A SEMI-EMPIRICAL FORMULA FOR REPRESENTING THE FULL ENERGY PEAK EFFICIENCIES OF PLANAR GE DETECTORS

Abstract

The non destructive assay of special nuclear materials in storage containers or as waste items often calls for the full energy peak efficiency to be estimated in geometries which may be adequately described by the far field approximation. The principle energy range of interest for materials such as Pu + ²⁴¹Am and HEU is below 500 keV. Small volume LEGe detectors were once required for such applications where high resolution was needed to extract information from the complex spectral regions. Recently, large volume planar detectors called Broad Energy Ge (BEGe) detectors have become available. BEGe detectors offer high resolution at low energy, as with LEGe detectors, but with higher efficiency based on greater solid angle and thickness. However, significantly changing detector dimensions requires an examination of the adequacy of functions used to estimate and trend efficiencies. In this work we discuss how the full energy peak efficiency of such planar detectors may be estimated simply from the crystal and encapsulation dimensions. A new semi-empirical formula is presented for the calculation and parameterization of the characteristic far field full energy peak efficiency for energies below the pair production threshold. The formula is an extension of the any interaction model with allowance for the escape of fluorescent x-rays and secondary scattered radiation. A database of sixteen such planar detectors with a wide variety of dimensions, covering volumes from ~8 to ~150 cm³, is used to validate and verify the method. In principal, this simple and quick to apply method is absolute given accurate dimensions of the active volume, thickness of any frontal dead layer and details of the end cap. Alternatively it can be used as a fitting function to interpolate or extrapolate experimental data. The results show that under the conditions examined, the formula is capable of reproducing measured efficiencies to within a few percent over the energy range of interest.

Introduction

The non destructive assay of SNM in storage containers or as waste items often calls for the full energy peak (FEP) efficiency to be estimated in geometries which may be adequately described by the far field approximation (source to detector separation much larger than detector dimensions) and sources primarily in front of the detector. The principle energy range of interest for materials such as Pu + ²⁴¹Am and highly enriched uranium (HEU) is below 500 keV. This range also covers the primary range for low energy mode relative isotopic measurements of Pu by multi-group analysis methods. Small volume LEGe detectors were once popular for such applications where high resolution was needed to extract information from the complex spectral regions. Recently large volume planar detectors, so called Broad Energy Ge or BEGe detectors, have become available. These offer high energy resolution at low energies as before but with higher efficiency because of solid angle and thickness.

In this work it is discussed how the FEP efficiency, ξ FEP, of such planar detectors may be estimated simply from the crystal dimensions and those of its encapsulation. The approach may be used to estimate the absolute efficiency from fabrication information, as a means to fit absolute experimental data or to fit relative efficiency profiles as would be called for in relative isotopics analysis codes.