Proposition for a new method for measuring short half-lives

NUCLEAR

INSTRUMENTS

3 (1958)

49-51;

NORTH-HOLLAND

PUBLISHING

CO.

-

AMSTERDAM

PROPOSITION FOR A NEW METHOD FOR MEASURING SHORT HALF-LIVES B.

JOH.XNSSOS

and T. ALVdGER

Nobel Institute of Physics, Stockholm 50 Received

In the usual method of measuring lives,

employing

multipliers,

fast

scintillators

the measurements

16 January

1958

with e, it will also obtain zero deflection,

short half-

but if

it had been emitted a short time later (e’,), then it would have obtained a deflection proportional

and photo-

are limited by the

decay time of the scintillation flash and more seriously by the time-spread in the photomultipliers. These complications seems to make it impossible to measure half-lives shorter than about 5 x IO-l1 s. In other indirect ways, as e.g. in resonant scattering, it is possible to estimate half-lives which are at least a factor of 10 faster, but this is limited to some very special cases. With the method proposed here, which in a direct way determines the half-lives, it is hoped that isomeric states decaying slower than lo-l4 s could be reached. The principle is as follows. Suppose that an element emits two K-conversion electrons in cascade. The time between these two events can then be determined in the following way. The start time of the first electron is determined by its phase-position in a high-frequency vroltage supplied between two condenser-plates. The second electron emitted in coincidence with the first one obtains a deflection which is a function

to the shaded area, A,, indicated in the sinecurve. Thus, if the coincidence counting-rate versus the position of the aperture, a2, along the line L is measured, a coincidence resolution curve will be obtained. A test arrangement with two sector-magnets before the deflecting plates is in the process of being constructed at the Nobel Institute. The condensers C, and C,, indicated in the figure, are connected to the same high-frequency source.The phase-difference between the voltage on the two condensers will be made variable in order to obtain an artificial delay. The angle, 0, is chosen to be 90” in order that the electrons will pass through as little material as possible. A frequency of 144 Rlc;s of the HF-source will be employed with an estimated voltage of 10 kV. With a distance of 60 cm between the condenser and the detector the resolving-time z of the arrangement for 1 MeV electrons can be estimated to be 0.1 mps. The figure is calculated

of the phase difference with respect to the first one. The principle is indicated in the fig. 1, which shows a block-diagram of the test-arrangement. (The magnetic focusing is necessary in practice, but not in principle.) For simplicity the source, S, is assumed to emit two electrons of the same energy in coincidence with each other. The plane parallel condensers C, and C, are connected to a high-frequency AC source. If the electron, e,, reaches C, at time t,, indicated in the sine-curve, it will undergo zero deflection. (This will be the most sensitive point and will be used in practice.) If e2 is an electron in prompt coincidence

from the following expression : ilb r=-++t 8

where db = the width of the spectrometer-line at half maximum. 6 = deflection sensitivity at the detector in mm;‘mps (at t = tJ. At = the difference in the transit time of the electrons through the magnet. In the actual case: db = 1 mm corresponding to a transmission of about 0.2oj, 6 = 20 and At = 0.05 m,us. The H.F.-deflection is carried 49

B.

50

JOHANSSON

AKD

out after the magnetic deflection because this will give the highest deflection sensitivity or time-dispersion

and

because

an

energy diswill be

crimination before the H.F.-deflection obtained. The differences in length

Magnet

of

the

1

T.

ALV.&GER

Because these differences of CCthey can be corrected

are linear

functions

for by using a small

angle magnet with reversed field-direction in front of the spectrometer. By properly chosen parameters,

this will not cause a serious decrease

Magnet 2

A

Fig. 1. A. Block-diagram of the test arrangement. S = sample; C,,, = deflection condensers; D,,, = detectors; a, aI 2 = apertures; e, 2 = electron paths ; K = coincidence unit. (The resolving time is equal to one half-period of the H.F:-voltage. Thus, t’h c ante -- t.) B. The high frequency voltage which is supplied to the condenser plates C, and C,. t, is the transit time of the electron through the condensers.

electron paths in the magnet are with good approximation (CXis small) equal to cc[R( 1 - co@) + I, sir@], where R = radius of curvature of the electron paths, a = angle between the electron paths (at S), B = angle of sector magnet, I, = source to magnet distance.

of the dispersion. However, a better method is to use two magnets with the same field-direction before the deflection plates, arranged in such a way that a first focus is obtained in between them. An aperture in the first focus will allow electrons with one energy only (within the energy resolution) to pass on to the second

PROPOSITION

FOR

.I NEW

magnet.

The differences

electron

path will then be corrected

in the

length

METHOD

of the

for by the

second magnet and moreover the final lineshape will be improved, which is important for the time-determination. However, the resolving

FOR

MEASURING

flection-method

SHORT

HALF-LIVES

51

this mixing can be held within

the energy-resolution of the spectrometer and furthermore, the time-dispersion for the detlection-method is much modulation conditions.

larger

for the

same

time is of less importance in the time-measurement provided that the deflection is small

In further development of the method, doublefocusing magnets will be employed, and by in-

within the condenser-plates

creasing the frequency and the voltage it seems to be possible to decrease the resolving time to

and that the resolu-

tion curve is sharp. Another method to obtain the

focus

is to modulate

a displacement the

energy

electronst. This will, however, give rise mixing of electrons with different energies that

the time-dispersion

is limited.

of

of the to so

In the de-

t Energy modulation in order to determine short halflives has been proposed by Gerholm and Tove, to be used in connection with lens spectrometers (Ark. f. Fysik 11 (1956) nr. 2, p. 75). A possible resolving time of t = 0.3 m,us was estimated for an electron-energy at 100 keV. The frequency required is 500 MC/S.

about

lo-l2

set and the

shortest

measurable

half-life to about IO-l* set for 1 MeV electrons and may be still less for lower energies. The sector-magnets will give low transmission and thus low coincidence counting rate, but fortunately the arrangement described above is very convenient to supply with a multi-channel (or multi-detector) system. Then it should be possible to obtain all points of the coincidence resolution-curve at the same time.