The parity of the 4.97 MeV level in Ne20

I I.E.I: I 2.K [

Nuclear Physics 41 (1963) 448

~60; ~ ) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

T H E P A R I T Y O F T H E 4.97 M e V L E V E L I N N e 2° H. E. GOVE, A. E. LITHERLAND and M. A. CLARK t Atomic Energy of Canada Limited, Chalk River, Ontario, Canada

Received 1 October 1962 Abstract: The parity of the level at 4.97 MeV in Ne ~° has been determined to be negative by measuring the linear polarization of 3.34 MeV gamma rays emitted when this level decays to the first excited state of Ne 2° at 1.63 MeV. The level was excited by the reaction Nea°(p, p'y) at an incident proton energy of 7.20 MeV. At this energy, the direct angular distribution of the 3.34 MeV gamma rays with respect to the proton beam was measured and was not isotropic. The linear polarization correlation was measured by the method of Compton scattering and this combined with the direct correlation established that the 4.97 MeV level had opposite parity to that of the 1.63 MeV state. Since the latter is positive, the parity of the 4.97 MeV level is negative. Previous experiments had shown that its spin is 2 and this combination of spin and parity excludes the 4.97 MeV level from participation in helium thermonuclear reactions.

1. Introduction T h e level 1) at 4.969 M e V in N e 2° lies closest to 4.753 MeV, the binding energy o f a n a l p h a particle in N e 2° (see fig. 1) a n d could therefore play a d o m i n a n t role in the f o r m a t i o n o f N e 2 o b y the reaction O t6 (5, 7)Ne 2° in stellar interiors after h y d r o g e n is exhausted if it has the right spin a n d p a r i t y c o m b i n a t i o n , eg. 0 ÷, 1 - , 2 ÷ etc. Several experiments have been a t t e m p t e d to d e t e r m i n e the spin a n d p a r i t y o f this level. I n one o f these the r e a c t i o n F19(p, ~,)Ne 2° was studied 2) at two resonances a n d it was concluded t h a t the m o s t likely assignment to the 4.97 M e V was 2 ± o r 3 ÷. M o r e recently the reaction Ne2°(p, p ' ) was e m p l o y e d to excite the 4.97 M e V level a n d coincidence correlations between 3.34 a n d 1.63 M e V g a m m a rays arising f r o m its decay t h r o u g h the first excited state o f N e 2 o were m e a s u r e d 3). The results u n a m b i g u ously indicated a spin assignment o f 2 a n d gave a q u a d r u p o l e - d i p o l e a m p l i t u d e ratio o f a b o u t 8 % for the 3.34 M e V r a d i a t i o n on the a s s u m p t i o n t h a t octupole r a d i a t i o n was negligible. I t was t e m p t i n g to conclude that this was an E 2 - M 1 mixture with positive parity for the 4.97 M e V level, particularly since this would readily p e r m i t N e 2° f o r m a t i o n b y helium t h e r m o n u c l e a r reactions 4). Recently, however, the lifetime o f this level has been m e a s u r e d 5) by the D o p p l e r shift a t t e n u a t i o n m e t h o d . It was f o u n d to be 1.9_+31o5X10 -12 sec a n d this, c o m b i n e d with the q u a d r u p o l e dipole a m p l i t u d e o f 8 % yields an E2 intensity o f only 0.15 % o f the W e i s s k o p f unit 6) if the level has positive parity. This w o u l d be the slowest E2 transition yet observed in light nuclei s), a p a r t i c u l a r l y r e m a r k a b l e result since, in this same nucleus, t w o t Now at Aerospace Corporation, Los Angeles, California. 448

449

P A R I T Y I N N ¢ g°

other E2 transitions, that between the first excited state and ground and between the second and first excited states, are enhanced by a factor s) of about 30 over the Weisskopf unit. On the other hand, if the level had negative parity the E1 and M2 transition rates would be reasonable. This would however, exclude this level from stellar helium thermonuclear reactions and the astrophysical implications of this are considerable. 9.577 9.179\

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From certain symmetry arguments also 7), it would be rather surprising to find a level of parity ( - ) J + l lying so low in energy in Ne 2°. For these reasons it was decided to make a direct measurement of the parity difference between the 4.97 and 1.63 MeV levels by using the Cornpton scattering process to determine t linear polarization of the 3.34 MeV gamma rays 8, 9). 2. Method and Apparatus For the Compton scattering method of measuring linear polarization to be effective, it is necessary to excite the level in question in such a way that the angular correlation t

See MeCallum a) for the appropriate formulae.

450

GOVe et aL

H.E.

of the gamma ray from its decay is not spherically symmetric (except in the unusual case that the spherical symmetry is a result of a particular multipole mixture). The reaction Ne2°(p, P'7) at a proton bombarding energy of about 7.2 MeV fulfils this condition 3 ) a n d was therefore chosen for the linear polarization measurements. The method employed is illustrated diagrammatically in fig. 2. The incident 7.2 MeV protons from the Chalk River tandem accelerator pass through a 6.4 x 10 -3 cm thick tantalum window into a cell filled with natural neon gas to a pressure of about 1 arm and are stopped in a gold backing. The path length is 1 cm. Gamma rays emitted vertically enter a 5.1 cm diameter by 7.6 cm long NaI(T1) crystal and are scattered through a mean angle 0 into a second crystal 7.6 em in diameter by 7.6 cm long.

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The spectrum of electrons measured in the first crystal in coincidence with voltage windows set on eight energy intervals of the spectrum of Compton scattered gamma rays measured in the second crystal was recorded in a 900-channel two dimensional pulse amplitude analyser lo). This instrument was operated in its 9 x 100 mode; the spectrum o f Compton scattered gamma rays from the second crystal in coincidence with all pulses above about 200 keV in the first crystal plus those from a Na 22 source located so that it could be seen by both crystals was displayed on the first 100 channels. Eight voltage windows were set as desired on this spectrum and pulses from electrons in the first crystal in coincidence with each of the voltage windows were displayed in the eight remaining 100 channels. To reduce the chance coincidence rate a pulse from a fast coincidence circuit i t) was also required. The second crystal which was shielded by lead from the target could be rotated about the vertical axis and measurements were made with the second crystal in the position shown in fig. 2 (N(0°)) and at right angles to the indicated position (N(90°)). In addition to the two crystals which comprised the polarimeter shown in fig. 2, a third NaI(TI) crystal 12.7 em in diameter by 10.2 em long was mounted in the horizontal plane containing the beam. It could be moved in angle about the target and was used to measure the direct correlation of the gamma rays. This angular distribution for the 3.34 MeV gamma ray, combined with the measured quadrupole-

PARITY IN Nc ~°

451

dipole amplitude ratio 3), permit the ratio N(O°)/N(90°) determined in the polarization experiment to be calculated for the cases of parity change and no parity change 9). In order to check the polarimeter alignment two other reactions were also studied. These were N14(p, p'y) Q = - 2 . 3 1 MeV and C12(p, p'~) Q = - 4 . 4 3 MeV where, in both cases, a gas target could be used, in the first case nitrogen and in the second CO2. At a proton energy of 5.15 MeV the 2.3t MeV 0 + level in N l't is strongly excited. The direct correlation of the 2.3l MeV gamma ray with respect to the incident beam is spherically symmetric and so is the polarization correlation - both, of course, as a consequence of zero spin for the emitting state. This reaction then serves to measure any asymmetries in the polarimeter. The second reaction was measured at a proton energy of 5.75 MeV where the 2 + level in C 12 at 4.43 MeV is fed strongly and where the pure E2 radiation from the decay o f this level in C 12 to the 0 + ground state has a pronounced angular correlation with respect to the incident beam. A measurement of this direct correlation combined with the known pure E2 character of the radiation permits N(O°)/N(90°) measured by the polarimeter to be predicted uniquely. 3. Experimental Results

For angles of Compton scattering between 45 ° and 70 ° and primary gamma ray energies between 2.3 and 4.4 MeV, the energy of the scattered gamma rays lies in the range 0.6 to 1.14 MeV and hence the Na 22 spectrum provides a very convenient scale on which to set gates on the scattered spectrum. The Na 22 source was located such that it could be seen by both NaI(TI) crystals in the polarimeter. The fast coincidence circuit was arranged so that all pulses above about 200 keVproduce a fast coincidence pulse and the bottom group o f 100 channels in the two-dimensional pulse-height analyser was arranged to record the spectrum from the second crystal in coincidence with all fast coincidence pulses. In each case then, this spectrum is essentially that of Na 22. Fig. 3 shows the 9tXl-channel display from the polarimeter obtained from the reaction N14(p, p'y) at Ep = 5.15 MeV. The polarimeter angle in this case is 90 °. The bottom spectrum has been described above, and the eight gates set on the spectrum of scattered gamma rays are shown shaded. The next eight 100-channel spectra from the bottom to the top are electron spectra from the first crystal in coincidence with each of the gates from left to right and also in coincidence with pulses from the fast coincidence circuit. In the first two of these, one can see two high energy peaks due to 2.31 MeW gamma rays producing positon-electron pairs in the first crystal followed by annihilation quanta of 0.51 MeV entering the second crystal. The situation is complicated by the fact that gates on the bottom spectrum set on the 0.51 MeV peak also produce pulses of 1.28 MeV energy in the second crystal from the Na 22 source. As the gates move above the 0.51 MeV peak, however, the true electron spectrum from Compton scattering of 2.31 MeV gamma rays appears. As the gate moves

452

n . E . GOVE e t al.

higher in energy on the spectrum of scattered gamma rays the electron peak moves lower in energy in accordance with the Compton scattering energy relationship. In effect what one is doing is selecting different mean scattering angles which are permitted by the finite size of the two counters and, in each case, the angle is indicated beside each spectrum. A 0.51 MeV peak appears as well in each of the electron spectra 1.33

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Fig. 3. The 900-channel pulse amplitude analyser display from the polarimeter for the reaction N~4(p, p'y), E r = 2.31 MeV, F~ = 5.15 MeV. The second crystal is located at 90 ° to the reaction plane. The bottom spectlum displays pulses from the second crystal gated by all fast coincidences. The next 8 spectra are from the first crystal in coincidence with the 8 gates shown on the bottom spectrum. The top 7 spectra are labelled with the equivalent Compton scattering angle as described in the text,

and is due to coincidences between 1.28 and 0.51 MeV gamma rays from Na 22. In the analysis of the data, the area under each electron peak was measured at 0 ° and 90 ° and the ratio calculated. It was found in the case o f N 14 that this ratio varied smoothly as a function of Compton scattering angle by about 40 ~o from one extreme to the other. The results for C 12 and N e z ° were then corrected for this variation. The variation was presumably due to inaccurate alignment to the polarimeter.

PARITY

IN

453

N e 20

Fig. 4 shows similar results for the reaction C12(p, P'7) at a proton energy of 5.75 MeV and a polarimeter angle of 90 °. Again the bottom spectrum is that from the second crystal in coincidence with all fast pulses. This spectrum was gated as before except now, due to slightly lower gain for the second crystal, the first gate encompasses the 0.51 MeV peak. In the second spectrum from the bottom (pulses from the 800

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Fig. 4. The 900-channel pulse amplitude analyser display from the pom~imeter for the reaction C'2(P, P'7), Er = 4.43 MeV, Ep = 5.75 MeV. The second crystal is located at 90 ° to the reaction plane. See caption to fig. 3 for description of spectra.

first crystal in coincidence with the first gate) one can now clearly see the two peaks from a 4.43 MeV gamma ray entering the first crystal and producing positon-electron pairs. Gamma rays from the positon annihilation escape and enter the second crystal producing, in the coincidence spectrum, the so-called single and double escape peaks. The remaining spectra show, as before, the electron peak from the Compton scattering which gradually decreases in energy as the gate on the spectrum in the second crystal is moved higher in energy. The ratio N(O°)/N(90 °) was calculated for various values of the Compton scattering angle and then corrected for instrumental asymmetry by dividing by the ratios found from nitrogen discussed previously.

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Fig. 5 shows the results for the reaction Ne2°(p, p'y) at a proton energy of 7.20 MeV and a polarimeter angle of 0 °. The gates on the spectrum from the second crystal were set the same as for the carbon case and again the single and double escape peak from the 3.34 MeV g a m m a rays is observed in the second spectrum from the bottom. The spectra following this show the electron peak due to Compton scattering

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Fig. 5. The 900--channel pulse amplitude analyser display from the polarimeter for the reaction N e ~ , p'~), E~ = 3.34 MeV and 1.63 MeV, Ep = 7.2(I Me"/. The second crystal is located in the reaction plane. See caption to fig. 3 for description of spectra.

of the 3.34 MeV g a m m a rays ranging in energy from 2.63 to 2.20 MeV as well as the electron peak from C o m p t o n scattering of 1.63 MeV g a m m a rays ranging in energy from 0.94 to 0.73 MeV after which it gets obscured by the 0.51 MeV g a m m a ray peak from N a 22. This 1.63 MeV g a m m a ray results from inelastic proton scattering from the first excited state in Ne 2°. The energy of this peak in the electron spectrum is given by Eelectron 1.63

l'63--(3"34--Ea.aa ); electron

=

PARITY IN Ne 2°

455

the observed energies correspond reasonably well to this relationship. Again the ratio N(O°)/N(90°) was calculated at the various Compton scattering angles and then divided by the corresponding ratio for nitrogen. The direct angular correlations of the gamma rays with respect to the incident proton beam were measured for both the 4.43 MeV gamma my from C12(p, p'~) ,

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456

et al.

n.E. o o w

T h e p o l a r i z a t i o n results are s h o w n in fig. 8 for n e o n a n d c a r b o n corrected b y the nitrogen results. I n fig. 8, the r a t i o N(O°)/N(90 °) is p l o t t e d against the C o m p t o n scattering angle. This process o f n o r m a l i z i n g b y the n i t r o g e n d a t a u n f o r t u n a t e l y increases the statistical errors on the points. I n general the extreme C o m p t o n scattering angles are o m i t t e d since they m u s t c o r r e s p o n d to scattering near the edges o f the crystals a n d are p r o b a b l y n o t very reliable.

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Fig. 8. Results of the polarization measurement for the 4.43 MeV level in C 12 and the 4.97 MeV level in Ne 2°. The ratio of coincidence counts in the first crystal when the second crystal is in the reaction plane N(0 °) to that when it is at right angles to the reaction plane N(90 °) is plotted against the effective Compton scattering angle 0. The solid and dashed curvcs are predicted values calculated as described in the text.

4. T h e o r y and C o m p a r i s o n with E x p e r i m e n t

T h e simplest case to analyse is that for c a r b o n since the g a m m a r a d i a t i o n is pure E2. I t can be shown 12) t h a t the ratio N(O°)/N(90 °) is given b y

N ( 0 ° ) / N ( 9 0 o) -

PS+ 1 P+S

w h e r e S is the ratio o f the intensity o f C o m p t o n scattered r a d i a t i o n parallel to the electric vector o f the incident r a d i a t i o n to that p e r p e n d i c u l a r to the electric vector. It is a function o n l y o f the C o m p t o n scattering process a n d d e p e n d s b o t h on the g a m m a r a y energy a n d the angle o f C o m p t o n scattering la). F o r a pure electric

PARITY

457

1N N e ~

quadrupole radiation emitted at 90 ° to the beam direction, P is given by p_

l+a2+a4

1-2a2-¼a4 ' where a2 and a 4 are the coefficients o f the Legendre polynomials describing the direct correlation o f the g a m m a ray with respect to the incident beam

W(O) =

1 + a2 P2(cos 0)-b a 4 P4(cos 0).

I f the radiation were magnetic, P would be given by the inverse o f the above expression. Using the measured values o f a2 and a4 for the c a r b o n case * and the k n o w n variation o f S with C o m p t o n scattering angle the quantity N(O°)/N(90 °) can be calculated and the results are s h o w n as the dashed lines on fig. 7. The agreement with experiment is reasonably g o o d and confirms the positive parity assignment for the 4.43 MeV level in C 12. In the case o f the transition between the 4.97 and 1.63 MeV states in Ne 2°, the situation is complicated by the occurrence o f a quadrupole-dipole mixture in the 3.34 MeV radiation and it is, therefore, m o r e convenient to use the expressions quoted by M c Callum 9). In what follows, it will be assumed that one is dealing with a g a m m a ray emitted from a single initial state o f total angular m o m e n t u m J to a single final state o f total angular m o m e n t u m L It will further be assumed that the radiation contains only quadrupole-dipole mixtures and that the intensity o f the quadrupole to dipole is less than 10%. This latter condition is k n o w n to be fulfilled 3). Under these conditions, the quantity P for a g a m m a ray emitted at 90 ° to the beam direction when there is no parity change between initial and final states is given by (-)'-'(2J+

(p20~ { Z t ( 1 J 1 J ' 1 2 ) + 2 d Z l ( | J 2 J , I2)} 1)½ - \~--~]

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(p20~ Z,(1JIJ, (--)J-z(2J+1)½+2 \~--~]

I2)

where 6 is the amplitude ratio o f quadrupole to dipole for the g a m m a radiation **, Z 1 is a coefficient defined and tabulated by Sharp et aL 14) and given by M c C a l l u m 9). It is related to the F coefficients o f Ferentz and Rosenzweig is) as discussed by Biedenharn 16). The statistical tensor pko which describes the orientation o f the g a m m a t The correct procedure for taking finite solid angle into account is to first correct the direct angular distribution coefficients appropriately for the geometry and crystal size employed in this measurement to yield the values for an infinitely small solid angle (in this case the attenuation factors were J~]Jo= 0.95 and ldJo = 0.87) and then to apply to these corrected coefficients the attenuation factors appropriate to the geometrical arrangement of the polarimeter. This latter calculation is a difficult one to make and has been ignored on the grounds that the first crystal of the polarimeter subtends a rather small solid angle at the target. This may account for the small disagreement between theory and experiment shown in fig. 7. t* The sign of ~ differs from that of McCallum ~) but is the same as that used by Litherland and Ferguson xs).

458

n. ~. c o v e et aL

ermtting state may be expressed in terms of the populations of the magnetic substates of the initial state 9) j. If there is a parity change between the initial and final states then the expression for P(90 °) is just the inverse of that given above. As before the measured ratio N(O°)/N(90 °) is given by (PS+ 1)/(P+S). Similarly the direct angular correlation of the gamma ray with respect to the incident beam is given by

W(O) = ( - y-'(zl +

p20 {Z,(IJIJ, 12)-26Z,(IJZI, 12)}P2(cos0),

where all the quantities are defined above. The equations for 147(0)and P(90 °) can be solved simultaneously for the quantities p20/pO0 and 6 for both parity change and no parity change and they can be compared with those obtained previously 3) at a proton bombarding energy of 7.15 MeV. The results are shown in table 1. This clearly eliminates the possibility that the parity of the TABLE 1 Comparison between p20/t~)O and 6 obtained in this experiment for the 4.97 MeV level in Ne 2° assuming no parity change and parity change and the values obtained by Broude and Gore 3) at a slightly lower bombarding energy Experiment present present B~oude and Gove s)

Parity change no yes

p20]pO0

q- 0.17 -- 0.43 --0.77

6 + 1.2 q- 0.02 +0.08

4.97 and 1.63 MeV states is the same since all the experimental evidence shows that dipole radiation is overwhelmingly dominant in the 3.37 MeV radiation. An amplitude ratio of quadrupole to dipole 6 equal to 1.2 is also inconsistent with the approximations employed for W(O) and P(90°). If it is assumed, however, that the parity of the two levels is different the results of this experiment at Ep = 7.2 MeV and the previous measurements of Broude and Gove 3) at 7.15 MeV are compatible. In both eases, a very small positive 6 is observed and this, of course, should not depend on bombarding energy. The value obtained in the present experiments however, is less accurate than that obtained previously 3). The statistical tensors, on the other hand, depend in an unpredictable way on the bombarding energy and it is not too surprising that they are different. The predicted curves for Ne 2° shown on fig. 8 are calculated in a somewhat different fashion. The value for 6 = 0.08 obtained previously 3) was assumed and the above equation for I4/(0) was solved for p20/pO0 using the value of a2/ao obtained from the direct angular correlation measured in this experiment. These values for 6 and p20/pO0 (the value obtained in this way for p20/pO0 w a s - 0 . 5 6 ) were then substituted in the equation for P(90 °) and from this the predicted N(O°)/N(90 °) was

PAXr~I IN N¢~

459

obtained. Again it is very clear that the parity of the 4.97 and 1.63 MeV levels in Ne 2° must be different. The results of the present experiment show conclusively that the first excited state o f C 12 at 4.43 MeV has the same parity as the ground state and the 4.97 MeV level in Ne 2° has the opposite parity from the first excited state. 5. Discussion

In the course of measuring the lifetimes of the 1.63, 4.25 and 4.97 MeV levels in Ne2 o by the Doppler shift attenuation method s), the coincidence correlation between alpha panicles detected at 0 ° to the b e a m and g a m m a rays from the reaction C 12 (C12~?)Ne 2° was also measured 17). These correlations are particularly easy to interpret la) since three of the particles involved have spin and parity 0 + and all the particles move along the beam axis. The measurements established spin and parity of 2 + and 4 +, respectively, for the 1.63 and 4.25 MeV states. The results for the 4.97 MeV level, however, could not be fitted by assuming 2 + for the level. It was then realized 19) that if the level had parity (--)~+I no alpha particles from the C 12(C12~) Ne 2° reaction could be emitted at 0 °. The fact that they were observed however, was due to the finite solid angle of the particle detector. When this fact was taken into account an unambiguous assignment of 2 - to the 4.97 MeV level could be made 17). In point of fact however, the parity assignment ( - ) J + l had already been established by measurements 2o) of the angular distributions of the alpha particles to the 4.97 MeV level from this same reaction at a number of incident C 12 energies where it was observed that a pronounced minimum in intensity of the emitted alpha group at 0 ° occurred at all energies. When one considers the above evidence along with the previous 3) spin assignment of 2 and the results of the present experiment it appears that a spin and parity assignment of 2 - for the 4.97 MeV level in Ne 2° is incontrovertible. The astrophysical consequences of this as regards the production of neon in stars by the helium thermonuclear process have been discussed 2~). In summary it is concluded that the stellar temperatures required to form Ne 2° by the reaction 016 (~, 7) via the levels at 5.631 and 5.80 MeV which have parity 22) ( _ ) J are above 5 x I0 a °K and such temperatures imply 2s) supernova explosions. The beta decay of F ~9 proceeds only to the 1.63 MeV J = 2 + level t in Ne 2° with a log f i of 4.99. The fl-? angular correlation indicates 25, 26) a spin and parity o f 2 + for the ground state of F 2°. The l o g f t for the fl decay to the ground state of Ne 2° is greater than 9 while that to the level at 4.97 MeV is greater than 6.5. This latter result would be difficult to understand if the spin and parity of the 4.97 MeV level were 2 + but is quite compatible with the assignment of 2 - . Recently Peaslee 7) has estimated the position of the first 2 - level in Ne 2° from general considerations of maximal space symmetry as well as on the basis of three t See Ajzenberg-Selove and Lauritsen ~4) for references.

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H. ~. ~OVE e t aL

models; the extreme hydrodynamic model, the alpha-particle model and the shell model and concludes that it should not occur below about 7 MeV. He contends that the observation of a 2 - level at 4.97 MeV means that the simple qualitative picture of an approximate Serber force in nuclei is inadequate. Finally it should be noted that t h e present information about spins and parities of some fifteen levels in Ne 2° lying between the ground state and about 9 MeV leads to an interpretation in terms of rotational bands 27). References 1) 2) 3) 4) 5) 6) 7) 8) 9)

10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27)

W. W. Buechner and A. Sperduto, Phys. Rev. 106 (1957) 1008 H. E. Gove, A. E. Litherland and A. J. Ferguson, Phys. Rev. 124 (1961) 1944 C. Broude and H. E. Gove, to be published E. E. Salpeter, Phys. Rev. 107 (1957) 516; A. G. W. Cameron, Chalk River Report CRL-41 (AECL No. 454) (June 1957) M. A. Clark, H. E. Gore and A. E. Litberland, Can. J. Phys. 39 (1961) 1241 D. H. Wilkinson, in'Nuclear spectroscopy, Part B, ed. by F. Ajzenberg-Selove (Academic Press, New York, 1960) D. C. Peaslee, private communication A. E. Litherland and H. E. Gove, Can. J. Phys. 39 (1961) 471 G.J. McCallum, Phys. Rev. 123 (1961) 568; S. Devons and L. J. B. Goldfarb, in Handbuch der Physik, Vol. XII/(Springer-Verlag, Berlin, 1957) p. 326 T. K. Alexander and L. B. Robinson, Nucleonics 20 (5) (1962) 70 R. E. Bell, R. L. Graham and H. E. Petch, Can. J. Phys. 30 (1952) 35 H. E. Gove and A. E. Litherland, in Nuclear spectroscopy, Part A, ed. by F. Ajzenberg-Selove (Academic Press, New York, 1960) R. D. Evans, The atomic nucleus (MeGraw-HiU Book Co., NewYork, 1955) chapt. 23, eq. (2.3) W. T. Sharp, J. M. Kennedy, B. J. Sears and G. M. Hoyle, Chalk River Report CRT 556 (1954) M. Ferentz and N. Rosenzweig, Argonne National Laboratory Report ANL 5234 (1953) L.C. Biedenharn, in Nuclear spectroscopy, Part B, ed. by F. Ajzenberg-Selove (Academic Press, New York, 1960) H. E. Gove, A. E. Litherland and M. A. Clark, Can. J. Phys. 39 (1961) 1243 A. E. Litherland and A. J. Ferguson, Can. J. Phys. 39 (1961) 788 A. E. Litherland, Can. J. Phys. 39 (1961) 1245 E. Almqvist, D. A. Bromley, J. A. Kuehner and B. Whalen, to be publisl~ed H. E. Gore, A. E. Litberland and M. A. Clark, Nature 191 (1961) 1381 J. A. Kuehner, Phys. Roy. 125 (1962) 1650 A. G. W. Cameron, private communication F. Ajzenberg-Selove and T. Lauritsen, Nuclear Physics 11 (1959) 1 F. Boehm, V. Soergel and B. Stech, Phys. Rev. Lett. I (1958) 77 M. Gell-Mann, Phys. Roy. 111 (1958) 362 A. E. Litherland, J. A. Kuehner, H. E. Gore, M. A. Clark and E. Almqvist, Phys. Rev. Lett. 7 (1961) 98