Corrections to coaxial Ge(Li) detector solid angle correction factors

NUCLEAR INSTRUMENTS AND METHODS 87 (I970)

I47--I48;

© NORTH-HOLLAND PUBLISHING CO.

C O R R E C T I O N S T O COAXIAL Ge(Li) D E T E C T O R SOLID ANGLE C O R R E C T I O N FACTORS* D.C. CAMP and A. L. VAN LEHN Lawrence Radiation Laboratory, University of California, Livermore, California, U.S.A. Received 22 July 1970 This letter discusses additional corrections needed for solid angle correction factors for coaxial detectors.

We acknowledge the error noted by Ani6in and Bikit 1) in our earlier work2). That is, we did not account for the attenuation of radiation which passes through the coaxial core before reaching active material. Thus eq. (9) and the bracketed term in eq. (A1) of ref. 2 for the integration of zone 1 (fig. 10, ref. 2) should include an attenuation factor: e -'(e)ox(') ( 1 - e-'(E)ox(')'),

(1)

where x(a)t is given by expression (A10) and x(a), the path length for inactive material, is given by

x(a) = ( r - n - d d ) c o s e c a - s sec a.

(2)

The same notation used in ref. 2 is used here. This modification decreases the solid angle corrections given in our tables. The amount of change increases as the energy, source distance, and detector depletion depth decrease, and as the detector length increases. The major changes occur at low energies and for large inactive or core solid angles. The percentage decreases shown in the detector * This work was performed under the auspices of the United States Atomic Energy Commission. s ~

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example of Ani6in and Bikin are essentially correct; however, the value of their J2/Jo and Jl/Jo corrections differ from ours. We believe this is due to the theoretical z(E) they used. For the case they cited, the decrease in the corrections does not exceed 4% at 5 cm, but is 14% at 3 c m and 30keV. For a 50ram diameter detector with a 16 mm depletion depth at 3 cm source distance for 30 keV radiation, the decrease is 43.5%. We have recalculated the correction coefficients and provide in the figures and table below a means of correcting our former tabular values for coaxial detectors. The new J2/Jo and J4/Jo values (subscript v) are obtained from the former values using the following equations:

(J2/J4)v = (J2/Jo)tab R2(E),

(3)

(J4/J2)v = (J4/Jo)tab R4 (E) .

(4)

The R,(E) are percentage reduction factors in the former (J,/Jo) tabular values as given in ref. 2. Explicitly R4(E) = 1 - (P.L.D.S), (5) Rz(E) ~ [1-¼(P.L.D.S.)], except for q~ = 40 mm at 3 cm, which is (1 - ½ P.L.O.S). (6)

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3

50, 8, 5.74, --37, 12, 5.67,

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34, II, 5.36, 3

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2.0 ~

7, %05, 3

50, 16, 5.04, 5 -45, I~, ~.70, 5

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30

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60

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200

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300

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1000

Fig. 1. Part of the correction needed for the solid angle correction factors for coaxial detectors. See text for complete expression.

147

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Fig. 2. Part of the correction needed for the solid angle correction factors for coaxial detectors. See text for complete expression.

148

D. C. C A M P

AND

A. L. V A N

LEHN

TABLE I

for

(mm) s > S

50 5 cm 25

45 5 cm 25

40 3 cm 9

37 3 cm 9

34 3 cm 9

30 3 cm 9

26 3 cm 9

(1.15 s) 2

(1.13 s) 2

(1.34 s) 2

(1.27 s) 2

(1.21 s) 2

(1.3 s) g

(1.15 s) 2

Here P is obtained from fig. 1 below, L is the reciprocal of F which is obtained from fig. 2. The abscissa of fig. 2 is the ratio of length of the new detector to the length of the standard detector sizes shown in fig. 1. D is given by [ v/ side2. O =,rclrc 1~,,

rc =

(r-n-dd),

(7)

where restd is calculated from one of the standard depletion depths shown in fig. 1, and S is given in table 1. If the source-to-detector distance is equal to the distances shown above, S is 1. Because of the very large solid angle correction factors which result for distances less than those shown above, we strongly recommend not using these detectors closer than 3 or 5 cm as indicated.

Ani6in and Bikit state that similar changes occur for five-sided detectors. This is true only if the coaxial or p-type core end faces the detector. The solid angle corrections given in our tables were all for the closed or totally active end oriented toward the source. Our new calculations with modifications similar to those above indicate no changes at all are required for "five-sided" detectors of either cylindrical or trapezoidal geometry with the closed end oriented toward the source. References 1) I. V. Ani~in and I. S. Bikit, Nucl. Instr. and Meth. 87 (1970) 145. 2) D. C. C a m p and A. L. Van Lehn, Nucl. Instr. and Meth. 76 (1969) 192.