A Catalog of XRF-Escape Peaks from Radiation Detectors Compounds for Nuclear Molecular Medicine and Gamma-Ray Spectrometry

Raffaele Scafè; Marco Puccini; Rosanna Pellegrini; Roberto Pani

doi:10.20944/preprints202510.2250.v1

Submitted:

24 October 2025

Posted:

29 October 2025

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Abstract

A catalog of values of predicted energies of the K-XRF escape-peaks from compounds, used for radiation detectors, is presented for given incident gamma-rays suited for nuclear molecular medicine and low-energy spectrometry. The information relating to the compounds adds to that relating to the individual natural elements recently posted [RSC2025a]. The results of powerfunctions best-fit of XRF energy values vs. Z are listed in Table 1 for Kα2 orbital and Kedge. These expressions, allow simple calculations, avoiding the development of complex software. An extensive literature survey has been carried out mainly considering text-books, review articles and research reports. A final number compounds (Nc) equal to 729 has been obtained, whose distribution per number of constituting elements (Ne) is reported in Table 2. The predicted energy peaks are arranged in Tables 3 to 7 per Ne in the range from 2 to 8, showing the average value of 3.92 elements per compound. The catalog is conceived for nuclear molecular medicine and gamma-ray spectrometry where such peaks need to be recognized and their underlying area known in order to allow quantitative information.

Keywords:

radiation detector

;

nuclear molecular medicine

;

gamma-ray spectrometry

Subject:

Physical Sciences - Radiation and Radiography

Introduction

Since the XRF photons are typical of the element making-up the detector, the escape-process changes the detector response function by moving away events from the full-energy peak towards an additional peak, sometimes completely separate from the photopeak, located at Egamma-EXRF, for Egamma > EXRF. Due to this reason, the evaluations based on the value of the integral of the counts underlying the full-energy peak are systematically underestimated if the escape photons corrections are not taken into account.

In particular assemblies (like thin and/or discretized detectors) the number of events whose energy falls under the escape peak may even equal or even exceed that of photons under the full-energy peak making necessary to apply corrections [PAX1954].

It must be remarked that this is due to unavoidable edge-effect since a real detector has limited dimensions and fluorescence photons undergo to non-zero probability to escape from the sensitive volume, not being revealed. Only the ideal case of a detector with infinite dimensions is free from this effect, as schematized in [JBR1954].

It is to be noted that the emissions from the L and the other lower-energy orbitals are discarded in the present evaluation since the involved values are negligible with respect to the K-ones, and so also occur for the respective fluorescence yields.

The values of energy of K-XRF-escape gamma-ray are predicted per 12 incident photons-energy values from 100 to 700 keV. Results are presented in Tables 3 to 7, arranged per Ne = 2, … , 8 and per compound id. This will confirm as the detector transfer function is perturbed more and more as Ne increases, due to the multiple presence of escape energies in the pulse-height spectrum.

The elements sequence utilized in the chemical formula, from left to right, is the same identifying the lines from top to bottom.

The first line of the compound shows, from left to right, the compound-id and the citing reference.

The format of the compound id. takes into account the different symbol-length by doubling the single-character ones (so, as an example, BB stays for B – boron and so on).

The format of reference code (AAAYYYYa) is made by sub-strings related to (a) first-Author, (b) year of first publication, and (c) a code of multiple publication in the year.

The following Ne rows of the compound show, from left to right.

- the atomic number Z of the element and their symbol;

- the value of the energy-spread (in keV) between Kedge and Kα2 lines, representing the gap of the rest of K-orbital emissions, i.e. Kβ2, Kβ1, Kβ3, and Kα1; and

- a dozen of numbers representing the escape-peak energy predicted for the correspondent mono-energetic incident photons.

Policies

Literature Coverage

Fundamentals of radiation detection including the concepts herein exposed are deeply and clearly given in Ref.[GKN1999]. The basic X-rays data are from Kaye & Laby, UK National Physical Laboratory [K&L2013], whose completeness and accuracy fulfill the requirements of the Catalog. The other literature citations are from text-books, review articles, research reports, conference papers, etc… whose titles are reported in the Reference list.

Data Selected

Data for this catalog are taken from [K&L2013], limited to those of XRF energy in the columns Kα2 and Kedge (for 4 ≤ Z ≤ 92) that are used for power-function best fit performing whose parameters are needed for calculations.

Incident Gamma-Rays

Listed in each result Table is the header specifying the dozen of values of mono-energetic incident gamma-rays considered for the calculations of escape-peaks of different elements.

The values considered in calculations are: 100, 125, 150, 175, 200, 250, 300, 350, 400, 500, 600 and 700 keV. The range includes the energies from all the radio-isotopes used for tracing pharmaceutical administered in SPECT and PET protocols. The last interval is extended up to 700 keV for considering also the 662 keV photons from Cs-137 sources, widely used for energy-calibration.

Escape-Energy Uncertainty

The uncertainty of 0.2-0.3 keV can be assumed, despite submission to the fitting process. On the other hand the tabulated X-rays can be considered affected by uncertainties in the order of a few eV because they are listed in keV with 3 decimal places.

Escape Gamma-Ray Intensity

The intensity of escape-gamma-ray cannot be easily estimated like their energy. Appropriate Monte Carlo simulation studies of the detector-source systems must be performed aimed to predict intensity values.

Element and Compound Identification

Both the atomic number Z and the symbol of chemical element are given in the results Tables 3 to 7.

The format of the compound id. takes into account the different symbol-length by doubling the single-character ones (so, as an example, BB stays for B – boron and so on).

Photo-Electric Peak

The response of a detector to mono-energetic gamma-rays Eγ is mainly made, in an ideal pulse-height spectrum, of a vertical segment, representing the photo-electric interactions, whose abscissa is proportional to Eγ and whose length is proportional to the number of incident gammas. In the reality, the segment becomes a Gaussian curve, due to the enlargement produced by the detector-energy-resolution.

Compton-Effect

Another process affecting the detector response is the Compton scattering, that produces a continuum ranging from zero to the so-called Compton-edge, arising at the end of this continuum. The energy-distance between the Compton edge and the centroid of photo-electric peak can be calculated as (see [GKN1999], p.310):

EC = Eγ / ( 1 + 2 ( Eγ / m0 c² ) ) , that is < Eγ .

Detector Response-Function (DRF)

If Eγ < 2 m0 c² the response function shows only the two items above described. Based on these values it is reasonable, in a first approximation, to localize the energy at which a valley occurs between the photoelectric-peak and the Compton-edge, as: Evalley ≈ ½ ( Eγ + EC ).

Escape Peaks

Energies of gamma-ray peaks which result from escape of XRF photons from the detector are calculated, according to [GKN1999], as: EEscape = Eγ - EXRF , for Eγ > EXRF . Based on the energy of a given escape photon and on the above considerations regarding the DRF, these photons can be classified according to their position on the DRF. The three following styles are used in Tables 3 to 7 to show the predicted values of escape photon energy: (a) for values overlapping the Compton continuum; (b) for those falling in the region between Compton edge and photo-electric peak; (c) for those overlapped to the photo-peak left-tail.

Table 1. Results of power-function best fit of XRF energy vs. Z for Kα2 orbital and Kedge. See Policies and Explanation

K Orbital	a (keV)	b	Rsquare
α2	0.00560144430106232	2.19086250995425	0.99995
edge	0.00628705594993865	2.12213694400228	0.99990

XRF characteristic energy Vs. atomic number, for a given orbital:

EXRF = a * (Z ^ b), where a and b characterize the orbitals for Z = 4 to 92.

Table 2. Statistics of compounds per number of elements Ne = 2, …, 8, See Policies and Explanation.

N° of elements Ne	N° of compounds Nc	Table
2	77	III
3	198	IV
4	222	V
5	179	VI
6	43	VII
7	9	VII
8	1	VII
Total	729

The distribution shows the average value of 3.92 elements per compound.

Table 3. part (1/5) – Predicted values of XRF-escape energy Eγ-EKα2 for two-component detectors.