Alpha spectra from the decays of Li8 and B8

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2-C

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Nuclear Phys,cs 15 (1960) 6 2 6 - - 6 3 5 , ( ~ North-Holland Pubhsh:ng Co, Amsterdam

Not to

ALPHA

be reproduced by photopnnt or n~crofflm

SPECTRA B

FROM J

FARMERI

THE

w~thout written ~

DECAYS

o n

from the pubhsher

O F Li s A N D

Bs

a n d C M CLASS

The Rzce Institute, Houston, Texas t t R e c e i v e d 7 D e c e m b e r 1959

Abstract:

T h e s p e c t r a of a l p h a p a r t i c l e s a c c o m p a n y i n g t h e d l s s o c l a t m n of B e s, f o l l o w m g t h e b e t a d e c a y s of LI s a n d B s, h a v e b e e n m e a s u r e d T h e s p e c t r a were f o u n d to be e s s e n t i a l l y l d e n t m a l , c o n f i r m i n g t h e e x p e c t e d s y m m e t r y m t h e d e c a y s c h e m e s of L1s a n d B s T h e s p e c t r u m a s s o c i a t e d w i t h t h e d e c a y of L1s h a s b e e n c o m p a r e d w i t h t h a t g i v e n b y t h e m o d f f m d single level of W h e e l e r T h e s p e c t r u m is n o t a d e q u a t e l y a c c o u n t e d for b y t l n s f o r m u l a ff c u r r e n t v a l u e s of t h e p a r a m e t e r s a r e u s e d to describe t h e 2 + a n d 4 + levels a t 2 9 a n d 11 7 M e V m Be s w h i c h a r e a s s u m e d to b e p a r t i c i p a t i n g A n a l t e r n a t i v e d e s c r i p t i o n of t h e a l p h a s p e c t r u m , r e v o l v i n g o n l y t h e 2 + levels m Be s a t 2 9 a n d 16 7 MeV, h a s b e e n g i v e n r e c e n t l y b y B l e d e n h a r n a n d Grlffy T h e i r e x p r e s s m n s a r e f o u n d to be m a g r e e m e n t w i t h t h e d a t a o v e r a n e n e r g y r a n g e of m o r e t h a n 10 MeV, a n d h e n c e m a y b e t a k e n as t h e p r e f e r r e d d e s c r i p t i o n of t h e process

1. I n t r o d u c t i o n

The ground states of the mirror nuclei Li* and B s are the T, = ± 1 members of the isobaric spin triad of mass number eight, and are expected to decay symmetrically to the same final states in Be s. The evidence available hitherto from the beta decay of Li 8 has indicated that less than 1 ~/o of the transitions go to the ground state of Be 8, that about 90 ~/o of the transitions occur to the broad 2+, T = 0 level located at 2.9 MeV, and the remainder are to unidentified levels at an excitation energy in Be s of 10 MeV or more 1). The broad level in Be 8 at 2.9 MeV is particularly interesting since it dissociates into alpha particles which are distributed in energy up to about 7 MeV *). The efforts to account theoretically for the shape of this continuous alpha spectrum have not met with very much success 3), although, to be sure, a plausible empirical modification of the expression of Wheeler reproduces the trends in the data for alpha energies up to about 3 MeV reasonably well. At higher energies, however, the expression accounts for only a fraction of the observed yield. In the past, conclusions regarding the adequacy of the modified Wheeler formula over the entire range of energy could not be drawn because of the uncertainty as to the number and location of higher lying states in Be 8, I :Now w i t h t h e C h a n c e - V o u g h t A~rcraft C o m p a n y , Dallas, T e x a s . t i S u p p o r t e d in p a r t b y t h e U S A t o m i c E n e r g y C o m m l s m o n 626

ALPHA

SPECTRA

FROM

THE

DECAYS

OF

LI 8 A N D

B8

6~7

which might be contributing to the alpha yield. This uncertainty has been removed b y recent investigations on the basis of which it is known that only one level occurs in the relevant region of the Be 8 spectrum at 11.7 MeV having a spin of 4+ 4) With this in mind, how to account for the higher energy portion of the alpha distribution in terms of the Wheeler formulation becomes quite perplexing, since beta transitions to the 4+ state are second forbidden 4) so that few, if any, alpha particles should be contributed b y this state. Recently the problem of the continuous alpha spectrum has been re-examined b y Grlffy and Biedenharn6). They have obtained an expression for the alpha distribution b y making use of the d-wave phase shifts, obtained from alpha-alpha scattering, to more precisely characterize the 2+ level at 2.9 MeV. On the basis of this semiempirical approach, an essentially satisfactory fit to the data over the entire energy range is achieved, which requires only an additional minor contribution of alpha particles from the 2+, T = 1 state at 16.7 MeV to be exact This agreement will be illustrated in the following discussion with data obtained in the present work. For comparison, an analyms based on the formula of Wheeler will also be shown. It is a common feature of all theories for the continuous spectrum that the alpha intensity is proportional to (Q--2E~) 5 where Q is the total disintegration energy and E~ is the energy of the alpha particle. Since the Q values differ in the cases of L1s and B 8 b y almost 1 MeV, the two spectra will be expected to have somewhat different trends with energy. The possibility of an additional difference between the two spectra arises from the fact that B 8 is energetically allowed to decay to the mirror T ---- 1 level in Be 8 at 16.7 MeV. Even though this transition is strongly unfavoured because of the small energy difference ( ~ 300 keV) and the break-up of the state into two alphas xs inhibited b y the isobaric spin selection rule, a small contribution to the yield of alphas might still be expected, because of the large matrix element for a super-allowed beta transition. To investigate these questions, the alpha spectra from both decays were obtained over as wide an energy range as possible. While the measurement of the continuous alpha spectrum is a classic problem, repeatedly investigated when associated with the beta decay of Li 8, the spectrum accompanying the positon decay of B 8 has been measured only once e), no doubt owing to the inability to make B 8 conveniently. This situation was remedied recently when He 3 became commonly available, since B 8is readily made b y means of the He 3 (L1e, n) reaction at bombarding energies of 3 MeV or more With the availability of B 8, it is now possible to compare the alpha spectra from the two modes of decay with much improved accuracy. From the experimental point of view, this comparison is greatly aided b y the use of a scintillation counter together wlth a multi-channel analyzer which enable all parts of the spectrum to be recorded simultaneously under Identical conditions.

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B. J

F A R M E R AND C. M

CLASS

2. Experimental Methods The alpha spectra were obtained with a crystal scintillation spectrometer consisting of a 5 mil thick CsI (TII) crystal detector attached to a DuMont 6363 photomultiplier tube used in conjunction with a 256-channel pulse-height analyzer. The spectrometer was inserted into a port in the target chamber so as to view the target at 90 ° with respect to the direction of the beam. In order to avoid the interference from competing reactions, advantage was taken of the approximately 0.8 second half lives of B s and Li 8 to observe the alpha particles with the beam off the target. To accomplish this both the counter and the beam from the accelerator were pulsed at the convenient frequency of 5 cycles per second. The pulsing was controlled by a variable frequency oscillator which drove two square wave-forming circuits. One square wave output switched the voltage applied across a set of beam deflection plates between 2 and 6 kV. The former voltage deflected the charged part of the beam onto the target in oorrder to e l i m i n a t e ~ h e small neutral portion of the beam as a possible source of background. The' latter voltage deflected the beam off the target and onto a tantalum beam stop for the counting portion of the cycle. The second square wave output was used to control a gate circuit for the photomultiplier tube. This gate was phased with respect to the deflection of the beam such that counting commenced approximately 10 milliseconds after the beam was off the target and ended approximately 10 milliseconds before it was deflected back on. The photomultiplier tube switching was accomplished by reversing the voltage on the focus electrode with respect to the photo-cathode. This method, winch has been discussed in the literature ~), served not only to inhibit counting during the beam-on portion of the cycle but also to prevent 'fatiguing' of the photo-cathode and dynodes resulting from the high intensity of particles, incident on the crystal during the 'beam-on' period. The background caused by delayed beta and gamma activity in the target, was reduced by the use of a thin CsI(TlI) crystal. The remaining background was significant only for pulse heights corresponding to alpha particle energies of less than 1.5 MeV and was allowed for by subtracting from the gross spectrum the yield obtained when the alphas were screened out by a thin foil of Ni interposed between the counter and crystal. In the case of the B s spectrum, due to the relatively lower yield of alphas, the background subtraction was more sensitive to the running conditions and not as reliable as in the case of Li s. The response of a CsI(TII) crystal is not a linear function of alpha particle energy so that it was necessary to obtain a calibration curve. The points for this curve, giving pulse height as a function of alpha energy as shown in fig. 1, were obtained at 5 MeV and less by elastically scattering alpha particles from a thin layer of gold evaporated on a VYNS film s). The points at 6.05 and 8.78 MeV were obtained with a T h ( B + C + C " ) source. When the calibration curve

ALPHA

SPECTRA

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THE

DECAYS

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LI 8 AND

B8

629

was used subsequently to assign energies to the alphas from Be 8, the pulse height scale was normalized to the check points obtained with the thorium source measured with the counter operating in the pulsed mode. Two additional check points at 3.92 and 7.21 MeV were obteuned b y placing a 3 4 mg/cm * aluminium foil between the source and the crystal 9).

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Fig. l. The relative pulse height as a function of energy for alpha particles mczdent on a 5 roll ttnck CsI(TII) crystal

The reactions used to produce the B 8 and Li 8 nuclei were Lie(He 3, n) and LiT(d, p), respectively. The target material for the former reaction was metallic hthium enriched to 96 % in Li e and that for the latter reaction was natural lithium metal. The targets were prepared in identical fashion b y evaporating the metal onto thin (m 200/~g/cm 2) carbon foils while in place in the reaction chamber. Under the conditions of the evaporation, the lithium layers deposited were partially oxidized. The thicknesses of the targets were measured with the aid of the scintillation spectrometer b y means of deuterons e]~s-tically scattered from the carbon backing. The position of the well resolved elastic peak was determined before evaporation with the target oriented at 45 ° to the direction of the beam. After evaporating the lithium, the target again was positioned at 45 ° to the beam but so arranged that the lithium was on the back side of the foil with respect to the beam and facing the scintillation crystal Then the scattering was repeated and from the shift of the peak due to the absorption of energy b y the lithium and/or lithium oxide layer, it was possible to calculate the thickness of this layer using the experimentally determined stopping

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CLASS

power for deuterons 10) To check the result from this measurement, the thickness was also estimated from the yield of deuterons elastically scattered from the lithium, assuming the Rutherford scattering cross-section and making use of the known solid angle of the detector. The values of the thicknesses obtained in this manner agreed satisfactorily with those obtained with the above method when the uncertainties in the scattering cross-section and the target composition were taken into account. The target thicknesses used when observing the alpha spectra ranged from 300 to 500 (+50)/~g/cm ~.

3. R e s u l t s

The spectra of alpha particles accompanying the decays of B s and Li s are displayed in fig. 2. The distribution associated with the Li s decay contains on !

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Fxg. 2. The energy spectra of alpha partmles from the LlS(fl-)BeS(~)~ and BS(~+)BeS(~)~ decays. Note t h a t the intenmty scale IS loganthmm The upper curve, to which the B s data has been normalized at 3 MeV, was calculated from the best fit to the L # data with the md of eq (4).

the order of 2 × 105 alpha particle counts while that associated with the B 8 decay contains about 2 × 10~ counts. Both distributions have been observed several times with substantially the same results. The smaller number of counts in the B s alpha spectrum is due partly to the small cross section of the (He 3, n) reaction at convenient bombarding energies, and partly to the loss of many alpha particles because the parent B s nuclei were ejected from the target due to the large recoil momenta imparted b y incident He 8 beam. The spectra have been corrected for small distortions which result from (1) the finite target thickness, (2) the dissociation of the Be 8 nucleus in flight, the motion here

ALPHA SPECTRA FROM THE DECAYS OF LI8 AND B8

631

resulting from the recoil momentum imparted b y the beta and neutlano in the preceding decay, and (3) the effect of counter resolution. The correction to the spectrum arising from the finite target thickness takes two effects into account: (a) a shift in the observed energy to compensate for the energy loss of the alpha particles emerging from some average depth within the target and (b) the spread in energy about the mean value due to alphas originating at various depths within the target. The corrections for both of these effects were relatively small except at the lower energies because in the counting arrangement used the alphas needed to traverse only the thin lithium target layer. Indeed, the effective thickness of the layer to the alphas was further reduced in accord with the dynamics of the recotling nuclei, which required that these nuclei either come to rest in a surface layer or be ejected from the target altogether. B y taking into account the measured thicknesses of the targets, the average recoil energies of the Li s and B 8 nuclei, and avaalable range-energy data for lithium nuclei n), it was estimated that the alphas in both the spectra penetrated on the average about 150 #g of material. The corresponding energy losses for various energy alpha particles are given in table 1. TABLE 1 Corrections to a l p h a spectra E a (MeV) T a r g e t correction E n e r g y shift (MeV) E n e r g y b r o a d e n i n g (MeV) Betn~-neutrmo b r o a d e n i n g (MeV) C o u n t e r b r o a d e n i n g (MeV) A E (R M S. e n e r g y b r o a d e n i n g in MeV) Change in ordinate, eq (2)

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013 0 10 0 14 0 20 0 22

0 0 0 0 0

16 13 14 13 23

+16%

-05%

10 08 10 27 30

-09%

These losses have been determined from an experimental stopping power curve extrapolated to low energies on the basis of other complete curves lo). The inaccuracy of the stopping power obtained in this w a y for the lower energy alphas causes about a 15 % uncertainty in the energy for a 1 MeV alpha. The spread in the energy of the alphas due to production at different depths in the target layer was also estimated in the same manner. This spread effectively reduced the intrinsic counter resolution and was applied with the counter resolution correction. The magnitude of this effect is also indicated In table 1 for various alpha particle energies. The Li 8 and B s nuclei are at rest when their beta decays occur; however, the recoil momentum of the beta and neutrino sets the residual Be 8 nucleus in motion. Due to the extremely short life-times of the states in Be s, the dissociation of the nucleus occurs while it is in flight cansmg a slight shift in the

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energies of the alphas. The resulting distortion to the spectrum has been calculated by Frost and Hanna 2) and may be described in terms of a loss of energy resolution. It was thus possible to include this effect also in the counter resolution correction. The magnitude of this energy broadening is given in table 1 for several energies. The true counter resolution was determined from the calibration data. The resolution at the 8.78 MeV was 3.7 % and was found to follow closely the familiar E-½ energy dependence observed with such crystal spectrometers. The magnitude of this energy broadening is included in table 1 for several energies. Also included in the table are the root-mean-square values of all three broadening effects. The resolution correction was applied by a method which involves the fitting of the experimental curve by analytical expressions z2). The expression for the true undistorted spectrum T(E=) is related to the experimental curve S(E=) by the following integral equation

S(E'=) = f o T(E=)R(E=, E'=)dE=

(1)

where R (E~,, E'~,) is the resolution function. If the resolution function is assumed to be Gaussian, the undistorted spectrum is given by

d~S(E'=) 4

(2)

where AE',, is the width of the resolution function at half maximum. Although the uncertainties were considerable in estimating the magnitudes of the individual contributions to the energy broadening, the resulting correction to 5

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F i g 3 L o g a m t h m l c p l o t of t h e c u r v e s for t h e L # ( ~ - ) B e S ( ¢ ) c t s p e c t r a of v a r z o u s a u t h o r s . R = R u m b a u g h , R o b e r t s , a n d H a f s t a d , F = p r e s e n t a u t h o r s , B = B u n n e r a a/., a n d F H = F r o s t a n d H a n n a T h e c u r v e s h a v e b e e n s h x f t e d v e r t i c a l l y (or c o n v e n i e n c e o( d i s p l a y .

ALPHA SPECTRA FROM THE DECAYS OF L18 AND B 8

633

the spectrum shape was small, as is indicated in table 1. The corrected spectra from both the Li s and B s decays are shown in fig. 2. Fig. 3 shows the results of the present work on Li s, denoted b y F, compared to those of Bonnet et al. (B), Frost and H a n n a (FH), and Rumbaugh et al. (R)2). 4. D i s c u s s i o n

Under the assumption that the beta decay and alpha dissocmtlon are two very close b u t separate events as opposed to a four-body dissociation of two alphas, a beta, and a neutrino, the alpha spectrum resulting from the population of a single level in Be s has been given b y Wheeler 3) and modxfled b y Bonner et al. 2) through the inclusion of a penetrability factor. The resulting expression for the number of alphas N~ as a function of dissociation energy 2E~ is

(Q--2E~)s

N~dE. = [(2E~--Egs)--Eo]~+~-/"2P,dE~

(3)

where Q is the relevant disintegration energy, E 0 is the energy of the level in Be s, Es~ is the excitation energy of the ground state of Be s (94 keV), F is the wadth of the level in Be s, and P l is the penetrability of one alpha in the field of another. The first step an the analysas of the spectra was a test of the (Q--2E~) 5 dependence *. Since the parameters in the denominator of eq. (3) and Pz concern only Be s, they will be the same for both the Li s and B s decay schemes, giving for the intensity ratio of the spectra

LQL,a--2E~I

(4)

The test of this expression is displayed with the data in fig. 2. The hne through the Li a data represents the best fit while the line through the B s data was obtained b y multiplying the orchnates of the lower curve b y the ratio given m eq. (4). It is seen that the calculated upper curve agrees well with the data except possibly at the high energy end where the counting statistics are poor. The adequacy of the fit tends to confirm the expectation that apart from an energy dependent factor the alpha spectra obtained from the decays of B s and Li s should be identical. Equation (3) was next evaluated for the L1s decay assuming only the first excited state m Be 8 to be participating and using for values of the level parat As m e n t l o n e d a b o v e , a n y e x p r e s s i o n d e s c r i b i n g t h e d m t r l b u t l o n m e n e r g y of t h e a l p h a s m u s t contaan a f a c t o r ( Q - 2 E ~ ) 6 to t a k e i n t o a c c o u n t t h e d e n s i t y of e l e c t r o n - n e u t r i n o s t a t e s m t h e f i n a l s y s t e m as r e q m r e d b y t h e t h e o r y of b e t a d e c a y T h e d m c u s s l o n m t h i s p a r a g r a p h m, t h e n , rodep e n d e n t of t h e p a r t m u l a r form of t h e e x p r e s s m n for N ~ d E ~

634

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meters those obtained from alpha-alpha scattering experiments 4). The result of this calculation is shown in fig. 4, along with the data for comparison. It is evident that the agreement is poor. Some improvement can be achieved in the higher energy region if eq. (3) is used to describe an additional contribution to the spectrum arising from the now well established broad, 4+, second excited state at 11 7 MeV. However, even a contribution from this state of 10 % of the total alpha intensity z, ~) does not lead to a satisfactory fit. It must also be kept in mind that what agreement is achieved is done so by overlooking the second forbidden character of the beta transition to the 4+ state. I

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2£,= (MeV} Fzg 4 A c o m p a r i s o n of t h e a l p h a p a r t m l e s p e c t r u m o b t a i n e d m t i n s w o r k w i t h t h a t p r e d m t e d b y W ~ e e l e r =), B o n n e r et a/ t), a n d Grfffy a n d B m d e n h a r n s) - Present experzment ~¢Vheeler's T h e o r y . . . . . B o n n e t ' s modzflcatzon - Grlffy a n d B m d e n h a r n - Grfffy a n d B m d e n h a r n i n c l u d i n g transztzons t o t h e T = 1 s t a t e

As mentioned earlier, an alternative description of the alpha spectrum has been provided in the recent work of Griffy and Biedenharn 5), which makes use of the d-wave phase shifts available from alpha-alpha scattering. Their expression for the spectrum is sin S ~2+ N=dE= :- k(Q--2E=) 6 -

P~

(5)

ALPHA

SPECTRA

FROM

THE

DECAYS

O F Lt s A N D

B8

035

where k is an arbitrary normalization constant, 02+ is the d-wave phase shift taken from alpha-alpha scattering data, and P2 is the penetrability factor for l = 2 alpha particles. In fig. 4 this formula is shown for comparison with the data. It is seen that the agreement is much improved in comparison to the foregoing analysis over an energy interval of nearly 8 MeV. Grlffy and Bledenh a m have also shown that the agreement m a y be extended to the high energy limit of the spectrum b y adding a term to eq. (5) to account for a contribution from the first T = 1, 2+ level in Be s at 16 7 MeV, which is sufficiently broad to influence the upper portion of the spectrum. The calculated dlstrlbutlon, when corrected in this manner, agrees quite well with the experimental data, as shown in fig. 4 The remaining discrepancy between the calculated and observed distributions is within the experimental error but appears exaggerated when the curves are shown on a logarithmic scale. In the high energy region in particular, the differences between the distributions in terms of the actual numbers of counts is exceedingly small. References 1) W H o r n y a k and T Launtsen, Phys Rev 77 (1950) 160 2) See for example W A Fowler a n d C C Launtsen, Phys Rev 51 (1937) 1103, Rumbaugh, Roberts and Hafstad, Phys Rev 54 (1938) 657, C L S m i t h and W Y Chang, Proc. Roy Soc A 156 (1938)415, ]3onner, Evans, Mahch and Rinser, Phys Rev 73 (1948) 885, C W L1 and W Whahng, Phys Rev 81 (1951)661, Frye, Armstrong and Rosen, Phys Rev 98 (1955) 241(A), T Frost and S S Hanna, Phys Rev 99 ( 1 9 5 5 ) 8 3) C Klttel, Phys Rcv 55 (1939) 55, J A Wheeler, Phys Rev 59 ( 1 9 4 1 ) 2 7 4) F. Ajzenberg-Selove a n d T Laurltsen, Nuclear Physms U (1959) 1 5) T A G n f f y and L C Bmdenharn, Nuclear Physms 15 (1960) 636 6) F C Gilbert, Phys Rev. 93 (1954) 499 7) U F a r m e l h and R Malvano, Rev Scl I n s t 29 (1958)699 8) ]3. D P a t e and L Yaffe, Can J. Chem 33 (1955) 15 9) Aron, Hoffman and Wllhams, A E C U -663 (1951) I0) W Whaling m Encyclopedla of Physms, Vol 34 (Springer Verlag, Berhn, 1958) 11) Neuendorffer, Inghs and Hanna, P h y s Rev 82 (1951) 75 12) K L1den and N Starfelt, Arklv fur Fymk 7 (1954) 427