00(M

AE-282UDC 539.f7t.0tS:

539.125.5.162.5

LU Polarized Elastic Fast-Neutron Scattering

off 12C in the Lower MeV-Range

I. Experimental Part

O. Aspelund

AKTIEBOLAGET ATOMENERGI

STOCKHOLM, SWEDEN 1967

AE-282

POLARIZED ELASTIC FAST-NEUTRON SCATTERING OFF C

IN THE LOWER MeV-RANGE. I. EXPERIMENTAL PART

O Aspelund

ABSTRACT

Practical as well as more fundamental interest in low-energy1 2 .

n- C elastic scattering motivated the execution of comprehensive

polarization studies between 1 . 062 and 2. 243 MeV. Seven complete

polarization angular distributions were obtained from experimental

finite-geometry left-right ratios at each energy observed at six or

seven laboratory scattering angles between 30 and 129 , using

polarized fast-neutrons emitted at 8, = 50 (lab. syst. ) from the7 7

Li(p, n) Be-reaction. Proper corrections were applied for finite-

geometry and polarized multiple-scattering effects as well as for

the presence of the first-excited state group of fast-neutrons in

the incident beams. The magnitude of the polarization effects are

sufficiently large to ensure the potentialities of C as an acceptable

fast-neutron polarization analyser in the energy range under con-

sideration.

Furthermore, on the basis of the above-mentioned polariza-

tion data as well as on the basis of total and differential scattering

cross section data available in current literature reliable phase

shifts were determined. These phase shifts are only in partial agree-

ment with the ones of Wills, Jr. et al. , and in definite disagreement

with the extrapolated phases of Meier, Scherrer, and Trumpy. Their

energy variations will be predicted in the theoretical part of this

contribution.

Printed and distributed in May 1967.

LIST OF CONTENTS

Pau,

1.

2 .

3 .

4 .

5.

6.

7.

8.

9.1 0 .

10.1

1 1 .

11.1

1 2 .

1 3 .

IntroductionTheory

Experimental facility-

Experimental procedure and data reduction technique

Experimental results

Phase analysis

Discussion

Summary

Acknowledgements

Appendix I

List of BT -coefficients for L ^ L =8L maxAppendix II

List of CT -coefficients for L ^ L =8L maxReferences

Figure captions

3

5

8

8

11

22

11

31

32

3 3

33

35

35

37

41

- 3 -

1 . INTRODUCTION

5 5 13 13The properties of the mirror nuclei He - Li, C - N,

17 17O - F, etc. , are of particular interest in nuclear structure

theory. Because of the exceptional stabilities of the doubly-magic4 ^2 16

nuclei He, C, O, etc. , it is to be expected that the salient

features of the corresponding mirror nuclei are well described by

means of independent-particle models. The interaction Hamiltonian

between the doubly-magic core and the odd nucléon is then in addi-

tion to the usual relative positional dependence augmented by a term

describing the coupling between the intrinsic spin of the nucléon and4 12 16

its orbital angular momentum. Consequently, when He, C, O,

etc., are used as sample nuclei in suitable scattering experiments,

the elastically scattered nucléons will become partially polarized,

provided that the selection rules pertaining to polarized scattering12

are fulfilled. In the particular case of n + C elastic scattering

at fast-neutron energies these selection rules are known to be

satisfied, because in addition to potential s-scattering there is a

contribution from resonant split d-scattering caused by even-parity

levels corresponding to the fast-neutron energies 2.076 MeV,

2.95 MeV, and 3.67 MeV. Furthermore, there is also a distinct

admixture of odd-parity (mainly -i = 1) scattering- also split—,

although the magnitude of the splitting is highly uncertain. The

origin of the I = 1-scattering is not yet known.

The net result of the split even- and odd-parity contribu-

tions is a rather large polarization above 2 MeV, although quite

variable with angle and energy. This feature is the reason why12

C was used as an analyser-after independent proposals of M.

Verde [1] and of E Baumgartner and P Huber [2 ]-in the pioneering

fast-neutron polarization experiments conducted by the Basel and

Zürich groups [3, 4, 5, 6, 7 ]. However, the absolute polarization

values quoted by these groups are generally quite uncertain, limiting12

the usefulness of C as a polarization analyser. The major part

of this uncertainty is caused by the insensitivity of the differential

scattering cross section to the small admixture of p-scattering,

making a reliable assessment of the p, /„- and p„ /_ - phases

virtually impossible. This is particularly true below 2 MeV

- 4 -

12where no resolved resonances in n + C scattering are known

to occur [8, 9, 10 1, so that the scattering is almost completely

determined by the ? -phase alone, leaving the remaining part too /L/2 3/2

be determined about equally much by the small f ' - , £. ' - ,•2 / o c / O 1 1

f>? - , and f_' -phases. Obviously, this is the reason why an

eventual phase analysis will be particularly unreliable - if pos-

sible at all-for fast-neutron energies below 2 MeV, if no special

precautions are taken.

The theory outlined below suggests a phase analysis not only

based on differential scattering cross sections but also on meas-

ured polarizations. This approach should enormously reduce the

uncertainties in a phase shift determination, and in particular

remove a number of ambiguities inherent in an ordinary phase

analysis. This reasoning incidentally supplies the objective of the

present report, being the determination of relatively accurate an-

gular distributions of the polarizations at various fast-neutron

energies between 1 and 2 MeV . The ultimate purpose is finally

an assessment of reliable phase shifts in the same energy range.

Needless to say, once this information is available the question12

of the use of C as a fast-neutron polarization analyser in therelevant energy range may be settled.

IF)Preliminary accounts of this work are found in refs. l i a - 17b.

- 5 -

2. THEORY

Invariance considerations applied to the kinematics of elastic

nuclear scattering of neutral non-relativistic spin-1/2 particles

by spin-0 nuclei yield the following transition matrix [l 8]

E ) (n a)

where

8 = scattering angle in the c. -of-m. system

E = energy of incident fast-neutron beam

- complex amplitudes, both functions of 9 and En

n = unit vector normal to the scattering plane

The positive direction of n is defined according to the

Basel convention [19], viz.,

[kxk' ] [kxk' ]n = •

[kxkr ] | k sine

where

—»k = c. -of-m. wave vector of incident fast-neutron

beam

and

—*t

k = c. -of-m. wave vector of scattered fast-neutron

beam

I = 2x2 unit matrix—*a = Pauli's spin matrix operator

Obviously, a complete determination of the transition matrix

T, being dependent on two complex amplitudes g and h, requires

three independent measurements at any arbitrary energy E and

at any arbitrary scattering angle 6, even if no consideration is

paid to an unimportant common complex phase factor. It turns

out that three appropriate experiments, respectively denoted

single-scattering, double-scattering, and triple-scattering ex-

periments, are the measurements of

- 6 -

V^ the differential scattering cross section (-̂ =r) for unpolarized

incident fast-neutrons

—•

2. the polarization P acquired by unpolarized incident fast-neu-

trons undergoing scattering under conditions identical to those

under J_.

3^ the spin rotation parameter ß_, also to be obtained under condi-

tions identical to those under T_.

These three parameters are respectively expressed by [20]

P - P n - 2 g # g fh#£ n (3)

a g*g - h*h , , xcosß= * K " , (4a)

(g*g + h*h)Vl-P

( 4 b )

Hardly for any sample nucleus are these parameters avail-

able, mainly because formidable experimental difficulties preclude

successful ß-measurements, but also because of the slow rate of

collection even of polarization data. In this state of affairs the

remedy is the execution of a phase analysis, the success of which

is due to the short range of nuclear forces, so that at least at

low energies only a few terms of the series presented below are

required. This approach, however, will in general lead to ambi-

guities [21 ], but no theoretical considerations will be given to

the uniqueness problems here.

Separation of the amplitudes g and h into partial waves

yields the following expressions [22]

i 2iô. 216- ,y I / « , i \ i- JLc (7 -f + 1~\\- P ( Q\ (^ }

=0.f . _l-e "Hpl(cose), (5b)

- 7 -

where 6, and 6» are the respective phase shifts for the intrinsic

spin parallel or anti-parallel to the orbital angular momentum.

Substitution of these expressions into (2) and (3) and invok-

ing the powerful methods of Racah algebra alternative formulas

f o r <dH>o a n d P W

3 ü o r

k

whereBT =S T. 2 S \z{l, J,-toJo; 7L))2 • sinô,1 • sinô,2xJ l J2 l] lZ 1 2

J l J?x c o s ( ô ' - ô / ) (8)

a n d

r --4 ^ I y y

L-\2L(L+I)J f fJ l J2

)J

J1 J2 J1 J2

xsinô» • sinô» • sin(6„ - 6 » ) (9)

In the phase analyses reported on below, however, we used

the original formulas (5a) and (5b) in conjunction with (2) and (3)

because of their compatibility with our digital computer. Never-

theless, in Appendices 1 and 2 resp. we reproduce complete

lists of the BT ' s andCT 's for any L^L =8. Their inclusionLi L ' max

in the present report is motivated by their utility for rough

estimates of the variations induced in respective quantities by

changes of the magnitudes of given phase shifts. Besides, it is

felt that these lists represent useful extensions of similar for-

mulas presented in ref. 7.

- 8 -

3. EXPERIMENTAL, FACILITY

The fast-neutron polarization facility of the Studsvik Van

de Graaff laboratory, where the whole body of experimental data

was obtained, has been thoroughly described elsewhere [23, 24,

25 ]. Only a rudimentary description in connection with the ex-

perimental procedure outlined below will therefore be reproduced

here.

4. EXPERIMENTAL PROCEDURE AND DATAREDUCTION TECHNIQUE

Partially polarized fast-neutrons were obtained at 50 (lab.

syst.) from the Li (p, n) Be-reaction, using the pulsed proton

beam from the Studsvik 6 MeV Van de Graaff^). The repetition

frequency was 1 Me/sec, and the minimum pulse width was about

10 nsec . Litium films of appropriate thicknesses were evaporated

in situ on the tantalum backing of an oscillating target assembly

closely resembling the original Argonne design [25], The colli-

mated polarized fast-neutrons were elastically scattered from

cylindrical reactor graphite samples. Several dimensions of

these were available, allowing a check of the reliability of our

Monte Carlo corrections for finite-geometry and polarized

multiple-scattering effects [26a,b]. Finally, the scattered fast-

neutrons were detected at equal nominal scattering angles by

means of NE 102 A plastic scintillators coupled to Philips AVP

56 photo-multiplier s by means of light guides. Fast time-of -

flight technique was utilized in order to time-discriminate

against target y-rays and unwanted in-scattered fast-neutrons

and Y"rays. Some reduction of the influence of the first-excited

state group of fast-neutrons was also accomplished by this meth-

od. Complete elimination of the effect of this group, however,

was not possible, because the flight path was too short to time-

separate it from the ground state group even when the minimum

*) Model CN, delivered by High Voltage Engineering Corporation,Burlington, Massachusetts, USA.

- 9 -

pulse width was used. To this end of course also ordinary energy-

discrimination was executed, the discriminator level correspond-

ing to a fast-neutron energy approximately equal to 0.6 MeV.

Systematic errors and unequal detector efficiencies were elimi-

nated by means of a transverse magnetic field acting on the

fast-neutron beam between target and sample [24].

Beam monitoring was accomplished by means of a conven-

tional long counter of our own design, also used for determina-

tion of the target thickness according to the familiar zero-degree •

rising yield curve method. As an important part of the experimen-

tal routine the target thickness was always checked before and

after each running period in order to preclude the possibility of

harmful target deterioration caused by proton bombardment.

The proton energy calibration was for obvious reasons

based upon the extrapolated low-energy end-point of the afore-

mentioned yield curve at zero-degrees, any actual proton en-

ergy E being found by means of the relation

where

Eth = 1 - 8 8 1 M e V = threshold energy

f , = threshold frequency-reading of the analysing magnet

NMR instrument

f = actual frequency-reading

Of course, this energy calibration rests on the assumptions

that for two arbitrary proton energies

1 . the protons are entering the analysing magnet in identical

fashions

2. the field configurations of the analysing magnet are identical

No investigation of to what extent these assumptions were fulfilled

was performed, however.

As for the determination of the associated fast-neutron

energy due regard was taken to the higher penetrabilities of

protons in litium for increasing proton energies [27]. The mean

- 10 -

fast-neutron energies quoted in this report have been reduced

from the ones determined by the reaction kinematics by an

amount equal to half the actual target thickness.

The data acquisition routine was the following one: First,

after demagnetization, the precession magnet was left in the

demagnetized state, and the scattering sample was brought

into the "in" position by means of a remotely controlled pneu-

matic valve. Secondly, the number of counts in Left Detector

and in Right Detector was recorded for some preset number of

monitor counts. Further, the sample was brought to the "out"

position, and a background run was made, allowing a détermina-

tion of the net number C , resp. C of fast-neutrons elastically

scattered into left, resp. right detector. The ratio of these

numbers is denoted X > viz. ,

Then the precession magnet was set at an induction value

24)

B close to the ideal one determined by the relation (see ref.

B = 3718 VE Gauss (E in MeV) (12)rr • n v n ' v '

Again the ratio

C L

of the counting rates of scattered fast-neutrons was determined.

We particularly point out that a separate background run was

made when the magnet was in the magnetized state.

From the above measurements the finite-geometry left-NL

right ratio (-TJ—) was approximately determined by means of theR

expression (see ref. 24)

- 11 -

(14)

A correction for non-ideal magnetic induction was finally-

applied, using the relations

«B

O 1 2 TT ( ] 5 )

C O S

TT

and

( N ) T 0 )iNR 1+(P,P2)

5. EXPERIMENTAL, RESULTS

The experimental finite-geometry left-right ratios are sum-

marized in tables la, 4b, and 2. We note that the major part of

the whole body of data was obtained by means of Sample C40, whereas

various thinner samples were utilized in order to supply experimen-

tal checks on the influence of finite-geometry as well as of multiple-

scattering effects on the observed left-right ratios [26b].

Below 2 MeV our measurements were performed at rather

closely spaced energies in order to ascertain the expected smooth

energy variations of the experimental quantities in an energy re-

gion notoriously free of resonances. We regard the present series

of measurements as a proof of the non-existence of spurious wiggles

on the energy patterns of the observed finite-geometry left-right

ratios. This fact we interpret as another indication of the absence

of experimental short-comings of the fast-neutron polarization

facility with which our data was obtained. The bearing on the re-

liability of the present data is obvious.

The presence of the J n = 7 level at E = 2.076 MeV causes

abrupt variations of the experimental left-right ratios in the energy

region close to the resonance energy. No detailed investigations

of these variations were however performed because of insufficiently

narrow energy resolution.

- 12 -

For energies above 2.076 MeV only one polarization angular

distribution has been obtained so far, namely the one at 2. 243 MeV.

The experimental data - except for the ones in the close

vicinity of the 2. 076 MeV resonance and a part of the ones obtained

by means of the thinner samples - were finally corrected for finite-

geometry as well as for polarized multiple-scattering effects, using

the elaborate Monte Carlo routine MULTPOL. Simultaneously, cor-

rections were also applied for effects on the finite-geometry left-

right ratios caused by the presence of the first-excited state group

- assumed unpolarized - in the incident fast-neutron beam. The

details of our Monte Carlo procedure have been published elsewhere

[26a, b ] and are therefore not reproduced here.

Computer-simulated left-right ratios are summarized in

tables 3a, 3b, and 4, whereas corresponding corrected polariza-

tions are displayed in tables 5a, 5b, and 6. At those energies

where complete polarization angular distributions are available

the smoothed corrected polarizations are depicted in the £. -parts

of figures 1 - 7 . These distributions form the important part of

the total body of corrected experimental data. Once obtained in

order of increasing energies and stored in the computer core

memory they were used during the determination of simulated

finite-geometry left-right ratios at intermediate energies. The

corresponding polarizations were found by linear interpolation

in data tables pertaining to figures 1 - 7 .

As for the absolute values of the polarizations quoted in

this report they are based upon an assumed known proton energy

dependence of the polarization P. of the ground state group of

fast-neutrons emitted at the laboratory reaction angle 6 = 507

from the p+ Li-reaction. For the energies of interest in

the present context a quadratic law was found sufficiently adequate.

Its parameters were determined by means of a least-squares fit

to all available experimental data in the relevant energy region

[28 - 35] (see fig. 8). The polarization properties of the incident

fast-neutron beams used during the determination of the experimen-

tal left-right ratios of tables la, lb, and 2 were subsequently calcu-

lated from our quadratic law and tabulated in table 8. The polari-

zation of the first-excited state group of fast-neutrons was regarded

- 1 3 -

as negligible in the relevant energy region [29, 36] , a feature of

in teres t during the cor rec t ion for the effect of this group on the

simulated lef t-r ight r a t i o s . It should however be noted that even

if the polarizat ion of the f i rs t -exci ted state group was non-negl i -

gible, proper correc t ions for its presence could sti l l have been

applied, provided that its polarizat ion had been sufficiently well

known (see re fs . 26a, b). T-LAs for the s ta t i s t ica l uncertaint ies A^rr- of the co r rec ted

NT N R

left-r ight rat ios -^— these were calculated by means of the formulaiNR

Vs

(17 a, b)

alternative a) or b) to be chosen whichever rat io is the l a rges t ,

in order to ensure a conservative es t imate of A"rvj—. Arguments

for the choice of this formula for AM— are presented in ref. 26b.R

The s ta t is t ical uncertainty AP of P is finally obtained

from, the expression

{ (1 + P P ) 2 N 2 2 , 1/2

- U T1 A N ^ + ( p Ä p i ) J1 R

Table la

E ^LX

(MeV)

1 .062

1-317

1.639

1.736

1-753

1 .807

1.890

1.938

1-983

2.005

2.005

2.041

Lat

±

±

±

±

±

±

±

±

±

±

±

0.027

0.024

0.021

0.017

0.025

0.020

0.016

0.025

0.016

0.021

0.021

0.018

30.0

1 .018

1 .048

1 .060

1.079

1.075

1.117

1.124

±

±

±

±

±

±

±

0

0.008

0.007

0.018

O.OlG

0.019

0.010

0.017

41

1.017

1.043

1.106

I.096

1 .105

1.110

1.131

1.165

1.144

1.119

1.148

1 .092

.8

±

±

±

±

±

±

±

±

±

±

±

0

O.008

0.006

0.011

0.015

0.006

0.014

0.012

0.012

0.013

0.013

0.011

0.015

56

1 .001

1.013

1.083

1 -037

1 -073

1 .121

.0°

±

±

±

±

0.011

0.009

0.020

0.016

0.011

0.012

85

O.962

0.950

0.974

0.962

0.951

0.933

0.940

0.996

.2

±

±

±

±

±

±

±

0

0.012

0.019

0.023

0.020

0.011

0.013

0.011

0.028

115

0.9'iO

O.89O

0.880

0.886

0.846

0.819

•7

±

±

±

±

±

±

0

0.023

0.024

u.024

0.022

0.012

0.012

129

0.914

0.908

0.864

0.895

0.851

0.846

0.847

0.812

0.807

0.861

0.873

. 0

±

±

±

±

±

±

±

±

±

±

0

0.031

0.023

0.016

0.022

0.011

0.018

0.012

0.020

0.011

0.018

0.019

blab

1 .062

1-317

I.639

1 -736

1.753

1.807

1.890

1.938

1.983

2.005

2.005

2.041

in

(MeV)

±

±

±

±

±

±

±

de

±

±

±

0.027

0.024

0.021

0.017

0.025

0.020

0.016

0.025

0.016

0.021

0.021

0.018

Table lb

(MeV) ^V*o^S s^

2.243 ± 0.023

30.0°

1.261 ± 0.009

45.0°

1.311 ± 0.009

60.0°

1-235 ± 0.012

85.0°

O.974 ± (i.Oll

110.0°

0.751 ± 0.010

120.0°

0.749 ± 0.011

129.0°

0.739 ± 0..-11

tilab E ^^"^^ n^^ -^ tMeV)

2.243 ± 0.023

Summary of experimental finite-geometry left-right ratios obtained by means of oample C40.

- 15 -

Table 2

n(MeV)

1

1

1

2

.482

.755

•958

.005

^ab

± 0

± 0

± 0

± 0

.028 1

.025 •

.025 '

.021 *

4

1.065

. 1.098

1 .090

1 .094

1.120

1.105

1.105

1.127

1.176

1.195

1.165

1.184

1.165

1.177

1.148

l.i

-H

-H

±

±

±

à

±

±

±

±

±

±

±

à

à

3°

0.026

0.016

0.090

0.021

0.019

0.022

0.006

0.021

0.029

0.017

0.012

0.025

0.029

0.017

0.011

1

0

0

0

85.

.908 ±

.955 ±

.996 ±

2°

0.026

0.015

0.028

0

0

0

0

0

0

0

0

0

0

0

129.

.875

.850

.851

.857

.8n

.818

.812

.722

.752

.843

.861

±

±

±

±

±

±

db

à

±

±

è

0°

0

0

0

0

0

0

0

0

0

0

0

.058

.027

.011

.049

.045

.025

.020

.045

.051

.012

.018

lab S a m p l e

CO25

c 25

c 18

C025

c 25

co4o

C 40

C025

c 25

C04()

C 40

C025

c 25

C040

C 40

Summary of experimental finite-geometry left-right ratios obtained by

means of different samples under otherwise identical conditions at the

fast-neutron energies quoted.

Table 3a

Xi

(MeV)

1.062

1.317

I.639

1.736

1.753

1 .807

1 .890

1.938

1.983

2.005

2.005

2.04l

l a b

±

±

±

±

±

±

±

±

±

±

±

±

0.027

0.024

0.021

0.017

0.025

0.020

0.016

0.025

0.016

0.021

0.021

0.018

30

1 .041

1.057

I.O78

I.O87

1.084

1 .110

1.153

.0

±

±

±

±

±

±

0

0.015

0.009

0.015

0.007

0.015

0.014

0.010

4 i

1 .012

1.064

1 .082

1.097

1.067

1.101

1.140

1.149

1.173

.8

à

±

±

±

±

±±

±

±

0

0.013

0.022

0.015

0.011

0.014

0.010

0.012

0.010

0.014

56

1 .001

1.034

1.081

1.093

1.113

1.115

. 0

±

±

±

±

0

0.022

0.018

0.018

0.015

0.017

0.017

85

0.927

O.961

0.986

O.969

0.972

0.941

0.931

.2

±

±

db

±

±

±

±

0

0.023

0.023

0.030

0.017

0.018

0.010

0.012

115

0.895

0.914

0.881

0.873

O.84i

0.819

•7

±

i

±

±

±

±

0

0.034

0.015

0.021

0.021

0.014

0.020

129

0.903

0.862

0.868

0.868

0.856

0.839

O.852

0.812

0.811

. 0

±

±

±

±

±

±

0

0.026

0.014

0.018

(̂ .019

0.011

0.017

0.021

0.010

0.020

6lab

1 .062

1.317

1.639

1.736

1.753

1.807

1 .890

1.938

1 .983

2.005

2.005

2.04l

E'n

(MeV)

±

±

±

±

±

±

±

±

±

±

±

±

0.027

0.024

0.021

0.017

O.O25

0.020

0.016

0.025

0.016

0.021

0.021

0.018

Table 3b

E\labn N.

(MeV) ^ \ ^ ^

2.243 ± 0.023

30.0°

1 .298 ± 0.013

45.0°

1.334 ± 0.017

60.0°

1.262 ± 0.014

85.0°

0.971 ± 0.022

110.0°

O.763 ± 0.012

120.0°

0.727 ± 0.011

129-0°

0.720 ± o.ou

eiab E ̂ ^^^ n^ ^ ( M e V )

2.243 ± 0.023

Summary of simulated finite-geometry left-right ratios obtained by means of Sample C4o.

- 17 -

Table 4

(MeV)

1

1

1

2

.482

•75^

•9^8

.005

l a b

± 0

± 0

± 0

± 0

.0281

.025 À

•

.025«

*

.021 *

1

1

1

1

1

41

.067

.165

.161

.162

.149

•

±

±

±i

±

8°

0 .

0 .

0 .

0 .

0 .

014

005

005

005

010

85.2°

0.942 ± 0.0080.941 ± 0.010

0

0

0

0

0

129.

.856

.789

.798

.808

.812

±

±

±

è

è

0°

0 .

0 .

0 .

0 .

0 .

011

006

007

007

010

l a b Sample

C025

c 25

p 1 Q.

C025

c 25p nil i ")

C 40

C025

c 25

C040

C 40

C025

c 25

C 40

Summary of simulated finite-geometry left-right ratios obtained by means

of different samples under otherwise identical conditions at the fast-

neutron energies quoted.

Table 5a

n^>(MeV)

1.062

1.317

1.639

1.736

1-753

1.807

1.890

I.938

1.9832.005

2.0052.041

]

S

±

±

±

±

±

±

±

±

±

±

±

Lab

\

0.0270.024

0.02]

0.017

0.025

0.020

0.016

0.0250.016

0.02]

Pi C\O"\

0.018

30

-0.052

-0.102

-0.173-0.149

-0.186-0.230

-0.256

. 0 c

è

±

±

±

±

±

±

>

0.027

0.0150.030

0.022

0.030

0.022

0.026

41

-O.O5I

-0.112

-O.198

-O.168

-O.I78

-0.211

-O.262

-O.276

-O.288

.8C

è

±

±

±

±

±

±

±

>

0.024

0.031

0.023

O.O23

0.020

0.022

0.022

0.020

0.025

56

-0.027-0.091

-0.179-0.143

-0.230

-0.247

.0°

±±

±

±

±

±

0.0390.028

0.0330.029

0.027

0.027

85.

+0.090

+0.052

+0.018

+0.056

+0.063

+0.084

+0.103

2°

±

±

±

±

±

±

0.046

0.044

0.051

0.036

0.0300.024

0.025

115

+0.199+0.206

+O.239

+0.258

+0.343

+0.406

7C

±

è

±

±

±

±

0.0740.045

0.048

0.046

0.031

0.041

129

+0.208

+0.225+0.269

+0.281

+0.290

+0.320

+0.367

+O.39I+0.415

. 0 c

±

±

±

±

±

±

±

±

±

>

0.0720.044

0.0370.045

0.025

0.040

0.040

0.0390.041

l a b

1 .062

1.317

1.639

1.736

1-753

1.807

l .890

1.938

I.9832.005

t— • \J\J\}

2.041

- n(MeV)

±

±

±

±

±±

±

±

±

0.0270.024

0.021

0.0170.025

0.020

0.016

0.025

0.016

0.021n noiU • v c J

0.018

00

I

Table 5b

(MeV) \ * ^

2.243 ± 0.023

30.0°

-0.561 ± 0.027

45.0°

-O.66O ± 0.032

60.0°

-O.585 ± 0.031

85.0°

+0.036 ± 0.040

110.0°

+0.605 ± 0.038

120.0°

+O.687 ± 0.041

129.0°

+0.710 ± 0.041

lab ^^T^^ n^ s ^ (MeV)

2.243 ±0.023

Summary of corrected polarization data obtained by means of Sample C 40

- 19 -

Table 6

n ̂ X>1

(MeV)

1.482

1.753

I.938

2.005

9lab

±

±

±

±

0

0

0

0

.0281

.025'

.025-

.021J

-0

-0

-0

-0

-0

41

.178

.276

.276

.276

.276

±

±

±

8°

0.

0.

0.

0.

0.

020

028

035022

020

85.20

+o.o84 ± 0.043

+0.084 ± 0.024

+0

+0

+0

+0

+0

129.

.290

.391

.391

.391

.391

±

±

±

±

±

0°

0.

0.

0.

0.

0.

025

085

078

045

039

8lab ^ ^ ^^ ^ a m p l e

CO25

c 25

C 18

C025

c 25

C04()

C 40

C025

c 25

CO4o

C 40

C025

C 40

Summary of corrected polarization data obtained by means of different

samples under otherwise identical conditions at the fast-neutron energies

quoted.

Note that the experimental data summarized in table 6 were obtained atenergies not coinciding with those at which complete polarization an-gular distributions were determined. For this reason the corrected po-larizations of table 6 were found by linear interpolations in appro-priate data tables pertaining to figs. 1-7. This fact explains theidentity of the corrected polarizations for different samples, at agiven fast-neutron energy. The experimental uncertainties, however,were calculated in the usual way, viz., by means of formulas (17a, b).

- 20 -

Table 7

Code

C 18

C025

c 25

CC&O

C 40

Dimensions :

Height: 80 mm

Inner

diameter(mm)

0

12

0

20

0

Outer

diameter(mm.)

18

25

25

40

40

Sample key

- 21 -

Table 8

EP

(MeV)

2.9873-2613.446

3.6133-7123.740

3-7933.880

3.9433.9844.0124.0494.277

Ground Sta te Group

En

(MeV)

1.062 ± 0.027

1.317 ± 0.024

1.482 ± 0.028

1.639 ± 0.021

1.736 ± 0.017

I.753 ± 0.025

1.807 i 0.020

1.890 ± 0.016

1.938 ± 0.025

I.983 ± 0.016

2.005 ± 0.021

2.04] ± 0.018

2-243 ± 0.023

P/5O 0 )

0.3162 ± 0.0152

0.3586 ± 0.0094

0.3737 ± 0.0087

0.3790 ± 0.0094

0.3779 ± 0.0099

0.3771 ± 0.0100

0.3747 ± 0.0103

0.3685 ± 0.0106

0.3641 ± 0.0107

0.3590 ± 0.0108

0.3564 ± 0.0108

0.3515 ± 0.0109

O.3152 ± 0.0109

Fi r s t -Exc i ted Sta te Group

E'n

(MeV)

0.620 ± 0.027

0.880 ± 0.024

1.049 ± 0.028

1.210 ± 0.021

1.305 ± 0.017

1.323 ± 0.025

1.377 ± 0.020

1.461 ± 0.016

1.510 ± 0.025

1.556 ± 0.016

1.577 ± 0.021

1.6l4 ± 0.018

1.818 ± 0.023

P*(50°)

ooooooooooooo

Summary of data pertaining to the energy and polarization properties

of the incident fast-neutron beams utilized during the determinations

of the experimental finite-geometry left-right ratios summarized in

tables la, lb, and 2.

- 22 -

6. PHASE ANALYSIS

Although the execution of a phase analysis is a standard pro-

cedure for providing input polarization as well as rotation param-

eter data to MULTPOL, as already reported in refs. 26a, b, we

still consider it justified to summarize the essential features of

our method here. It is based upon the formulas alluded to previous

ly in this report, and uses the following input data:

1. ae

3 ^ -NR

4 P

Total elastic cross sections were found by interpolation in

the compilation of R JHowerton [37], and the experimental as well

as the fitted a -values are quoted in the b^-parts of the respective

figs. 1-7. - Similarly, interpolated differential scattering cross

sections were extracted at eight scattering angles from ANL -

6172 [38]. Additional input data were our own iterated left-right

ratios as well as the associated P. -values determined as previous-

ly described, both sets of data together yielding relevant polariza-

tion data through the relation

N R

PT1 1 +N R

Needless to say, the phase shifts quoted in table 9 are the

ones reproducing the smooth corrected curves of figs. 1-7, ex-

cept for the ones in the respective a^-parts labelled "smoothed

uncorrected left-right ratios".

The practical execution of the phase analysis at a particular

fast-neutron energy was performed digitally, using the IBM-7044

routine PHASE. PHASE is written in the FORTRAN IV language

- 23 -

and produces a set of phases together with their standard devia-

tions from the afore-mentioned input data and a set of approximate

input phase shifts [39 ]. The method used may briefly be summa-

rized as follows: The relevant mathematical expressions are lin-

earized around the approximate input phase shifts, whereafter

iterated phase shifts are deduced by means of simultaneous search

in all phase shifts considered. Repeated linearization and iteration

is performed until standard least-squares requirements are sat-

isfied. As for the uniqueness of the phases quoted in table 9 no

such problems were encountered at any of the fast-neutron ener-

gies at which a phase analysis was executed.

The accuracies of the phase shifts reported in table 9 are

expected to be quite high because of the large amount of experi-

mental information used for their determination, although we can-

not quote any figures for the particular set reproducing the smooth

corrected curves of figs. 1-7. Notwithstanding the fact that PHASE

produces both the phases themselves as well as their standard de-

viations from a given set of input data (including the uncertainties

of these data), we are faced with the facts that no representative

figures for the input uncertainties of the iterated left-right ratios

can be quoted until we intercompared the simulated and the experi-

mental finite-geometry left-right ratios. We circumvented this

state of affairs by always using as the uncertainties of the iterated

left-right ratios the ones of the experimental left-right ratios. In

principle, therefore, the uncertainties of even that particular set

of phases yielding acceptable simulated finite-geometry left-right

ratios are left undetermined. Acceptable is here used in the sense

of personal judgement, because for computer economy reasons

no least-squares criterion could be invoked for deciding when the

simulated finite-geometry left-right ratios were mathematically

acceptable. -

Nevertheless, representative uncertainties of the phase

shifts determined were obtained as follows: Once an acceptable

set of simulated finite-geometry left-right ratios with associated

uncertainties was available, the corrected left-right ratios with

relevant uncertainties as calculated by means of formula [l7a,b]

- 24 -

were used as input data for a final phase analysis, yielding new

phase shifts and associated uncertainties as collected in table 10.

Obviously, the differences between respective phase shifts of

tables 10 and 9 are within the limits of error of the former, for

whLch reason we shall regard these uncertainties as representa-

tive for that particular set of phase shifts reproducing the smooth

curves of figs. 1-7.

A more fundamental reason for regarding these limits of

error as very good first approximations to a set of experimental

uncertainties determined according to a simple least-squares

criterion may be obtained as follows: Namely, from the phase

shifts of table 10 a set of input data to MULTPOL (barely differ-

ent from those represented by the smooth curves of figs. 1-7)

may be produced, yielding new simulated finite-geometry left-

right ratios with associated errors. These data as well as the

experimental left-right ratios and the new corrected left-right

ratios will then supply sufficient data for another phase analysis,

the results of which to be summarized in another table of phase

shifts with associated uncertainties. This procedure may then be

repeated until the data of successive tables are sufficiently equal

to each other to satisfy a standard least-squares criterion, al-

lowing an unbiased determination of the phase shifts and their

uncertainties, again usable as objective criteria for the stop of

the iteration chain of MULTPOL. Computer economy reasons

do of course not allow such a comprehensive procedure, but the

above reasoning substantiates our previous choice of experi-

mental uncertainties as a representative one.

En

(MeV)

1.062 - 0.027

1.317 - 0.024

1.639 - 0.021

1.736 - 0.017

1.890 - 0.016

1.983 - o .oi6

2.243 - 0.023

J/2ô0

( °)

- 67.27

- 73-10

- 79.49

- 82.95

- 89.63

- 92.81

- 93-76

*r( °)

- 3.39- 4.92

- 6.15

- 6.51

- 7.95

- 9.45

- 1 . 8 0

J/261

( °)

- 6.16

- 6.54

- 6.71

- 8.19

- 9.81

-12.55

- 7.95

,5/2

( °)

- 1.22

- 1.29

- 2.27

- 2.48

- 3.29- 3.22

+ 170.90

.3/262

( °)

+ 1.10

+ 1.90

+ 2.44

+ 2.02

+ 3-36

+ 4.56

+ 7.71

Table 9

Phase shifts reproducing the smooth corrected curves of figs. 1-7

En

(MeV)

1.062 - 0.027

1.317 - 0.024

1.639 - 0.021

1.736 - 0.017

I.89O - 0.016

I.983 - 0.Q16

2.243 - 0.023

fV2

( °)

- ^7.27 - 0.44

- 73.1L - 0.80

- 79.56 - 2.07

- 83.03 t 2.13

- 69.81 - 2.01

- 92.88 - 2.36

- 93-03 - 2.45

3/21

( °)

- 3.41 - 0.24

- 4.70 - 0.46

- 5.91 - 1.03- 6.25 - 0.94

- 7.83 t 0.58

- 9-39 - 0.63

- 6.97 - 0.83

1/2

( °)

- 6.21 t 0.32

- 6.34 - 0.55

- 6.46 - 1.24

- 7.91 - 1.09

- 9.67 - 0.66

-12.51 - O.69

- 8.14 - O.99

5/22

( °)

- 1.20 - 0.25

- 1.52 - 0.57

- 2.60 - I.38

- 2.85 - 1.28

- 3.52 - 0.82

- 3.32 - 0.84

+171.10 - 0.82

( °)

+ 1.11 - 0.26

+ I.69 - O.56

+ 2.11 - 1.36

+ 1.66 - 1.25

+ 3.15 - 0.80

+ 4.45 i 0.63

+ 7.90 - O.70

Table 10

Phase shifts resulting from a phase analysis oased upon fully corrected left-right ratios with associated

uncertainties + additional input data identical to those used during the determination of the phase shifts

of table 9.

- 27 -

7. DISCUSSION

Some features of the polarization pattern in n+ C-scattering

at fast-neutron energies below 2 MeV [40, 41 , 42, 43] were known

prior to the start of the present series of experiments, although

lack of complete polarization angular distributions limited the val-

ue of this information considerably. Furthermore, some of the

previous polarization data suffered both from large experimental

uncertainties as well as from unreliable corrections for finite-

geometry and polarized multiple-scattering effects. Thus, the

prime objective of our measurements was to fill a gap of incom-

plete knowledge, using comparatively advanced experimental

technique in order to acquire high-accuracy angular distribu-

tions reasonably fast. Furthermore, comprehensive computer

processing of the experimental data allowed truely quantitative

results to be quoted. An important part of the data processing

procedure was then determination of reliable phase shifts at

seven fast-neutron energies in the energy range under considera-

tion. Ultimately, they form a convenient body of experimental

data, expressing the salient features of the low-energy fast-

neutron interaction with carbon. It should in this connection be

pointed out that phase analyses solely based upon differential

scattering cross section data have hitherto been unsuccessful

for fast-neutron energies below 2 MeV [44,45], perfectly under-

standable because of small absolute values of the 6, - and em-

phases. Indeed, the present investigation in a convincing way

demonstrates the power of combined cross section-polarization

measurements for assessment of reliable phase shifts in an en-

ergy region where several phases make small yet significant

contributions to the scattering process. An attractive feature

of our procedure is that by invoking strictly quantitative methods

in the course of data processing we also are able to quote rep-

resentative statistical uncertainties of the respective phase

shifts.

The general conclusion to be drawn from our data, namely1 2

that the low-energy fast-neutron- C interaction is very well

described by means of orbital angular momenta not exceeding

- 28 -

-t = 2, is another indication of the non-presence of any J = y1 -} '-•

level in C at low excitation energies [8 , 9, 10, 46, 47, 48, 49, 5 0 ] .

The substantial polarizat ions observed in cer ta in angular ranges

even at the lowest fast-neutron energy considered is solely caused

by interference between p-sca t t e r ing and s - and d-sca t te r ing . As

was to be expected, d-scat ter ing gradually loses importance for

decreasing energ ies , although it cer tainly st i l l is felt at 1 MeV.

It would be worthwhile to extend the-present work to energies

below 1 MeV, where one from the t rend at energies between 1

and 2 MeV should expect the negative-going polarizat ions at

scat ter ing angles in the forward hemisphere to disappear . At

what energy this would take place, is a question of the p e r s i s t -

ence of the admixture of d ' -waves, again dependent on theTT 5+ 13

effect of the J =-5- level at E = 3 . 850 MeV in C. v i z . , belowX 3/2

the neutron separat ion energy. The d ' -admixture , however,

is expected to rapidly become unimportant below 1 MeV.

Both p-phases are slowly varying in the energy range under

investigation, so that the 90 (c . -of-m. syst . ) polarizat ion caused

by their nearly constant splitting should be a measurable effect

for fas t -neutron energies substantially less than 1 MeV. Con-

siderable ca re should therefore be exerc ised in the use of c a r -

bon as a 90 "null" ana lyser . In the past a number of fas t -neu-

t ron polarizat ion facili t ies was checked for false a symmet r i e s

by this method, (see f .ex . [51 ,52 ,53] ) , although more careful

studies with bet ter s ta t is t ics at the relevant energies probably

should have revealed left-right ra t ios different from unity. Ob-

viously, the pers i s t en t low-energy p-sca t te r ing is caused by

the two p- levels below the neutron separat ion energy in C,n 1 ~

namely by the ground state (J =— ) and by the second-excited

state (J =1- ) at E =3.680 MeV.

As for the smoothness of the energy variat ions of the p -

phases it is acceptable as long as the splitting of the d-phases

stays smal l . The cause of the slight departure from smoothness

at higher energies must be t raced back to too few polarizat ion

and differential c r o s s section observations at scat ter ing angles

around 90 (c . -o f -m r syst . ). We recognize the wel l -es tabl ished

- 29 -

problem of reliable p-phase determinations at fast-neutron ener-

gies above 2 MeV, where the even-parity contributions from s-

and d-waves become particularly dominant. Special attention

will therefore be paid to this problem in a series of polarization

studies at energies between 2 and 3 MeV soon to be initiated.

The rather rapid increase of the polarization at forward

scattering angles for increasing energies is caused by increasing

splitting of the d-phases. It is however remarkable that the ab-

solute values of these are smaller than those indicated by Wills,

Jr. et al. [54] and substantially smaller than the extrapolated

phases of Meier, Scherrer, and Trumpy [7]. Particularly for3/2

the ô? -phase this implies a much smaller effect at low energiesTT 3"*~

from the J = -̂ levels at the fast-neutron energies 2. 95 and 3. 67

MeV than found by these workers. Furthermore, in conflict with

the findings of Wills, Jr. et al. we obtain a negative d -phase

below 2 MeV, making our data compatible with about 50 % larger

polarizations at both forward and backward scattering angles.

The s ' -phase, however, is in good agreement with the one of

Wills, Jr. et al. The general conclusion can therefore be drawn

that although the fast-neutron-carbon interaction between 1 and

2 MeV essentially is an s-wave one, it nevertheless contains

sufficiently large admixtures of split p- and d-waves to make

carbon an acceptable polarization analyser. Thus, carbon serves

as a useful low-energy substitute to helium, whose analyser

characteristics are inferior below 2 MeV because of small recoil

energies of the a's usually observed.

The agreement between our polarization data and those of

other workers is considered to be satisfactory below 2 MeV. This

is particularly well borne out in fig. 9, where we intercompare

our data at 41 .8° (45.0°) and 85.2° (85.0°) (lab.syst.) with those

of Elwyn and Lane [41 ], respectively observed at 45. 0 and

90.0 (lab.syst.). Potential sources of systematic discrepancies

between both sets of data may either be those caused by the an-

gular variations of P, and P and/or lack of proper recognition

of polarization effects in the higher scattering orders during

the correction of Elwyn and Lane's data. Obviously, within the

- 30 -

experimental uncertainties stated (in the case of our data herein

also included the finite correction accuracies) none of these ef-

fects are sufficiently large to entail any significant different es

between both sets of data. - Above 2 MeV our data are too sparse

to make an intercomparison worthwhile until more experiments

have been performed.

In order to complete the picture of the low-energy fast-

neutron interaction with C we not only draw up the smooth

polarization angular distributions reproducing the simulated

finite-geometry left-right ratios of the EU -parts of figs. 1 -7

but also the respective differential scattering cross sections as

well as the rotation parameters, all smooth curves obtained by

means of the phase shifts of table 9. As was to be expected,the se

phase shifts yield cross sections that are in excellent agreement

with the experimental data of Lane and coworkers [38] and with

the data of Howerton's compilation [.37], Naturally, the differ-

ential cross sections reflect effects explicity delineated in table

9, e.g. the increasing importance of even-parity scattering for

increasing fast-neutron energies. The rotation parameters display

smooth angular distributions, although the maximum ß-value s

usually do not exceed about 1 0 . In other words, the spin-orbit

force may very well yield substantial polarizations without essen-

tial alterations of the spin directions of the fast-neutrons in the

incident beam.

Finally, an inspection of figs. 1 -7 does not reveal any

other simple interrelations between corresponding (TÖ) ' s,

P s, and ß s than those expressed by (2), (3) and (4a, b). Indeed,

our figures may be regarded as a demonstration of the non-

validity of Rodberg's rule [55]

dëWo7 Wo

This is perfectly understandable because it would require

CT/BT =const., independent of L , (21)

a condition easily obtained by intercomparison of

- 31 -

) = - - i 7 E BT P I (coso _, 2 T _ , L L v

a n d

k L=1

No reason, however, can be seen for the general validity

of (21). The trend of the angular distributions of (-rpr) , P, and

(3 to become more complicated in order as indicated is ascer-

tained by the shapes of eqs. (2), (3) and (4a, b) themselves, and

does not require any specific assumption on the underlying fast-

neutron - C interaction [56],

8. SUMMARY

The fast-neutron interaction with C was investigated at

energies between 1. 062 and 2. 243 MeV by means of polarized

elastic scattering, using fast-neutrons emitted at the nominal

laboratory reaction angle 9, = 50 from the Li(p, n) Be-reaction.

At seven energies complete polarization angular distributions

were obtained from the finite -geometry left-right ratios ob-

served at six or seven nominal scattering angles between 30

and 129 (lab. syst. )„ Proper corrections were applied for fi-

nite-geometry and polarized multiple-scattering effects as well

as for the presence of the first-excited state group of fast-neu-

trons in the incident beams. Reliability checks of the digital

correction methods invoked were performed by means of addi-

tional experimental data observed at selected energies and scat-

tering angles.

Notable features of the afore-mentioned complete angular

distributions are significant non-zero polarizations at 90

(c. -of-m. syst. ), indicating substantial admixtures of split p-

scattering. The contribution from even-parity scattering in-

creases with increasing energy, whereas the odd-parity contri-

bution stays practically constant. The resulting effect of the

interfering even- and odd-parity scatterings is a steadily in-

creasing polarization with increasing energy, the increase being

- 32 -

particularly pronounced at scattering angles in the forward hem-

isphere. - The measurements reported demonstrate the useful-

ness of C as a fast-neutron polarization analyser in the energy

range under consideration.

Finally, the afore-mentioned polarization data as well as

total and differential scattering cross section data available in

current literature were used as input information for digital de-

termination of reliable phase shifts. These are only in partial

agreement with the ones of Wills, Jr. et al. , and in definite dis-

agreement with the extrapolated phases of Meier, Scherrer and

Trumpy. - A description of the energy variations of the phase

shifts determined will be given in a forthcoming theoretical part

of this contribution.,

9. ACKNOWLEDGEMENTS

The author wishes to express his gratitude to L Aringe and

to P Tykesson and his accelerator crew for their active assistance

during the data-taking process. Splendid coding work of G Näslund

as well as general interest of Dr. R Pauli were vital to the success

of this work and are highly appreciated. Thanks are further extended

to Dr. R O Lane and coworkers for supplying the author with indis-1 2

pensable data on n- C elastic scattering. Also, valuable informa-

tion on the p+ Li-reaction furnished by the groups at Duke University

and at University of Wisconsin is greatfully acknowledged.

- 33 -

10. A P P E N D I X I

10 .1 L i s t of B T - coef f i c ien t s for L ^ Lm a x

^ 2 > J 2 J l J 2 J l J 2Ao T = sinô» • sinô» • cos(Ôp - ôp )—*f, T -V — — — ^ — — \f— J \ , *fj '

1)J1 1 2 1 ^f

„ . 1 , 1 / 2 , 0 . 1 , 3 / 2 o . 2 , 3 / 2 8 . 2 , 3 / 2 , 7 2 . 2 , 5 / 2 ,B l = 4 V 1/2 + 8 V 1/2 + 8 Al ! 1/2 + 5 Al ! 3/2 + ~ Al ! 3/2 +

+ I I A 3 ' 5 /2 + 36 A3, 5/2 ]_44 3, 7/2 + 144 ^4, 7/2

5 ü2,3/2 35 2,5/2 7 2,5/2 7 ß3, 5/2

+ l i A 4 , 7 / 2 80 4,9/2+ 21 A3, 7/2 + 3 A3,7/2

2 » 3 / 2

_L i •> A 2 . 5 / 2 . D A 1 » V 2 x i 9 A 3 , 5 / 2 , . A l , 3 / 2 ,

0 ; 1/2 + 1 2 A0 ; 1/2 + 8 L l , 1/2 + 1 2 A l , l /2 + 4 A l , 3/2 +

+ M A3» 5/2 ^44 3,7/2 2,3/2 24 2,5/2 ++ 7 A l , 3 / 2 + 7 A l , 3 / 2 + 4 A2,3/2 + 7 2,3/2

L44 .4,7/2 48 A2 , 5/2 16 .4, 7/2 200 4, 9/2

+ 7 A2,3/2 + ~ A 2 , 5 / 2 + T " A 2 , 5 / 2 + ~7~A2,5/2 +

. M 3, 5/2 16_ 3, 7/2 200 3, 7/2 200 ,4, 7/2+ 7 A3, 5/2 + T " A3, 5/2 + T T A3, 7/2 + " I T A4, 7/2 +

40p_A4,9/2 400 A4,9/2+ 231 4,7/2 + 33 4,9/2

_ , _ A 3 , 5 / 2 3 , 7 / 2 , , _ . 2 , 5 / 2 ^ . , . 4 , 7/2 72 . 2 ,B 3 = 1 2 A 0 , l / 2 + 1 6 A0 1/2 + 1 2 A l 1/2 + 1 6 A l 1/2 + - A l

48 2, 5/2 16. A4, 7/2 80 .4, 9/2 48 .3, 5/25 A l , 3 / 2 + ~ A l , 3 / 2 + T " A l , 3 / 2 + 5 A2, 3/2

- 34 -

Ü A . 3 , 7 / 2 32. 3 ,5/2 ^ ^3 , 7/2 u ^4, 7/23 A 2 ,3 /2 + 5 Û 2 ,5 /2 + i b Ù2, 5/2 + l b Û 3 ,5 /2

40 A4,9/2 48 A4,7/2 240 .4,9/2nA3,5/2+rrA3,7/2 + TT A3,7/2

, .4 , 7/2 A 4 ,9 /2 , . 3 , 7/2 144 3, 5/2 80. 3, 7/2B 4 ~ l b A O , l / 2 + 2 0 A0, l / 2 + l ö A l , l / 2 + ^ T A l , 3 / 2 + 7 A l , 3/2

+ I 4 4 A2» 5 / 2 + 80 .4, 7/2 8£ 4, 9/2 36. .2, 5/2+ 7 Û2,3/2 + 7 A2,3/2 + 11 Û2,3/2 + 7 A2,5/2 +

720. A4, 7/2 1440 4, 9/2 36 ,3, 5/2 720 3, 7/2+ T T A2, 5/2 + ~TT A2, 5/2 + T Ä3, 5/2 + T T A3, 5/2 +

648 .3, 7/2 648 4, 7/2 6480. 4, 9/2 1620 4, 9/277 3,7/2 + 77 Ü4, 7/2 1001 4, 7/2 143 4,9/2

_ 20 A4' 9 / 2 + M A4> V 2 + 40 A4, 9/2 80 .3, 7/2 200 3, 5/2B5 ~ 2 ° A l , l / 2 + ~ A l , 3 / 2 + 3 A l , 3 /2 + ~ A 2 , 3/2 + 7 A2, 5/2

80 .3, 7/2 80 4, 7/2 160 4, 9/2 120£ 4, 7/2+ 7 A2,5/2 + T A3,5/2 + T T A3, 5/2 + 91 A3, 7/2 +

240 A4,9/213 3,7/2

A 4 ' 9 / 2 + ̂ ° ^ A 4 ' 7 / 2 + Ü P - A 4 ' 9 / 2 + 4 1 ° - A 3 ' 7 / 2 | 2 0 Q A 3 ' 7 ^ 2A 2, 3/2 + 11 û 2 , 5 / 2 + 11 A 2 , 5/2 + 11 Û 3 , 5/2 + 33 3 ,7 /2

200 4, 7/2 560 .4, 9/2 32^ .4, 9/233 ü 4 , 7 / 2 + 33 Ü4, 7/2 + 33 Û4, 9/2

6300 . 4 , 9 / 2 , 19600 . 4 , 7 / 2 5600 . 4 , 9 / 27 ~ T 4 T Û 3 , 5/2 + 429 Û 3 , 7/2 + "l29~ 3, 7/2

R 7840 . 4 , 9 / 2 980 . 4 , 9 / 28 ~ 143 4, 7/2 "̂ 143 " 4 , 9/2

- 35 -

11. APPENDIX II

11.1 List of C. -coefficients for L ^ LL max-

2 ' J 2 J l J2 J l J 2T = sinô,, sin6„ sin(50 - 6P )

'Y7"Jï *! ^2 *ï ^2

_ 1,1/2 1,3/2 2,3/2 8 2,3/2 L8 2,5/2C l - " 2 V 0 , l / 2 + 2 V 0 , l / 2 Z V l , l / 2 5 V l , 3/2 + 5 1,3/2

18. 3,5/2 Ü 3,5/2 36 3,7/2 3^ 4, 7/25 2,3/2 " 35 2,5/2 7 2,5/2 " 7 3,5/2

_ 32 v 4,7 /2 20 v 4,9 /221 3,7/2 3 3,7/2

C - - 2 V 2 ' 3 /2 + 2 V2, 5/2 1,3/2 3,5/2 _ 1 ^ 3,5/2U2 " Z 0,1/2 + Z 0,1/2 + ù 1,1/2 1,1/2 7 1, 3/2

24 3,7/2 10 2,5/2 24 4, 7/2 4 4, 7/2+ 7 V l , 3 / 2 + ~ V 2 , 3 / 2 " ~ V 2 , 3 / 2 " 3 V2, 5/2 +

100 4,9/2 4 3,7/2 100 y 4,9 /221 2, 5/2 + 3 3,5/2 + 77 4,7/2

3, 5/2 3, 7/2 2, 5/2 _ 4, 7/2 12. 2, 3/20 ,1 /2 + L V0, 1/2 + Z V l , 1/2 Z V l , 1/2 5 Vl , 3/2

2. v2' 5 / 2 - i v4' 7 / 2 + 10 v4' 9^2 - 2 v3' 5 / 2 + 4 v3' 7 / 2

5 1,3/2 3 1,3/2 + 3 1,3/2 5 2, 3/2 + 3 2, 3/2

i 7 3 , 5/2 2 3, 7/2 _ 2 4, 7/2 40 4 ,3 /2 _ 16. 7 4 , 7/25 V 2 , 5 / 2 + 3 2 ,5 /2 3 V 3, 5/2 + 33 3 , 5/2 l l V 3 7 / 2

i £ v , /11 3 ,7 /2

2 V 4 ' 7 ^ 2 + 2 V 4 ' 9 / 2 + 2 V 3 ' 7 / 2 Ü V 3 ' 5 / 2 + 1 v 3 ' 7 / 2 +Z V0, 1/2 + Z V0, 1/2 + Z V l , 1/2 7 V l , 3/2 + 7 V l , 3/2 +

, H V2, 5/2 4 4, 7/2 14 4, 9/2 18. 4, 7/2 72 4, 9/27 2,3/2 ' 7 2,3/2 11 2,3/2 " 11 2,5/2 + 77 2, 5/2

18. 3,7/2 ,1458. 4,9/211 3, 5/2 1001 4, 7/2

1,1/2 3 1,3/2 + 3 1,3/2 + 3 2 ,3 /2 7 2, 5/2

+ ± . v3 ' 7 / 2 J _ v 4 ' 7 / 2 + 64 4 ,9 /2 160 4 ,7 /2

+ 21 2 ,5 /2 " 2 1 3 ,5/2 39 3 ,5 /2 91 3 ,7 /2

±- v /13 3, 7/2

30 V4,9/2 _ 100 4, 7/2 10 4,9/2 100. 3, 7/2 2£ 4, 9/211 2,3/2 33 2, 5/2 33 2, 5/2 + 33 3, 5/2 + 11 V4, 7/2

45£ 4,9/2 1400 4, 7/2 50 „4,9/2143 3,5/2 429 3, 7/2 429 3, 7/2

C - 490 v4 '9 /28 143 4,7/2

- 37 -

12. REFERENCES

1. VERDE M,Nuovo Cim. , Ser. 9 , 9_ (1952) 376-379.

2. BAUMGARTNER E and HUBER P,Helv. Phys. Acta 2_5_ (1952) 626 -628.

3. HUBER P and BAUMGARTNER E,Helv. Phys. Acta 26_ (1953) 420-422.

4. RICAMO R,Helv. Phys. Acta 26_ (1953) 423-424.

5. RICAMO R,Nuovo Cim. , Ser. 9 ,10 . (1953)1607-1615.

6. BAUMGARTNER E and HUBER P,Helv. Phys. Acta 2_6 (1953) 545 -562.

7. MEIER R W, SCHERRER P, and TRUMPY G,Helv. Phys. Acta 2J7 (1 954) 5 77-61 2.

8. HUDDLESTON C M et al. ,Phys. Rev. 1J_7 (1959) 1055-1056.

9. WILENZICK R M et al. ,Phys. Rev. 1_21_ (1961) 1150-1158.

10. SETH K K, BILPUCH E G, and NEWSON H W,Nucl. Phys. £7 (196 3) 137-149.

l i a . ASPELUND O,talk given at the Biannual Meeting of the Swedish PhysicalSociety, Gothenburg 4-7 June 1963.

l i b . ASPELUND O,Arkiv Fysik 2_6_ (1964) 236-237.

12a. ASPELUND O,talk given at the Annual Meeting of the Norwegian PhysicalSociety, Bergen 6-8 June 1963.

12b. ASPELUND O,Phys. Norv. 1_ (1961-65) 173.

13. ASPELUND O,in Compt. Rend. Congrès Int. Phys. Nucl., Vol. 2.,1964.Ed. P Gugenberger, Éd. Centr. Nat. Rech. Scient., Paris1964, p. 897-899.

14. ASPELUND O,lecture delivered in the Physics Seminar, Fysisch Labora-torium, Rijks-Universiteit te Utrecht, Utrecht 16 September1965.

- 38 -

15. ASPE LUND O,lecture delivered in the Physics Seminar , Natuurkundig Labora-tor ium, Rijks-Universi tei t te Groningen, Groningen 17 September1965.

16. ASPELUND O,in Proc . 2 n d Int. Symp. Pol. Phen. Nucl., Kar ls ruhe , 6-10Sept. 1965. Ed. P Huber and H Schopper, Birkhäuser Verlag,Basel-Stut tgar t , 1966, p. 474.

17a. ASPELUND O,talk given at the Annual Meeting of the Norwegian PhysicalSociety, Kjeller and Oslo 1-3 June 1966.

17b. ASPELUND O,Phys. Norv» 2_ (1967) 124.

18. WOLFENSTEIN L,Phys. Rev. 7^(1949)1664-1674.

19. P roc . Int. Symp. Pol. Phen. Nucl.»Basel, 4-8 July I960.Ed. P Huber and K P Meyer, Birkhäuser Verlag, Base l -Stuttgart, 1961, p. 436.

20. WOLFENSTEIN L,Phys. Rev. 96. (1954) 1654-1658 (Erra tum: Phys. Rev. 9_8(1955) 1870).

21 . van WAGENINGEN R,Thesis , Rijks-Universi tei t te Groningen. s-Gravenhage, 1957.

22. LEPORE J V,Phys. Rev. 79_(1950) 137-142.

23. ASPELUND O,(1962) (AE-97) and Nucl. Instr . and Meth. 2_3(1963) 1-9.

24. ASPELUND O, BJÖRKMAN J, and TRUMPY G,(1965) (AE-189) and Nucl. Instr . and Meth. 3i6_ (1965) 245-254.

25. ASPELUND O and TRUMPY G,to be published.

26a. ASPELUND O and GUSTAFSSON B,in P roc . 2 n d Int. Symp. Pol . Phen. Nucl. Kar ls ruhe , 6-10Sept. 1965. Basel-Stut tgart , 1966, p. 475-478.

26b. ASPELUND O and GUSTAFSSON B,AB Atomenergi, Sweden. Internal report FFN-66 (1967) andto be published.

2 7. WHALING W,in Encyclopedia of Physics , Vol. 34. Ed. S Flügge, Springer-Verlag, Berl in-Gött ingen-Heidelberg, 1958, p. 193-217.

28. STRIEBEL H R, DARDEN S E, and HAEBERLI W,Nucl. Phys. 6_(1958) 188-195.

- 39 -

29. CRANBERG L,Phys. Rev. 114 (1959) 174-175.

30. BAICKER J A and JONES K W,Nucl. Phys. 1_7 (I960) 424-434.

31. AUSTIN S M et al. ,Nucl. Phys. 2_2 (1961) 451-467.

32. BENENSON W, MAY T H, and WALTER R L,Nucl. Phys. .32 (1962) 510-516.

33. ANDRESS, J r . W D et al. ,Nucl. Phys. 7£(1965) 313-320.

34. MINZATU I et al. ,Nucl. Phys. 4£ (1963) 347-352.

35. MINZATU I et al. ,Phys. Letters 4 (1963) 357-358.

36. MORGAN G L, HOLLANDSWORTH C E, and WALTER R L,in Proc. 2 n d Int. Symp. Pol. Phen. Nucl. , Karlsruhe, 6-10Sept. 1965. Basel-Stuttgart, 1966, p. 523-525.

37. HOWERTON R J,(1959) (UCRL-5226, revised).

38. LANE R O et al. ,Ann. phys. N. Y. ]_2 (1961) 135-171. (Internai report ANL-6172, I960.)

39. IBM-7044 routine PHASE, written by G Näslund.

40. STRIEBEL H R and HAEBERLI W,Bull. Am. Phys. S o c , Ser. II, 2_(1957) 234.

41. ELWYN A J and LANE R O,Nucl. Phys. 21(1962) 78-117.

42. BEGHIAN L E et al. ,Nucl. Phys. 42_ (1963) 1-20.

43. OLNESS R J, SETH K K, and LEWIS H W,Nucl. Phys. 52_(1964) 529-541.

44. ASPELUND O,unpublished.

45. PISENT G and SARUIS A M,Nuovo Cim. , Ser. 10, 2_8 (1963) 600-61 3.

46. GREEN T S and MIDDLETON R,Proc . Phys. Soc. (London) A69 (1956) 28-42.

- 40 -

47. YOUNG T E et al. ,Phys . Rev. 116 (1959) 962-969.

48. GORODETZKY S et al . ,J. Phys . Radium 22_ (1961) 573-575.

49. GALLMAN A et al . ,Phys . Rev. 1_29_ (1963) 1765-1770.

50. CHRISTENSEN P R and COCKE R L,Phys . Le t t e r s 22_ (1966) 503-505.

51. BROWN D, FERGUSON A T G, and WHITE R E,in P r o c . Int. Symp. Pol . Phen. Nucl. , Base l , 4-8 Jul\Base l -S tu t tgar t , 1961, p . 291-302.

52. BROWN D, FERGUSON A T G, and WHITE R E,Nucl. Phys . 25 (1961) 604-610,

53. FERGUSON A T G and WHITE R E,Nucl. Phys . 3_3_ (1962) 477-481.

54. WILLS, J r . J E et al . ,Phys . Rev. H)9_(1958) 891-897.

55. RODBERG L S,Nucl. Phys . l_5_(1960) 72-78.

56. HÜFNER J and DE-SHALIT A,Phys . Le t t e r s 15 (1965) 52-55.

- 41 -

13. FIGURE CAPTIONS

Figs . 1-7 Experimental data relevant to the fast-neutron interaction12with C at the energy quoted in the respect ive f igures .

a Left-right rat io

observed in elast ic scat ter ing, using polarized fast-neutrons emitted

at the nominal reaction angle 9 = 50 from the Li(p,n) Be-reac t ion .

1. Experimental f ini te-geometry left-right rat io } o

2 . Computer-s imulated finite-geometry left-r ight rat io } x

3. Correc ted angular distribution }

4. Uncorrected smoothed angular distribution } — — —

b Differential elastic scat tering c ross section for unpolarized

incident fast-neutrons, T

1. Experimental data of Elwyn and Lane i °

2. Correc ted angular distribution }

c Polarizat ion acquired by unpolarized incident fast-neutrons

1. Correc ted experimental data } 9

2. Correc ted angular distribution }

d Spin rotation pa ramete r

1. Correc ted angular distribution }

Angular distributions designated "cor rec ted" have been reproduced

from the phase shifts of table 9.

Fig. 8 Polarizat ion versus incident proton energy for the ground

state group of fast-neutrons being emitted at the laboratory

react ion angle 9.. = 50 from the p+ Li - reac t ion .

Fig. 9 Intercomparison of experimental polarization products of

this work and those observed by Elwyn and Lane.

300

12

Ni

iM.O( 1

0.9

0.8

P,= 0.3162 * 0.0152

I1.2 £250

•h1.1 200

1.0TN, 150-

• 0.9 100

0-8 50

(Experimental* 2 51 t013h

'i = 2 51b

300

ca

1Si

250^ 050o

I

200 0.25

00 -025

50 -050

E = 1.062 ± 0.027 MeV

0.50

025 10

-0 25 -10'

•050

Fig. 1

: 3 0 O

[Experimental : 2.13iCuO5b.°V (pitted "2.20 b .

-Tk

08 50

k ^

ni . . . .l 6 ' ' ' ' -|0

300 g

O«

tA

2 5 o |

Ê

200 Q25

100 -0.25

50

4-

= 1.317± 0.02A MeV

0.25 10V

P p

025 -10'

10"

10*

Fig. 2

-.300

1 2

0.8 L

0.50

[Experimental ') 76*005 b"•'Ipltted :189b

-0 50

cos 9 .

10'

En=1.639± 0.021 MeV

Fig. 3

300,-

0.81- '08 50

fExperii* :]Fitted

mental 0 72*0 05b183 b

8250^ 050

1

200 0.25

444

300 r

100 -0 25

50 -f) 50

0 -1

cos9c „

0.50

0.25 10«

_Jo|p pjo-

-0.25 -10"1-

J-0 50

0cos 6,

10'

o Tp

E = 1.736 t 0.017 MeV

F i g . 4

-,1.3 300i'Experimental:1.70±O05b

>:lFitted : 1 7 6 b

300

-]0.50

50 -0.50L J-0.5O

-, ' • ' ' A ' ' ' ' . ' o

En= 1.890* 0.016 MeV

Fig. 5

§300

250

200

'Experimental :" l"l*i 05b°*.: JFiHed -1 73 b

300 c

-, 0.50 20'

1ü0 -0 25

50 -0 50 J-0 50 -20*

cos 9,

20"

10'

En= 1.983 ± 0.016 MeV

Fig. 6

16

En=2.2A3i 0.023 MeV

20-

Fig. 7

0.50 T

Z!p'

0.40--

0.3O - -

0.20

O.io -•

02.5

ei

0

P, =-1.584 + 1.089 Ep-0.151 Ep

O H.R. Striebel, S.E.Darden, and W. Haeberli (1958)

0 L. Cranberg (1959)

a ü. A. Baîcker and K.W. Oones (1960)

s S. M. Aust in et al. (1961)

V W. Benenson, 3.H. May, and R.L.Walter (1962)

A W. D. Andress, Or. et al. (1965)

3.o 3.5 4.o 4.5 5.o

T 0 . 5 O |

- 0.4o

• 0-30

- • 0. 20

- 0. io

05.5

PMeV

0.10

0.05

P.P

-0.05

-0.10

x

I I1 Ï

II T

• * ^ >

> »

i

1.5H h

TH h

Ifi

2.0

i *

2.5 3.0

MeV

En

-0.15

-0.20

T: P, (51°) P(A5°)

: P, (51e) P(90»)1

JH=P, (50°) P(41.8') ;I-ÎH:R(50O) P(45°)

Elwyn< and

Lane

t i : f ( 5 0 ' ) P(85.20)J+«H:F»(50°) P(85°)

Present

work

T

l 1

Ti

-0.25

F ig . 9

LIST OF PUBLISHED AE-REPORTS

1—200. (See the back cover earlier reports.)

201. Heat transfer analogies. By A. Bhattacharyya. 1965. 55 p. Sw. cr. 8:- .202. A study of the "384" KeV complex gamma emission from plutonium-239.

By R. S. Forsyth and N. Ronqvist. 1965. 14 p. Sw. cr. 8 : - .203. A scintillometer assembly for geological survey. By E. Dissing and O.

Landström. 1965. 16 p. Sw. er. S:—.204. Neutron-activation analysis of natural water applied to hydrogeology. By

O. Landström and C. G. Wenner. 1965. 28 p. Sw. cr. 8 : - .205. Systematics of absolute gamma ray transition probabilities in deformed

odd-A nuclei. By S. G. Malmskog. 1965. 60 p. Sw. cr. 8:- .206. Radiation induced removal of stacking faults in quenched aluminium. By

U. Bergenlid. 1965. 11 p. Sw. cr. 8 : - .207. Experimental studies on assemblies 1 and 2 of the fast reactor FRO. Part 2.

By E. Hellstrand, T. Andersson, B. Brunfelter, J. Kockum, S-O. Londenand L. I. Tirén. 1965. 50 p. Sw. cr. 8 : - .

208. Measurement of the neutron slowing-down time distribution at 1.46 eVand its space dependence in water. By E. Möller. 1965. 29 p. Sw. cr. 8:—.

209. Incompressible steady flow with tensor conductivity leaving a transversemagnetic field. By E. A. Witalis. 1965. 17 p. Sw. cr. 8 : - .

210. Methods for the determination of currents and fields in steady two-dimensional MHD flow with tensor conductivity. By E. A. Witalis. 1965.13 p. Sw. cr. 8 : - .

211. Report on the personnel dosimetry at AB Atomenergi during 1964. ByK. A. Edvardsson. 1966. 15 p. Sw. cr. 8 : - .

212. Central reactivity measurements on assemblies 1 and 3 of the fast reactorFRO. By S-O. Londen. 1966. 58 p. Sw. cr. 8 : - .

213. Low temperature irradiation applied to neutron activation analysis ofmercury in human whole blood. By D. Brune. 1966. 7 p. Sw. cr. 8:- .

214. Characteristics of linear MHD generators with one or a tew loads. ByE. A. Witalis. 1966. 16 p. Sw. cr. 8 : - .

215. An automated anion-exchange method for the selective Sorption of fivegroups of trace elements in neutron-irradiated biological material. ByK. Samsahl. 1966. 14 p. Sw. cr. 8 : - .

216. Measurement of the time dependence of neutron slowing-down and therma-lization in heavy water. By E. Möller. 1966. 34 p. Sw. cr. 8 : - .

217. Electrodeposition of actinide and lanthanide elements. By N-E. Bärring.1966. 21 p. Sw. cr. 8:- .

218. Measurement of the electrical conductivity of He1 plasma induced byneutron irradiation. By J. Braun and K. Nygaard. 1966. 37 p. Sw. cr. 8 : - .

219. Phytoplankton from Lake Magelungen, Central Sweden 1960-1963. By T.Willen. 1966. 44 p. Sw. cr. 8:- .

220. Measured and predicted neutron flux distributions in a material surround-ing av cylindrical duct. By J. Nilsson and R. Sandlin. 1966. 37 p. Sw.cr. 8 : - .

221. Swedish work on brittle-fracture problems in nuclear reactor pressurevessels. By M. Grounes. 1966 34 p. Sw. cr. 8:—.

222. Total cross-sections of U, UOi and ThOi for thermal and subthermalneutrons. By S. F. Beshai. 1966. 14 p. Sw. cr. 8:- .

223. Neutron scattering in hydrogenous moderators, studied by the time de-pendent reaction rate method. By L. G. Larsson, E, Möller and S. N.Purohit. 1966. 26 p. Sw. cr. 8:- .

224. Calcium and strontium in Swedish waters and fish, and accumulation ofstrontium-90. By P-O. Agnedal. 1966. 34 p. Sw. cr. 8:- .

225. The radioactive waste management at Studsvik. By R. Hedlund and A.Lindskog. 1966. 14 p. Sw cr. 8:- .

226. Theoretical time dependent thermal neutron spectra and reaction ratesin HiO and DiO. S. N. Purohit. 1966. 62 p. Sw. cr. 8:- .

227. Integral transport theory in one-dimensional geometries. By I. Carlvik.1966. 65 p. Sw. cr. 8:- .

228. Integral parameters of the generalized frequency spectra of moderators.By S. N. Purohit. 1966. 27 p. Sw. cr. 8 : - .

229. Reaction rate distributions and ratios in FRO assemblies 1, 2 and 3. ByT. L. Andersson. 1966. 50 p. Sw. cr. 8 : - .

230. Different activation techniques for the study of epithermal spectra, app-lied to heavy water lattices of varying fuel-to-moderator ratio. By E. K.Sokolowski. 1966. 34 p. Sw. cr. 8:- .

231. Calibration of the failed-fuel-element detection systems in the Agestareactor. By O. Strindehag. 1966. 52 p. Sw. cr. 8:—.

232. Progress report 1965. Nuclear chemistry. Ed. by G. Carleson. 1966. 26 p.Sw. cr. 8 : - .

233. A summary report on assembly 3 of FRO. By T. L. Andersson, B. Brun-felter, P. F. Cecchi, E. Hellstrand, J. Kockum, S-O. Londen and L. I.Tirén. 1966. 34 p. Sw. cr. 8 : -

234. Recipient capacity of Tvären, a Baltic Bay. By P.-O. Agnedal and S. O. W.Bergström. 1966. 21 p. Sw. cr. 8:- .

235. Optimal linear filters for pulse height measurements in the presence ofnoise. By K. Nygaard. 1966. 16 p. Sw. cr. 8:- .

236. DETEC, a subprogram for simulation of the fast-neutron detection pro-cess in a hydro-carbonous plastic scintillator. By B. Gustafsson and O.Aspelund. 1966. 26 p. Sw. cr. 8 : - .

237. Microanalys of fluorine contamination and its depth distribution in zircaloyby the use of a charged particle nuclear reaction. By E. Möller and N.Starfelt. 1966. 15 p. Sw. cr. 8:- .

238. Void measurements in the regions of sub-cooled and low-quality boilinq.P. 1. By S. Z. Rouhani. 1966. 47 p. Sw. cr. 8 : - .

239. Void measurements in the regions of sub-cooled and low-quality boiling.P. 2. By S. Z. Rouhani. 1966. 60 p. Sw. cr. 8 : - .

240. Possible odd parity in " 'Xe. By L. Broman and S. G. Malmskog. 1966.10 p. Sw. cr. 8 : - .

241. Burn-up determination by high resolution gamma spectrometry: spectrafrom slightly-irradiated uranium and plutonium between 400-830 keV. ByR. S. Forsyth and N. Ronqvist. 1966. 22 p. Sw. cr. 8 : - .

242. Half life measurements in <"Gd. By S. G. Malmskog. 1966. 10 p. Sw.cr. 8:—.

243. On shear stress distributions for flow in smooth or partially rough annul!.By B. Kjellström and S. Hedberg. 1966. 66 p. Sw. cr. 8 : - .

244. Physics experiments at the Agesta power station. By G. Apelqvist, P.-A.Bliselius, P. E. Blomberg, E. Jonsson and F. Akerhielm. 1966. 30 p. Sw.cr. 8 : - .

245. Intercrystalline stress corrosion cracking of inconei 600 inspection tubes inthe Agesta reactor. By B. Grönwall, L. Ljungberg, W. Hübner and WStuart. 1963. 26 p. Sw. cr. 8:- .

246. Operating experience at the Ägesta nuclear power station. By S. Sand-ström. 1966. 113 p. Sw. cr. 8:- .

247. Neutron-activation analysis of biological material with high radiation levels.By K. Samsahl. 1966. 15 p. Sw. cr. 8:- .

248. One-group perturbation theory applied to measurements with void. By RPersson. 1966. 19 p. Sw. cr. 8:- .

249. Optimal linear filters. 2. Pulse time measurements in the presence ofnoise. By K. Nygaard. 1966 9 p. Sw. cr. 8:- .

250- The interaction between control rods as estimated by second-order one-group perturbation theory. By R. Persson. 1966. 42 p. Sw. cr. 8:—.

251. Absolute transition probabilities from the 453.1 keV level in 183W. By S. GMalmskog. 1966. 12 p. Sw. cr. 8 : - .

252. Nomogram for determining shield thickness for point and line sources ofgamma rays. By C. Jönemalm and K. Malén. 1966. 33 p. Sw. cr. 8 : -

253. Report on the personnel dosimetry at AB Atomenergi during 19S5. By K. A.Edwardsson. 1966. 13 p. Sw. cr. 8 : - .

254 Buckling measurements up to 250°C on lattices of Âgesta clusters and onD J O alone in the pressurized exponential assembly TZ. By R. Persson,A. J. W. Andersson and C.-E. Wikdahl. 1966. 56 p. Sw. cr. 8:- .

255 Decontamination experiments on intact pig skin contaminated with beta-gamma-emitting nuclides. By K. A. Edwardsson, S. Hagsgärd and A. Swens-sOii. 1963. 35 p. Sw. cr. 8:- .

258. Perturbation method of analysis applied to substitution measurements ofbuckling. By R Persson. 1966. 57 p. Sw. cr. 8:- .

257. The Dancoff correction in square and hexagonal lattices. By I. Carlvik. 196635 p. Sw. cr. 8:- .

253. Hall effect influence on a highly conducting fluid. By E. A. Witalis. 196613 p. Sw. cr. 3:- .

259. Analysis of the quasi-elastic scattering of neutrons in hydrogenous liquids.By S. N. Purohit. 1966. 26 p. Sw. cr. 8:~.

260 High temperature tensile properties of unirradiated and neutron irradiated20Cr-35Ni austenitic steel By R B Roy and B Solly. 1966. 25 p. Sw.cr. 8:- .

251. On the attenuation of neutrons and photons in a duct filled with a helicalplug. By E. Aalto and A. Krell. 1986. 24 p. Sw. cr. 8:- .

262. Design and analysis of the power control system of the fast zero energyreactor FR-O. By N. J. H. Schuch. 1966. 70 p. Sw. cr. 8 : - .

263. Possible deformed states in '" In and ' " In . By A. Bäcklin, B. Fogelberg andS. G. Malmskog. 19S7. 39 p. Sw. cr. 10:- .

264. Decay of the 16.3 min. '"Ta isomer. By M. Höjeberg and S. G. Malmskog.1967. 13 p. Sw. cr. 10:-.

265. Decay properties of " 'Nd . By A. Bäcklin and S. G. Malmskog. 1967. 15 p.Sw. cr. 10: - .

266. The half life of the 53 keV level in '"Pt. By S. G. Malmskog. 1967. 10 p.Sw. cr. 10:-.

267. Burn-up determination by hight resolution gamma spectrometry: Axial anddiametral scanning experiments. By R. S. Forsyth, W. H. Blackadder andN. Ronqvist. 1967. 18 p. Sw. cr. 10:- .

268. On the properties of the s,^2 >- d 3 / 2 transition in 1"Au. By A. Bäcklinand S. G. Malmskog. 1967. 23 p. Sw. cr. 10:- .

259. Experimental equipment for physics studies in the Agesta reactor. By G.Bernander, P. E. Blomberg and P.-O. Dubois. 1967. 35 p. Sw. cr. 10:—.

270. An optical model study of neutrons elastically scattered by iron, nickel,cobalt, copper, and indium in the energy region 1.5 to 7.0 MeV. By B.Holmqvist and T. Wiedling. 1967. 20 p. Sw. cr. 10:- .

271. Improvement of reactor fuel element heat transfer by surface roughness.By B. Kjellström and A. E. Larsson. 1967. 94 p. Sw. cr. 10:- .

272. Burn-up determination by high resolution gamma spectormetry Fission pro-duct migration studies. By R. S. Forsyth, W. H. Blackadder and N. Ron-qvist. 1967. 19 p. Sw. cr. 10:-.

273. Monoenergetic critical parameters and decay constants for small spheresand thin slabs. By I. Carlvik. 24 p. Sw. cr. 10:-.

274. Scattering of neutrons by an anharmonic crystal. By T. Högberg, L. Bohlinand I. Ebbsjö. 1967. 38 p. Sw. cr. 10:- .

275. The I A K I = 1 , E1 transitions in odd-A isotopes of Tb and Eu. By S. G. Malm-skog, A. Marelius and S. Wahlborn. 1967. 24 p. Sw. cr. 10:-.

276. A burnout correlation for flow of boiling water in vertical rod bundles. ByKurt M. Becker. 1967. 102 p. Sw. cr. 10:-.

277. Epithermal and thermal spectrum indices in heavy water lattices. By E. K.Sokolowski and A. Jonsson. 1967. 44 p. Sw. cr. 10:-.

278. On the ds,2-<-~>"97/2 transitions in odd mass Pm nuclei. By A. Bäcklin andS. G. Malmskog. 1967. 14 p. Sw. cr. 10:- .

279. Calculations of neutron flux distributions by means of integral transportmethods. By I. Carlvik. 1967. 94 p. Sw. cr. 10:-.

280. On the magnetic properties of the K = 1 rotational band in '"Re. By S. G.Malmskog and M. Höjeberg. 1967. 18 p. Sw. cr. 10:-.

281. Collision probabilities for finite cylinders and cuboids. By I. Carlvik. 1967.28 p. Sw. cr. 10:-.

232. Polarized elastic fast-neutron scattering off 12C in the lower MeV-range.I. Experimental part. By O. Aspelund. 1967. 50 p. Sw. cr. 10:- .

Förteckning over publicerade AES-rapporter

1. Analys medelst gamma-spektrometri. Av D. Brune. 1961. 10 s. Kr 6:- .2. Bestralningsförändringar och neutronatmosfär i reaktortrycktankar - nâgra

synpunkter. Av M. Grounes. 1962. 33 s. Kr 6:- .3. Studium av sträckgränsen i mjukt stâl. Av G. Dstberg och R. Attermo

1963. 17 s. Kr 6:- .4. Teknisk upphandling inom reaktoromrâdet. Av Erik Jonson. 1963. 64 s.

Kr 8:-.5. Ägesta Kraftvärmeverk. Sammanställning av tekniska data, beskrivningar

m. m. för reaktordelen. Av B. Lilliehöök. 1964. 336 s. Kr 15:—.6. Atomdagen 1965. Sammanställning av föredrag och diskussioner. Av S

Sandström. 1966. 321 s. Kr 15:-.Additional copies available at the library of AB Atomenergi, Studsvik, Ny-köping, Sweden. Micronegatives of the reports are obtainable through Film-produKter, Gamla Iandsvägen 4, Ektorp, Sweden.

EOS-tryckerierna, Stockholm 1967