A figure of merit for gamma-ray polarimeters

NUCLEAR

INSTRUMENTS

AND

METHODS

A FIGURE OF MERIT

B. A Umu

(1973) 603-604;

108

0

FOR GAMMA-RAY

LOGAN

and

R. T

NORTH-HOLLAND

PUBLISHING

CO

POLARIMETERS

JONES

of Ottawa - Carleton Umv Nuclear Physzcs Group, Physzcs Deparfment,

Umverszty

of Ottawa,

Ottawa

2, Ontano,

Canada

A LJUBICIC Znstrtute RudJer BoikovrC, Zagreb, Recewed

16 January

Yugoslavza

1973

A figure of merit for gamma-ray polarlmeters IS proposed. Various polarlmeters are analysed on the basis of the proposed figure of ment

In recent years several gamma-ray polanmeters with good energy resolution have been developed’-“). Although the polarlzatlon sensitivities of the polanmeters have usually been investigated thoroughly only a few comparisons of their respective detection efficlencles have been made’,“). The quality of a polanmeter depends on both its polarization sensitivity and its detection efficiency It 1s the purpose of this note to propose a figure of merit which allows a quantitative comparison of the qualities of different polarlmeters Polarlmeters are designed to given an asymmetry A A 1s equal to the product QP. Q IS the polarization sensltlvlty of the polarlmeter (0 < Q < 1) and P 1s the linear polarization of the photons (0

If o~/A 1s to be determined necessary that T>

(1)

T = (N,+N,)

(C)-l I-‘.

of A, 1s

(2)

I 1s the number of photons per umt time incident on the polarlmeter and I 1s the average full energy peak detection efficiency.


It 1s

(3)

This suggests that a suitable figure of merit for a polanmeter will be EQ2 as increasing this product by some factor will decrease the time necessary to acheve ca/A < x by approximately the same factor A slmllar criterion 1s well known m the case of polarlmeters designed to measure the polanzatlon of proton and neutron beams”). The proposed figure of merit neglects the term (1 - Q2 P2) If P M 1, a figure of merit CQ’/(l - Q”) could be used

N, and N2 are the counts accumulated m equal time intervals when the polarlmeter has two different onentatlons with respect to the plane of polarization of the photons. Often Q 1s known reasonably accurately and the relative statlstlcal uncertainty a,/P 1s limited by uA/A It can be shown that

for the measurement

l-Q2P2 (2Q2) (1p2) x2 *

A=-. N,-N2 N, +N2

T, the time necessary given by

to some value

The analysis above assumes that uncertamtles m P are dominated by the uncertainty m A and this assumes that Q has been determined accurately. Q 1s often determined by measuring the asymmetry produced by photon beams of known polarization. The statistical arguments outlined above also apply to the expenmental determination of Q and polarlmeters with higher values of .CQ2 will be easier to calibrate accurately. In this context the relatlonshlp (3) also shows that the quality of a photon beam used for cahbratlon IS measured by the product IP’. Using the proposed figure of merit as a basis for comparison it has been shown that a polarlmeter constructed with two Sl(Ll) detectors 1s supenor to a polarlmeter which uses only one Sl(Ll) detector’) Slmllar conclusions were made m the case of NaI(T1) polarimeters’2). More recently Twin has measured the detection efficiencies of several polarlmeters of known polarlzatlon sensitivity and has used the product EQ as a measure of the quality of a polanmeter”) Other workers have used the same cntenon2) Twm concluded

603

604

B. A. LOGAN

that the 3.5 cm x 1.5 cm x 0 6 cm planar Ge(L1) polanmeter mvestlgated was only 13% as good at 0.8 MeV as a conventional Compton polanmeter constructed with a 48 cm3 Ge(L1) scattermg counter and a 35 cm3 side counter At 3 MeV the planar detector was only 4% as good as the conventional polanmeter. These figures Include a potential factor of two increase m the detectlon efficiency of a conventional polarlmeter when two side counters are used If the proposed figure of merit 1s used as a basis of comparison the planar detector 1s only about 2% as good as the conventional polarlmeter at 0 8 MeV and 1% as good at 3 MeV Larger planar Ge(L1) detectors than that used by Twm are avallable6s7) No experlmental measurements of the detection efficlencles of these larger planar detectors have been reported but, If it 1s assumed that the detection efficlencles are approximately proportional to the detector volumes, an Increase m the detectlon efficiency of about a factor of 4 3 IS expected The polarlzatlon sensltlvltles of the larger detectors have been mvestlgated thoroughly and are about the same as that of the detector of Twm. The figures of merit of these larger planar polarlmeters are still an order of magmtude below the conventional polan-

et al

meter Apphcatlon of the proposed figure of merit gives results that mdlcate that the advantages of smgle detector polarlmeters are probably limited to the slmphclty of the auxlhary apparatus and to the shghtly superior energy resolution which can be attained

References 1) A E Lltherland,

G T Ewan and G A Bartholomew, Bull Am Phys Sot 13 (1968) 1405 2) J Honzatko and J Kajfosz, Czech J Phys B19 (1969) 1281 and 3) C Broude, 0 Hausser, H Malm, J F Sharpey-Schafer T K Alexander, Nucl Instr and Meth 69 (1969) 29 4) G E Owen and Y K Lee, Nucl Instr and Meth 82 (1970) 173 5) B A Logan, Nucl Instr and Meth 82 (1970) 149 9 A. E LItherland, G T Ewan and S T Lam, Can J Phys 48 (1970) 2320 7) H Ropke, H Grawe and G Hammel, Nucl Phys Al72 (1971) 499 8) B A Logan, Can J Phys 49 (1971) 2612 9 A LJublEIC and B A Logan, Nucl Instr and Meth 96 (1971) 441 lo) P Twm, Nucl Instr and Meth 103 (1972) 613 11) L Wolfer&em, Phys Rev 75 (1949) 1664 9 A LJublElC and B A Logan, Nucl Instr and Meth 99 (1972) 269