Re-determination of the β-energy of tritium and its relation to the neutrino rest mass and the Gamow-Teller matrix element

Re-determination of the β-energy of tritium and its relation to the neutrino rest mass and the Gamow-Teller matrix element

4.C ] Nuclear Physics A138 (1969) 417--428; (~) North-HollandPublishiny Co., Amsterdam Not to be reproduced by photoprint or microfilm without writ...

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4.C

]

Nuclear Physics A138 (1969) 417--428; (~) North-HollandPublishiny Co., Amsterdam Not

to be reproduced by photoprint or microfilm without written permission from the publisher

R E - D E T E R M I N A T I O N OF T H E / ~ - E N E R G Y OF T R I T I U M A N D ITS RELATION TO T H E N E U T R I N O REST M A S S A N D THE G A M O W - T E L L E R MATRIX E L E M E N T R. C. SALGO and H. H. STAUB Physik-lnstitut der Universitiit Ziirich Received 9 June 1969 Abstract: The upper energy limit of the fl-particles of 3H is determined with a retarding field spectrometer. Without having to rely on any assumptions concerning the structure of the sourcc or of the resolving power of the instrument, art upper limit (80 % confidence) of 200 cV for the rest mass of the antineutrino or its Fermi energy is found. Assuming that this mass is actually zero, a value for the maximum fl-encrgy of 18.72.'-_0.05 keV is found. The correspondingft value is 1159 -- I 1 s. This result together wittt the very much lower half-life of the neutron by Christcnsen et al. gives a value of the square of the GT matrix element of 2.844=-0.06. This practically removes the discrepancy with the prcdiction of the PCAC hypothesis concerning the enhancement of the GT matrix clement by pion exchange.

1. Introduction Except for the neutron the fl-decay of tritium, T - ~ 3 H e + e - + ~ , is the allowed fl process with A I = 0 = A T and mixed Fermi or vector and Teller or axial vector interaction. From an accurate determination of the energy Eo and the maximum energy Emax of the fl-particles one can obtain

simplest Gamowreaction the mass

TABLE 1 References Jenks et al. 2) Langcr et al. a) Gregory et al. *) Friedman et al. s) Popov et al. 6) Porter 7) Pillinger et al. s) Moreland et al. 9)

Method calorimeter magnetic spectrometer calorimeter mass spectrometer calorimeter magnetic spectrometer calorimeter mass spectrometer

Eo (keV) 18.6 4-0.2 17.95-L0.1 18.21 --0.03 18.65-'- 0.2 18.15 ± 0.03 18.61 5=0.1 18.46 :-0.06 18.47--0.17

of the antineutrino. Perhaps a more important factor today is the connection with elementary particle physics or current algebra as pointed out by Blin-Stoyle and Tint t). From the vaIues of the reduced lifetime ( f t ) of the neutron and tritium decays, which require the a.:curate determination of the maximum fl energy and the halfqife one can obtain the value of the G T matrix element MA. For tritium this quantity 417

418

R. C. SALGO AND H. H. STAUB

depends markedly on pion exchange between the nucleons which can be calculated fi'om high-energy pion production data on the basis of the partially conserved vector current hypothesis. Table 1 shows the more recently published values of Eo. There are three obviously low values with rather small limits of error, and it was felt that a re-determination of E0, with a different experimental method should be undertaken.

2. Experimental method The accurate determination of the maximum kinetic energy of fl-particles is always quite difficult since finite resolution and thickness of the source will lead to a spectrum with zero slope at the point of maximum kinetic energy. The subsequent rise of the number of recorded particles is determined by the true shape of the differential spectrum and the details of the spectrometer, its resolving power and energy dependence of the angle of acceptance and conditions of the source. A finite but small neutrino mass m,. on the other hand leads to a faster drop of the spectral distribution towards the true end-point of the fl-spectrum, which is the maximum kinetic energy of the fl-partieles given by: Ema x ~

where ligible For of the

Eo-.~vc2-ER~

Eo+mo c2 is the total energy available in the fl-reaction, ER the usually negrecoil energy imparted to the residual nucleus and mo the electron rest mass. an allowed (AI = 0, i; An : no) transition, the shape of the spectrum in terms kinetic energy E of the electron with ER = 0 is given by: d--n-n= const F(E, Z)(E + mo c2)(E- Eo)Ex./E(E + 2too c

dE

1 - (_m,.c-_ ~-.

\E o - E!

For tritium near the maximum energy one has: Ema x =

- - - oc (Eo--E) 2

dE

I/L

Eo-mvc 2,

E o - E << Eo

<< moc 2

= (Emax-E+mvc 2) \7(Em, x-E)(Emax-E+Zmvc2 ).

\E o - E~

"

The effect of a finite neutrino mass is therefore twofold: It lowers the value of E~.~x and at the same time modifies the very end of the spectrum to rise proportionally to x'E,,,x ± E instead of (E,,,.~- E) z as in the case of m,. = 0. Degeneracy of the antineutrinos leads to the same modification. In the case of the tritium decay the recoil energy is always smaller than 3.5 eV and is thereforc negligible. The experimental difficulties encountered with a detailed study of the shape of the spectrum near its endpoint are greatly reduced since Eo, the sum of antineutrino rest energy and maximum kinetic energy of the electron is rather acct:rately known from ti:e Q-values of the reactions 3H(p, n)3He [ref. 1o)] and n(p, 7)d [ref. ~1)] and the mass spectroscopic value, AM, the difference of the

fi-ENERGY

OF

TRITIUM

419

masses of the hydrogen molecule and the deuterium atom 12). If m3n and m3nc are the nuclear masses of 3H and 3He respectively (in energy units), Eo is: E 0 ~

YY]3H - - I'F/3H c --/,'/7, 0 .

The Q n value for 3H(p, n)ZHe of Salgo et al. lo) was not corrected for electronic binding energies and is therefore Q, -- m m + m n - m m ~ - m, = - 763.77_+ 0.08 keV, where m H and m, are proton and neutron masses respectively. The value of Qv [ref. 11)] is independent on electronic binding energies: Q,, = rn, + r n n - m d = 2224.668_+0.046 keV.

The doublet difference AM is AM = M , ~ -

~ I d ----- 2ma

+ 2too - 2B. - B n ~ - m d - - lTqo + B n = 1442. l 3_+ 0.05 keV,

where BH is the binding energy of the electron in the hydrogen atomic ground state (13.5 eV) and B.~ the molecular binding energy of H , (4.5 eV). Combining these values one obtains Eo = Q , + Q ~ - A M - ( B ~ , + B n 2 )

= 18.75+0.ll keV.

(1)

t

The upper limit for the mass of the antineutrino can therefore be determined rather accurately by simply measuring E,,a, as the highest energy at which electrons can be found in the fl-spectrum, without having to take recourse to some extrapolation proccdure which is strongly affected by the measuring instrument, the theoretical shape of the fl-spectrum and source conditions. 3. Spectrometer and sources

In view of the above considerations the spectrometer was designed for a source as strong as possible, spread over a wide area and a large solid angle of acceptance. These requirements are met by the electric retarding potential spectrometer as it was used previously by Hamilton, Alford and Gross 14). Since we directed our attention solely to the value of Em~x we chose a plane arrangement instead of a spherical one, although of course a further modification of the spectrum is introduced by the dependence of the solid angle on the energy and the retarding potential. Fig. 1 shows the arrangement schematically. The pure TzO ice source was evaporated on a gold plated circular source holder of 5.5 cm radius in thermal contac:, with a liquid nitrogen cold trap. It was kept at ground potential. The cold trap with the source holder can be rotated by 90 ~ into a position opposite a nozzle through which T 2 0 vapor was deposited on the source holder. The rctarding potential - Vo was applied to a grid at 11.0 cm from the plane of the source holder and parallel to it. Eight ring electrodes connected appropriately to a potential divider across the voltage

420

R . C. S A L G O A N D 11. H . S T A U B

V0 give a fairly linear potential drop. This arrangemcnt ensures parabolic trajectories of the electrons. It also avoids points of high electric field strength near the source which could lead to uncontrollable field emission of electrons near the source. The grid consisted of a square mesh of steel wires with a diameter of 0.04 m m and 0.125 mm distance. The optical transparency at perpendicular incidence is therefore about 45 ~ . The potential at the center of an opening differs from that of the wire by AV/Vo < 3" 10 -4. On the side of the grid opposite to the source a focussing elec-

[..(~.Ui Digital Voltmeter H.V.Supp|y ,~--Lt-'~'~'-R~ ~ for retsrding potential

, ili,ii,,i

)lllllllk

] Electronmultiplier

ource in

fPr°sletla°Pn°rCafts°nUr ce i

I I

'//F"Elect . . . . . rod~ ing

"~ Topump I T2o Fig. 1. Retarding potential spectrometer (schematic). trode, connected electrically to the grid forms a strongly demagnified rough image of the source from the electrons which have passed the grid. The detector opening is placed at the point where this image is formed. It consists of an open ended Cu-Be electron multiplier with the first dynode at ground potential. Since the nmltiplication factor of Cu-Be is very small, perhaps l0 -3 for 18 keV electrons, it was originally planned to reduce the energy and to produce additional multiplication by placing a nickel foil of suitable thickness and at a potential of about - 500 V in front of the multiplier, ltowever this scheme had to be abandoned. Although the desired increase in detection efficiency was observed, the background without the tritium source increased even more. The background, which contributed almost 99 ~ to the counting rate even at the point of lowest retarding voltage at 17.4 keV represented a major problem. It must of course be remembered, that the portion of the spectrum above this energy contains

fl-ENERGY OF TRITIUM

421

less than 10 .3 of the total intensity. The background could be reduced to this still high but tolerable level only by improving the vacuum of the system to 10 - s Torr with a titanium ion getter pump. By the use of metal and viton gaskets it was possible to bake out the complete vacuum system at 200 °C. A further reduction was achieved by avoiding any sharp corners of parts at negative voltage, where electrons could be released by cold emission. The background could be measured separately before the active material was deposited on the source holder. It decreased linearly with the retarding potential over the voltage region 16.5 to 20.7 keV and the spectrum measured with the source above 18.8 keV showed exactly the same linearity and slope. Since the background rer, rcsented the major part of the recorded particles and was certainly subject to slow variations with time the measurements could only be taken by rapid and repeated scanning of the region of interest from 17.4 to 20.2 keV. The source material T 2 0 was prepared as described previously 10) by oxidizing pure T 2 gas in excess oxygen on a hot platinum wire catalyst. A small portion of T 2 0 (about 0.1 Ci activity) was placed into a flask attached to the evaporation nozzle through which the water vapor was condensed on the cold source holder turned in front of the nozzle. The total amount of 39 ~tg of T 2 0 was not evenly distributed over the source holder. From the appearance of interference fringes we estimate the thickness at the center to be about 20 pg- c m - 2 dropping off very quickly to the edge. Serious consideration had to be given to the problem of the charging up of the insulating layer of active material by the emission of/?-particles and thereby changing the actual value of the retarding potential. Although the conductivity of ice by protons at a few °C below zero is quite high it will be extremely small at - 1 9 0 ° C. However the high activity of the material causes ionization within the insulating layer itself, raising electrons from the valence to the conduction band. Their lifetime can easily be estimated and their mobility will probably not differ very much from that in other insulating crystals ( ~ 100 em2/Vs). From this it follows that the positive potential at the surface of the ice is probably less than 10 . 3 V if one assumes that one half of the fl-particles leave the source and that each particle of the other half produces about 15 ion pairs within the insulating layer. The variable retarding voltage was derived from a well regulated and thermally insulated power supply. The almost linear variation of the voltage by 2.4 kV was obtained by the full 10 turns of a I00 k~, helipot. A 50 Hz synchronuous motor rotates the helipot at uniform speed and simultaneously operates a mechano-optical timer which divides the complete range of 2.4 kV in 100 equal intervals of 24 V with equal and constant time of passage. At the end of each interval a 2 msec signal stops the counter fed by the electronmultiplier, transfers the counts accumulated during the passage time of about 2 sec to the appropriate channel of a magnetic core memory and resets the counter for the next interval. A potential divider of high quality resistors with a ratio of about 1 : 120 delivered a fraction of the total voltage to a digital voltmeter. I11 order to avoid errors introduced by voltage dependence of the resistors, the system was calibrated absolutely

422

R . C. S A L G O A N D II. H . S T A U B

with the i s o s c h r o m a t s of the unresolved Kxlce 2 and fl3fll doublets o f M o and Z r [ref. ~3)] by a p p l y i n g the voltage to a X - r a y tube with M o and Z r anodes respectively. A single crystal calcite s p e c t r o m e t e r with a scintillation detector was set at a voltage well a b o v e the c o r r e s p o n d i n g K limit on the m a x i m u m o f the line in first o r d e r and the voltage lowered until complete d i s a p p e a r a n c e o f the r a d i a t i o n was observed. Fig. 2 shows an i s o c h r o m a t o f M o Ka o b t a i n e d in this manner. A sufficient Nd,

20 10 16

12 IO

8

6 /.

2 I

161

162

I

I

163

164

165

166

167

168

I

169

170 tl

Fig. 2. Isochromatof the Mo Kk, line. Abscissa: digital voltmeter reading U of the divided voltage V0. The full curve is calculated for a Gaussian resolution of AU == 0.99 V. TASTE 2 Line Zr K~ Mo K~

Zr K~, Mo K// shortwave limit

Energy (keV) 15.747 17.444 17.663 19.602 16.625 17.918 18.403 18.923

f 118.35 '-0.15 118.29~0.15 118.30-:0.17 118.52~0.16 118.75 -'0.20 117.96_-?:0.16 118.63 ~0.20 118.27 :- 0.19

.I,_'_o-: )r = 118.37 !:0.06 U p o r t i o n between threshold and excitation o f the line shows g o o d linearity to allow tor precise e x t r a p o l a t i o n . The r o u n d i n g oil" at the threshold can be explained by a s s u m i n g a G a u s s i a n resolution exp [-(E--Eo)Z/2A 2] with a width A = 0.117 keV

/5'-]-NERGY OF TRITIUM

423

as shown by the solid line. This value is compatible with the geometry of the Bragg spectrometer. Since the ~.~ :~, and the flail1 doublets were unresolved, the energy of the maximum of the resultant peak was assumed at E = E , , - ½ ( E = , - / z ; 2 ). The four K-lines were also used to determine the positioning of the spectrometer at the diffraction angles corresponding to short wave length limit at 4 arbitrary fixed voltages. The eight calibrations of the voltage divider gave for the ratio of the actual full voltage Vo to the reading of the digital voltmeter U the values shown in table 2. With this factor the mean value of each voltage interval was determined from its corresponding voltmeter reading. 4. Results Fig. 3 shows the energy distribution of the counts for the total of 3600 passages of the retarding potential between 17.4 and 19.85 keV after subtracting the background whose value was determined from the data between 18.80 and 19.84 keV. Due to the high background the counting rate was almost constant at about 3 • 1 0 6 N ~103 3o

20

,0 °

htJ!Jtli!!!}! t,, t t ,14ttt t iil't'ttt' ti *'t ill it' l

' I

17.5

T

,

,

,

I

18.0

,

,

,

,

l

18.5

,

,

,

,

I

19.0

~

,

,

,

I

19.5

,

,

,

T

key -V 0

Fig. 3. Recorded spectral distribution o f the fl-particles o f tritium after subtraction o f b a c k g r o u n d as determined f r o m m e a s u r e d values at Vo >- 18.75 keV. Full curve: Least-square fit o f 4th order parabola. T h e arrow m a r k s the value o f Eo.

counts per channel with a constant statistical standard error of a = +_ 1700. In order to determine the lower limit of Er, ax, the energy at which no //-particles are observed, we used an integral method rather than collecting the data of several points in groups, since the choice of their size might introduce some bias. Unless one makes the rather improbable assumption that in the fl- process a neutrino is absorbed from a sea of degenerate neutrinos rather than an antineutrino emitted,

424

It. C . S A L G O A N D I f . I t . S T A U B

Ema~ is smaller than Eo and the measured spectral distribution is a monotonically increasing function of Emax-E. Consequently we used the points with E > Eo = 18.75 keV for determining magnitude and uncertainty of the background or zero line. The values N j ( E j ) of the measured distribution were added up to define new average values,

NK = ~ t Nj_+

+zl~,

where, assuming a normal distribution as evidenced by the raw data, the statistical error is quadratically composed of the background error Ao and the error Aj of the Nj values. The -NK valucs will also increase monotonically and will differ from zero with increasing probability as E decreases. By this procedure, which is free from any assumption on extrapolation or on the spectral shape one obtains: /=max = > 18.57 keV with 80 O//oprobability, Emax _~ 18.46 keV with 90 % probability. If one assumes a normal distribution of crrors in the measurement of E o = 18.75_+ 0.11 keV in (1) one obtains for the limits of the antineutrino mass or in the case of degeneration its Fermi energy: m~,cz < 200 eV with 80 % probability, mv c2 < 320 eV with 90 ~ probability.

If this mass is actually zero, which is not contradicted by any experiment, the data of fig. 3 can be represented by an expansion in a power series of the form: N (E) = at (Co - E) + a2 (Eo - E) z + a3 (Eo -- E) a + ag(Eo - E)4 with Ema~ = E o. The fourth power is justified by the fact that the spectrometcr integrates over the energy interval from E 0 to E and that the thickness of the source varics locally and is thin or thick depending on the encrgy. As is to be expected the first coefficient a I is zero within the limits of uncertainty. The result of the least-

square fit with the parameters a l , a2, a3, a4 and Eo yields Ema, = Eo = 18.704-0.06 keV. The resultant curve is shown in fig 3. The small contribution to the uncertainty f r o m f a n d Vo are included in the error. 5. Diseussion

The present result for the upper limit of the antineutrino mass is considerably lower than the previous values of Langer and Moffat 3) and Hamilton, Alford and Gross 14) which were placed a t mvc 2 < 1 keV at 90 }~ confidence level by Daniel 15). Shortly

,S-ENERGY OF TRITIUM

425

after completion of the present work Bergkvist 16) presented a result m,,c 2 < 60 eV at 90,%o confidence level. This author also used tritium sources and a combined magnetic and electric spectrometer of high resolution and large aperture. The limit for the antineutrino mass is deduced from the deviation of the Kurie plot from a straight line. However as pointed out by Bergkvist a deviation caused by a finite neutrino mass can be seriously altered or even masked by the conditions of the source and its surface. The energy loss of the/3-particles in the material of the source is l=articularly important, if the source is very thin as in the work of Bergkvist. If the source has actually a thickness of 2 #g. cm -2 the mean energy loss might be as low as 10 to 20 eV. However due to the finiteness of the energy loss in individual collisions the spread or straggfing of the energy can be considerably larger and thereby lead effectively to a much straighter end of the Kurie plot for my > 0. The present work on the other hand is fi'ee from any assumption concerning the source and its thickness except that no appreciable amount of foreign material is deposited on it (which would actually increase the limit) and that no change of the monotonic shape of the spectral distribution is introduced by the spectrometer. As a result of this independence from assumptions the upper limit for the antineutrino mass is larger than Bergkvist's value by about a factor of five, which could perhaps be reduced to two by a further drastic reduction of the detector background. If we assume now that the four independent measurements indicate that the antineutrino mass is indeed zero we can combine the present value of Emax = Eo with that from the reaction and mass spectrometer data (1) and obtain Emax = Eo = 18.72+0.05 keV. The determinations of t h e f t value of tritium from this value of Emax can most conveniently be carried out with the exact numerical values fi'om the work of Bahcall 17) where the dependence of the f-value on Emx is given for several nuclei. A small radiative correction of + 1.5 % was added according to an estimate from K~.ll6n's work is). The most accurate value for the half-life of tritium is still that of Jones 19) viz. t = (3.8695+0.0013). l0 s s. T h e f t value for tritium is thus found to be 3H : ( f t ) = 11594-11 s. Blin-Stoyle 1) and Wilkinson 2o) have pointed out that the value of the GamowTeller matrix element IMA[2 of tritium offers a rather sensitive test for the partiall¢ conserved axial vector current hypothesis (PCAC). Whereas this matrix element is exactly 3 in the case of a single nucleon, e.g. the neutron, it would be considerably lowered in the three-particle structure of tritium. If the state of tritium is predominantly a full symmetric I2S state in Blin-Stoyle's notation, this author 2a) concludes that IM°[ 2, the matrix element without exchange contribution must be certainly smaller than 2.76 and probably even smaller than 2.70. A further and considerable modification arises from pion exchange between the nucleons. Assuming P C A C to hold

426

R. Co S A L G O A N D 1f. I t . S I ' A U B

and using the experimental values of the pion production amplitude of the reaction p + p ~ ~t+ + d , Blin-Stoyle 1) has shown that pion exchange can further change the value of [M°[ by a fraction

6 = IM~'I-M° varying from at most + 2 °/ /o to - 2 5 % depending on the values of the range parameter ,:t and the uncertainties of the constants A~ and All. Previous data zt) gave IM°l , -3.3+_0.15 and would therefore have required an enhancement of IM°I due to pion exchange of about + I0 °/o. The matrix element MA of tritium is related to its ]'t value by

ft -

2n3h 7 In 2 1 mSoC, G2vIA,IvI2q_GIIMAI2,

(2)

whcre Gv and GA are the vector (Fermi) and GA the axial vector (Gamow-Teller) coupling constants and My the vector matrix element. Conserved vector current theory requires IMvl z = 1. The quantity Gv is obtained from the pure Fermi transition 0 ÷ ~ 0 + of t 40. Its decay energy has recently bcen determined by Freeman et al. z2) from the Q-value of the reaction 14N(p, n ) t 4 0 and the measurement of the 7-ray energy of the T = 1 ~ T = 0 transition of 14N*. The decay energy is given as E o = 1809.1 + 1.5 keV. Previously Bardin et al. 23.) had found E0 from the Q-values of the reactions ~2C(3He, p)14N* and IEC(3He, n)140 and gave Eo = 1812.6+1.4 keV. Using the weighted average of the two energy determinations as 1810.9_+ 1.0 keV one obtains t h e f v a l u e again from Bahcall's ~7) calculation. The radiative correction has rccently been recalculated by Jaus 24) to be + 1.9+_0.5 %. With the half-life given by Bardin et aL 23) t = 71.36+_0.09 s one finds for t40: f t = 3117.0+ 18 s. Since MAz = 0 and Mvz = 2 one obtains G~, =

1

2rc3h7 In 2 _ (l.973+_0.11)

• 10 -98

erg 2"

cm 6

2(f0 ,-g¢" or:

Gv = (1.404-t-0.004)

x I0 -49

erg-

c m 3.

The axial vector coupling conszant is most accurately determined from the.It value of the free neutron, which has been drastically reduced by the new and more accurate value determined by Christensen el al. 25). The decay energy is 1293.56+0.07 keV from the latest measurement of the deuteron - H z [re£ 12)] mass doublet and the energy of the n-p capture 7-ray1*). The f-value of Bahcall 17) is therefore increased by 0.28 % but lowered by 0.23 % due to the not entirely negligible recoil effects and finally increased by 1.2 % for the radiative correction as estimated from K'/illdn's 18) work. With the new t-value one obtains f t = 1108.5_+16.4 s,

E-ENERGY OF TRITIUM

427

and since: [MA] 2 ~---3, [Mvl2 = 1

G]/G~

1. F2(ft) 'o 11 =

= ~ [_ i f ~

1.545.+0.028.

Putting the data into eq. (2) we can write for the matrix element ]MA] 2 of tritium in terms of t h e f t values of 3H, n and 140: IMAI2

F2_(ft)140-(ft)3H7 (ft)n = 3 1_ 2(ft)l*O-(ft)n _] (/t)3H

_ 2.844-0.06.

It is therefore definitely smaller than 3. If we assume an upper limit for IM°l z = 2.76 we find the enhancement which should be caused by mesonic exchange to be = +0.5.+].2)%

or with I M ° 1 2 = 2 . 7 0 : 6

= +(2.6+1.2)%.

Thus the large enhancement of + 10 o/ /o which was in disagreement with the predictions of PCAC theory has been strongly reduced. The main contribution stems from the much lower value of the neutron lifetime but the small but very effective increase of the tritium/~-energy has also lowered the value of IMAJ. The authors are very much indebted to Prof. G. Rasche and Dr. W. Jaus for many valuable discussions of the theoretical aspects of this work. The assistance of Dr. H. Koller, Dr. F. Zamboni and W. Auwfi.rter is gratefully acknowledged. The work has been financially supported by the Schweizerische Nationalfonds.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

R. J. Blin-Stoyle and M. Tint, Phys. Rev. 160 (1967) 803 G. I-L Jenks, F. H. Swceton and J. A. Ghormley, Phys. Rev. 80 (1950) 990 L. M. Langer and R. J. D. Moffat, Phys. Rev. 88 (1952) 689 D. P. Gregory and D. A. Landsman, Phys. Rev. 109 (1958) 2091 L. Friedman and L. G. Smith, Phys. Rev. 109 (1958) 2214 M. M. Popov, I. V. Gagarinskij, M. D. Senin, I. P. Mikhalenko and I. M. Morozov, Atom. Energ. 4 (1958) 296 F. T. Poltcr, Phys. Rev. 115 (1959) 450 W. L. Pillinger, J. J. Hentges and 3. B. Blair, Phys. Rev. 121 (1961) 232 P. E. Moreland and K. T. Bainbridge, Proc. 2nd Conf. on nuclear masses, Vienna (1963) 423 R. C. Salgo, H. H. Staub, H. Winklcr and F. Zamboni, Nucl. Phys. 53 (1964) 457 A. W. Taylor, N. Neff and J. D. King, Phys. Lett. 2AB (1967) 659 W. H. Johnso:a, M. C. Hudson, R. A. Britten and D. C. Kayser, Proc. 3rd Int. Conf. on atomic masses (1967) 793 J. A. Bearden, Rev. Mod. Phys. 39 1967) 78 D. R. Hamilton, W. P. Alford and L. Gross, Phys. Rev. 92 (1953) 1521 H. Daniel, Rev. Mod. Phys. 40 (1968) 659 K. E. Bergkvist, CERN Report 69-7 (1969) 91 J. N. Bahcall, Nucl. Phys. 75 (1966) 10 G. Kiillen, Nucl. Phys. B1 (1967) 225

428 19) 20) 21) 22)

R. C. S A L G O A N D H . H . S T A U B

W. M. Jones, Phys. Rev. 100 (1955) 124 D. H. Wilkinson, Proc. Int. Conf. on nuclear structure, Tokyo (1967) 469 R. J. Blin-Stoyle and S. Papageorgiou, Nucl. Phys. 64 (1965) 1 J. M. Freeman, J. G. Jcnkin, D. C. Robinson, G. Murray and W. E. Burcham, Phys. Lctt. 27B (1968) 156 23) R. K. Bardin, C. A. Barnes, W. A. Fowler and P. A. Seegcr, Phys. Rev. 127 (1962) 583 24) W. Jaus, Nucl. Phys. B6 (1968) 402 and private communication 25) C. J. Christensen, A. Nielsen, A. Bahnsen, W. K. Blown and B. M. Rustad, Phys. Lett. 26B (1967) 11