63:). This is of most interest in terms of radiation interaction with composite materials. For bulk interaction properties, it can be useful to define an effective atomic number for a composite medium and, depending on the context, this may be done in different ways. Such methods include (i) a simple mass-weighted average, (ii) a
67:
type method with some (very approximate) relationship to radiation interaction properties or (iii) methods involving calculation based on interaction cross sections. The latter is the most accurate approach (Taylor 2012), and the other more simplified approaches are often inaccurate even when used in
412:
interact with a substance, as certain types of photon interactions depend on the atomic number. The exact formula, as well as the exponent 2.94, can depend on the energy range being used. As such, readers are reminded that this approach is of very limited applicability and may be quite misleading.
416:
This 'power law' method, while commonly employed, is of questionable appropriateness in contemporary scientific applications within the context of radiation interactions in heterogeneous media. This approach dates back to the late 1930s when photon sources were restricted to low-energy
239:
433:
between Z has been shown for a limited number of compounds for low-energy x-rays, but within the same publication it is shown that many compounds do not lie on the same trendline. As such, for polyenergetic photon sources (in particular, for applications such as
404:
312:
O), made up of two hydrogen atoms (Z=1) and one oxygen atom (Z=8), the total number of electrons is 1+1+8 = 10, so the fraction of electrons for the two hydrogens is (2/10) and for the one oxygen is (8/10). So the
83:
447:
by weighting against the spectrum of the source. The effective atomic number for electron interactions may be calculated with a similar approach. The cross-section based approach for determining
71:
In many textbooks and scientific publications, the following - simplistic and often dubious - sort of method is employed. One such proposed formula for the effective atomic number,
454:
is obviously much more complicated than the simple power-law approach described above, and this is why freely-available software has been developed for such calculations.
327:
302:
269:
672:
Taylor, M. L. (2011). "Robust determination of effective atomic numbers for electron interactions with TLD-100 and TLD-100H thermoluminescent dosimeters".
27:
within that medium. There are numerous mathematical descriptions of different interaction processes that are dependent on the atomic number,
707:
Taylor, M. L.; Smith, R. L.; Dossing, F.; Franich, R. D. (2012). "Robust calculation of effective atomic numbers: The Auto-Zeffsoftware".
234:{\displaystyle Z_{\text{eff}}={\sqrt{f_{1}\times (Z_{1})^{2.94}+f_{2}\times (Z_{2})^{2.94}+f_{3}\times (Z_{3})^{2.94}+\cdots }}}
616:"Electron Interaction with Gel Dosimeters: Effective Atomic Numbers for Collisional, Radiative and Total Interaction Processes"
438:), the effective atomic number varies significantly with energy. It is possible to obtain a much more accurate single-valued
429:
which incorporates a ‘constant’ of 2.64 × 10, which is in fact not a constant but rather a function of the photon energy. A
571:
Taylor, M. L.; Franich, R. D.; Trapp, J. V.; Johnston, P. N. (2008). "The effective atomic number of dosimetric gels".
761:
674:
Nuclear
Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
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681:
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32:
24:
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48:
724:
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638:
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488:
56:
36:
280:
247:
748:
Eisberg and
Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles.
720:
685:
634:
484:
755:
20:
658:
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435:
399:{\displaystyle Z_{\text{eff}}={\sqrt{0.2\times 1^{2.94}+0.8\times 8^{2.94}}}=7.42}
546:
23:
of a material exhibits a strong and fundamental relationship with the nature of
693:
533:
Spiers, W. (1946). "Effective atomic number and energy absorption in tissues".
471:
Murty, R. C. (1965). "Effective Atomic
Numbers of Heterogeneous Materials".
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52:
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Taylor, M. L.; Franich, R. D.; Trapp, J. V.; Johnston, P. N. (2009).
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409:
16:
Approximate atomic number calculated for materials with many elements
47:
in this context is equivalent to the atomic number but is used for
418:
60:
573:
Australasian
Physical & Engineering Sciences in Medicine
408:
The effective atomic number is important for predicting how
514:
Mayneord, W. (1937). "The significance of the Röntgen".
39:), one therefore encounters the difficulty of defining
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86:
398:
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35:(i.e. a bulk material composed of more than one
8:
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68:a relative fashion for comparing materials.
421:units. The exponent of 2.94 relates to an
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271:is the fraction of the total number of
304:is the atomic number of each element.
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516:Unio Internationalis Contra Cancrum
14:
275:associated with each element, and
55:of different materials (such as
308:An example is that of water (H
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1:
535:British Journal of Radiology
547:10.1259/0007-1285-19-218-52
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694:10.1016/j.nimb.2011.02.010
45:effective atomic number
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25:radiation interactions
427:photoelectric process
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297:{\displaystyle Z_{n}}
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264:{\displaystyle f_{n}}
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31:. When dealing with
721:2012MedPh..39.1769T
686:2011NIMPB.269..770T
635:2009RadR..171..123T
485:1965Natur.207..398M
431:linear relationship
623:Radiation Research
585:10.1007/BF03178587
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729:10.1118/1.3689810
479:(4995): 398–399.
423:empirical formula
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80:, is as follows:
51:(e.g. water) and
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715:(4): 1769–1778.
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762:Atomic physics
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21:atomic number
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522:: 271–282.
458:References
370:×
351:×
273:electrons
221:⋯
192:×
153:×
114:×
65:power-law
49:compounds
756:Category
737:22482600
659:27139580
651:19138053
601:23619503
593:18697704
555:21015391
425:for the
53:mixtures
717:Bibcode
682:Bibcode
631:Bibcode
501:2175323
481:Bibcode
410:photons
37:element
735:
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649:
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473:Nature
241:where
57:tissue
655:S2CID
619:(PDF)
597:S2CID
497:S2CID
419:x-ray
43:. An
733:PMID
647:PMID
589:PMID
551:PMID
394:7.42
385:2.94
378:2.94
359:2.94
226:2.94
213:2.94
174:2.94
135:2.94
61:bone
59:and
19:The
725:doi
690:doi
678:269
639:doi
627:171
581:doi
543:doi
489:doi
477:207
452:eff
444:eff
367:0.8
348:0.2
337:eff
319:eff
93:eff
77:eff
758::
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449:Z
441:Z
391:=
374:8
364:+
355:1
342:=
333:Z
316:Z
310:2
290:n
286:Z
257:n
253:f
218:+
209:)
203:3
199:Z
195:(
187:3
183:f
179:+
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164:2
160:Z
156:(
148:2
144:f
140:+
131:)
125:1
121:Z
117:(
109:1
105:f
98:=
89:Z
74:Z
41:Z
29:Z
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