Polarization of neutrons produced in the D—D reaction

Nuclear Physics 10 (1959) 429

~39;~North-Holland PublishingCo., Amsterdam

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

POLARIZATION

OF N E U T R O N S P R O D U C E D REACTION

IN THE

D--D

P. P. K A N E t

Wesleyan University, Middletown, Conn., U.S.A. R e c e i v e d 8 J a n u a r y 1959 P o l a r i z a t i o n of n e u t r o n s f r o m t h e d(d, n) H e r e a c t i o n w a s m e a s u r e d a t a n a v e r a g e d e u t e r o n e n e r g y of 93 k e V a n d e m i s s i o n a n g l e s of 43 ° a n d 53 ° in t h e l a b o r a t o r y s y s t e m . T h e v a l u e s of P n are f o u n d to be - - 1 0 . 6 ~ o ± 2 . 3 ~o a n d - - 9 . 5 ~/o =[=3.7 ~/o respectively. T h e s e a r e in e x c e l l e n t a g r e e m e n t w i t h p r e v i o u s r e s u l t s a t h i g h e r energies. T h e r e s u l t s of all e x p e r i m e n t s s u g g e s t t h a t t h e p o l a r i z a t i o n is i n d e p e n d e n t of d e u t e r o n b o m b a r d i n g e n e r g y b e t w e e n 93 k e V a n d 700 keV.

Abstract:

1. I n t r o d u c t i o n During the last few years, the production and use of medium energy polarized neutrons have resulted in a substantial contribution to our understanding of nuclear forces. Schwinger 1) proposed the scattering of nucleons from helium as a mechanism for the production of polarization. This method of producing polarization, although successfully utilized at first by Heusinkveld and Frier 2) and later by other workers for protons, is not particularly suitable for neutrons of a few MeV energy. The efficiencies of most detectors are only of the order of a few per cent and therefore it has not been possible so far to detect neutron polarization obtained in the above manner in the MeV region of kinetic energies. However, according to the original prediction of Wolfenstein s), the d(d, n)He 3 reaction has proved to be a convenient source of polarized neutrons in the energy range under consideration. The Li (p, n) Be T reaction 4-~) has also been used extensively for o b t ~ f i n g polarized neutron beams. Our experiments are concerned exclusively with the d - - d reaction. The polarization of d - - d neutrons has been studied by m a n y workers s_ls). Only the first of these experiments attempted to utilize deuteron bombarding energies less than 200 keV. At an energy of about 100 keV, Longley et M. s) obtained a value for P1(45 °) of 4 0 i 2 0 ~o. Here, P1(45 °) is the polarization of neutrons at 45 ° in the centre of mass system. The experiments at higher deuteron energies give for the maximum neutron polarization a rather precise value in the neighbourhood of 10 ~ . Therefore, in order to understand t W o r k s u p p o r t e d in p a r t b y a g r a n t f r o m t h e R e s e a r c h Corporation. 429

430

p . p . maNE

better the dependence of the neutron polarization on the incident deuteron energy, it seemed necessary to us to increase the precision of the measurement of the neutron polarization at low incident deuteron energies. Our result for the neutron polarization at an average deuteron energy of 93 keV is in good agreement with the precise results obtained at the higher energies. The disagreement between our result and t h a t of Longley et a/. might be attributed to the large statistical error of the latter measurement or to the difference in technique. Following a suggestion of Schwinger le), Longley et al. employed the small angle scattering from a lead nucleus to detect the neutron polarization. This technique involves difficulties associated with very strong background and was therefore not used in the more recent experiments. Since the properties of carbon as an analyser had been studied in detail b y Meier eta/. n), we decided to employ carbon as an analyser. Among earlier workers, Pasma and Levintov e t a / . used scattering from helium for a s y m m e t r y measurements. The others used carbon scatterers. Previous work, particularly that of Levintov et a/., had shown that the results for neutron polarization obtained with thin deuterium targets were substantially the same as those obtained with thick targets. Therefore, no attempt was made to use thin targets. The theoretical ideas underlying the experiment are well-known and are mentioned briefly in section 2. The experimental details are outlined in Section 3. Results and conclusions are presented in the fourth section. 2. T h e o r y The notation is described in the caption to fig. 1. If Pn(01) is the polarization of the neutron beam incident on the carbon target, we have the relation Pn(01) = exPn(Ox)

(1)

)

Fig. 1. D i a g r a m m a t i c r e p r e s e n t a t i o n of t h e a n g l e s i n v o l v e d in t h e e x p e r i m e n t , d a n d n repres e n t t h e i n c i d e n t d e u t e r o n a n d t h e e m i t t e d n e u t r o n . 01 is t h e a n g l e w h i c h t h e e m i t t e d n e u t r o n m a k e s in t h e c e n t r e of m a s s s y s t e m w i t h t h e d i r e c t i o n of i n c i d e n c e of t h e d e u t e r o n . 0t is t h e a n g l e t h r o u g h w h i c h t h e n e u t r o n is s c a t t e r e d b y t h e c a r b o n n u c l e u s in t h e c e n t r e of m a s s f r a m e of t h e n e u t r o n a n d t h e n u c l e u s . Directions, r i g h t a n d left, a r e defined in t h e d i a g r a m .

POLARIZATION OF N E U T R O N S P R O D U C E D I N T H E D - - D

REACTION

481

where

e I = kd X kn/Jkd X kn[.

(2)

Here kd is the wave vector of the deuteron and kn is the wave vector of the emitted neutron. Let Pc(02) be the polarization of an initially unpolarized neutron beam aRer scattering from carbon through 02. Then we can write Pc(0n) as

e2Pe(02)

Pc(0~) =

(3)

where e s = k n xk'n/[k n Xk'nl.

(4)

In eq. (4), kn and k'n are the wave vectors of the incident and scattered neutrons respectively. The differential cross section for the scattering of a polarized neutron beam is given b y the formula 17) ¢(02, 4) = ~u(Os){l+Pn(01) " Pc(On)}

(5)

where ~u(02) is the differential cross section for the scattering of an unpolarized neutron beam at 02 and ~bis the azimuthal angle. In our experiment, scattering takes place in the plane defined b y the direction of the deuteron beam and that of the emitted neutron. The asymmetry e is given b y the formula :

=

=

=

~(01, 02) :

(6) (o2,

From the eqs. (1) to (6), we can derive the relation

*(01, 02) = Pn(0x)Pc(0s).

(7)

If Pc(02) is known, experimental measurements of e can be used to determine the required polarization Pn(01). Along with McCormac d aL, we assume the validity of the phase shift analysis of Meier d a/. for the scattering of neutrons from carbon between 2.4 and 3.6 MeV. On the basis of this assumption we get the relation Po(O~) ~ --sin(202). (8) In deducing the polarization PE(01) from measurements of the asymmetry e, we assumed complete equality between the two sides of (8). 3. E x p e r i m e n t a l

Details

A beam of deuterons, accelerated through 120 kV, was aLLowed to impinge on an occluded deuterium target. The target was formed b y adsorbing deuterium in an alumim'um disc ~ inch thick. After the target had been bombarded b y a 100 pA deuteron beam for about l0 hours, it did not reveal a n y noticeable fluctuations i n the deuterium content for at least two or three days. The experimental arrangement is shown in fig. 2. Europium

432

P.P.

KANE

activated lithium iodide scintillator, available from Harshaw Chemical Company, was used for monitoring the neutron beam. The lithium iodide scintillator was a cylinder of diameter 1{ inches and thickness ½ inch. Pulses from the lithium iodide counter were amplified and then fed to a discriminator. The bias of the discriminator was set below the pulse height corresponding to the dissipation of the kinetic energies of the product triton and alphaparticle within the scintillator. Therefore, the lithium iodide monitor counts were rather insensitive to fluctuations in the gain of the electronics. This feature of the lithium iodide counter made it a satisfactory neutron monitor. Neutrons, used for a s y m m e t r y measurements, were collimated as shown in fig. 2. The vertical height of the collimator was one inch all along its length. The maximum height of the neutron beam at the centre of the carbon target was somewhat less than 1½inches. An optical spectrometer was modified so

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Fig. 2. A r r a n g e m e n t of s h i e l d i n g a n d c o u n t e r s , d r e p r e s e n t s t h e d e u t e r o n b e a m , T t h e d e u t e r i u m t a r g e t , C t h e c a r b o n t a r g e t a n d A t h e a n t h r a c e n e c o u n t e r . T h e l i t h i u m iodide c o u n t e r w a s placed a t a d i s t a n c e of 58 i n c h e s f r o m T in t h e direction of I.

as to support the carbon scatterer and the detector for scattered neutrons. The cylindrical carbon target was 1~ inches in diameter. It had an average density of 1.76 g/cm ~. The spectrometer table had on it accurately marked circular grooves. So the target could be positioned quite accurately with reference to the centre of the spectrometer table. The scattered neutrons were detected with the help of an anthracene crystal, l½ inches in diameter and ~ inch thick, mounted on a Dumont 6292 photo-multiplier. The anthracene counter was mounted in the movable arm of the spectrometer. The pulses from the anthracene counter were amplified and the amplified output was fed simultaneously to a single channel analyser and a discriminator. For given values of 01 and 03 , counts were taken for an assigned number of

POLARIZATION

OF N E U T R O N S

PRODUCED

IN

THE

D--D

REACTION

4~

monitor counts on the right (4 ---- 0) with and without the carbon target and on the left (4 = ~) again with and without the target. Such a set of four readings was repeated between ten to twenty times for each combination of 01 and 82 values. In order to cancel the effect of irregularities, the carbon target was rotated through approximately 180 degrees between successive sets of readings. From the above sets of observations, scattered neutron counts and asymmetries were determined in a straightforward manner. Only the single channel analyser counts were used in the measurement of the asymmetries. The counts obtained with the help of the discriminator were only used to s t u d y the effects of fluctuations in electronic gain. The values of asymmetries determined with the help of the discriminator for different bias settings were in agreement with the more reliable single channel values. The pulse height response of an anthracene counter to neutrons elastically scattered from carbon showed a rather flat distribution up to a certain critical value and then dropped off sharply. The window of the single channel analyser was set to accept only those pulses that had a height somewhat smaller than this critical value. This procedure helped considerably in reducing the number of unwanted background counts. From previously published results on the scattering of 2.65 MeV neutrons n), it was expected that a systematic error of ½ degree in the determination of zero degree scattering position would lead to asymmetries of about +0.01 at the values of 03 used in our measurements. Therefore, it was necessary to ensure accurate alignment of the scatterer and the detector with the beam axis. Accurate alignment of the centre of the spectrometer with the beam axis was achieved b y means of an optical telescope. The correct zero degree positionwas determined b y rotating the anthracene counter through small angles about the expected zero degree position and observing the approximate symmetry of the curve giving neutron count as a function of angle. The data are shown in fig. 3. The angles could be read to about one tenth of a degree on the spectrometer scale. The zero degree position, determined in this manner, was expected to be accurate to a quarter of a degree. A second check was provided b y repeating the beam profile measurements with the carbon target in place. The zero degree position determined b y the last procedure was found to be the same as that determined in the absence of the carbon target, thus revealing a proper alignment of the carbon target as well. The zero degree positions, determined before and after a series of asymmetry measurements, were found to be the same, indicating the absence of systematic drifts in the deuterium target or deuteron beam focus. Two separate methods were used to detect instrumental asymmetries that might be present in spite of these careful alignment procedures. When O~ is zero, one would expect the polarization P . of the emitted neutrons to vanish on the basis of eqs. (1) and (2). Therefore, asymmetry values for any

-434

P . P . KANE

value of 0s should also vanish. The asymmetries, measured under these conditions, gave an average value of 0.0044-0.019. Further, eq. (8) suggests that Pc(90 °) should be zero and hence the asymmetry for a 02 value of 90 ° :should also be zero. The experimental result is 0.007-4-0.021, These measurements ensure the absence of appreciable instrumental asymmetries. An additional precaution was taken in the measurement of the non-vanishing asymmetries. From eqs. (1) to (6), we get the relation

~(0~, 02)

=

0~).

+~(--0~,

(9)

In the case of the two values of 0z employed in our experiments, asymmetry measurements were made for the corresponding --0 z values as well. The results satisfied eq. (9) within the experimental error. The values reported RELATIVE NEUTRON NTENSITY

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ANGLE OF ROTATION,

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(Oegreol)

Fig. 3. B e a m profile o b t a i n e d w i t h t h e h e l p of t h e a n t h r a c e n e c o u n t e r . T h e s y m m e t r y of t h e profile w a s u s e d to d e t e r m i n e t h e zero degree s c a t t e r i n g position.

for the asymmetries in table 1 are the means of the two values of e for #1 and --01. The background was about 80 % of the counting rate in the presence of the carbon target. Under such conditions, the background m a y be substantially altered in an unpredictable manner b y the use of the carbon target. For 0s larger than about 25 degrees, the background was almost independent of angle. This observation suggests that any asymmetries introduced b y background differences were negligible.

POLARIZATION OF NEUTRONS PRODUCED IN THE D --D REACTION

435

The carbon target subtended an angle of 4-2 degrees at the centre of the deuterium target. The emission of neutrons from the d - - d source is not isotropic. In a separate experiment, we have determined the angular distribution of neutrons emitted in the d - - d reaction at an accelerating voltage of 120 kV. The anisotropy of the d - - d source contributed an absolute asymmet r y of about 0.003 in our experiment. In view of the fairly large statistical errors of the measurements, this correction has been considered to be negligible. However, it should be remarked here that the correction is of such a sign as to increase the observed asymmetries. Appreciable multiple scattering of neutrons was present. However, an argument, t h a t has been proposed before 1~), suggests t h a t the measured asymmetries were probably not in error on this account. Since a thick, adsorbed deuterium target was used in these experiments, it was desirable to know the average deuteron energy for neutron production. A knowledge of the dependence of the d(d, n)He 3 reaction cross section on deuteron energy was necessary in the calculation of the average energy of the deuterons. No previously published results were available at these energies t. So an auxiliary experiment was carried out to determine the energy dependence of the reaction cross section. For this purpose, the lithium iodide counter was placed at an angle of 90 ° in the laboratory system to the deuteron beam. A long boron tri-fluoride counter of the type suggested by Hanson and McKibben is) was also put at 90 ° to the deuteron beam on the other side. The insensitivity of such a long counter to neutron energy is well known. We also verified experimentally the absence of the dependence of the long counter sensitivity on neutron energy for a range of at least about 200 keV. If the energy of the deuterons is varied from 30 keV to 130 keV, the maximum variation in the energy of the neutrons emitted at 90 ° in the laboratory ~ystem is about 20 keV. The energy insensitivity of the long counter within such a narrow range could therefore be safely assumed. Lithium iodide and boron tri-fluoride counts were then taken for fixed intervals of time and for fixed values of deuteron current as the accelerating voltage was varied from 30 kV to 130 kV. The maximum variation in beam current was ± 1.5 during these measurements. The mean value of the current was known probably to better than 1 % . Observations taken at a given voltage both before and after the complete set of readings revealed no significant fluctuations in the electronic gain. The data obtained with the long counter are presented in fig. 4. A moderately good fit to the data is obtained, if we take the d(d, n)He reaction cross section to be proportional to E ~.4 where E is the f NoU added in f~oo/: T h e w o r k of I. B e r t h o l d s o n a n d G. C a r l s o n u) h a s r e c e n t l y c o m e t o Cur a t t e n t i o n . A l t h o u g h no a t t e m p t w a s m a d e i n t h a t w o r k t o o b t a i n a n e x p l i c i t f u n c t i o n a l relationship between the r e a c t i o n cross s e c t i o n a n d d e u t e r o n e n e r g y , our r e s u l t s a p p e a r t o b e i n agreemen~t w i t h t h o s e of a b o v e a u t h o r s .

436

P. ~,. ~.Z,T~,

bombarding deuteron energy. The same energy dependence was shown within the experimental error b y the lithium iodide counter, suggesting an absence of variation of the response of such a counter within a range of at least 20 keV in neutron energy. From the observed energy dependence of the reaction, we calculate the average deuteron energy to be 93 keV at an accelerating voltage of 120 kV. The error in the determination of the average deuteron energy is expected to be less than 7 keV. Among the earlier workers, Levintov e ~ . 14) had assumed a linear dependence of the reaction u~

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Fig. 4. V o l t a g e d e p e n d e n c e of t h e p r o d u c t i o n of n e u t r o n s for a fixed b e a m c u r r e n t a n d a fixed i n t e r v a l of t i m e . T h e s t r a i g h t line f i t to t h e d a t a s u g g e s t s a n E L • d e p e n d e n c e of t h e d---d r e a c t i o n cross section a t low d e u t e r o n energies E. T h i s e n e r g y d e p e n d e n c e h a s b e e n u s e d to c o m p u t e t h e a v e r a g e e n e r g y of d e u t e r o n s effective in p r o d u c i n g n e u t r o n s .

cross section on voltage. But they used deuteron energies in the neighbourhood of 1 MeV. Further it should be pointed out that our determination of the energy dependence was achieved only with the help of a thick deuterium target. 4. R e s u l t s and D i s c u s s i o n

The results are summarized in table 1. The observed polarization is in excellent agreement with other measurements both as regards magnitude and sign. Our value for the polarization is the same within the experimental error as that of Meier a ~. 11) around 600 keV, those of McCormac et ~ . 12) between 500 and 700 keV, that of Levintov et ~ . 14) at 400 keV and finally those of Pasma 15) between 300 and 500 keV. An essential constancy of the polarization within the deuteron energy range 93 keV to 700 keV is suggested b y all the experiments including the present one. Meier eJ ~ . analyse the

POLARIZATION OF NEUTRONS PRODUCED IN THE D--D REACTION

437

earlier results of Huber and Baumgartner 10) b y using the revised phase shift calculations and give a value of - - 1 1 % 4 - 5 % for the polarization at an energy of 600 keV and a laboratory emission angle of 45 °. An earlier measurement of the polarization at 200 keV 15) gives the somewhat lower value of TABLE 1 E x p e r i m e n t a l results for t h e polarization of n e u t r o n s generated in a d---d reaction a t a n average d e u t e r o n energy of 93 keV in the l a b o r a t o r y system. O1L

01

OI

e

Pa(01)

Mean Pn(Oz)

43.0 °

45.7 °

27.0 ° 32.4 ° 43.0 ° 53.7 °

0.082 ± 0.044 0.104±0.032 6.085±0.031 0.116±0.033

-- 10.1% ± 5.4% --11.5% ± 3 . 5 % -- 8 . 5 % ± 3 . 1 % --12.2% ± 3 . 5 %

--10.6%±2.3%

32.4 ° 48.4 ° 53.7 °

0.130±0.054 0.010±0.050 0.124±0.044

--14.4%~6.0% -- 1 . 0 % ± 5 . 0 % --13.0%±4.6%

-- 9 . 5 % ~ 3 . 7 %

53.0 °

56.2 °

0~ is t h e angle in the centre of m a s s frame t h a t t h e n e u t r o n m a k e s w i t h of t h e incident deuteron. 0IL is t h e corresponding angle in the l a b o r a t o r y the angle t h r o u g h which t h e n e u t r o n is scattered b y t h e c a r b o n nucleus in m a s s f r a m e of t h e n e u t r o n a n d t h e nucleus, e is the observed a s y m m e t r y . T h e are o n l y statistical, e is given b y t h e relation

e(O. 0,) =

t h e direction system. 02 is t h e centre of errors q u o t e d

a(O,, ~ = o ) - a ( O , , ¢ = =) a(O,, ~ = o)+a(O,, ~ = =)

The reported values for e are the averages of the a s y m m e t r i e s for 01 and - - O r

--5.8 %-4-2.5 % b u t the relative statistical error of the measurement is quite large. In view of the suggested independence of the polarization from energy, an average of all measurements mentioned in this paragraph was taken. This average value of the polarization at a laboratory emission angle between 43 ° to 50 ° turns out to be --9.6 % ! 0 . 7 %. The suggested energy independence of the polarization could explain very well the fact that Levintoy eta/. noticed no significant changes in the polarization when thick deuterium targets were used instead of thin ones. The polarization of protons from the companion reaction d(d, p ) H s has been measured previously lg-zl), although not with the same degree of precision. The proton polarization is of the same order of magnitude as the neutron polarization and is also found not to change rapidly with energy. This similarity is to be expected on the basis of charge independence of nuclear forces. On the basis of the theory of the d - - d reaction developed b y Beiduk et al. 22), Blin-Stoyle ~, 24) deduced the following relation giving the neutron polarization as a function of energy E of the deuteron and centre of mass emission angle 01 of the neutron:

438

P.P. KANE

A ( E ) Sill 20101 for E < 300 keV. P,~(Ox) = B I + A (E) cos 2

(10)

In the above formula, the constant B depends upon a knowledge of the nuclear wave functions and so cannot be calculated at present. The coefficient A (E) depends on the energy of the deuterons and is the same as the coefficient of cos~(0x) in the expression I + A ( E ) c o s 2 01, which gives the angular distribution of the emitted neutrons. The suggested absence of the energy dependence of the polarization would imply in this theory a not too rapid variation of the coefficient A (E) with energy. Since there was considerable disagreement between the measurements of the coefficient A in this energy region, it was determined by us in a separate experiment which will be reported shortly. Our value for A is in the neighbourhood of 0.9. It is higher than that reported earlier by some workers m). But it will extrapolate quite well to those of Preston e~ a/. ~) between 156 and 270 keV and those of Chagnon and Owen IF) between 400 and 600 keV. Therefore, it appears that A varies between 0.9 and 1.8 as the deuteron energy is varied from 93 keV to about 400 keV. In that case, the form of eq. (10) certainly suggests a rather slow variation of the polarization with energy. The apparent lack of dependence of the experimentally observed polarization on energy is however not adequately explained at present. A further refinement of the theory is necessary before definite conclusions can be reached. We determined the polarization only for two values of 01 and therefore cannot make a significant comparison with the angular dependence exhibited in eq. (10). It is a pleasure to thank Dr. F. I. Boley for making available the facilities of the electrostatic accelerator, Mr. B. D. Day, Mr. T. R. Fisher and Mr. J. A. Palsedge for assistance in taking data and Mr. D. B. Colby for some of the computations. References I) J. Schwinger, Phys. Rev. 69 (1946) 681 M. Heusinkveld and Frier, Phys. Rev. 85 (1952) 80 L. Wolfenstein, Phys. Rev. 75 (1949) 342 Vv'illard, Bair and Kington, Phys. Rev. 95 (1954) 1359 Adair, Darden and Fields, Phys. Rev. 96 (1954) 503 A. Okazaki, Phys. Rev. 99 (1965) 55. 7 Striebel, D a r d e n a n d Haeberli, Nuclear Physics 6 (1958) 188 8 Longley, Little and Slye, l~nys. Rev. 86 (1952) 419 9 R. Ricamo, Nuovo Cimento 10 (1953) 1607 10 E. Baumgartner and P. Huber, Helv. Phys. Acta 26 (1953) 545 11 Meier, Scherrer and Trumpy, Heir. Phys. Acta 27 (1954) 577 12 McCormac et a/., Phys. Rev. 104 (1956) 718 13 Levintov et al., Nuclear Physics 3 (1957) 221 14 Levintov eta/., Nuclear Physics 3 (1957) 237 2 3 4 5 6

POLARIZATION

15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28)

OF NEUTRONS

PRODUCED

IN

THE

D--D

REACTION

P. J. Pasma, Nuclear Physics 6 (1958) 141 J. Schwinger, Phys. Rev. 73 (1948) 407 J. v . Lepore, Phys. Rev. 79 (1950) 137 A. O. Hanson and J. L. McKibben, Phys. Rev. 72 (1947) 673 Bishop eS al., Natulre 170 (1952) 113 R. E. Sege] and S. S. Hanna, Phys. Rev. 106 (1957) 536 B. Maglic and J. Vukovic, Nuclear Physics 6 (1958) 443 Beiduk et al., Phys. Rev. 77 (1950) 822 R. J. Blin-Stoyle, Proc. Phys. Soc. A b4 (1951) 700 R. J. Blin-Stoyle, Proc. Phys. Soc. A 65 (1959) 949 Fuller, Dance and Ralph, Phys. Rev. 108 (1958) 91 Preston, Shaw and Young, Proc. Roy. Soc. 226 (1954) 212 P. R. Chagnon and G. E. Owen, Phys. Rev. 101 (1956) 1798 I. Bertholdson and G. Carlson, Arkiv f. Fysik 2 (1950) 289

439 D