Precision energy measurement of γ rays from short-lived activities

Nuclear I n s t r u m e n t s and Methods 178 (1980) 4 4 3 - 4 4 9 © North-Holland Publishing C o m p a n y

PRECISION ENERGY MEASUREMENT OF ~' RAYS FROM SHORT-LIVED ACTIVITIES E.K. WARBURTON and D.E. ALBURGER Brookhaven National Laboratory, Upton, N Y 11973, U.S.A. Received 10 March 1980 and in revised form 25 June 1980

I n the precision energy m e a s u r e m e n t using Ge(Li) detectors o f a 3" ray emitted following a short-lived # activity there are several problems encountered which are n o t usually of consequence. We consider two of them. First, when using the m i x e d source technique, the counting rate and the fraction o f c o u n t s due to the short lived activity will decrease during the counting cycle and any c o u n t rate dependence o f the system gain will lead to an error. Second, short lifetimes are usually accompanied by large #-energies and the associated Doppler effects m u s t be considered. As an example, the energy of the 3" ray from the first-excited state o f 11 B was determined after formation via the #--decay of 13.8 s 11 Be. The result is (2124.473 -+ 0.027) keV.

gain will lead to an error in the extracted 3' ray energy. * Second, the recoil momentum given to the 7-emitting nucleus by the emission of a/3,u pair can result in a Doppler shifted 7 ray. Since the amount of the Doppler shift is proportional to the recoil velocity, it is most evident for light nuclei and for large ~3 energies-which means short lifetimes. We consider the effect on precise 7 ray energy measurements of these phenomena in turn. To exemplify the effects we describe an energy measurement for the 3' ray from the first excited state of 11B after formation via the/T-decay of 13.8 s 11Be.

1. Introduction In recent years there have been considerable advances made in the precision energy measurement of 7 ray energies using Ge(Li) detectors. In particular, the work of Helmer, Greenwood and Gehrke and their co-workers [ 1 - 5 ] and of Meyers [6] has resulted in a set of energy standards for E3"< 3.5 MoV with uncertainties below 5 ppm. These Ge(Li) results are obtained by the mixed source technique in which two or more radioactivities are detected simultaneously and 7 ray energies from one activity are measured relative to one or more of the others. At a precision of 5 ppm many possible sources of error must be considered. A good example is the dependence of pulse height on source-detector geometry [4]. Because of this effect it is important to consider carefully any differences in the positions of the various sources used in the measurement. In order to extend the set of precise energy standards to energies of 3.5 MeV and higher, it is expedien{ to study rather short-lived activities in the lighter nuclei. We consider here two effects which are usually negligible for long-lived activities but which should be considered when designing and analyzing precise 7 ray energy measurements using short lived activities. First, when using the mixed source technique, the counting rate and the fraction of counts due to the short lived activity will decrease during the counting cycle and any count rate dependence of the system

2. Count rate dependence of energy separation measurements We denote the total counting rate in the Ge(Li) detector by

i q ) = Z)

e- a,

(1)

i

where Ar~i) is the contribution at t = 0 of the activity * The possibility for error in the m e a s u r e m e n t of energy differences of 3' lines with different half-lives is, of course, more general. A n y time dependent gain or base-line shift will affect the two lines differently, hence causing an error. The c o u n t rate dependence considered here is the m o s t obvious example o f a n o n r a n d o m effect which cannot be averaged o u t by repeated measurement. 443

E.K. Warburton, D.E. Alburger / Precision energy measurement

444

with decay constant Xi (meanlife Ti=~kil), We assume a linear dependence of gain on counting rate, that is, the peak position of the ]th peak in the spectrum is taken to be

x/(t) : x~j) + S " U ( t ) .

(2)

We are interested in the mean value of x/(t) for a counting period At:

(x/) = f At xi(t) Ar0")(t) d t / s t Nff)(t) d t ,

(3)

0

and using eqs. (1) and (2) we fred N~O/)Xj {1 e-(~'i+xi)At t (X]) = X~ ) + S ~i ~ki + ~kj i -- ~ J" -

(4)

Eq. (4) is sufficiently geneial to cover most cases of interest. The simplest application and probably the most common is the case of one short-lived activity with decay constant Ls and one long-lived activity for which XL = 0 can be assumed Qver the counting period At. We are interested in the channel separation between a peak x L associated with the longqived activity and a peak xs associated with the short4ived activity, i.e., Ax(t) = XL(t) -- xs(t). The mean value of &x(t) over the counting interval !s, from eq. (4), ( A x ) - - ( x L) - (Xs)=X~ L ) - x~s) - SN~S)g(XsAt),

(5)

where

g(z) .

1 +e -z

.

2

.

1 -e -z

.

.

z

(6)

For a counting interval smaller than the meanlife r, i.e., for z < 1, an expansion of eq. (6) in powers of z gives

g(z)

6(n + 1) zn . =z~2 ~ (-1)n (n + 2)!(n + 3) 12 n=o

(7)

The first few terms of eq. (7) are

g(z) -

Z2

Z3

12

24

ratio of the counting interval to the meanlife of the activity squared. The correction is, of course, easily converted to energy units using the energy dispersion (e.g., in keV/channel) evaluated at x~s). Application of this result will be illustrated in section 4.

3. Doppler broadening o f r a d i o a c t i v e T-rays Gamma-ray sources from radioactive nuclei can be categorized by the meanlife r of the emitting excited state relative to the slowing down time rs of the recoiling nuclei in the source material. If r>> rs then the recoiling nucleus will have become totally stopped before emission of the 7 ray and the 7-ray line shape will show no effects of the momentum transferred to the nucleus by the emission process. If r ~ rs, the line shape of the "),-transition N(E,y) will reflect the partition distribution of beta and neutrino energies and any angular correlation between the beta and neutrino and between the recoiling nucleus and the 7 ray. If r--~ rs then N(E,,/) will also depend on the slowing down process for the recoiling nuclei in the source or surrounding material. We consider here the Doppler line shape, N(E~,), for r ~ %. We adopt the usual units customary in /3-decay [7], namely h = c = me = 1. The following definitions are usual: E0 = m a x i m u m kinetic energy of the /3-ray, W0 = E0 + 1 = total energy of the 13-ray, Pe = ~3-ray momentum = x/(W 2 - 1), p , = neutrino momentum = Wo W, P R = momentum of the recoil nucleus, --PR = Pe + Pv. In the/3-decay process Jx ~ J 2 , the nucleus in the state with spin J2 is given a recoil momentum which depends on the partition in energy between the emitted electron and neutrino and on the angle q5between them

pR = Pe + pv ;

p~t = p2e + p2v + 2pepv cos ~ .

(10)

Z4

+ - - --.... 80

(8)

If now the level J2 decays by 7-emission to a state J3, the energy of the 7-rays will be governed by the Doppler relation

(9)

E~, = E,,/o(1

Thus, for Xs At < 1 a useful approximation is < ~ ) ~ x~L) - x~s) - hSN~S)(Xs At) z .

To summarize, for the conditions cited above, the count-rate dependence of the amplifier-detector system gives rise to a correction to the channel separation (Ax) which is approximately proportional to the counting rate of the short-lived activity and to the

+ / ~ R COS O) ,

(l])

where Evo is the 7-ray energy for emission from a nucleus at rest, fir PR/MN,withMN the mass of the recoiling nucleus, and 0 the angle between PR and the > r a y momentum K~. We define the probability distribution of E.y for a =

E.K. Warburton,D.E. Alburger / Precision energy measurement /rv

given magnitude of fiR by

P(E~, PR) d~'.y = 14/09R,K~t) d~20 ,

(12)

where W(pR,/(7) is the angular correlation function of PR and K 7 and d~0 is the solid angle interval around 0. By differentiation of 0 with respect to ET, eq. (11) gives 1

Isin 0 d0l --- 2 d~20 - ETO~R ,

(13)

and MN

P(E.r, P R) dE7 - - -

2E~.0PR

W(E'r, P R) dE.y ,

(14)

where we assume that eq. (11) can be used to make the indicated change of variables in the angular correlation function W. Thus, the ")'-flux for a given magnitude ofPR wil be confined to the bounds ETo(1 - 13R)~
(15)

and will have a shape determined by the angular correlation o f p R and K.r. The 3'-ray line shape N(ET) observed experimentally will be given by a convolution of the probability distribution P(ET, PR) with the differential probability G(pR)dPR that the recoil momentum lies in the interval between PR and PR + dpR. Kofoed-Hansen [8] has derived the form of G(PR) for allowed transitions under the good approximation that the mass of the recoil nucleus is infinite. The result is easily generalized to include forbidden transitions: w+ G(PR)

;

g(W, PR) dW,

(16)

W_

N(ET,/3max) = f

W± =

2(W0 + p~,)

P(ET, PR) G(pR) dPR.

ET0(1--13max)

(19)

In general N(E.r) will be a quite complicated function of the nuclear matrix elements contributing to the fl-decay process. For instance, W(PR, K 7) of eq. (12) is dependent on the matrix elements of rank 1 and 2 which enter into J1 ~ J2 and is not necessarily isotropic for allowed transitions as is the correlation between Pe and K 7 or Pu and K 7 [7]. Likewise G(PR) contains a strong dependence on the correlation between Pe and p~ [through the coefficient a of eq. (18)] which depends on the ratio of matrix elements of different ranks. It also depends on these matrix elements through the spectral shape factor C(W) [7]. To illustrate the calculation of the 7 line shape, we assume the simplest case possible, (1) an isotropic correlation between PR and KT, i.e. W(ET, pR ) = 1 in eq. (14), (2) an allowed spectral shape (not necessarily an allowed transition), (3) the Coulomb effect on the spectral shape can be neglected, i.e., F(Z, I4I)= F(O, W) = 1. With these assumptions eq. (16) can be integrated analytically to yield [8-10]

a(pR) =p~ ( X - 1) 2 X3 I X ( X - 1) + 2W2o(X+ 2)] 6ct p 2 (X - 1)2 , l+a X

(20)

where X = W2o- p~ and the normalization is now arbitrary. The convolution integral of eq. (19) is, with our simplifying assumptions, an integral in PR space of G(PR)/p R which is easily evaluated to yield

W(~, t3max)

where (Wo +-pR) 2 + 1

445

= ,

(17)

g(W, PR) = ½F(Z, W) C(W)

1

-3X+-+31nX+~+2W~(X+ X

l+a6a

and

X [pRWpv + (½a) PR(.P~ " p2e -- p2)] ,

[_~

[_~2

where F(Z, I40 is the Coulomb function, C(W) the spectral shape factor, and a the Pe, Pv angular coefficient [7]. N(E~,) will be symmetric about Evo and is given for E-r
1

X2

2X+lnX+~]

(allowed shape, z = O) , (18)

3

X

(21)

where PR varies linearly with E 7 from PRo = (Wg 1) 1/2 at ET=ETo(1-/3max) to P R = 0 at E.r=E ~ . The e - p correlation coefficient a is +1 for a pure rank 0 transition and - ~ for a pure rank 1 transition. The approximations made in obtaining eq. (21) are not usually adequate for detailed comparisons;

3,3

446

E.K. Warburton, D.E. Alburger / Precision energy measurement

however, the result is very useful for estimating the magnitude of Doppler effects. Utilization of eq. (21) will be illustrated the next section.

4. Energy measurement of the 11B 2 1 2 4 - + 0 keV transition 4.1. Experiment The 2124 keV "), ray from the decay of the firstexcited state of I~B was produced by the/3-decay of 11 Be [ 11 ]. 11Be, with f r = 1/2 +, decays with an halflife o f 13.8 s. The first-forbidden branch to the f r = 1/2- 2124 keV first-excited state of 11B is 29%. A further 4.3% is contributed to the 2124 keV transition from allowed /3-transitions to higher-lying levels followed by 7-cascade through the 2124 keV level. The /3 ray end-point energy for/3-decay to the 2124 keV level is 9.38 MeV. l l B e was formed via the 9Be(t, p ) l l B e reaction with 1.5 g A of a 3.1 MeV triton beam from the BNL 3.5 MV Van de Graaff accelerator. A 50 cm 3 Ge(Li) detector was situated 4 m from the target chamber and on the other side of a concrete wall. The target was mounted on a "rabbit" which was shunted pneumatically between the bombard and count positions. The target consisted o f a self-supporting foil of 4.7 mg/cm 2 9Be. A full b o m b a r d - c o u n t cycle was as follows: 0 - 7 s bombard, 7 7.5 s transfer, 7.5 12 s wait, 12 19 s count, 1 9 - 1 9 . 5 s transfer. The front face o f the ORTEC true coaxial Ge(Li) detector was ~ 3 cm from the 9Be foil ( l l B e source) in the count position. A S6Mn source (half-life: 2.58 h) was placed immediately behind the l lBe source together with a mixed S6Co-6°Co source. The counting rate due to these three long lived sources was 6 kHz while that due to a 1Be at the start of the count cycle was 2 kHz. Pulses from the Ge(Li) preamplifier (cooled FET) were fed to an ORTEC 472 spectroscopy amplifier and thence to a Northern Econ lI series 4096-channel ADC and pulse height analyzer operated with 8192 channel conversion gain and a digital offset of from 3840 to 4096 channels. The energy separation, A(2124 2113), of the 11B 2124 keV 7 ray from the S6Fe (2113.107-+ 0.012) keV [3] 7 ray from S6Mn decay was determined from six spectra taken with different amplifier gains and digital offsets. The energy dispersion was ~0.3 keV/ channel. Gamma rays from S6Co and 6°Co with accurately known energies [3] provided the secondary

energy calibration. The different sources were carefully placed so that the uncertainty due to different s o u r c e - d e t e c t o r geometries [4] could be neglected. Peak channels were determined using the fitting routine SAMPO [12] and a quadratic least squares fit of Ey versus peak channel was made for each of the six spectra. The mean energy separation A ( 2 1 2 4 2113) was found to be (11.366 -+ 0.024) keV where the external uncertainty of the six determinations is quoted because the normalized Xz was slightly greater than one. Combining this result with the S6Fe ~, ray energy we obtain (2124.473 + 0.027) keV for the l i B 3' ray. Correcting for the nuclear recoil in the 7-emission process results in an excitation energy for this first-excited state of 2124.693 + 0.027 keV. The best previous value was (2124.7 + 0.4) keV [13]. We now wish to consider the uncertainty due to count rate dependence of the systems gain (section 2).

4.2. Effect o f counting rate variation The count rate dependence of the gain was determined by varying the distance of a S6Co source from the detector. (In separate tests it was found that the dependence [4] of the gain on the s o u r c e - d e t e c t o r distance was negligible compared to the count rate dependence being determined.) The count rate was varied from 1.5 to 21 kHz and the peak positions of the S6Co 3, rays of 1771, 2035, and 2598 keV were determined with SAMPO [12] as a function of count rate. For each, the linear relationship of eq. (2) was found to be well obeyed and a linear interpolation gave S = 23 eV/kHz in the 2 1 1 3 - 2 1 2 4 keV region. Using eq. (9) with A~s) = 2 kHz, XsAt = 7/(13.8/ ln2) = 0.35, we find a counting rate effect on the present energy separation of 0.47 eV which is negligible. The effect is small because the counting interval was only 35% of the meanlife and the counting rate was kept small.

4.3. Doppler effects One of the six measurements o f the S6Mn 2113= ~lBe 2124 keV doublet is shown in fig. 1. It is apparent that the width of the 2124 keV line is greater than that o f the 2113 keV line. Except for the tails, both peaks are well reproduced by Gaussians. From the six determinations of A ( 2 1 2 4 - 2 1 1 3 ) we find an average fwhm (full-width-at-half-maximum) for the S6Mn 2113 line of 2.50 keV which we take to be the instrumental width for the 2124 keV line. Assuming

447

E.K. Warburton, D.E. Alburger / Precision energy measurement 104~

'

I

'

'

'

I

'

'

'

I

'

'

'

I

liB

'

'

I

[

2124 KeY

I0

I

I

I a=+l

56Fe 2115.107 KeV 5.78 KeV

Ji,i Z Z

8

/

/i I

\\\

2.89 KeV

"I£2

6 ~-

/

201

15

m lO 3 1,3 r~

Z GAUSSlAN ///:' "-f(FWHM = 2.49 KeY)

\

Z O C)

e.

. . ~&".'~"_ _ 102

'24160 '

_ _ _

"-"

'2180

, ,12500, '

,

I

2520

,

,":'T

~

2540

CHANNEL NUMBER

Fig. 1. Portion of a "r-ray spectrum showing the S6Fe 2113 keV and 11B 2124 keV peaks. The least squares fits are Gaussians and the widths are from these fits.

addition in quadrature a Doppler width for the 2124 keV line of 2.30 keV was extracted. This value includes some effect (~13%) due to 3,-feeding from higher-lying levels fed by allowed 13decay. Correcting for these branches (assuming the same ratio of fwhm/ /3max tbr the partial line shape due to all branches) gives a Doppler broadened width of 2.49 keV for the line shape of the 2124 keV line formed by direct t3-feeding. In fig. 2 this result is compared to the simplified expression for the Doppler line shape given in eq. (21). For the ttBe-decay to the 2124 keV level of 11B the energy, m o m e n t u m and velocity parameters needed for application of eq. (21) are W0 = 19.362, PRO = (Wg -- 1) 1/2 = 19.337, /3max = ( m J M N ) P R 0 = 0.96 X 10 -a, flmaxET0 = 2.047 J~eV. Because the riB 2124 keV level has J = 1/2, the angular correlation W(PR, K.r) of eq. (12) is isotropic. The two extreme possibilities for the Doppler line shape indicated were calculated assuming Z = 0 and an allowed/3-spectral shape. Also shown is a Gaussian (dashed curve) with the fwhm appropriate to the measured Doppler width. (Note: A Gaussian is used for simplicity; there is no experimental or theoretical reason to expect a Gaussian shape.) Considering the assumptions made in applying eq. (21), it appears that the Doppler width observed experimentally for the I~B 2124 keV line is adequately explained, but that the ambiguities due to ignorance of the beta ma-

EyO (I-/~rn o x )

I0

5

0 ETO

5

I0

15

!0

Eyo ( I +/~mo x)

Fig. 2. Doppler line shapes for the llB 2124 keY "r ray following formation via 11 Be/3 decay. The full curves are from eq. (21) and assume an allowed shape and Z= 0 for the /3-spectrum. The values of a are for the two extreme possibilities (see text). The Gaussian (dashed curve) is shown for comparison only; it has the width observed experimentally for the transition.

trix elements preclude a more detailed comparison. * Our first comment concerning the effect of the observed Doppler broadening on the energy measurement is the obvious one that the extra width of the 11B lines must be allowed for in the peak fitting procedure-as it was in this analysis. This caution is hardly necessary when the effect is as noticeable as it is for tlBe ~ decay; however, it is worth recalling for those cases where the increased line width due to Doppler effects is present but not so apparent. A much more serious potential Doppler-connected source of error in precision energy measurements is that due to the combination of source inhomogeneity and finite lifetime. One might be temped to conclude from fig. 2 that the rank 1 matrix elements (a = -1/3) dominate the rank 0 matrix elements (a = +1). However, the possible effects of the neglected spectral shape factor C(W) of eq. (18) are large enough to negate this conclusion. For instance, the rank 0 first-forbidden shape factor is of the form K(1 + a/W) and it is possible for the W-1 term to reduce the width of the rank 0(a = +1) line shape considerably. Nevertheless, the Doppler effect does contain information on the ~ matrix elements and further studies to extract this information axe being considered. The correction due to Coulomb effects, i.e., Z ¢ 0, is quite small for 1lB.

448

E.K. Warburton,D.E. Alburger /Precision energy measurement

To illustrate this effect imagine the idealized situation of a source consisting of a thin film deposited on a thick backing viewed at right angles to the interface and through the backing (this geometry we refer to as the "interface" geometry). Also imagine a meanlife ~for the 3,-emitting state much longer than the stopping time of the recoiling nuclei in the backing but much shorter than the stopping time in air. Then for all angles 0 > 90 ° the recoil momentum will be unaffacted by the stopping medium while for 0 < 90 ° all 3' rays will be emitted after the recoiling nuclei stop. The measured 7-ray energy will no longer be ETo but the mean of the distribution from ETo to ETo(1 /3max) in fig. 2. To estimate this effect we assume a Gaussian line shape and average the energy over the lower half yielding (E 7) = ETo - 0.34(fwhm), where 0.34 = (4n In 2) -1/2. For the present lIB 2124 keV line with fwhm = 2.30 keV, the error generated by the source inhomogeneity in this idealized case would be 0.78 keV. The extreme conditions assumed to obtain this result are not likely to be met in practice; however, the effect is so large that even a small percentage of it would be nonnegligible. A rough guide for estimating this effect in other cases is AE(source, r >> rs)iN ~ 0.4Eo, o/3max ,

(22)

where the notation is intended to recall the origin of the effect and the fact that it applies to the "Interface" (IN) geometry. In the present laB case, the meanlife of the 2124 keV level is 4.8 fs [13] and a more meaningful estimate of AE(source, r) is obtained by calculating the attenuation of the liB recoils in the Be averaged over the meanlife. We estimate this attenuation by a calculation using the approach of Blaugrund [14] and assuming a recoil velocity of 0.68PRo. The result is an attenuation of ~8% so that the effect calculated for the ~lBe decay to the lIB 2124 keV level for the "interface" geometry would be AE(source, Texp)iN ~ 0.08 X 780 = 62 eV. In any practical case the "interface" geometry is imperfectly realized and the important parameter is the ratio of the range R of the recoils to the source thickness d. Recoil ranges are of the order 0.1-10/~g/ cm 2 and for R / d < 1 an estimate of the maximum possible effect gives

AE(source, ~exp) < (R/d) AE(source, 7"exp)iN . In the present measurement the i1Be activity was produced right through the 9Be foil since the energy loss of 3.1 MeV tritons in 4.7 mg/cm 2 of 9Be is ~850 keV. For a lIB recoil velocity/3ma x = 0.96 × 10 -3 we estimate [15] a mean range of 3.2 #g/cm 2 in 9Be and thus R/d ~ 0.7 × 10 -3 and AE(source, rexp) will be negligible.

5. Conclusions

5.1. Count rate effects As far as we know, a quantitative evaluation of the effect of a count-rate dependent gain on 3' ray energy measurements has not been given previously. The dependence of the uncertainty introduced by the effect on the counting rate and counting interval is not surprising. However, the formulae expressing this dependence-eqs. (4) to (9) allow an easy evaluation of the effect. The only additional measurement needed is the slope of the energy (or channel) versus count rate curve in the region of interest. Perhaps an interesting result is that the calculated uncertainty is independent of the counting rate of any long-lived activities (i.e., those with r>~ At) as long as the assumption of a linear dependence of peak position on counting rate [eq. (2)] is valid. Finally, we note that these results should find application with relatively long lived sources as well as short lived ones-the parameter of interest being the ratio of the counting interval to the meanlife of the activity being studied.

5.2. Doppler Effects It is shown that the possible energy shift due to source inhomogeneities is quite large even for quite short lifetimes for the 7-emitting state. This effect is proportional to ( W ~ - 1)I/2[MN and thus is not so important for heavier nuclei and those /3-emitters whose long lifetimes are due to a small energy release. As an example, consider the /3-decay branch of S6Co(ti/2 = 78 d) to the 4 ÷ second excited state of S6Fe. For this branch the recoil velocity connected with ~ m a x is f i r = 2.6 × 10 -s and the estimate of eq. (22) for the maximum energy shift due to source inhomogeneity is 13 and 9 eV for the 4 ÷-+ 2 ÷ 1238 keV and 2 ÷-+ 0 ÷ 847 keV 7 rays, respectively. Thus

E.K. Warburton, D.E. Alburger / Precision energy measurement for this example it would be difficult to fabricate a source for which the energy shift would be non-negligible. * It can be anticipated that even for large values of (W2o - 1)l/2/m N the inequality R i d ~ 1 will pertain and AE(source, r) will be negligible. However, two types of radioactive sources routinely used for which R i d 2 1 could be obtained are easily called to mind. The first is a continuously flowing radioactive gas system with the detector viewing a gas reservoir. Any activity that sticks to the walls of the reservoir will probably have R i d > 1. A second type is the He-jet system which is currently in extensive use at this laboratory [16]. In the BNL system a He-jet carries the radioactivity from the target and deposits it on an aluminized mylar tape. Measurements [17] on the 7Li and a groups emitted in 1aBe ~ aaB ~ 7Li + a set an upper limit of 20 /~g/cm 2 on the aaBe source thickness d and it could be considerably less than this.

5.3. Summary In summary, the two sources of uncertainty considered here should be kept in mind but can be rendered negligible quite easily. In the measurement of the 11B 2 1 2 4 - + 0 keV transition used as an example, both effects were negligible. The energy of this 7 ray transition was found to be (2124.473-+ 0.027) keV corresponding to an excitation energy for the l i B first-excited state of (2124.693 + 0.027) keV.

* Note, however, that the half-life of the S6Fe 2+ state is ~6 ps-a value for which the effect would be near maximum if such a source were encountered.

449

References [1] R.G. Helmer, J.E. Cline and R.C. Greenwood, in The electromagnetic interaction in nuclear spectroscopy (ed. W.D. Hamilton; North-Holland Publ. Co., Amsterdam, 1975) p. 775. [2] R.G. Helmer, R.C. Greenwood and R.J. Gehrke, Nucl. Instr. and Meth. 155 (1978) 189. [3] R.C. Greenwood, R.G. Helmer and R.J. Gehrke, Nucl. Instr. and Meth. 159 (1979) 465. [4] R.G. Helmer, R.J. Gehrke and R.C. Greenwood, Nucl. Instr. and Meth. 123 (1975) 51. [5] R.G. Helmer, J.W. Starner and M.E. Bunker, Nucl. Instr. and Meth. 158 (1979) 489. [6] R.A. Meyer, Multigamma-ray calibration sources, Lawrence Livermore Laboratory, Report M-100 (Dec. 1, 1978). Additional references reported within. [7] H.F. Schopper, Weak interactions and nuclear beta decay, (North-Holland Publ. Co., Amsterdam, 1966). [8] O. Kofoed-Hansen, Vgl. Dan. Vid. Selsk. Mat. Fys. Medd. 28, no. 9 (1954). [9] C.H. Johnson, F. Pleasonton and T.A. Carlson, Phys. Rev. 132 (1963) 1149. [10] O. Kofoed-Hansen, Phys. Rev. 74 (1948) 1785. [ll]D.E. Alburger and D.H. Wilkinson, Phys. Rev. C 3 (1971) 1492. [12] J.T. Routti and S.G. Prussin, Nucl. Instr. and Meth. 72 (1969) 125. [13] F. Ajzenberg-Selove,Nucl. Phys. A248 (1975) 1. [14] A.E. Blaugrund, Nucl. Phys. 88 (1966) 501. [15] K.B. Winterbon, Ion implantation range and energy deposition distributions (Plenum, New York, 1975), Vol. 1. [16] D.E. Alburger and T.G. Robinson, Nucl. Instr. and Meth. 164 (1979) 507. [17] D.E. Alburger, D.-J. MiUener and D.H. Wilkinson (to be published).