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# Mass attenuation coefficient

### NIST: X-Ray Mass Attenuation Coefficients - Table

1. X-Ray Mass Attenuation Coefficients Table 3. Values of the mass attenuation coefficient, μ/ρ, and the mass energy-absorption coefficient, μ en /ρ, as a function of photon energy, for elemental media. Atomic absorption edges are indicated by the shell designation
2. Tables and graphs of the photon mass attenuation coefficient μ / ρ and the mass energy-absorption coefficient μen / ρ are presented for all of the elements Z = 1 to 92, and for 48 compounds and mixtures of radiological interest. The tables cover energies of the photon (x-ray, gamma ray, bremsstrahlung) from 1 keV to 20 MeV
3. The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). The attenuation of gamma radiation can be then described by the following equation: I=I0.e- (μ/ρ).ρl, where ρ is the material density, (μ/ρ) is the mass attenuation coefficient and ρ.l is the mass thickness
4. Mass attenuation coefficient Andrew Murphy ◉ and Dr Zemar Vajuhudeen ◉ et al. The mass attenuation coefficient (also known as the mass absorption coefficient) is a constant describing the fraction of photons removed from a monochromatic x-ray beam by a homogenous absorber per unit mass

### X-Ray Mass Attenuation Coefficients NIS

• X-Ray Mass Attenuation Coefficients. 3. The Mass Energy-Absorption Coefficient, μen/ρ. The methods used to calculate the mass energy-absorption coefficient, μen/ρ, are described perhaps more clearly through the use of an intermediate quantity, the mass energy-transfer coefficient, μtr/ρ. The mass energy-transfer coefficient,μtr/ρ, when.
• The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). The attenuation of X-rays can be then described by the following equation: I=I0.e- (μ/ρ).ρl, where ρ is the material density, (μ/ρ) is the mass attenuation coefficient and ρ.l is the mass thickness
• The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). Material Properties X-rays , also known as X-radiation , refers to electromagnetic radiation (no rest mass, no charge) of high energies
• hazards within the desired limit. Quantities of materials that need to be known include mass attenuation eff) and effective electron density (Ne). Attenuation coefficient was defined as the probability of a radiation interacting with a material per unit path length [Woods, 1982]
• For the mass attenuation coefficient, see Mass attenuation coefficient. The linear attenuation coefficient , attenuation coefficient , or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light , sound , particles , or other energy or matter . [1
• The mass attenuation coefficient is a measure of the probability of the interaction that occurs between incident photons and the matter of the unit mass per unit area

The investigated results are being used in medical physics for developing improved and sensitive techniques and minimizing radiation exposure. In this study, mass attenuation coefficients of.. CALCULATION OF TOTAL MASS ATTENUATION COEFFICIENTS, EFFECTIVE ATOMIC NUMBERS AND EFFECTIVE ELECTRON DENSITIES FOR THE EARTH ATMOSPHERE Y. ELMAHROUG1, B. TELLILI2 & C. SOUGA3 1Université De Tunis El Manar, Faculté Des Sciences De Tunis, Unité De Recherche De Physique Nucléaire Et Des Hautes Energies, 2092 Tunis, Tunisi Mass attenuation coefficients of the given materials have been calculated by the DOS based compilation XCOM (Berger and Hubbell, 1987; Hubbell and Seltzer, 1995) - provides total mass attenuation coefficient and total attenuation cross section data for about 100 elements as well as partial.

The mass attenuation coefficient is a normalization of the linear attenuation coefficient per unit density of a material producing a value that is constant for a given element or compound (i.e., independent of density of the material) 1,3 In the literature, there is no experimental value registered for mass attenuation coefficient of PLA. However, in the NIST platform it is possible to calculate the mass attenuation coefficient of compounds by entering the weight fractions of the absorber material. Therefore, it was possible to compare simulation results with NIST Themassattenuationcoefficient,/i/p,andthemassenergy-absorptioncoefficient,p en/p, arebasic quantities used incalculations of the penetration and the energy deposition byphoton This constant is known as the mass attenuation coefficient and has units of cm 2 /gm. To convert a mass attenuation coefficient to a linear attenuation coefficient (μ), simply multiply it by the density (ρ) of the material. Use of Linear Attenuation Coefficients Keywords: Mass attenuation coefficient, Tissue equivalence, Geant4 simulations, XCOM 1 Introduction In the biological and medical context, mass attenuation coefficient is a key parameter used to characterize the radiological properties of various dosimetric materials1−4. Since it is defined by takin The mass attenuation coefficient is obtained from the formula. µ r LI I= no{ } where I o is the intensity, n Lis the transmission intensity, ρ is the density of mass and is the thickness obtained x from the mass m and area a of the liquid film as Figure 1 Mass attenuation coefficient 1 Mass attenuation coefficient The mass attenuation coefficient is a measurement of how strongly a chemical species or substance absorbs or scatters light at a given wavelength, per unit mass. In addition to visible light, mass attenuation coefficients can b The Linear Attenuation Coefficient for Air is the product of the Mass-Attentuation Coefficient of Air and the density of Air. The density of air is 0.001293 g/cm3 Berger, M.J. et al. (2005). XCOM: Photon Cross Section Database (ver.y1.3). [Online] Available: http://physics.nist.gov/xco

The mass attenuation coefficients used in the calculations were obtained using the Monte Carlo N-Particle (MCNP5) simulation code. The MCNP5 calculations of the attenuation parameters for the Rhizophora spp. samples were plotted graphically against photon energy and discussed in terms of their relative differences compared with those of water and breast tissue The mass attenuation coefficient is conventionally given by the symbol $[\mu/\rho] = \sigma/(uA)$, where $\sigma$ is the cross-section in barns/atom (1 barn = $10^{-24}$ cm 2), $u$ is the atomic mass unit, and $A$ is the relative atomic mass of the target element (i.e. in amu; the mass. The mass attenuation coefficient, or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. A new method to measure mass attenuation coefficient of - particles covering end point energies 0.318 to 2.28 MeV for elements H, C, O, Al, Cl, Cu and Ag from compounds and salts has been described. The measured mass attenuation coefficients of beta particles have been compared to the values given in previous work X-Ray Attenuation and Absorption for materials of Dosimetric Interest. J. H. Hubbell and S. M. Seltzer Tables and graphs of computed photon mass attenuation coefficients and mass energy-absorption coefficients from 1 keV to 20 MeV are presented for all of the elements (Z = 1 to 92) and for 48 compounds and mixtures of radiological interest

### What is Mass Attenuation Coefficient - Definitio

1. All Answers (10) There isn't quite a direct relationship between mass-attenuation coefficient and dose, since not every attenuated photon deposits all it's energy in the medium (e.g. for Compton.
2. Context: The study of photon interactions with biological materials is essential in radiation medicine and biology, nuclear technology and space research, since radioactive sources are used. Aims: A study of mass attenuation coefficient, effective atomic numbers (Z eff) and electron density of some commonly used skeletal muscle relaxants. Materials and Methods: We have measured the mass.
3. affect the stopping power of radiation, and (6) to measure radiation attenuation coefficients for beta particles and gamma rays. Theory There are two primary types of radiation that originate from the nucleus of the atom, Yet another useful concept is the mass attenuation coefficient.
4. The mass attenuation coefficient, or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. The SI unit of mass attenuation coefficient is the square metre per kilogram (m 2 /kg)
5. Mass attenuation coefficients as a function of photon energy for the CT contrast agents by Geant4 simulations. The Geant4 simulation data of the mass attenuation coefficients has been compared with the theoretical values of XCOM program in Fig. 2
6. Mass attenuation coefficients (μ/ρ values) for various human tissues can be found at: X-Ray Mass Attenuation Coefficients. The density (ρ values) for various human tissues can be found at: X-Ray Mass Attenuation Coefficients. They are taken from the ICRU Report 44 (1989). HU values are coumputed as follows: HU x = 1000 μ x-μ water μ wate

Mass attenuation coefficients, effective atomic numbers and electron densities of thermoluminescent dosimetric compounds (Shivaliga et al., 2004) have also been obtained. The mass attenuation coefficients, and effective atomic and electron numbers for some alloys such as Cr, Fe and Ni at different energie Mass attenuation coefficient Mass energy absorption coefficient. NPRE 441, Principles of Radiation Protection, Spring 2020 Chapter 4: Interaction of Radiation with Matter -Interaction of Beta Particles Mass Energy Absorption Coefficient FigurefromAtoms,Radiation,andRadiationProtection,JamesETurner,p19 Mass Attenuation Coefficient. When characterizing an absorbing material, we can use sometimes the mass attenuation coefficient. The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). The attenuation of gamma radiation can be then described by the following equation

Massdämpningskoefficient - Mass attenuation coefficient Från Wikipedia, den fria encyklopedin Den massdämpningskoefficient , mass extinktionskoefficient , eller massan smal stråle dämpningskoefficient av volymen av ett material karakteriserar hur lätt den kan penetreras av en stråle av ljus , ljud , partiklar , eller annan energi eller materia MASS ATTENUATION COEFFICIENT : µ/Þ Unit - g/cm² Mass attenuation coefficient is independent of the density of the absorber MASS ATTENUATION COEFFICIENT 9. (I) Energy of the radiation (II) Density (III) Atomic number (IV) Electrons per gram FACTORS AFFECTING ATTENUATION 10.

The mass attenuation coefficient, or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation (such as X-rays), sound, or any other beam that can be attenuated Abstract. In this study, the total mass attenuation coefficients (μ m) for some homo- and hetero-chain polymers, namely polyamide-6 (PA-6), poly-methyl methacrylate (PMMA), low-density polyethylene (LDPE), polypropylene (PP) and polystyrene (PS) were measured at 59.5, 511, 661.6, 1173.2, 1274.5 and 1332.5 keV photon energies.The samples were separately irradiated with 241 Am, 22 Na, 137 Cs.

The mass attenuation coefficient, or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light,. The mass attenuation coefficient is a measurement of how strongly a chemical species or substance absorbs or scatters light at a given wavelength, per unit mass.In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation (such as X-rays), sound, or any other beam that attenuates.. The mass attenuation coefficient is also called mass absorption. The mass attenuation coefficient or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation (such as X-rays), sound, or any other beam that attenuates (a) Mass attenuation coefficient of aluminum. (b) mass attenuation coefficient of copper. (c) mass attenuation coefficient of lead CONCLUSION The mass attenuation coefficients for 3 high purity elemental materials Al, Cu and Pb were measured in the gamma energy range from 81 up to 1333 keV using a NaI(Tl) scintillation detector ### Mass attenuation coefficient Radiology Reference Article

mass attenuation coefficient: The measure of a chemical species' or other substance's ability to absorb or scatter electromagnetic radiation in any form (e.g., light, sound, X-rays, etc.) per unit of mass From optimization model of the double-layer shielding design and selection of lead and iron cylindrical container by MATLAB software to store the radioactive waste at 1.3325 MeV and 100 mSv/hr, we have found that the mass attenuation coefficient and exposure buildup factor were 0.056601 [cm.sup.2]/g for lead, 0.051862 [cm.sup.2]/g for iron and 4.7316 for lead, 1.6681 for iron, respectively In Fig. 2, the variation of mass attenuation coefficients versus for partial as well as total photon interaction processes with incident photon energy in the range from 1 keV to 100 GeV has been shown for PVC. It has been observed that the mass attenuation coefficient (Âµm) for PVC decreases rapidly upto 100 keV The Linear attenuation coefficient , and how to find the Mass attenuation coefficient, knowing their Densities? I have been searching everywhere, in books, from the internet. It is unbelievable, there is not a single place that have the information. Please help me to find it. If you have the source, please give me its webpage as well ### NIST: X-Ray Mass Attenuation Coefficients - Section

The mass attenuation coefficient, mass extinction coefficient, or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. 48 relations mass attenuation coefficient of leaves of Indian medicinal plant collected in different regions. For the determination of the experiment of mass attenuation coefficient, the authors used a 241Am source, which produced X-rays in the range of 8 to 32 keV, using targets of Cu, Rb, Mo, Ag and Ba Mass attenuation coefficients of investigated materials are determined by the transmission method according to Beer-Lambert's law: where and are the incident and attenuated photon intensity, respectively, (cm 2 ·g −1) is the mass attenuation coefficient, and is the thickness of the slab Y123 and Y358 high-temperature superconductor phases have experimental mass attenuation coefficients (MAC) determined at 46.5, 81, 122, 302, 356, 383, 662, 1173, and 1332 keV photon energies. The experimental values have been compared with theoretical values acquired employing the XCOM software and database. It has been observed that the theoretical and the empirical results were in perfect.

### Linear and Mass Attenuation Coefficient - X-rays nuclear

1. A new method to measure mass attenuation coefficient of particles covering end point energies 0.318 to 2.28 MeV for elements H, C, O, Al, Cl, Cu and Ag from compounds and salts has been described. The measured mass attenuation coefficients of beta particles have been compared to the values given in previous work. A good agreement is found with (Thummel, 1974) empirical relation
2. For attenuation coefficient as it applies to electromagnetic theory and telecommunications see propagation constant. For the mass attenuation coefficient..
3. English examples for mass attenuation coefficient - Since the mass attenuation coefficient is the ratio of these two, we find that it has units of (length-squared) per mass. The mass attenuation coefficient is also called mass absorption coefficient or mass extinction coefficient. This is a convenient concept because the mass attenuation coefficient of a species is approximately independent.
4. The mass-attenuation coefficients of gold are tabulated at 91 energies between 14 keV and 21 keV. In columns 1 and 2, the x-ray energy and mass-attenuation coefficient are listed along with the 1 standard deviation uncertainty in the least significant digit(s), which is given in brackets
5. ed mass attenuation coefficients for different bone

### What is Linear and Mass Attenuation Coefficient - X-rays

NationalBureauof Stanaaros Library.MlMmin.Bids-gEP251969 r'' NSRDS-NBS29 A111D1^67174 i tiotonCrossSections, NBS AttenuationCoefficients,and NATLINSTOFSTANDARDS& TECHRTC. 1 1 _nergyAbsorptionCoefficients From10keVto100GeV U.S.DEPARTMENTOFCOMMERCE NATIONALBUREAUOFSTANDARDS XJ. j mass attenuation coefficients of silver, 11 keV 28 keV, and development of an all-energies approach to local dynamical analysis of bond length, revealing variation of effective thermal contributions across the L J Tantau, C T Chantler, J D Bourke et al.-X-ray mass attenuation coefficient of silver C Q Tran, C T Chantler, Z Barnea et al. The mass attenuation coefficient is a measure of the probability of the interaction that occurs between incident photons and the matter of the unit mass per unit area. The knowledge of the mass attenuation coefficients of X and y-ray in biological and other important materials is of significant interest for industrial, biological, agricultural, and medical applications The mass attenuation coefficient, or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation (such as X-rays), sound, or any other beam that can be attenuated. Tables of x-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z = 1 to 92 and 48 additional substances of dosimetry interest by Hubbell, J. H.; Seltzer, S. M Linear and mass attenuation coefficients are the coefficients used most often. The equation I = Ioe-mu x expresses the exponential relationship between incident primary photons and transmitted photons for a monoenergetic beam with respect to the thickness of the absorber and thus may be used to calculate the attenuation by any thickness of material Mass attenuation coefficient is a measurement of how strongly a chemical specie or substance absorbs or scatters radiation at a given wavelength, per unit mass. Mass attenuation coefficient is an useful parameter to derive many other physical parameters. Linear attenuation coefficient (µ l) describes the fraction of

### Mass Attenuation Coefficients, Effective Atomic and

Once you have determined the value of the mass attenuation coefficient you can obtain the linear attenuation coefficient, μ, by multiplying by the density of the brass. The half-value layer, HVL, for the primary photon energy of interest may then be obtained using the simple relationship between linear attenuation coefficient and HVL—i.e. The mass absorption coefficient µ (cm2/g) is related to the transmitted intensity through a material of density r (g/cm3) and thickness d by I = I0e-µρd. (1) Thus, the linear absorption coefficient is µ (cm-1) = µr. For a pure material, the mass absorption coefficient is directly related to the total atomic absorption cross section LINK OF BETA DECAY AND TYPES OF BETA DECAY VIDEO https://youtu.be/HN3n7UmIwZY LINK OF NUCLEAR FISSION REACTOR, PART- 1 VIDEO https://youtu.be/hnWRaGr.. The probability of a photon interacting in a particular way with a given material, per unit path length, is usually called the linear attenuation coefficient (μ), and it is of great importance in radiation shielding. Plates of barite concrete with different thickness were fabricated in order to determining their mass attenuation coefficients at different energies Getting and plotting the Mass Attenuation Coefficient Edit on GitHub import numpy as np import matplotlib.pyplot as plt import astropy.units as u from astropy.visualization import quantity_support quantity_support () from roentgen.absorption import MassAttenuationCoefficient cdte_atten = MassAttenuationCoefficient ( 'cdte' ) energy = u

### Attenuation coefficient - Wikipedi

We use the x-ray extended-range technique (XERT) [Chantler et al., Phys. Rev. A 64, 062506 (2001)] to measure the mass attenuation coefficients of molybdenum in the x-ray energy range of $13.5--41.5\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ to 0.02--0.15 % accuracy. Measurements made over an extended range of the measurement parameter space are critically examined to identify, quantify, and. An X-ray fluorescent (XRF) configuration was used to measure the mass attenuation coefficient of materials at low energy photons. An Americium-241 ( 241 Am) annular source was used in conjunction with niobium, palladium, molybdenum and tin plates that provided K α1 photons with energies between 16.59 and 25.26 keV. The transmitted photons were measured by using a low energy Germanium (LEGe. The neutron-radiation mass attenuation coefficients of 10B atoms are the second largest among those of all elements.13. Continue Reading. The Impact Of Nde On Food Industry 1403 Words | 6 Pages. in the location of foreign bodies in food, edible fats and oils were analysis by the size of droplet in emulsions (Sherwin and Nicol, 1998)

The linear attenuation coefficients for each phase were cal-culated (Table III) from published mass attenuation data (McMaster et al.1969) for 22.105 keV x-rays. These were used to calculate the linear attenuation coefficient for each simulated bone specimen using Eq. 8 (Tables I and II). Results No PMMA Infiltratio What is the abbreviation for mass attenuation coefficient? What does M&SOL;R stand for? M&SOL;R abbreviation stands for mass attenuation coefficient A plot of the total mass attenuation coefficient vs. gamma energy for some common shielding materials is provided in Figure 3. For low gamma energies (<500 keV), higher atomic number elements, such as lead, bismuth, and tungsten have much higher mass absorption coefficients and shield low energy gamma.

The mass attenuation coefficient of a compound or mixture can be obtained from the mass attenuation coefficients of its constituent elements using the following mixture rule: (2) 3. Results and Discussion In Fig. 2, the variation of mass attenuation coefficients versus for partial as well as total photon interactio Mass attenuation coefficients, half value layers and effective atomic numbers have been determined for the prepared samples at photon energies 238, 583, 661, 911, 1173, 1332 and 2614keV. The results are compared with the corresponding theoretical calculations. In additio mass attenuation coefficients are higher at this energy. As the energy value increases Compton scattering becomes more dominant and mass attenuation coefficients decrease with increasing gamma ray energy. The concrete samples containing TCW in small rates more absorbed photon than the ordinary concrete. Th I don't like the mass attenuation coefficient; it bugs me and it has weird units.Yet researchers studying the attenuation of x-rays in materials usually quote the mass attenuation coefficient rather than the linear attenuation coefficient in their publications. As x-rays pass through a material, they fall off exponentially as exp(−μL), where L is the distance (m) and μ is the linear.

### The Mass Attenuation Coefficients, Electronic, Atomic, and

Then, for mass attenuation coefficient k (which has units of area over mass), the probability of interaction is. P = 1 − e − k ρ ℓ. As you can see, the interaction probability approaches zero as the length goes to zero, and it approaches 1 as the length goes to infinity. Share. Improve this answer Journal of Biomimetics, Biomaterials and Biomedical Engineering Materials Science. Defect and Diffusion Foru on linear and mass attenuation coefficient of soil samples have been investigated at eight gamma ray energies from 123 keV to 1280 keV. These parameters usually depend on the energy of the radiations and composite materials of the soil and are useful for quantitative evaluation of interaction of gamma rays with various components in the soil samples The mass attenuation coefficient of binderless and PLA added oil palm trunk particleboards were observed as nearest to the calculated XCOM value from water in the 16.59 - 25.26 keV photon energies range. It is considered that oil palm trunk particleboard as a significant and reliabl The photon mass attenuation coefficient, effective atomic number and electron density are the basic quantities required in determining the penetration of X-rays and gamma photons in matter. The mass attenuation coefficient (µ/ρ) is a measure of probability of interaction that occurs between incident photons and matter per unit mass per unit area

### (PDF) Mass Attenuation Coefficients of Human Body Organs

1. ed from the individual mass attenuation coefficients by the equation: This simply means that the overall mass.
2. Figure 4 gives the mass attenuation coefficient as a function of energy for several elements. This shows both the strong energy dependence of the absorption coefficient (mu/rho decreases with increasing energy) and the five to ten fold jumps in absorption at specific energies
3. Getting and plotting the Mass Attenuation Coefficient. import numpy as np import matplotlib.pyplot as plt import astropy.units as u from astropy.visualization import quantity_support quantity_support() from roentgen.absorption import MassAttenuationCoefficient cdte_atten = MassAttenuationCoefficient('cdte') energy = u.Quantity(np.arange(1, 1000. 1. o acids . [5
2. We define the mass attenuation coefficient as the linear attenuation coefficient divided by the material density; this quantity is more fundamental because it is independent of the actual density and physical state of the absorber 
3. Linear and mass attenuation coefficient for gamma rays for different materials and solutions plays an important role in RSID units. There are different measurement techniques to measure them. As the technology developed day by day, the gamma rays are used in many fields, like medicine, food preservation and with their measurement techniques are developed but we find these measurements can be.     The mass attenuation coefficient is the fraction of photons rem oved from the beam per density-weighted unit of absorber thickness. The density times the path length is the density-weighted path length, which is sometimes called the radiological path length For a given energy photon the mass attenuation coefficient may be determined by taking into account the weight percentages of the elements that make up the brass. The generalized expression that is usually applied is μ/ρ = Σ w i (μ/ρ) i Mass attenuation coefficients of x-rays in ISO quality concrete in barite of different regions of Brazil 13 - 18 May 2012 Glasgow Scotland 1.INTRODUCTION The probability of a photon interacting in a particular way with a given material, per unit path length, is usually called the linear attenuation coefficient (µ), and it i attenuation coefficient for a material depends on the incident photon energy, the effective atomic number and the density of the material. Susan  measured the gamma ray mass attenuation coefficients for industrial materials such as n-pentane, ethanol, toluene, olein, oil sludge, polyethylene, distilled water, cement, brick an Then, the mass attenuation coefficient of Eremurus spp. root was measured by X-rays in 16.63 keV - 25.30 keV energy range, and was compared with the theoretical values for water and young-age breast with 75 % muscle and 25 % fat that is called Breast 1 [7, 13] calculated by the XCOM computer program 

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