in this energy region. 3.2. THE C12(Hea, p)N 14 REACTION WITH PROTON GROUPS CORRESPONDING TO THE FORMATION OF THE N ~4 G R O U N D STATE AND EXCITED STATES AT 2.311, 3.945, 4.91, 5.10, 5.69, 5.83, 6.23, 6.44 AND 7.03 MeV (DESIGNATED BY P0 TO P6, Ps, P9 AND pn, RESPECTIVELY)

Pronounced and broad resonance structures appear in most of the groups, extending over the whole energy range. But many resonance positions vary from angle to angle

490

HSrN-~tN KUAN et aL

and group to group, so t h a t there is uncertainty in the resonance positions• More detailed descriptions of the results on the proton groups individually are given below• 3.2.1. The C12(He 3, po)N 14 (ground state)• Differential cross sections at 01,b = 76 ° and 159.4° and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20, and 4.88 are shown

,oo•

• ~.~

Ci2(He ~ He3)C, 2 o.

~...

O(CM.)= 8 4 . 5 o -

200

~

z <_

-~

......

-

C

'

.

~

.....

FIT

I

FIT

2

RUTHERFORD

e{C. M.) = 9 0 °

C3 <~ n=,l -

(n

"5

o

-60

.......

"40

.zo

..-. ::._..--.:~.~_._~ ....

#(C.M.) = 1 2 2 . 3 "

-60 .40

-2o

8(C.M.I • 1 5 4 . 5 °

~°

..,°

"40

8(C.M.) = 164.5"

" • -.-'- . . . . . . . . . . .

2.0

.0

HELIUM-3

ENERGY

"---.'.--".',L.,. . . . . 4,5

5.0

$.5

(MeV)

Fig. 6. Differential elastic c.m. scattering cross sections o f CXS(I-Ies, Hes)C *= at c.m. angles 84.5 °, 90 °, 122.3 °, 154.5 ° a n d 164.5 °. T h e lines are theoretical fits (s¢¢ text a n d table l) a n d R u t h e r f o r d c r o s s sections.

in fig. 7. The results are in good agreement with the work of Johnston et al. 2) in the 2 to 5 MeV region. The angular distribution at 4.88 is quite like that at 5.98 MeV in the work of Hinds and Middleton 5). The general features of the angular distribu-

clS~-

491

He s REACTIONS

tions are that there is no consistent peaking forward, and that the shape does not vary very much from resonance to resonance. 3.2.2. The C 12 (He 3, Pl) N14. (2.311 MeV state). Differential cross sections at 01,b -76 ° and 159.4 ° and angular distributions at 2.49, 2.88, 2.99, 3.15, 3.50, 4.20 and 4.88

Ct 2 (He3,p.) Nt4(GROUND STATE)

2.49 MeV

s 2,88MsV -s~t2"99 2 ~MI~

'

-I

at" bJ I--

i

m

:5.50MeV -6

b

4.20MeV ~1~

@

2

b

.

~

i

i

i

4.88 MeV

"

-0.4

30

i

~

-3.2

L

910

i

i

150

i

30

90

i

~'o

14o

C.M.ANGLE(DEGREES)

i

i

,'o

'

!

i

i

4.0

4.5

5.0

'

150

I--

4 O(Lob)=159.4 b Z.O

2.5

i 5.0

i 3.5

HELIUM-3 ENERGY(MeV)

5.5

Fig. 7. Differential cross sections at laboratory angles 76° and 159.4 °, and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20 and 4.88 MeV of the reaction CX2(He3, po)N 1~. The solid lines were drawn through the data points. The arrows marked the positions where angular distributions were measured.

MeV are shown in fig. 8. The results agree very well with the work of Johnston et al. 2). The general features of the angular distributions are the rapid variation in the 2 to 3 MeV regions and the consistent peaking forward above 4.8 MeV (fig. 8

RsrN-MrN ~UAN et al.

492

and ref. s)). The angular distribution at 2.99 MeV was measured very carefully 3 to 4 times for the purpose of making an analysis which, with the analyses o f the Pg, V6.,, and elastic He a data, would aid in making assignments at this energy. The angular distribution at 4.88 MeV is quite similar to that at 5.98 MeV obtained by Hinds and Middleton s) except that there is more peaking forward at 5.98 MeV. C=2(HeZ.pl)NI4*(2.31

"4

Z

2.49 MoV

J~

/

"k,,//

Q

~C

STATE)

MeV

#

\ //.

2.88 MeV

IM

I

i

I

i

i

-LO 3.15MeV 6

~.)/(~'k

-o.5

-z

-z ~

4 . 2 0 MeV

4.88 MeV

-\

b

to

~.

?~'i 3.50MeV

+

'

\,/

,,../ 50

z.o

90

~.5

150

30

90

t

150

;o

'

~

?-+ ~-~-t

'

~o

C.M. ANGLE (DEGREES)

3.0

3.5 HELIUM-3

4.~

4.0 ENERGY

5.0

a5

(MeV}

Fig. 8. Differential cross sections at laboratory angles 76 ° and 159.4 °, and angular distributions at 2.49, 2.88, 2.99, 3.15, 3.50, 4.20 and 4.88 MeV of the reaction C12(He a, pt)Nt~*(2.31 MeV state). The solid lines were drawn through the data points. The arrows marked the positions where angular distributions were measured. 3.2.3.

The C 1 2 ( H e 3, p 2 ) N 14. ( 3 . 9 4 5 M e V

state). D i f f e r e n t i a l

cross

sections

at

01,b = 76 ° and 159.4 ° and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20 and 4.88 MeV are shown in fig. 9. The angular distributions show three types o f shape. Those o f the first type, at 2.49 and 4.20 MeV, are probably due to the effects of resonances which can be seen at 2.40 and 4.40 MeV in the 159.4 ° excitation curve. Those of

CZ2-~Hea REACTIONS

493

the second type, at 2.88, 2.99 and 3150 MeV, have similar shapes, possibly associated with direct interaction since the excitation curves show no large variations in this energy region. A third type, at 4.88 MeV has a shape similar to the angular distribution at 5.98 MeV obtained by Hinds and Middleton 5).

C12(H~ P2)N+4*(3.945 MeV STATE)

2.49 MeV

+\ f

\

2.88 MeV

. i

n

E

X
i

,

\

i

i

I

i

3.50 Uov

i

i

~

\,

b

\~.#

l

I

°~

- °

i

~

i

i

+.2o M°V

/+

i

3o

9~

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4.88 MeV

-,

,5o

i

/

+

3~

2.99 MeY

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\..

"4

.o

#

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*

90

150

C.M. ANGLE (DEGREES)

.~

8(Lob)= 7 6 °

'~. ~-. •~ _ / " ~

./

-2 •

/ ..-

•

•/

L

i

i

+!5

~o

J3

E O(Lob)=159.4°

/

b

2.0

2!5

3~o

~ HELIUM-;5

/

/

Lo

~.s

ENERGY (MeV)

Fig. 9. Differential cross sections at laboratory angles 76 ° and 159.4 °, and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20 and 4.88 MeV of the reaction CZ2(He a, pz)NZ~*(3.945 MeV state). The solid lines were drawn through the data points. The arrows marked the positions where angular distributions were measured.

3.2.4• The C12(He3, pa)N 14. (4.91 MeV state). Differential cross sections at O~b = 76 ° and 159.4 ° and angular distributions at 2.49, 2.88, 2.99, 3•50, 4.20 and 4.88 MeV are shown in fig. 10. Two pronounced broad resonances appear in the 159.4 ° excita-

H$IN-MIN KUAN et al.

494

tion curve centred at 3.75 and 4.75 MeV. The angular distributions at 2.49,2.88, 2.99 and 3.50 MeV show larger cross sections at backward angles, and the two angular distributions at 4.20 and 4.88 MeV show resonance structure. The 4.88 MeV angular distribution has a shape similar to the one at 5.98 MeV obtained by Hinds and Middleton 5) up to 0~.,~. = 120 °. Hinds and Middleton show no data at backward angles. ClZ(He 3, p3)NI4*(4.91

2 . 4 9 MeV

r¢ tlJ

STATE )

I.O

BL O

z g5

MeV

MeV

2.88

2 . 9 9 MeV

,o.5 ,,

~1"

"1"

i

'

9o

i

/

t

I--

Q> b

3;

'

9b '

I~,o

5'o

i~o

50

90

150

C.M. ANGLE (DEGREES)

6(Lab} 7 6 *

-i z

•1[

• , "• =

• • ~

; 't- - - ' -

t.

i

i

i

i

4:0

4'5

5'o

W -6 i'--

5

J

11

0(Lab)=159.4*

"6 2

,'o

£5

3:o

315 HELIUM-5

55

ENERGY (MeV)

F i g . 10. D i f f e r e n t i a l c r o s s s e c t i o n s a t l a b o r a t o r y a n g l e s 7 6 ° a n d 1 5 9 . 4 °, a n d a n g u l a r d i s t r i b u t i o n s a t 2 . 4 9 , 2 . 8 8 , 2 . 9 9 , 3 . 5 0 , 4 . 2 0 a n d 4 . 8 8 M e V o f t h e r e a c t i o n C X ~ ( H e a, p a ) N X 4 * ( 4 . 9 1 M e V s t a t e ) , T h e s o l i d l i n e s w e r e d r a w n t h r o u g h t h e d a t a points. T h e a r r o w s m a r k e d t h e p o s i t i o n s w h e r e angular d i s t r i butions were measured.

3.2.5. The C~2(He 3, pg)N ~4. (5.10 MeV state). Differential cross sections at 0~b = 76 ° and 159.4 ° and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20 and 4.88 MeV are shown in fig. 11. In this proton channel, the excitation curves at 76 ° and 159.4 ° both show pronounced resonance structure, but there is little similarity

495

Cz2-~ He# REACTIONS

between them. There is a small resonance at 3 MeV in the 76 ° excitation curve. The small resonance at 4.30 MeV in the 159.4 ° excitation curve has been repeated five times to prove its existence, with good agreement. This small resonance does not appear at the same position as the one shown in 159.4 ° excitation curve of Pt group which

CI2(He 3, P4)NI4*( 5. I0 MeV STATE )

2 . 4 9 MeV

2 . 8 8 MeV

Z

.2 < 2 . 9 9 MeV m

i

i

i

i

i

i

"5

i

i

i

J

1

4

i

i

i

I

8

b

'3.50 MeV

4 . 2 0 MeV

3'0 '

9~

4 . 8 8 MeV

=5o

30

90

15o

C.M. ANGLE (DEGREES)

~l_ab)= 7 6 °

~4

4

8(Lob)= 159.4 °

~o

2!5

.

~o

.

~'5 HELIUM-3

4b ENERGY

4'5

5!o

~

(MeV)

Fig. 11. Differential cross sections at laboratory angles 76 ° and 159.4 °, and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20 and 4.88 MeV of the reaction CI=(He s, p~)N 14. (5.10 MeV state). The solid lines were drawn through the data points. The arrows marked the positions where angular distributions were measured.

496

KUAN e t al.

nS~-M~

also have been reported by Johnston et aL 2) at 4.35 MeV and was used by them to predict a state in O is. The angular distributions vary from energy to energy above 3 MeV. This is probably due to the presence o f many resonances which show in the excitation curves. The angular distributions show no consistent forward peaking, but, rather, backward

ps)NI4*(5.69MeV STATE)

C12(He3, A Z

-4

2 . 4 9 MeV

.4

2.88 MeV

"4

2"99MeV

~/;" /

'

"Z tO l-f4)

i

i

t

f

I

I

3,50 MeV

.

I

i

t

I

I

4 . 2 0 MeV

I

I

~,

I

I

4.88MeV

I

I

t

..d b -I

"2

'

~

'

,~o

4

~ ' 9'o ' ,~o C.M. ANGLE (DEGREES)

~o

8(Lob)=76 •

'

,/ /./

~'o

"

~

,~o

. ~N"

B

•

.

,0

HELIUM-3

ENERGY

4.5

~1.0

5.5

(MeVI

Fig. 12. Differential cross sections at l a b o r a t o r y angles 76 ° a n d 159.4 ° , a n d a n g u l a r distributions at 2.49, 2.88, 2.99, 3.50, 4.20 a n d 4.88 M e V o f the reaction CX~(He~, p6)Na4*(5.69 M e V state). T h e solid lines were d r a w n t h r o u g h the d a t a points. T h e arrows m a r k e d the positions where a n g u l a r distrib u t i o n s were m e a s u r e d .

peaking and structure. The angular distribution at 4.88 MeV has a shape somewhat different from the 5.98 MeV curve of Hinds and Middleton 5). 3.2.6. The Ct2(He 3, ps)N t4* (5.69 MeV state). Differential cross sections at 01=b = 76 ° and 159.4° and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20 and

C12--~-He 3 REACTIONS

497

4.88 MeV are s h o w n in fig. 12. I n a d d i t i o n to the two b r o a d resonance structures extending f r o m 2.3 to 3.8 M e V a n d from 4.5 to 5.4 M e V o n b o t h excitation curves at 76 ° a n d 159.4 °, there are n a r r o w e r resonances at 2.5 M e V o n b o t h curves, at 3.0 MeV o n the 159.4 ° curve, a n d at 4.2 M e V o n the 76 ° curve. T h e 4.2 M e V resonance c a n also be seen o n the 100.2 ° excitation curve (not s h o w n in the figure). D a t a in

-1

,

0

~

CJ2(He~ ps)NI4*(5.8 3 MeV STATE) 3

t

"4 "

Y

-I

~2 4 . 8 8 MeV

3o'

9b

~

3'o

'

'gb

C.M. ANGLE

3b '

,~o

'

'

z

~o

t\/

OlLab|= 7 6 "

~'~'''

<®~ ! L .J

'

./

z --< "

~,

(DEGREES)

-2

b

8(Lob) = 100.2"

81Lob)=159.4*

3.0

~k5 HELIUM-3

•

•

//

+

~

4.0 ENERGY

.

4.5 (MeVI

5.0

5.5

Fig. 13. Differential cross sections at laboratory angles 76°, 100.2° and 159.4°, and angular distributions at 2.99, 3.50, 4.20 and 4.88 MeV of the reaction C12(He3, pe)N 14. (5.83 MeV state). The solid lines were drawn through the data points. The arrows marked the positions where angular distributions were measured. this 4.0 to 4.5 MeV region were repeated four times to prove the real shape of the excitation curves, with good agreement. The width o f the 3 M e V resonance at 159.4 ° agrees with that o f P9 (below). The a n g u l a r distributions measured for the Ps g r o u p show wide variations. They are isotropic at 2.49 MeV, peak backward at 2.88, 2.99 a n d 3.50 MeV, peak at 0c.m. = 105 °

498

HSrN-MIN KUAN e t al.

at 4.2 MeV, and peak forward at 4.88 MeV. The angular distribution at 4.88 MeV is similar to the one at 5.98 MeV f r o m 0c.m. = 0 ° to 80 ° o f Hinds and Middleton s). 3.2.7. The C12(He3, p6)N14* (5.83 MeV state). Differential cross sections at 0t~b = 76 ° and 159.4 ° f r o m 2.9 to 5.4 MeV, at 01~b = 100.2 ° f r o m 4.0 to 4.5 MeV

3

3~

2.88 MeV

<

~

9~ bl

I--

Ci2(He3, pc)N1,4 (6.23MeVSTATE)

.!

I

~E

i

i

J

i

i

L

i

MeV

s

'

9'0

I-

I11

i

J

4 . 8 8 MeV

•

'

i~o

3o

9b

C.M. A N G L E

t~ Ilg W

i

'

,~o

~

'

9'0

'

i~o

(DEGREES)

i

i

i

i

i

i

i

i

i

i

4~5

~o

,I

'2

J q~

b

8(Lobl • 159.4"

a5

3'.o

~5 HELIUM-3'

4'o ENERGY

5.5

(MeVI

Fig. 14. D i f f e r e n t i a l cross s e c t i o n s at l a b o r a t o r y a n g l e s 76 ° , 109.3 ° , 146.6 ° a n d 159.4 ° , a n d a n g u l a r d i s t r i b u t i o n s at 2.88, 2.99, 3.50, 4 . 2 0 a n d 4.88 M e V o f t h e r e a c t i o n C12(He a, ps)N14*(6.23 M e V state). T h e solid lines w e r e d r a w n t h r o u g h the d a t a points. T h e a r r o w s m a r k e d the p o s i t i o n s w h e r e a n g u l a r distributions were measured.

and angular distributions at 2.99, 3.50, 4.20 and 4.88 are shown in fig. 13. The yields are low below 4.0 MeV in the excitation curves and start rising f r o m the 4.2 MeV reso-

CxtL-~- He a

499

REACTIONS

nance. The 4.2 MeV resonance appearing at 76 ° has the same position and width as it does in the excitation curve o f Ps. The yields at 159.4 ° o f these two groups are also similar. The laboratory width of the 4.2 MeV resonance is about 80 +_ 15 keV from the Ps and P6 data at 76 °.

CJ2(He3,P9)Nt4*(6.44 M eV STATE) "8

Z

-I

2.99 MeV

t<~ Y

P

~

II~

4

--

-3

THEORY o'(01=6.7 P,

E 30

150

C.M. ANGLE (DEGREES)

Q ~

<

" "

a

i

i

w

~~ , ,,. .h.~, . =,v~.o. ,~,~ I

.

.

fit)

-r"

f_°

0(L°b).,,e.,-

i

zs

~.o

35

HELIUM-3

4.0

i

45

i

5.0

5.5

ENERGY ( M e V )

Fig. 15. Differential cross sections at laboratory angles 76 °, 109.3 °, 146.6 ° a n d 159.4 °, a n d a n g u l a r distributions at 2.99, 4.20 a n d 4.88 MeV of the reaction C12(He s, p0)N~*(6.44 M e V state). T h e solid lines were d r a w n through the d a t a p o i n t s for all the curves except the 2.99 MeV a n g u l a r distribution. The solid line for the 2.99 MeV angular distribution was the theoretical fit (case 1 o f table 3). The arrows m a r k e d the positions where a n g u l a r distributions were m e a s u r e d .

The angular distributions vary from energy to energy. It seems that the 4.2 MeV angular distribution is mainly due to the 4.2 M e V resonance with some degree o f interference with neighbouring resonances. The 4.88 MeV angular distribution is

500

HSIN-MIN

et

KUAN

al.

similar in shape to the one at 5.98 MeV in the work o f Hinds and Middleton 2), but the cross sections are about 4 times higher at 4.88 MeV. 3.2.8. The C~2(He 3, p s ) N 14. (6.23 M e V state). Differential cross sections at 01~b = 76 ° and 159.4 ° f r o m 2.3 to 5.4 MeV and some results at 0~ b = 109.3 ° and 146.6 ° and angular distributions at 2.88, 2.99, 3.50, 4.20 and 4.88 are given in fig. 14. The yield curves have no narrow resonance structure except for a relatively narrow resonance appearing at 4.35 MeV in the b a c k w a r d angle data. The yields at backward angles rise above 5 MeV. All the angular distributions have forward peaking. CL2(He3' Pll ) N I 4 . ( 7 ' 0 3

MeV STATE)

.I.2

'0.6

06

0.4

4.20

3b

9b

,

C~4

MeV

'

~o

4 . 6 8 MeV

3b

'

9b

'

i~o

C.M. ANGLE (DEGREES) g(Lob) = 76 * j , . . o _ . _ _ . ; , _ , . . . . . . ~ o . - 2 . ~ .

i 0( L ab) =

109.3"

,. ~ . ~ _ . _ ~ .

i

i

~

...~__~_.-.- - , - ~ . - ~ ) " ~ - - ~ - " "--~-*-'-~"~'x. i

i

i

OlLab) = 146.6.

3.2

~ : 0 4 . 2 1

~l.o

,,~.~

HEUUM-3 ENERGY(u~) Fig. 16. Differential cross sections at laboratory angles 76°, 109.3° and 146.6°, and angular distributions at 4.20 and 4.88 MeV of the reaction C12(Hes, p~)N~4*(7.03 MeV state). The solid lines were drawn through the data points. The arrows marked the positions where angular distributions were measured. 3.2.9. The C12(Hea, pg)N14* (6.44 MeV state). Differential cross sections at 0~ab = 76 °, 109.3 °, 146-6 °, 159.4 ° and angular distributions at 2.99, 4.20 and 4.88 MeV are given in fig. 15. All the yield curves show a p r o n o u n c e d single resonance at 2.99 MeV and smaller yields in other regions, with indication o f resonance structure at 4.4 MeV. The angular distribution on the 2.99 M e V resonance was repeated four times to make sure o f its isotropic behaviour. The isotropic character o f this angular distribution is o f theoretical interest. This point will be discussed later. 3.2.10 The C12(He 3, p l l ) N 14. (7.03 MeV state). Differential cross sections at 0lab = 76 °, 109.3 °, 146.6 °, and angular distributions at 4.20 and 4.88 MeV are shown

CV'+

He a

501

REACTIONS

in fig. 16. T h e r e is no p r o n o u n c e d structure in the yield curves, although there is s o m e i n d i c a t i o n o f b r o a d r e s o n a n c e b e h a v i o u r at 4.4 an d 4.9 MeV. CIZ(He~,eo)CII(GROUND

STATE

)

¢

-16 2 . 4 9 MoV

2.88 MeV

2.99 MeV

'i ~t~+~

~/

A Z Q ,,¢[ n.* LU I-¢/) =E

,

i

i

1

i

r

r

i

r

=E b

4 , 2 0 MeV

4o\,,

, L J* ~ ,

i \/ i

\ -4o~

i

i

i

i

4.88 MeV

F2o

3.50 MeV

3"o

9b

'

'

~o

i

~

i

i

i

) 90 150 C.M. ANGLE (DEGREES}

30

90

150

-16

Z i

i

l,

r

i

r

J

16 I-II1

O(Lob)= 159.4"

8

qs

8(Lab) = 104.5 °

/.

/

b "8

i

HELIUM- 3

ENERGY (MeV)

Fig. 17. Differential cross sections at laboratory angles 76°, 104.5° and 159.4°, and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20 and 4.88 MeV of the reaction CI~(He~, ~0)Cll(ground state). The solid lines were drawn through the data points. The arrows marked the positions where angular distributions were measured. 3.3. THE CI~(Hea, ct)C11 WITH c¢ GROUPS TO THE C11 GROUND STATE AND FIRST EXCITED STATE AT 2.00 MeV A s in the case o f the p r o t o n o u t g o i n g channels, there are b r o a d resonances in the excitation curves, b u t the r e s o n a n c e positions vary with angle an d channel. In

502

HSIN-MINKUANet

aL

the angular distributions of Hinds and Middleton s), strong yields were observed in the forward angles, but the measurements extend only up to 120°, and hence it is not known whether the yields at backward angles stay small or go up again. The behaviour of these two reactions in the lower energy region of the present work seems somewhat different from their behaviour at higher energies as shown in the Hinds and Middleton results 5). 3.3.1. The CZ2(He3,~o)Cll (ground state). Differential cross sections at 0ja, = 76 ° and 159.4 ° from 1.8 to 5.4 MeV, at 0~ab = 104.5 ° from 4 to 4.5 MeV, and angular distributions at 2.49, 2.88, 2.99, 3.50, 4.20 and 4.88 MeV are shown in fig. 17. CI=(He3, clOCt 1~(2.00 MeV STATE)

+,>t'+

8

4.88 MeV

4

.Q

/

i

/ / +

+~./ l4

4"20 M~V

~

3'0 ' 9'o ' I~0 C.M. ANGLE (DEGREES)

•

t~

+

.-! "'*-.~~--,-_.

l+.~'+-.'': .

.

4.2

.

.

.

.

I

" ~

.

4.6 5.0 HELIUM-3 ENERGY (MeV)

1 I

I

5.4

Fig. 18. Differential cross sections at laboratory angle 76° and angular distributions at 4.20 and 4.88 MeV of the reaction CZ2(He3, cq)Cl1"(2.00 MeV state). The solid lines were drawn through the data points. The arrows marked the positions where angular distributions were measured. The interesting feature of this reaction at these energies is the presence of relatively narrow resonances and the rapidly varying angular distributions in the resonance region. This is shown in the data of the 2 to 3 MeV and the 4.5 MeV regions. This suggests compound nucleus formation in this reaction, although it was originally thought to proceed primarily via direct interaction. The resonance positions in the 159.4 ° data do not agree with those in the 76 ° data. The 4.88 MeV angular distributions has a different shape than the 5.98 MeV distribution of Hinds and MiddletonS). Another feature of this reaction is the large cross sections compared with the cross sections of other outgoing particle channels. 3.3.2. The C12(He3, (z1)C 11* (2.00 MeV state). Differential cross sections at 01=b = 76 ° and angular distributions at 4.20 and 4.88 MeV are shown in fig. 18. There is an indication of a resonance at 4.35 MeV in the yield curve. The angular distribu-

C1Z-~ He 3 REACTIONS

503

tion at 4.88 M e V has a shape similar to the 5.98 M e V distribution o f Hinds and Middleton 5). 3.4. GAMMA RAYS FROM C12-t-He3 REACTIONS In fig. 19(a) is shown the excitation curve o f g a m m a rays included in the w i n d o w marked in fig. 4 (mainly ?6.44) at 0jab = 90 ° f r o m 2.7 to 5.4 MeV. In the 3 M e V region the curve is due primarily to the ?6.44 and has a shape similar to that o f the excitation

(bl

. ,%

.

t

~ .

L

~

I 2.99

/\.~. "~" /" I .'-..~ .~. ..... / q <~"

(a)

f!

/*/"

l

/

40

MeV

4

- -

THEORY

....

eo + 0.43Tp=- o,zz7 P4 LAB

ANGLE

[

(DEGREES)

/ y

.J

....... i

I / ,

~

I/

(c)

)

-2O

laJ I )lU > I--

/'"

/

/

]XIO

d"

,,"

I

F"

"',,

d"

,/

/

/°

/

/

-Io

i

/...../

,o-

!

/

/

/

•'

J6, ........ -"s / i t ~

...........

......~;.~ '

/ Z

1.0

1.15

3.0

HELIUM-3 ENERGY (MeVl

4.0

415

5.0 i

Fig. 19. Gamma rays from CX2(Hes, p')N14*: (a) excitation curve of the 6.44 MeV gamma ray from C12(Hes, pgyG.44)NX4*(6.44 MeV state) with the window setting shown in fig. 4; (b) angular distribution of the 6.44 MeV gamma ray at 2.99 MeV resonance. The solid line was the theoretical fit (ease 1 of table 2), the dashed line was a least-squares fit of the experimental data points; (el excitation curves of gamma rays with energies greater than about 3 MeV (closed points) and of gamma rays with energies greater than about 4.5 MeV (open circles). curve o f the P9 proton group, as would be expected. The increase in g a m m a - r a y yield at the higher energies is presumably due to the effect o f the 6.23 M e V and other high energy g a m m a rays, which can appear in the pulse-height analyser w i n d o w set for ?6.44. This is m o r e clearly evident if o n e m a k e s a c o m p a r i s o n with the data on the corresponding proton groups.

504

HSIN-MIN KUAN e t al.

The angular distribution of the 76.4.4 on the 2.99 MeV resonance measured with the method described in section 2.2.3 is shown in fig. 19(b) and has very pronounced structure. The angular distributions of this 76.44 at other energies did not show pronounced structure. In fig. 19(c) is shown the 0 ° excitation curve from 1.2 to 5.4 MeV of all gamma rays with energy greater than 3 MeV and the 90 ° excitation curve from 2.4 to 5.2 MeV of all g a m m a rays with energy greater than 4.5 MeV. The first curve shows the resonances at 1.3, 2.1, 2.45, 3.0, 4.2, 4.4 and 5.1 MeV which appear in the various proton groups.

4. Analysis and Results in the 3 MeV Region The P9 proton group and the corresponding 76.44 both show a strong isolated resonance at 2.99 MeV He 3 energy. The elastic data show structure, and the angular distributions of other particle groups show rapid variations with energy in the 3 MeV region. Attempts were made to interpret these results on the assumption of compound nucleus formation. So far, the analysis has been quite promising in the cases of the elastic, no, p~, P9 and 76.44 data. From an examination of the experimental results for the other outgoing channels, it seems likely that some also have compound nucleus formation as the dominant reaction mechanism. It is true that some of the other outgoing channels do show general trends characteristic of direct interactions, and the D W B A interpretation may be the theoretical ground on which to discuss these reactions. The point of view in the present work was to see how far the analysis based on compound nucleus could be carried to obtain information on nuclear states. In the following sections, analyses of the experimental data in the 3 MeV region for elastic He ~, 76.44, P9, no and p~ taken together are discussed in that order. The choice of order is arbitrary, since all the analyses are required to make an unambiguous choice of the resonance parameters. 4.1. ANALYSIS OF ClS(Hea, Hes)CIs An analysis of the C12(He 3, He3)C t2 differential elastic scattering cross section using dispersion theory in the single level approximation was run on an IBM-709 computer. The expression for the differential cross section was the same as eq. (1) of Belote et al. 12). Hand calculations, using a graphical method, were used to check the computer calculations. Isolated resonance shapes, one for each l and J~, were first calculated. They are shown in fig. 20 for a resonance energy of 3 MeV. By comparing them with the experimental data, tentative initial assignments of the resonance parameters could be made. The computer calculations of course included interference between resonances. After m a n y trial calculations, the parameters given in table 1 were chosen. The fit using these parameters is shown by the curves in fig. 6. The results of the calculations show that the fit to the 2.99 MeV resonance is quite successful. As can be seen by comparison of the isolated resonance curves of fig. 20, the assignment of l = 2 from the elastic data at the 2.99 MeV resonance is unambiguous. J~ = 3 + with l = 2 could be made to fit the elastic data equally well by

C12 ~- He8 REACTIONS

I~ '

' ' '-

'''

' I ~''

' I

505

~

'

'

'

'

t

'

'

'

'

I

f'

i

r-

,..., " =

I/ 104

['- "a ~

J / /

I ~i ~° r~

ro

/

#"s

eJ 04

05 U

/ ///

//

// 1"/

+

//

/

d[.("4 ,

d

,

L

i °

L

i

,

,

i Iml i , r l I i L L

I

o

; (NVI(3V~I3,.LS/NN'9'8)

o

d NOIJ-93S

I (5

IH,,

SSON3

,J

o

.

506

I-/SIN-MIN KUAN e t al.

adjusting the elastic partial width, but the choice of J = ~ is required by the analysis of the 76.44 angular distribution. The resonance energy and width of the 2.99 MeV resonance were obtained from the 109 and 76.44 excitation curves; those of the 2.45 and 2.75 MeV resonances were obtained from the total C12(He 3, no)O 14 and

--25

(o) ELASTIC He:5

/ t

(b) OUTGOING Pl

(c) OUTGOING NEUTRONS

/L

-15

5

-60

/

3

/

-2o

4 HELIUId-3

2.2 2.6 ENERGY (MeV)

3.0

2.2

2.6

3.0

Fig. 21. H a r d sphere phases used in the analyses o f t he elastic H e 3, px a n d n e u t r o n d a t a o f the C~=+He s reactions.

TABLE 1 R e s o n a n c e parameters used for fits s h o w n in fig. 6

Curves

ER (lab) (MeV)

Fxab (keY)

l

J=

FMe3 F

Solid line (Fit 1)

2.99

125

2

~+

0.15

Dashed line (Fit 2)

2.99 2.75 2.45

125 420 200

2 0 1

~+ ½+ ~-

0.15 0.05 0.10

C12(He 3, p l ) N 14. cross-section excitation curves. The J~ and l values at 2.45 and 2.75 MeV were chosen for best fit both to the elastic data and to the C a2 (He 3, no)Or4 and C12(He 3, px)N t4* angular distribution data. The hard sphere phases 9~I were entered in the programme as a quadratic function of energy in which the coefficients were determined by a least-squares fit to the tabulated values 13). The values used are plotted in fig. 21(a). After choosing the resonance positions, widths, and l and J"

Clz--~He$ KEACTIONS

507

values, the best fit was obtained by varying the elastic partial widths. The small elastic partial widths given in table 1 are reasonable in view of the large cross sections in many of the reaction channels. The inadequacies of the fit above 3.5 MeV and below 2.5 MeV are apparent" from fig. 6. Deviations are to be expected, since there are many resonances above and below 3 MeV which could not be included in the calculations, so that it is perhaps surprising that the fit at 3 MeV is so good. In the case of the 164.5 ° data and curve of fig. 6, the fit is good at the 2.45 MeV resonance, but no combination could be found to remove the discrepancy at 2.75 MeV. The departure from the calculated Rutherford cross section, shown by the dashed line in fig. 6, cannot be taken as significant, since the contributions of resonances below 2.45 MeV and above 2.99 MeV were not taken into account. 4.2. A N A L Y S I S O F T H E 6.44 M e V ~,-RAY A N G U L A R RESONANCE

D I S T R I B U T I O N A T T H E 2.99 M e V

The experimental results (subsects. 2.2.3 and 3.4) show that the 2.99 MeV resonance in the v-ray excitation curve is due mainly to the 6.44 MeV Vray. It was shown also that the v-ray angular distribution of fig. 19(b) at 2.99 MeV is due to this V ray. The P9 proton group to the 6.44 MeV state shows a strong resonance at 2.99 MeV with relatively small cross sections above and below the resonance (fig. 15). It was therefore assumed that an analysis of the angular distribution of the 6.44 MeV V ray, as well as that of the P9 proton group, could be made on the assumption of an isolated compound nucleus state without interference from other states. A preliminary least-squares fit to the experimental angular distribution of the 6.44 MeV V ray showed no appreciable contribution from odd order Legendre polynomials or from even order polynomials of order higher than 4. The least-squares fit using even orders up to P4 is given by Po + 0-437P2 - 0.227P4. It is shown by the dashed line in fig. 19(b). Since the coefficient of P4 is of significant magnitude, it follows from general considerations that the incident I > 2 and that J > ~. (This can be seem from the fact that the Racah Z coefficient in the/'4 term of the angular distribution is non-zero only for 1 > 2 and J > ~). Since the fit to the elastic data required that l be 2 with J either ~ or ~, it immediately follows that the assignment is unambiguously J~ = ~+ for the state at 14.46 MeV in the compound nucleus 015 corresponding to the 2.99 MeV resonance. The analysis of the v-ray angular distribution was based on the expression for the angular distribution of an (a, by) reaction given by Krausetal. 14). For a single J and one value of the orbital angular momentum l and channel spin S in the incident channel, the differential cross sections are given by sums (added coherently or incoherently as specified below) of expressions of the form

508

HSIN-MIN

al,

et

KUAN

( - 1) 4 (2S~ + 1)~ (2S~ + 1)¢ C(LL1 - 1, AO) Z(lJlJ, SA) A !

t

t

¢

•

t

•

•

× W(JSxJS2,1 A) w ( g x j g 2 j , jb A)

x W(j'LjL, hA)P,~(cos 0).

(1)

Here C is the Wigner, or Clebsch-Gordan coefficient, Z and Ware the Racah coefficients, S = ½, l = 2 and J = ~:for the present case. The remaining symbols are defined as follows: S~ and S~ are the channel spins in the P9 + Nx4* channel, l' = is the orbital angular momentum in the P9 + N~4* channel, Jb is the spin of the outgoing proton, j is the spin of the 7-emitting state, j e is the spin of the final state, L is the multipolarity of the y ray, 2 = -½A +I'+ S+S~ - S ~ +Jb-Jr. The spins S~ and S~ can each take on the values { and 3, since the 6.44 MeV in N 14 has been shown ts) to have angular momentum 3. The choice of parity for this state and its implications have been discussed by Warburton and Pinkston ~6). The parity had not been determined at the time of this work. With positive parity for the 6.44 MeV state, essentially pure E2 radiation would be expected. With negative parity, the possibilities of M2 and E3 both have to be considered. Table 2 lists the expressions obtained by evaluating the coefficients in eq. (1) for the possible combinations of S~ and S~ and for t h e L and lower l' values allowed by both 3- and 3 + choices for the 6.44 MeV state of N ~4. TABLE

2

Calculated angular distribution of the 6,44 MeV gamma rays Case No.

l

J"

l'

S'1

S'2

L

3 + cases

1

2

~+

0

{

{

2

/'o+0.490 Pz--0.299/'4

2 3

2 2

~+ ~+

2 2

~ {

~ {

2 2

Po+O.O49Pz+O.150P4 Po+O.204P~+O.150P4

4

2

~+

2

{

½

2

-4-0.120 P~ 3- cases

5 6 7 8 9 10

2 2 2 2 2 2

~+ ~+ ~+ ~+ ~+ {+

1 1 1 1 1 1

~ { ~ ~ ~ {r

~ ~½ t { {-

2 2 2 3 3 3

Po+0.322/'2+0.043 P4 Po+0.437 P~--0.192 P4 -b0.094 P~zF0.191/'4 P0+0,424 P~--0.003/'4 /'o+0.575 P~+0.015 P4 4-0.124 P2~0.015 P4

In summing expressions from table 2 to obtain differential cross-section expressions, the amplitudes by which the contributions from the channel spin combinations are to be multiplied are expected to have relative phases 0 or 7r, while contributions from different l' are to be added incoherently x,). It is clear from the table that it is not possible to distinguish between 3- and 3 + for the 6.44 MeV state in N 14 on the basis of the ?-ray angular distribution alone, since the cases L = 2, l' = 0 with St = S~ = and L = 2, l' = 1 with St = S~ --- ~ with small admixtures of other allowed cases would fit the angular distribution equally well. The analysis of the P9 proton group is therefore required to resolve the ambiguity in the parity of the 6.44 MeV state in

C~+He s RF.ACTmNS

509

N ~ . The P9 analysis of the next section, taken together with the elastic analysis and the requirement J > ~ from the magnitude of the coefficient o f P 4 in the y-ray angular distribution, unambiguously assigns even parity to the 6.44 MeV state in N ~4, consistent with the fact that case 1 of table 2 fits the y-ray angular distribution. The analysis of the 6.44 MeV y-ray angular distribution at 2.99 MeV constitutes rather strong support of the results of the various other analyses. Many of the cases of table 2 do not give the large coefficients of P2 and P4 required by the experimental distribution. In the experimental distributions, a small background from lower energy y-rays would introduce an error .in the direction of increasing the measured cross section at 90 ° relative to forward and backward angles, as shown in subsect. 2.2.3, so that possible errors in the experimental distributions would result in an underestimate of the magnitudes of the coefficients of P2 and P4 required to fit the distributions. Alburger, Chase and Warburton 17) have recently established the fact that the 6,44 MeV y ray consists of pure E2 radiation. This not only determines L to be 2 but established the parity of the 6.44 MeV state as even. 4.3. ANALYSIS OF C12(Hea, p~)N14*(6.44 MeV STATE)

The analysis of the angular distribution of C12(He 3, pg)N 14. was based on eqs. (3.16), (4.5) and (4.6) of Blatt and Biedenharn is) which were derived on the basis of single level dispersion theory. For the C12(He 3, p9)N 1~* reaction and for a single J, the expression reduces on resonance to

E E (--

Z(IJIJ, SL)Z(I'JI'J, S'L)VL(COS0), (2)

S'F

with S = ½. From the elastic and 76.,,4 analyses, l = 2 and J = ~. S" and l' refer to the P9 + N14" channel, with S" taking on the values ~ and 7 as in the 76.4~ analysis. The approach in fitting the data was to calculate angular distributions for individual S' and for the lowest one or two l' values and to compare them with the experimental data. Hand calculations were made using the available tables 19) of Z coefficients. Since it has already been determined from the analysis of the elastic data that J~ = ~+ and that the incoming l = 2 for the 2.99 MeV resonance, only the cases for l = 2, j r = ~+ are given in table 3. TABLE 3 Calculated angular distributions of C12(Hes, ps)N x4* (6.44 MeV state) at 2.99 MeV resonance Case No.

S

1

J~

l'

S"

3 + cases

1

½

2

~+

0

~

eo

2 3

½ ½

2 2

~+ j+

2 2

~ ~

P0-- 0.407 P2+0.550 P4 Po--0.693 P2--0.164 P4 3- cases

4 5

½ ½

2 2

~-+ f]+

1 1

~ ~-

Po+0.913 P2 /o+0.286 Pz

510

HSIN-MIN K U A N et aL

By a comparison of the calculated angular distributions, given in table 3, and the isotropic experimental angular distribution, the only possibility is that of l' = 0, S' = ~+. An admixture of d-wave for the outgoing particle is not necessary. This is reasonable in view of the low energy of the P9 proton group. The final calculated angular distribution is isotropic, and the cross section is given by

a(O) = 6.7 Po mb/sr, using (Fnc32/F)(Fp9o/F) = 0.062, S' = ~+, 1' = 0. Comparison between theory and experiment is shown in fig. 15 where the solid line represents the calculated 6.7 mb/sr, independent of 0. The agreement is seen to be good. As the FHc32/F= 0.15 has been obtained from the calculation of elastic cross section, we have Fpgo/F = 0.413 and Fp9 = 51.5 keV (since F = 125 keV). As a final result of the elastic He 3, Y6.44 and P9 analyses, even parity can be assigned to the 6.44 MeV state in N 14, independent of assumptions of the multipolarity of the 6.44 MeV y-ray. The analyses are mutually consistent and constitute strong evidence that the compound nucleus reaction mechanism is dominant in the 3 MeV He3-energy region. 4.4. T O T A L CROSS SECTIONS O F T H E R E A C T I O N S ClS(He 8, no)O 1', CI~(He a, p 0 N x4* A N D Cl~(He s, po)N 1'

The purpose of this analysis was to assign resonnnce positions and widths to be used in the analysis of the no and Pl angular distributions and the He 3 elastic scattering data. The total cross sections for the emission of Po and Pl were obtained from the differential cross sections at six angles, 0~ b = 7 °, 30 °, 60 °, 90 °, 120°, 150°, measured by Johnston et aL e). Data points read from the curves were plotted as angular distributions and integrated numerically. The results are plotted in figs. 22(b) and (c). The curves were fit by a sum of Breit-Wigner single levels using an IBM-1401 computer. The final fits are the solid curves in fig. 22 using the parameters given in table 4. TABLE 4 Parameters used in fits o f the total cross sections o f C12(He a, n) 014, C12(He a, pl)N ~'* and C1S(He 8,po)N I'

-F'He3P# Eo (MeV)

(2Jq- I)

Fl~u (keV) no

2.45 2.75 2.99 3.28 3.60 4.60 5.10

200 420 125 280 500 480 680

0.0629 0.0807 0.0351 0 0 0 0

Pl 0.0521 0.0565 0.0307 0 0 0 0

_ps Po 0.0234 0.0807 O. 136 0.0216 O. 169 0.0809 0.164

511

C12~-He $ REACTIONS

N o attempt was made to fit the cross sections o f Pl and no at higher energies because the angular distributions of these two groups show forward peaking at higher energies 2, 4, 5, 20) which indicates the possible presence o f l = 0 stripping reaction.

O

U

2

Cl2(He 3,n)O 14

(o)

FITS

I

1

I

I

i

i

(b) CI2(He3,Pl)N 14"If

0 D:

")

- ,o

c)


30

CfZ(He~,p0 )N 14

°

2o

21o '

2!5

3.'o HELIUM-3

3.'5 ENERGY

,!o

,!3

3.0

(MeV)

Fig. 22. Theoretical fits of the total cross sections of the reactions C~2(He3, n)O x~, CX~(He3, p0N ~4., and C12(Hes, po)N~. The parameters used are given in table 4. The experimental data points for (Hes, n) are from ref. ~6). The (He 3, p~) and (Hea,P0) points were calculated from the excitation curves of Johnston et al?). But this is not the case for the Po g r o u p which shows strong evidence o f resonance p h e n o m e n o n 2, 5, zo). Thus, the fitting of the Po data was therefore extended to include resonances at 3.28, 3.60, 4.6 and 5.1 MeV. The 4.6 and 5.1 M e V resonances are not pronounced, and the parameters used are mainly to fit the smoothly rising yield.

512

H$1N-MIN KU^N e t al.

4.5. A N G U L A R DISTRIBUTIONS OF CZZ(Hd, no)C T M AND CZZ(Hea, Ih)N ~4.

The final states in these two reactions (the 2.31 MeV state o f N ~* and the ground state of O ~4) are members of an isobaric triplet with J = 0 + and T = 1. The reactions differ in the energies of the outgoing particles and the Coulomb force in the case of p~. The similarity in the experimental results for the two reactions can be seen by comparing the 90 ° and 0 ° yield curves ~' 4) from 2 to 5 MeV the 10° yield curves and angular distributions zo) from 5.7 to 11 MeV, and the total cross sections shown in fig. 22. The angular distributions in the 2 to 3 MeV region were fit using the single level dispersion theory expressions for the cross sections given by Blatt and Biedenharn is), "4

~/~/~. ~v

"2

2.49 MeV

2.68~v ~

~m~

t~

CI2(He3 pl)N 14.

,Y

Z

3.15 MeV

t

r~ rr hl I'-i

I

i

i

i

i

•3

i

.

3b

•

.

'

.

9b

i

i

2.66 M e V / ~

i

3

I

i

I

i

CI2(He3, n)O 14

2.B7 MeV

/

2.33 MeV

-2

•

i

•

.

• EXPERIMEHT [3J I MIV) X 2 - - F i T {,3.00MIIN) t ,

.

' ,~o

~'o

'

9'0

'

,~o

i

30

i

i

90

I

,I

130

.

30

90

150

C.M. ANGLE (DEGREES)

Fig. 23. Theoretical fits of the angular distributions of CXS(He8, px)N 1~* and CZ2(He8, n)OZ% The parameters are those given in table 5. The data for Pz were from the present measurement (fig. 8), those for neutron were from the results of Din, Kuan and Bonner ~). The same hard sphere phases were used as are shown in figs. 21(b) and 21(e).

as in the case of the P9 angular distributions. The calculations were carried out with an IBM-709 computer. The, programmed expression, which included interference between resonances, was the same as eq. (2) of Kashy et al. s). The hard sphere phases ~bz used for the incoming He 3 particles was the same as those used in elastic He 3 analysis. The ~b~, of the outgoing protons were calculated using a programme originally written by Harris 21). The values used in the computation are plotted in fig. 21(b). The ~bt, of the outgoing neutrons were obtained from the least-squares fit of a quadratic expression to the tabulated values 22). They are plotted in fig. 21(c). The positions and widths of the resonances were obtained from the Breit-Wigner fits to the total cross sections and from the P9 and 76.44 analysis• The products of the

I }

513

Clz-~ He s REACTIONS

He a and outgoing particle partial widths were obtained from the fits to the total cross sections. The I and J " of the 2.45 and 2.75 MeV resonances were chosen for best fit to these angular distributions and are the same as those used in the final fit to the elastic data. Actually the processes of fitting the angular distributions and total cross sections of no and Pl were carried out simultaneously, and the parameters were adjusted many times until the fits to both the total cross sections and the angular distributions were reasonably good when compared with the experimental data. The final parameters used for the fits shown in fig. 23 are given in table 5. It should be remarked that the use of ½+ for the 2.75 MeV resonance gives a much better fit than any other J ' , while the use o f ~ - or ½- f o r the 2.45 MeV resonance has not much effect on the shapes of the angular distributions above 2.3 MeV. TAm.E 5 Parameters used in fits of the angular distributions of CX2(Hes, Px) N z4* and CZ2(He s, no)O ~ eo (McV)

ri,b (keV)

.r,

r,:/~p, F'~

r.e3rno /'~

2.99 2.75 2.45

125 420 200

~+ ½+ j-

0.00512 0.02823 0.01303

0.00585 0.04035 0.01572

Since the angular distributions above 4.5 MeV show consistent peaking forward which indicates the possibility of 1 = 0 double stripping, no attempt was made to extend the above analysis to higher energies. Gibbs and Tobocman 23) have made some DWBA calculations (cf. ref. 4) also) for C 12(He 3, n)O 14 in the 2 to 5 MeV region. However, from the comparison with the experimental results, it seems that the interpretation of the rapidly varying angular distributions as due to interference between many broad compound nucleus states is likely to be successful.

5. Summary and Conclusions Protons to the 6.05 and 6.70 MeV states 6) of N t4 (P7 and Plo, taking the order of the excited states of N 14 as shown in fig. 1 from ref. 6)) were not observed. The two states were suggested by Burge and Prousse 24) and by Hossain and Kamal 2n) in their work on N14(p, p') with a cyclotron at 9.5 MeV. Although the identifications of the other proton groups up to pt 1(7.03 MeV state) were quite positive from comparisons of the positions of the groups in the spectra with the results of detailed calculations of the reaction kinetics, these two groups were not observed in any of the spectra taken. A general feature of the C t 2 + He 3 reactions is the appearance of broad resonances in most of the outgoing channels, suggesting compound nucleus formation. Dispersion-theory analyses to fit the elastic He 3, no, pt, and P9 differential cross-section data and the 76.~ angular distribution data were quite successful in the 3 MeV region.

514

H$IN-M1N

KUAN

et

a].

o~

O

O

O

O

.o O I i¢~

÷

o

O

z ÷ O t~

-H

-H

O ¢'4

o e3

r~

d -H

CI~-~- He8 REACTIONS

515

At the 2.99 MeV resonance, where the assignment J~ = 4 + for the corresponding state in the compound nucleus O is was obtained, the success and consistency of the analyses for the various channels strongly support the assumption of compound nucleus formation. The parity of the 6.44 MeV N 14 state 6, 15, 16) with J = 3 was determined to be even from the elastic He 3, P9 and ~:~.4~,analyses at the 2.99 MeV resonance. Table 6 gives a summary of the resonance parameters from the analyses in the 3 MeV region, including reduced widths, where they could be obtained, and the ratios of the reduced widths to the Wigner limit expressed in percent. In calculating the reduced widths, the reaction radii used were 5.4 fm for the elastic He 3 channel, 4.95 fm for the n o, Pl and P9 channels. The penetrabilities used were obtained from refs. 13, 21). The resonances in general show strong interference. Resonance energies vary from one channel to another and between angles in the same channel. An example is the 3 MeV resonance for the ~0 group at 159 °. At 76 ° the maximum occurs above 3 MeV. Data were taken simultaneously at two angles approximately 90 ° apart for all the charged particle groups, so that discrepancies are not due to relative errors in the energy. Table 7 contains estimates of positions and widths of resonances which appear TABLE 7 Resonances

of C18+Hea reactions not included in table

E~3 (MeV)

rt~b (keV)

~ ( O 15) (MeV)

4.20±0.01

80-/-15

15.43

4.37::[=0.04

100-4-30

15.57

4.6 :~0.1

15.75

5.0 ::t:0.1

16.07

6

Resonance appeared

at:

76° excitation curves of ps, pe and 159.4° excitation curve of u~ 159.4° excitation curves of Pl, P~, Ps, P9 and 0 ° and total cross section excitation curves of no (ref. 4)) 0° and total cross section excitation curves of no (ref. ~))

clearly indicated on one or more excitation curves. Those taken from differential cross section curves should be regarded as uncertain. In the early work on C l Z + H e 3 reactions, BromleyetaL 1) have reported resonances at 2.15, 2.52 and 2.70 MeV, and Johnston et aL 2) have reported resonances at 3.0, 3.6, 4.4 and 4.8 MeV. All the excitation curves plotted on the same He 3 energy scale for comparison are shown in fig. 24. Above, a corresponding 015 excitation energy scale is given, and on top is the total N14(p, n)O 14 cross section with a scale of proton energies corresponding to the compound nucleus 015 excitation-energy and the He3-energy scales below. The N14(p, n)O 14 total cross-section curve is taken from the following paper 26). The energies of the states on the O 1~ scale correspond to the C 12 + H e 3 resonances

(~.ev)

ITI

/

~E

I

I

io

I

NI4(p,n)O 14

~,l

i,z

I

40

-2o

~ i

I

I

TOTAL ,

PO

I

~

159.4°

.

159.4" _~ . . . . . .

P2

-,... 76 =

,4 "2

P3

4 2

P4

'42

~

/

/

t

P8 (

8 4

/

I

/

i

,~ .........

-~

.

I,

I

,lO

" "'l

I

I

i

I

I

HELIUM-3

,

Ct 0

I

I

ENERGY (MeV)

Fig. 24. Summary o f all the experimental results in the prcviotts fi@~res. The dashed lines az¢ the excitation curves at 76°. The energy vaJucs of the s~tcs in 01~ are from tables 6 a~(l 7.

C12-~HeS REACTIONS

517

of tables 6 a n d 7. A l t h o u g h m a n y of the resonances are n o t distinct, there are u n mistakable correspondences a m o n g the channels for most o f them. The a u t h o r s wish to acknowledge the generous help of Dr. T, A. Belote at the start o f the charged particle experiments a n d analysis, the help of Dr. J, P. Schiffer o f the A r g o n n e N a t i o n a l L a b o r a t o r y i n the ~-ray analysis a n d the use o f a c o m p u t e r o f the A r g o n n e N a t i o n a l L a b o r a t o r y , the courtesy of Dr. N. A. B r o w n in allowing the use of his version o f the Belote-Brown-Perry spin-½ scattering p r o g r a m m e for the IBM-709 computer, the D a t a Processing Center o f the Texas A, a n d M. E n g i n e e r i n g Experim e n t Station for time o n their IBM-709 computer, a n d Dr. E. K. W a r b u r t o n for a very stimulating discussion o f the possible assignments to the 6.44 M e V level of N la.

References

1) D. A. Bromley, E. Almqvist, H. E. Gore, A. E. Litherland, E. B. Paul and A. J. Ferguson, Phys. Rev. 105 (1957) 957 2) R. L. Johnston, H. D. Holmgren, E. A. Wolicki and E. Geer Illsley, Phys. Rev. 109 (1958) 884 3) J. H. Towle and B. E. F. Maeefield, Proc. Phys. Soc. 77 (1961) 399 4) G. U. Din, H. M. Kuan and T. W. Bonner, Bull. Am. Phys. Soc. 6 (1961) 236; Proc. Rutherford Jubilee Int. Conf. ed. by J. B. Birks. (Academic Press, New York, 1961) p. 499; Nuclear Physics 50 (1964) 267 5) S. Hinds and R. Middleton, Proc. Phys. Soe. 75 (1960) 745 6) T. Lauritsen and F. Ajzenberg-Selove, Nuclear Data Sheets, Sets 5 and 6, 1961; F. A. Ajzenberg-Selove and T. Lauritsen, Nuclear Physics 11 (1959) 1 7) E. H. Beckner, R. L. Bramblett, G. C. Phillips and T. A. Eastwood, Phys. Rev. 123 (1961) 2100 8) E. Kashy, R. R. Perry and J. R. Risser, Phys. Rev. 117 (1960) 1289 9) J. B. Marion, 1960 Nuclear Data Tables, Part 3, (National Academy of Sciences, National Research Council, Washington, D. C., 1960) p. 26 10) E. Kashy, R. R. Perry and J. R. Risser, Nucl. Instr. 4 (1959) 167 11) C. W. Reich, G. C. Phillips and J. L. Russell, Jr., Phys. Rev. 104 (1956) 143 12) T. A. Belote, E. Kashy and J. R. Risser, Phys. Rev. 122 (1961) 920 13) W. T. Sharp, H. E. Gove and E. B. Paul, Atomic Energy of Canada Limited Report AECL-268 50 (1964) 267 14) A. A. Kraus, Jr., J. P. Schiffer, F. W. Prosser, Jr. and L. C. Biedenharn, Phys. Rev. 104 (1956) 1667 15) H. J. Rose, W. Trost and F. Riess, Nuclear Physics 12 (1959) 510 16) E. K. Warburton and W. T. Pinkston, Phys. Rev. 118 (1960) 733 17) E. K. Warburton, private communication 18) J. M. Blatt and L. C. Biedenharn, Revs. Mod. Phys. 24 (1952) 258 19) L. C. Biedenharn, Oak Ridge National Laboratory Report ORNL-1501 (1953) unpublished; W. T. Sharp, J. M. Kennedy, B. J. Sears, and M. G. Hoyle, Atomic Energy of Canada Limited Report AECL-97 (1954) unpublished 20) H. W. Fulbright, W. P Alford, O. M. Bilaniuk, V. K. Deshpande and J. W. Verba, University of Rochester Report NYO-10034 (1962) 21) R. W. Harris, Ph.D. Thesis, Rice University (1961) 22) I. Bloch, M. M. Hull, Jr., A. A. Broyles, W. (3. Bouricius, B. E. Freeman and G. Breit, Revs. Mod. Phys. 23 (1951) 147 23) W. R. Gibbs and W. Tobocman, Bull. Am. Phys. Soc. 6 (1961) 236 24) E. J. Burge and D. J. Prowse, Phil. Mag. 1 (1956) 912 25) A. Hossain and A. N. Kamal, Ind. J. Phys. 31 (1957) 553 26) H. M. Kuan and J. R. Risser, Nuclear Physics 51 (1964) 518