Counting rate corrections

The counter characteristics are known for standard conditions, which means:

(i) C 02 gas free of (electronegative) impurities;

(ii) an atmospheric pressure of 760 torr;

(iii) a fixed filling pressure at 20°C;

(iv) a constant dead time caused by the Geiger counter blocking pulses.

Deviations from standard conditions inevitably occurring in routine operation must be corrected for.

The purity correction compensates for the influence of electronegative

im-purities in the counting gas (c.f. eq. 3.11). Their effect is essentially equivalent t o lowering the operating voltage (a certain decrease in voltage causes a decrease of the gas multiplication M by a certain factor). Thus impurities give a parallel shift of the characteristic curves (c.f. fig. 3.10) of both the coincidence (muon) and the anti-coincidence ( C beta) channel.

The parameters for p u r i t y , atmospheric pressure and filling pressure correction in use for the routine dating counters were established by Vogel. The purity correc-tion was described by Brenninkmeijer and Mook (1976). For the new counter G R A D A similar corrections are applied.

The purity correction procedure is as follows: The muon counting rate is measured at a fixed voltage at the steep slope of the curve (at three quarters of the plateau counting rate, c.f. fig. 3.10.a). First this counting rate is corrected t o a standard atmospheric pressure of 760 torr using a barometer dependence (d/V /dbj/N^ =

—2%/cm Hg (table 3.7). Then the curve shift due t o impurities is calculated f r o m the observed decrease in muon counting rate and the known slope. Knowing the curve shift we can correct the beta and the background counting rate using the voltage dependence of these quantities in the operating (= plateau) region (c.f.

table 3.4).

The purity correction equations are:

r = B+(Nz-NZo)(6B/6V)/(dN^/6V)maXf (3.22.a)

A=A' {l-{Nz-NZo)(dNp/6V)/A0(dN^/dV)max} . (3.22b)

Here the prime is used for the uncorrected values, Nz and NZo indicate the p u r i t y counting rate of the coincidence channel for the sample and for standard con-ditions, (6B/6V) is the slope of the background, (6N^l6V) that of the net standard beta plateau and ( d / VM/ d \ / )m a x that of the steep part of the muon curve, A represents the sample and AQ the net standard counting rate.

Because the correction applies t o both beta and background counting rate it is important for samples of all ages.

The procedure described above only gives good results if the impurities cause a parallel shift of the characteristic curves w i t h o u t affecting their shape. From fig. 3.20 it is obvious that this is an approximation, no longer true for very impure samples (c.f. Barendsen, 1955; Freundlich and R u t l o h , 1972). Therefore we have t o define a range for which the constant slope assumption gives a negligible error. For a normal counting period of one day the counting statistics give ONJNQ > 4 ° /0 0

(for a recent sample) and oB/B & 1.0%. As long as the change in slope yields a relative difference of < 1 %0 resp. < 4 % o , the error introduced by taking a con-stant slope is 3% or less of the total standard deviation and is therefore negligible.

100 150

Nz (cpm) ^{2 0 0 250}

Fig. 3.20. Relation between the maximum slope of the muon characteristic curve ( d A / ^ / d l / )m a x

and the 'purity counting rate' A/^; * — counter I, f — counter G R A D A .

The maximum increase of the muon counting rate w i t h voltage (d/V / d \ / )m a x varies w i t h the purity counting rate as

(d/VM/dV)r (1.61 ± 0.26) x 1 0 "3/ VZ + (0.361 ± 0.084). (3.23) The constants for the purity correction for the different counters are summarized in table 3 . 1 1 . From this table and eq. 3.23 we choose a counting rate of 70% of NZo (= 150 cpm for counter G R A D A ) as the lower limit of applicability of the purity correction. Here the use of the constant slope assumption gives an error of 0.80/0 0 and 3 %0 in N„ and B respectively.

The atmospheric pressure correction must be applied t o the background counting rate. The components of the background counting rate and their variation w i t h atmospheric pressure were discussed in a previous section. The P value of the least squares f i t of the background counting rate as a function of the atmospheric pres-sure is slightly better than as a f u n c t i o n of the muon counting rate. In view of this and t o c o n f o r m t o the correction procedure in use at the Groningen laboratory the background was corrected using the barometer reading only. If high accuracy is required, however, also the muon counting rate should be considered.

The atmospheric pressure correction is:

Bb = B-(76-b)6B/db, (3.24)

where b is the barometer reading in cm Hg. The constants are given in table 3 . 1 1 . The correction is important for low activity samples. For recent samples it is usually negligible.

The filling pressure affects the counting rate in t w o different ways. In the first place, for a constant operating voltage, the gas multiplication factor changes w i t h filling pressure. If we calculate the change in voltage necessary t o compensate for the pressure variation we f i n d 1.60 ± 0.07 V / t o r r for beta radiation in the operating region (V = 7800 V , p = 2917 t o r r ) . This effective change in operating voltage, how-ever, need not be corrected for separately since it is already included in the purity correction.

The second effect is the change in the amount of gas in the counter. In a first approximation this only affects the beta counting rate which is corrected by

A=A'pQ/p, (3.25)

where A' is the measured 1 4C activity o f the sample and pQ is the standard filling pressure.

The dead time caused by the anti-coincidence blocking pulses of the Geiger counter leads t o a loss in anti-coincidence counting rate in the proportional counter. Since the total dead time is directly proportional t o the Geiger counting rate /VG, the anti-coincidence counting rate of the proportional counter (N/t) has to be corrected for variations in the Geiger counting rate

NQ/t= N/t{l-(NG-NGo)r/60} > (3.26)

where the subscript o indicates standard conditions, (/VG—/VG o)/60 is the deviation f r o m the standard Geiger counting rate in counts per second and r is the dead time due t o the blocking pulse ( « 1 msec) triggered by a Geiger count in seconds per count.

Since the Geiger counter mainly detects cosmic ray muons, one source of varia-tions in Geiger counting rate is the variation o f the atmospheric pressure. With a dead time of 3.2% f o r G R A D A and 2.8% f o r RZ (c.f. sect. 3.2.3.1) and an atmospheric pressure dependence of —2.3%/cm Hg for muons, this gives a correction of 0.7 resp. 0 . 6 ° /0 0/c m Hg for the anti-coincidence channel counting rate.

This correction has t o be taken into account only w i t h high precision analyses of young samples (e.g. tree ring calibration).

The four corrections discussed above can be combined into one correction equation:

N

parameters as determined by Vogel

3.2.4. Conclusions

(i) From the results for the counters I and G R A D A (no. 6A and 6) it appears that counters with a background counting rate of approximately 2.5 cpm at an effective volume of 1.7 1 can be reproducibly constructed. Using these counters at a pressure

of almost 4 atmospheres poses no serious problems and gives a figure of merit of 27 resulting in an age range of about 53 000 years for a t w o days counting period, (ii) A n indirect determination of the gas multiplication factor makes possible a quantitative interpretation of the counter operating conditions. Standard condi-tions are a gas multiplication of 1.7 x 1 04 at 7800 V and 2917 torr at 20 °C w i t h a lower discriminator level corresponding t o a primary energy of w 1.0 keV or 30 primary ion-electron pairs.

(iii) Since the gas multiplication equation found gives good results when applied t o the earlier work of Barendsen as well as" to RZ it is of probably more general validity for C 02 proportional counters.

(iv) Interactions in the gas and in the wall of the counter both contribute t o the background counting rate.

(v) For muons interactions in the counter gas dominate at moderate and high pressures. Interactions in the counter wall become important only at very low pressures « 100 t o r r ) .

(vi) The background counting rate of the counter is mainly caused by cosmic radiation, especially muons. The radioactivity of the counter contributes < 30% to the background. This emphasizes the importance of using heavily shielded (under-ground) counting rooms.

Chapter 4