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XRF Escape-Peaks from Natural Elements for Nuclear Medicine Imaging and Gamma-Ray Spectrometry

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13 September 2025

Posted:

15 September 2025

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Abstract
A catalog of K-XRF escape-peak energy from natural elements and for several energies of gamma-rays incident on a single-element detector is presented. The parameters of a power-model are listed In Table I for predicting the energy of such peaks.In Table II predicted peaks are arranged in order of increasing atomic number (ranging from 4 to 92) of the detector component and for the Kα2 XRF main emission.This catalog is conceived for nuclear medicine and gamma-ray spectrometry where such peak need to be recognized and known as underlying area in order to gain advantage of quantitative analysis, but, also for detector-developers as well as for spectroscopists that should be interested in the issue.
Keywords: 
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Introduction

This catalog is conceived for nuclear medicine and gamma-ray spectrometry where the escape-peak need to be recognized and known as underlying area in order to perform quantitative analysis, but, also for detector-developers as well as for spectroscopists that should be interested in the issue.
The literature energy-emissions vs atomic number Z have been fitted to a power-model, whose parameters (listed In Table I) are used for predicting the energy of such peaks.
The quite-perfect agreement between the literature data and the power-model allows to calculate the wanted escape-peak energy without requiring specific software development.
The predicted values of XRF K-escape gamma-ray energy are presented in Table II per a dozen of incident mono-energetic photons-energies and per Z-values of single-natural element.
Each row shows, from left to right: (a) the values of Z; (b) the symbol of element; (c) the gap Kedge-Kα2 energies (where the rest of orbital emissions, i.e. Kβ2, Kβ1, Kβ3, and Kα1 are grouped); and (d) a dozen of numbers representing the escape-peak energy predicted for incident photons.
The L and M XRF emissions are ignored in this evaluation since their energy is negligible with respect to the K-ones, so also the respective fluorescence yields are equally negligible.
The physical process of the escape of the XRF of the materials constituting a detector has been held in a certain consideration to improve its performance, with particular regard to the ability to perform quantitative analyzes. This has been recently remarked in [SR25].
In fact, since XRF photons are characterized in energy, distinctive of the element of which the detector is made, the escape-process can also change, even significantly, the response function of the detector itself with the result of relocating events from the full-energy peak towards an additional peak, sometimes completely separate from the photopeak, located at lower energy. For this reason, evaluations based on the value of the integral of the counts underlying the full-energy peak are systematically underestimated if escape photons are not taken into account.
In particular cases (like thin and/or discretized detectors with identification of multiple interactions) 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 corrections [AP54].
It can be said that this is due to inevitable edge-effect since a real detector has limited dimensions and fluorescence photons undergo to non-zero probability to escape from its sensitive volume, not being revealed. Only the ideal case of a detector with infinite dimensions is free from this effect, how it is theorized in Ref.[BJ54].

Policies

Literature Coverage

Fundamentals of radiation detection including the concepts herein exposed are deeply and clearly given in Ref.[KG00]. The basic X-rays data are from Kaye & Laby, UK National Physical Laboratory, Ref.[KL13], whose completeness and accuracy fulfill the requirements of these Tables.

Data Selected

Data for this catalog are taken from Ref.[KL13], 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 and for evaluating the energy-gap, respectively.

Incident Gamma-Rays

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

Incident Gamma-Ray Energy

The considered values 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 reference.

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 Identification

Both the atomic number Z and the chemical symbol of the element are given Table II.

Photo-Electric Peak

The response of a detector to mono-energetic gamma-rays is mainly made, in an ideal pulse-height spectrum, of a vertical segment, representing the photo-electric interactions, whose abscissa is proportional to and whose length is proportional to the number of incident gammas. In the reality, the segment become a Gaussian curve, being 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 [KG00], 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 Ref. [KG00], as: EEscape = 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 Table II to show the predicted values of escape photon energy: (1) underscore for values overlapping the Compton continuum; (2) bold for those falling in the valley between Compton edge and photo-electric peak; (3) Italic for photons overlapped to the photo-peak left-tail.
Table I. Results of power-function best fit of XRF energy vs. Z for Kα2 orbitals. See pages 2-3 for Policies and Explanation.
Table I. Results of power-function best fit of XRF energy vs. Z for Kα2 orbitals. See pages 2-3 for Policies and Explanation.
orbital a b Rsquare
K-α2 0.00560144430106232 2.19086250995425 0.999952133940893
Input data are from Ref.[KL13]. The fitting has been limited to the elements having 4 ≤ Z ≤ 92.
Table II. Predicted values of XRF escape energy Eγ-Kα2 (keV) - part 1 of 2, for Z = 4 , ... , 50. See pages 2-3 for Policies and Explanation.
Table II. Predicted values of XRF escape energy Eγ-Kα2 (keV) - part 1 of 2, for Z = 4 , ... , 50. See pages 2-3 for Policies and Explanation.
Z-Sy Eedge-Kα2 incident-photon energy Eγ (keV)
(keV) 100.0 125.0 150.0 175.0 200.0 250.0 300.0 350.0 400.0 500.0 600.0 700.0
4-Be 0.006 99.9 124.9 149.9 174.9 199.9 249.9 299.9 349.9 399.9 499.9 599.9 699.9
5-B 0.005 99.8 124.8 149.8 174.8 199.8 249.8 299.8 349.8 399.8 499.8 599.8 699.8
6-C 0.005 99.7 124.7 149.7 174.7 199.7 249.7 299.7 349.7 399.7 499.7 599.7 699.7
7-N 0.004 99.6 124.6 149.6 174.6 199.6 249.6 299.6 349.6 399.6 499.6 599.6 699.6
8-O -0.002 99.5 124.5 149.5 174.5 199.5 249.5 299.5 349.5 399.5 499.5 599.5 699.5
9-F 0.015 99.3 124.3 149.3 174.3 199.3 249.3 299.3 349.3 399.3 499.3 599.3 699.3
10-Ne 0.010 99.2 124.2 149.2 174.2 199.2 249.2 299.2 349.2 399.2 499.2 599.2 699.2
11-Na 0.039 99.0 124.0 149.0 174.0 199.0 249.0 299.0 349.0 399.0 499.0 599.0 699.0
12-Mg 0.056 98.8 123.8 148.8 173.8 198.8 248.8 298.8 348.8 398.8 498.8 598.8 698.8
13-Al 0.076 98.5 123.5 148.5 173.5 198.5 248.5 298.5 348.5 398.5 498.5 598.5 698.5
14-Si 0.101 98.3 123.3 148.3 173.3 198.3 248.3 298.3 348.3 398.3 498.3 598.3 698.3
15-P 0.130 98.0 123.0 148.0 173.0 198.0 248.0 298.0 348.0 398.0 498.0 598.0 698.0
16-S 0.164 97.7 122.7 147.7 172.7 197.7 247.7 297.7 347.7 397.7 497.7 597.7 697.7
17-Cl 0.204 97.4 122.4 147.4 172.4 197.4 247.4 297.4 347.4 397.4 497.4 597.4 697.4
18-Ar 0.247 97.1 122.1 147.1 172.1 197.1 247.1 297.1 347.1 397.1 497.1 597.1 697.1
19-K 0.296 96.7 121.7 146.7 171.7 196.7 246.7 296.7 346.7 396.7 496.7 596.7 696.7
20-Ca 0.346 96.4 121.4 146.4 171.4 196.4 246.4 296.4 346.4 396.4 496.4 596.4 696.4
21-Sc 0.400 96.0 121.0 146.0 171.0 196.0 246.0 296.0 346.0 396.0 496.0 596.0 696.0
22-Ti 0.460 95.6 120.6 145.6 170.6 195.6 245.6 295.6 345.6 395.6 495.6 595.6 695.6
23-V1 0.519 95.1 120.1 145.1 170.1 195.1 245.1 295.1 345.1 395.1 495.1 595.1 695.1
24-Cr 0.582 94.7 119.7 144.7 169.7 194.7 244.7 294.7 344.7 394.7 494.7 594.7 694.7
25-Mn 0.649 94.2 119.2 144.2 169.2 194.2 244.2 294.2 344.2 394.2 494.2 594.2 694.2
26-Fe 0.721 93.7 118.7 143.7 168.7 193.7 243.7 293.7 343.7 393.7 493.7 593.7 693.7
27-Co 0.797 93.2 118.2 143.2 168.2 193.2 243.2 293.2 343.2 393.2 493.2 593.2 693.2
28-Ni 0.878 92.6 117.6 142.6 167.6 192.6 242.6 292.6 342.6 392.6 492.6 592.6 692.6
29-Cu 0.965 92.0 117.0 142.0 167.0 192.0 242.0 292.0 342.0 392.0 492.0 592.0 692.0
30-Zn 1.057 91.4 116.4 141.4 166.4 191.4 241.4 291.4 341.4 391.4 491.4 591.4 691.4
31-Ga 1.155 90.8 115.8 140.8 165.8 190.8 240.8 290.8 340.8 390.8 490.8 590.8 690.8
32-Ge 1.259 90.2 115.2 140.2 165.2 190.2 240.2 290.2 340.2 390.2 490.2 590.2 690.2
33-As 1.368 89.5 114.5 139.5 164.5 189.5 239.5 289.5 339.5 389.5 489.5 589.5 689.5
34-Se 1.485 88.8 113.8 138.8 163.8 188.8 238.8 288.8 338.8 388.8 488.8 588.8 688.8
35-Br 1.605 88.1 113.1 138.1 163.1 188.1 238.1 288.1 338.1 388.1 488.1 588.1 688.1
36-Kr 1.732 87.4 112.4 137.4 162.4 187.4 237.4 287.4 337.4 387.4 487.4 587.4 687.4
37-Rb 1.866 86.6 111.6 136.6 161.6 186.6 236.6 286.6 336.6 386.6 486.6 586.6 686.6
38-Sr 2.008 85.9 110.9 135.9 160.9 185.9 235.9 285.9 335.9 385.9 485.9 585.9 685.9
39-Y 2.155 85.1 110.1 135.1 160.1 185.1 235.1 285.1 335.1 385.1 485.1 585.1 685.1
40-Zr 2.305 84.2 109.2 134.2 159.2 184.2 234.2 284.2 334.2 384.2 484.2 584.2 684.2
41-Nb 2.464 83.4 108.4 133.4 158.4 183.4 233.4 283.4 333.4 383.4 483.4 583.4 683.4
42-Mo 2.628 82.5 107.5 132.5 157.5 182.5 232.5 282.5 332.5 382.5 482.5 582.5 682.5
43-Tc 2.797 81.6 106.6 131.6 156.6 181.6 231.6 281.6 331.6 381.6 481.6 581.6 681.6
44-Ru 2.973 80.7 105.7 130.7 155.7 180.7 230.7 280.7 330.7 380.7 480.7 580.7 680.7
45-Rh 3.156 79.8 104.8 129.8 154.8 179.8 229.8 279.8 329.8 379.8 479.8 579.8 679.8
46-Pd 3.344 78.8 103.8 128.8 153.8 178.8 228.8 278.8 328.8 378.8 478.8 578.8 678.8
47-Ag 3.540 77.8 102.8 127.8 152.8 177.8 227.8 277.8 327.8 377.8 477.8 577.8 677.8
48-Cd 3.742 76.8 101.8 126.8 151.8 176.8 226.8 276.8 326.8 376.8 476.8 576.8 676.8
49-In 3.951 75.8 100.8 125.8 150.8 175.8 225.8 275.8 325.8 375.8 475.8 575.8 675.8
50-Sn 4.167 74.7 99.7 124.7 149.7 174.7 224.7 274.7 324.7 374.7 474.7 574.7 674.7
Styles for estimated escape peak position Underscore: overlapped to the Compton continuum;
in the detector response function: Bold: in the valley between Compton edge and photo-electric peak;
Italic: overlapped to the photo-peak left-tail.
Table III. Predicted values of XRF escape energy Eγ-Kα2 (keV) - part 2 of 2, for Z = 51 , ... , 92. See pages 2-3 for Policies and Explanation.
Table III. Predicted values of XRF escape energy Eγ-Kα2 (keV) - part 2 of 2, for Z = 51 , ... , 92. See pages 2-3 for Policies and Explanation.
Z-Sy Eedge-Kα2 incident photon energy Eγ (keV)
(keV) 100.0 125.0 150.0 175.0 200.0 250.0 300.0 350.0 400.0 500.0 600.0 700.0
51-Sb 4.389 73.6 98.6 123.6 148.6 173.6 223.6 273.6 323.6 373.6 473.6 573.6 673.6
52-Te 4.616 72.5 97.5 122.5 147.5 172.5 222.5 272.5 322.5 372.5 472.5 572.5 672.5
53-I 4.851 71.4 96.4 121.4 146.4 171.4 221.4 271.4 321.4 371.4 471.4 571.4 671.4
54-Xe 5.092 70.2 95.2 120.2 145.2 170.2 220.2 270.2 320.2 370.2 470.2 570.2 670.2
55-Cs 5.341 69.1 94.1 119.1 144.1 169.1 219.1 269.1 319.1 369.1 469.1 569.1 669.1
56-Ba 5.597 67.9 92.9 117.9 142.9 167.9 217.9 267.9 317.9 367.9 467.9 567.9 667.9
57-La 5.860 66.6 91.6 116.6 141.6 166.6 216.6 266.6 316.6 366.6 466.6 566.6 666.6
58-Ce 6.131 65.4 90.4 115.4 140.4 165.4 215.4 265.4 315.4 365.4 465.4 565.4 665.4
59-Pr 6.408 64.1 89.1 114.1 139.1 164.1 214.1 264.1 314.1 364.1 464.1 564.1 664.1
60-Nd 6.691 62.8 87.8 112.8 137.8 162.8 212.8 262.8 312.8 362.8 462.8 562.8 662.8
61-Pm 6.981 61.5 86.5 111.5 136.5 161.5 211.5 261.5 311.5 361.5 461.5 561.5 661.5
62-Sm 7.278 60.1 85.1 110.1 135.1 160.1 210.1 260.1 310.1 360.1 460.1 560.1 660.1
63-Eu 7.584 58.8 83.8 108.8 133.8 158.8 208.8 258.8 308.8 358.8 458.8 558.8 658.8
64-Gd 7.898 57.4 82.4 107.4 132.4 157.4 207.4 257.4 307.4 357.4 457.4 557.4 657.4
65-Tb 8.221 55.9 80.9 105.9 130.9 155.9 205.9 255.9 305.9 355.9 455.9 555.9 655.9
66-Dy 8.553 54.5 79.5 104.5 129.5 154.5 204.5 254.5 304.5 354.5 454.5 554.5 654.5
67-Ho 8.894 53.0 78.0 103.0 128.0 153.0 203.0 253.0 303.0 353.0 453.0 553.0 653.0
68-Er 9.243 51.5 76.5 101.5 126.5 151.5 201.5 251.5 301.5 351.5 451.5 551.5 651.5
69-Tm 9.601 50.0 75.0 100.0 125.0 150.0 200.0 250.0 300.0 350.0 450.0 550.0 650.0
70-Tb 9.968 48.4 73.4 98.4 123.4 148.4 198.4 248.4 298.4 348.4 448.4 548.4 648.4
71-Lu 10.346 46.9 71.9 96.9 121.9 146.9 196.9 246.9 296.9 346.9 446.9 546.9 646.9
72-Hf 10.734 45.3 70.3 95.3 120.3 145.3 195.3 245.3 295.3 345.3 445.3 545.3 645.3
73-Ta 11.128 43.6 68.6 93.6 118.6 143.6 193.6 243.6 293.6 343.6 443.6 543.6 643.6
74-W 11.535 42.0 67.0 92.0 117.0 142.0 192.0 242.0 292.0 342.0 442.0 542.0 642.0
75-Re 11.952 40.3 65.3 90.3 115.3 140.3 190.3 240.3 290.3 340.3 440.3 540.3 640.3
76-Os 12.382 38.6 63.6 88.6 113.6 138.6 188.6 238.6 288.6 338.6 438.6 538.6 638.6
77-Ir 12.824 36.9 61.9 86.9 111.9 136.9 186.9 236.9 286.9 336.9 436.9 536.9 636.9
78-Pt 13.277 35.1 60.1 85.1 110.1 135.1 185.1 235.1 285.1 335.1 435.1 535.1 635.1
79-Au 13.739 33.4 58.4 83.4 108.4 133.4 183.4 233.4 283.4 333.4 433.4 533.4 633.4
80-Hg 14.215 31.6 56.6 81.6 106.6 131.6 181.6 231.6 281.6 331.6 431.6 531.6 631.6
81-Tl 14.700 29.7 54.7 79.7 104.7 129.7 179.7 229.7 279.7 329.7 429.7 529.7 629.7
82-Pb 15.204 27.9 52.9 77.9 102.9 127.9 177.9 227.9 277.9 327.9 427.9 527.9 627.9
83-Bi 15.725 26.0 51.0 76.0 101.0 126.0 176.0 226.0 276.0 326.0 426.0 526.0 626.0
84-Po 16.250 24.1 49.1 74.1 99.1 124.1 174.1 224.1 274.1 324.1 424.1 524.1 624.1
85-At 16.787 22.2 47.2 72.2 97.2 122.2 172.2 222.2 272.2 322.2 422.2 522.2 622.2
86-Rn 17.337 20.2 45.2 70.2 95.2 120.2 170.2 220.2 270.2 320.2 420.2 520.2 620.2
87-Fr 17.900 18.3 43.3 68.3 93.3 118.3 168.3 218.3 268.3 318.3 418.3 518.3 618.3
(*) 88-Ra 18.475 100.0 41.3 66.3 91.3 116.3 166.3 216.3 266.3 316.3 416.3 516.3 616.3 (*)
(*) 89-Ac 19.063 100.0 39.2 64.2 89.2 114.2 164.2 214.2 264.2 314.2 414.2 514.2 614.2 (*)
(*) 90-Th 19.689 100.0 37.2 62.2 87.2 112.2 162.2 212.2 262.2 312.2 412.2 512.2 612.2 (*)
(*) 91-Pa 20.312 100.0 35.1 60.1 85.1 110.1 160.1 210.1 260.1 310.1 410.1 510.1 610.1 (*)
(*) 92-U 20.947 100.0 33.0 58.0 83.0 108.0 158.0 208.0 258.0 308.0 408.0 508.0 608.0 (*)
(*) For Z ≥ 88 the value of Eγ is under the threshold of XRF K-emissions.
Styles for estimated escape peak position Underscore: overlapped to the Compton continuum;
in the detector response function: Bold: in the valley between Compton edge and photo-electric peak;
Italic: overlapped to the photo-peak left-tail.

References

  1. [AP54] Axel, P. Intensity Corrections for Iodine X-Rays Escaping from Sodium Iodide Scintillation Crystals. Rev. Sci. Instrum. 1954, 25, 391.
  2. [BJ54] Birks, J. B. Scintillation Counters. Pergamon Press LTD, London, 1954.
  3. [KG00] Knoll, G.F. Radiation Detection and Measurement, 3rd ed.; John Wiley & Sons, Inc.: New York, NY, USA, 2000; ISBN 0-471-07338-5.
  4. [KL13] Kaye & Laby. Tables of Physical & Chemical Constants, X-Ray Absorption Edges, Characteristic X-Ray Lines and Fluorescence Yields. National Physical Laboratory (NPL), Teddington, UK, 2013.
  5. [SR25] Scafè, R.; Puccini, M.; Pellegrini, R.; Pani, R. XRF-Escape Scintillator Footprints for Nuclear Medicine Imaging and Gamma-Ray Spectrometry. Photonics 2025, 12, 191.
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