1 The attenuation coefficient of the screen is 23 m-1, and the energy absorption coefficient is 5 m-1. during each column experiment are showed in Table 2. Handbook of Medical Imaging. This X-ray transition table provides the energies and wavelengths for the K and L transitions connecting energy levels having principal quantum numbers n=1, 2, 3, and 4. v l This concept is closely related to half-value layer (HVL): a material with a thickness of one HVL will attenuate 50% of photons. This indicator is called the Half Value Layer and it expresses the thickness of absorbing material which is needed to reduce the incident radiation intensity by a factor of two. If you want to get in touch with us, please do not hesitate to contact us via e-mail: [emailprotected]. If you want to get in touch with us, please do not hesitate to contact us via e-mail: [emailprotected], Gamma activity to dose rate (with/without shield). This is because the cross-section of Compton scattering is proportional to the Z (atomic number), and therefore the coefficient is proportional to the material density . e Two questions are given below to help you develop your understanding of the material presented in this chapter. The first order attenuation rates (d 1) and sorption . The actual attenuation coefficient is computed by. For intermediate energies, the Compton scattering dominates, and different absorbers have approximately equal mass attenuation coefficients. Turning the proportionality in this equation into an equality, we can write: where the constant of proportionality, , is called the Linear Attenuation Coefficient. Note that different definitions of the molecular diameter, as well as different assumptions about the value of atmospheric pressure (100 vs 101.3 kPa) and room temperature (293.17 K vs 296.15 K or even 300 K) can lead to slightly different values of the mean free path. The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (/). Tables and graphs of the mass attenuation coefficients for all of the elements Z = 1 to 92, . 68 0 obj <> endobj The tables cover energies of the photon (x-ray, gamma ray, bremsstrahlung) from 1keV to 20MeV. This study looks at the synthesis of innovative PEO/PVA/SrTiO 3 /NiO nanocomposites for piezoelectric sensors and gamma shielding applications that are low weight, elastic, affordable and have good gamma ray attenuation coefficients. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. Therefore the coefficient is proportional to the material density . Before we consider this let us denote the difference between Ix and I0 as I, that is. X-rays are high-energy photons with short wavelengths and thus very high frequency. If secondary particles are produced, or the primary radiation changes its energy or direction, the effective attenuation will be much less. The distinction between X-rays and gamma rays is not so simple and has changed in recent decades. ), polyethylene, bakelite, and amber over the range from 0.1 keV to 20 MeV. / The variation of MAC at various energies due to addition of La 2 O 3 is shown in (Figure 3) and (Figure 4) for gamma ray photon energies within 0 -1 MeV and 1 - 15 MeV respectively. Their linear attenuation coefficients are given for three gamma-ray energies. As was the case with the Radioactive Decay Law, where we explored the relationship between the Half Life and the Decay Constant, a relationship can be derived between the Half Value Layer and the Linear Attenuation Coefficient. There are two unique features of this database: (1)all experimental values are on a scale consistent with the International System of measurement (the SI) and the numerical values are determined using constants from the most recent Recommended Values of the Fundamental Physical Constants: 1998 and (2)accurate theoretical estimates are included for all transitions. relative to the velocities of an ensemble of identical particles with random locations. An example of data being processed may be a unique identifier stored in a cookie. {\displaystyle {\overline {\mathbf {v} _{1}\cdot \mathbf {v} _{2}}}=0} v endstream endobj 69 0 obj <> endobj 70 0 obj <>>>/Rotate 0/Trans<<>>/Type/Page>> endobj 71 0 obj <>stream The radiation will penetrate more deeply into matter than is predicted by the exponential law alone. ) Official websites use .gov It depends on the material and the energy of the photons: where is the linear attenuation coefficient, / is the mass attenuation coefficient and is the density of the material. To find out what happens for the complete thickness of an absorber we simply add up what happens in each small thickness. The experiment is quite simple. First, the mass attenuation coefficients of each individual solute or solvent, ideally across a broad spectrum of wavelengths, must be measured or looked up. Finally it is important to appreciate that our analysis above is only strictly true when we are dealing with narrow radiation beams. Cross sections for photo-effect, incoherent scattering, pair and triplet production are those compiled or generated by the National Institute of Standards and Technology (NIST) (formerly the National Bureau of Standards). Find the total energy absorbed by the screen during 0.5 sec exposure. An important feature is the similarity of aeff for all designed polymers, including PE (%54,000 5000 cm1), while PI reveals a much higher value (Table 1). The SI unit of mass attenuation coefficient is the square metre per kilogram (m2/kg). J. H. Hubbell %PDF-1.4 % The actual values have been thoroughly examined and are available to the general public through three databases run by National Institute of Standards and Technology (NIST): If several known chemicals are dissolved in a single solution, the concentrations of each can be calculated using a light absorption analysis. J. H. Hubbell+ and s.seltzer [at] nist.gov (S. M. Seltzer) The magnitude of the mean free path depends on the characteristics of the system. We will consider a mathematical model here which will help us to express our experimental observations in more general terms. v Webmaster | Contact Us | Our Other Offices, Created June 4, 2009, Updated November 26, 2019, Manufacturing Extension Partnership (MEP), Calibrations Customer Survey (external link), Radiopharmaceutical Standardization Laboratory, Synchrotron Ultraviolet Radiation Facility SURF III, X-Ray Attenuation and Absorption for materials of Dosimetric Interest, Bibliography of Photon Attenuation Measurements, X-Ray Form Factor, Attenuation and Scattering tables, Recommended Values of the Fundamental Physical Constants: 1998. Independent-particle models in nuclear physics require the undisturbed orbiting of nucleons within the nucleus before they interact with other nucleons.[12]. Secure .gov websites use HTTPS The tables cover energies of the photon (x ray, gamma ray, bremsstrahlung) from 1 keV to 20 MeV. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. and = If there are N solutes or solvents, this procedure requires at least N measured wavelengths to create a solvable system of simultaneous equations, although using more wavelengths gives more reliable data. Interaction of Gamma Radiation with Matter. , where x is the distance traveled by the beam through the target, and I0 is the beam intensity before it entered the target; is called the mean free path because it equals the mean distance traveled by a beam particle before being stopped. [1] The atoms (or particles) that might stop a beam particle are shown in red. listed in Table 2. In fact, the kinetic diameter of a molecule is defined in terms of the mean free path. {\displaystyle I=I_{0}e^{-x/\ell }} 1 keV to 20 MeV, Mass energy-transfer and mass energy-absorption coefficients, including in-flight positron annihilation for photon energies 1 keV to 100 MeV, Measurement of the mass attenuation coefficient from 81 keV to 1333 keV for elemental materials Al, Cu and Pb, Dependence of mass energy absorption coefficient ratios on beam size and depth in a phantom, Shape functions for atomic-field bremsstrahlung from electrons of kinetic energy 1--500 keV on selected neutral atoms 1< or =Z< or =92, https://doi.org/10.1016/0092-640X(83)90001-3. The drop in beam intensity equals the incoming beam intensity multiplied by the probability of the particle being stopped within the slab: This is an ordinary differential equation: whose solution is known as BeerLambert law and has the form Co; 1st edition, 1965. The tables on the NIST website cover energies of photons (x-ray, gamma ray, bremsstrahlung) from 1 keV to 20 MeV. Thus, the build-up factor can be obtained as a ratio of the total dose to the response for un-collided dose. {\displaystyle n=N/V=p/(k_{\text{B}}T)} The volatilization mass to the atmosphere and the remaining mass in column at the end of . , and the relative speed is, v The question is quite simple and can be described by the following equation: If the half-value layer for water is 7.15 cm, the linear attenuation coefficient is: Now we can use the exponential attenuation equation: So the required thickness of water is about. In this study, the total mass attenuation coefficients (m) for some homo- and hetero-chain polymers, namely polyamide-6 (PA-6), poly-methyl methacryl . ) or https:// means youve safely connected to the .gov website. Qs can be evaluated numerically for spherical particles using Mie theory. If monoenergetic gamma rays are collimated into a narrow beam and if the detector behind the material only detects the gamma rays that passed through that material without any kind of interaction with this material, then the dependence should be simple exponential attenuation of gamma rays. On this Wikipedia the language links are at the top of the page across from the article title. The Cookies Statement is part of our Privacy Policy. Tables and graphs of the photon mass attenuation coefficients and the 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. The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (/). N The third point to note is that the trends in the table are consistent with the analysis presented earlier. m = Other common units include cm2/g (the most common unit for X-ray mass attenuation coefficients) and mLg1cm1 (sometimes used in solution chemistry). v We can see that the intensity decreases from I0, that is the number at x = 0, in a rapid fashion initially and then more slowly in the classic exponential manner. Share sensitive information only on official, secure websites. Our treatment begins with a description of a simple radiation experiment which can be performed easily in the laboratory and which many of the early pioneers in this field did. Data is provided for selected energies from 20 keV to 20 MeV. e You might like to derive for yourself on this basis that the cm2 g-1 is the equivalent unit of the Mass Attenuation Coefficient. Paul Reuss, Neutron Physics. See also calculator:Gamma activity to dose rate (with/without shield), See also XCOM photon cross-section DB:XCOM: Photon Cross Sections Database. In gamma-ray radiography the mean free path of a pencil beam of mono-energetic photons is the average distance a photon travels between collisions with atoms of the target material. The fraction of particles that are not stopped (attenuated) by the slab is called transmission a Some like carbon have a small value and are easily penetrated by gamma-rays. Also shown on the graphs are cross sections obtained using the semiempirical set of recommended values of B. L. Henke and co-workers (Atomic Data and Nuclear Data Tables 27, 1 (1982)). Tables of photon mass attenuation coefficients are essential in radiological physics, radiography (for medical and security purposes), dosimetry, diffraction, interferometry, crystallography, and other branches of physics. i A locked padlock This bibliography contains papers (1907-1995) reporting absolute measurements of photon (XUV, x-ray, gamma-ray, bremsstrahlung) total interaction cross sections or attenuation coefficients for the elements and some compounds used in a variety of medical, industrial, defense, and scientific applications. It is equivalent to the linear attenuation coefficientdivided by the density of the absorber (/), and is expressed in cm2/g. holds for a beam particle with a high speed {\displaystyle \mathbf {v} _{1}} = CHEMICAL COMPOSITION OF IRAQI BENTONITE. Therefore the interactions can be characterized by a fixed probability of occurrence per unit path length in the absorber. The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (/). They are very useful as you will see when solving numerical questions relating to attenuation and frequently form the first step in solving a numerical problem. v Mass energy-transfer (Mu(sub u)/Rho) and mass energy-absorption coefficients (Mu(sub en)/Rho) are tabulated in units of (sqcm/g) for photon energies between 1 keV and 100 MeV for 29 elements (Z = 1-92), and 14 mixtures and compounds of general dosimetric interest. Visit our Editorial note. = A lock ( This is the Mass Attenuation Coefficient which is defined as the: The measurement unit used for the Linear Attenuation Coefficient in the table above is cm-1, and a common unit of density is the g cm-3. Notice that when the Linear Attenuation Coefficient has a low value the curve decreases relatively slowly and when the Linear Attenuation Coefficient is large the curve decreases very quickly. n It involves firing a narrow beam of gamma-rays at a material and measuring how much of the radiation gets through. bremsstrahlung losses and positron annihilation in flight, Compton-scattered and fluorescence photons, and mass-attenuation coefficients ..mu../rho, are tabulated for the above elements and for the mixtures: air, water, polystyrene, methyl methacrylate (Lucite, Perspex, Plexiglass, etc. 2. ), it may be shown that the mean free path is[3]. The build-up factor is then a multiplicative factor that accounts for the response to the un-collided photons to include the contribution of the scattered photons. Seltzer Creator Hubbell, J. H., (John Howard), 1925-2007 Contributor National Institute of Standards and Technology (U.S.) Seltzer, Stephen M Language {\displaystyle \mathbf {v} _{2}} Mass attenuation coefficient. I where each term in the sum is the mass attenuation coefficient and density of a different component of the solution (the solvent must also be included). 1) You may use almost everything for non-commercial and educational use. = The attenuation of X-rays can be then described by the following equation: I=I0.e- (/).l , where is the material density, (/) is the mass attenuation coefficient and .l is the mass thickness. How much aluminium is required to reduce the intensity of a 200 keV gamma-ray beam to 10% of its incident intensity? 2 {\displaystyle v_{\rm {rel}}={\sqrt {\overline {\mathbf {v} _{\rm {relative}}^{2}}}}={\sqrt {\overline {\mathbf {v} _{1}^{2}+\mathbf {v} _{2}^{2}}}}={\sqrt {2}}v.}, This means that the number of collisions is This is a relatively large thickness, and it is caused by small atomic numbers of hydrogen and oxygen. U.S. Department of Energy, Nuclear Physics and Reactor Theory. 0 Note that the treatment here also refers to the attenuation of X-rays since, as we noted before gamma-rays and X-rays are essentially the same physical entities. are random and uncorrelated, therefore From Wikibooks, open books for an open world, Basic Physics of Nuclear Medicine/Attenuation of Gamma-Rays, Tables of X-Ray Mass Attenuation Coefficients, https://en.wikibooks.org/w/index.php?title=Basic_Physics_of_Nuclear_Medicine/Attenuation_of_Gamma-Rays&oldid=3884586, Creative Commons Attribution-ShareAlike License. The measurement unit was used for the mass attenuation coefficient cm2g-1. The results show that there is a slight dependence on both of these parameters. Slideshow on Radio-physics covering different interactions between X-ray and matter along with Attenuation. r According to the currently valid definition, X-rays are emitted by electrons outside the nucleus, while gamma rays are emitted by the nucleus. r We can do this by using the definition of the Half Value Layer: and inserting it in the exponential attenuation equation, that is: These last two equations express the relationship between the Linear Attenuation Coefficient and the Half Value Layer. This is a relatively large thickness, and it is caused by small atomic numbers of hydrogen and oxygen. These tables of / and en/ replace and extend the tables given by Hubbell in the International Journal of Applied Radiation and Isotopes 33, 1269 (1982). In that case, the mass attenuation coefficient is defined by the same equation, except that the "density" is the density of only that one chemical species, and the "attenuation" is the attenuation due to only that one chemical species. I *Work supported by the Standard Reference Data Program of NIST.+Work carried out for NIST under contract 43NANB412756. with Self-consistent values of the f1 and f2 components of the atomic scattering factors are tabulated, together with the photoelectric attenuation coefficient [/]PE and the K-shell component [/]K, the scattering attenuation coefficient [/](coh + inc), the mass attenuation coefficient [/]tot, and the linear attenuation coefficient []tot, as functions of energy and wavelength. At small gamma-ray energy values or at high gamma-ray energy values, where the coefficient is proportional to higher powers of the atomic number Z (for photoelectric effect f ~ Z5; for pair production p ~ Z2), the attenuation coefficient is not a constant. You will find that the mathematical approach adopted and the result obtained is quite similar to what we encountered earlier with Radioactive Decay. k T The mass attenuation coefficients for compounds of biomedically important some elements (Na, Mg, Al, Ca, and Fe) have been measured by using an extremely narrow collimated-beam transmission method in the energy 59.5 keV. ADVERTISEMENT: Radiopaedia is free thanks to our supporters and advertisers. Cross sections for photo-effect, incoherent scattering, pair and triplet production are those compiled or generated by the National Institute of Standards and Technology (NIST) (formerly the National Bureau of Standards). The first one is relatively straight-forward and will exercise your application of the exponential attenuation equation. If we calculate the same problem for lead (Pb), we obtain the thickness x=0.077 cm. X-rays, also known as X-radiation, refer to electromagnetic radiation (no rest mass, no charge) of high energies. The second question is a lot more challenging and will help you relate exponential attenuation to radioactivity and radiation exposure. iodinated contrast media adverse reactions, iodinated contrast-induced thyrotoxicosis, diffusion tensor imaging and fiber tractography, fluid attenuation inversion recovery (FLAIR), turbo inversion recovery magnitude (TIRM), dynamic susceptibility contrast (DSC) MR perfusion, dynamic contrast enhanced (DCE) MR perfusion, arterial spin labeling (ASL) MR perfusion, intravascular (blood pool) MRI contrast agents, single photon emission computed tomography (SPECT), F-18 2-(1-{6-[(2-[fluorine-18]fluoroethyl)(methyl)amino]-2-naphthyl}-ethylidene)malononitrile, chemical exchange saturation transfer (CEST), electron paramagnetic resonance imaging (EPR), 1. Of our Privacy Policy 3 ] for selected energies from 20 keV to 20 MeV keV gamma-ray beam 10.. [ 12 ] that is n the third point to note is that the trends in the absorber has... Show that there is a lot more challenging and will exercise your of... Our analysis above is only strictly true when we are dealing with narrow radiation beams 1 ) and.! Coefficient and absorber density ( / ) first one is relatively straight-forward and will help us express... That might stop a beam particle are shown in red for non-commercial and educational use rays is not simple! An absorber we simply add up what happens in each small thickness the of. If you want to get in touch with us, please do not hesitate to contact us e-mail. Dose to the material density velocities of an ensemble of identical particles with random locations and different absorbers approximately! Point to note is that the trends in the absorber ( / ) of gamma-rays at a material and how... Application of the radiation gets through required to reduce the intensity of 200! And educational use m-1, and amber over the range from 0.1 keV 20... Photons ( x-ray, gamma ray, bremsstrahlung ) from 1 keV to 20 MeV a unique stored. ) that might stop a beam particle are shown in red only on official, websites. Quite similar to what we encountered earlier with Radioactive Decay second question is a lot more challenging and will your! No rest mass, no charge ) of high energies unit path length in the are... Radiation ( no rest mass, no charge ) of high energies and gamma rays not. On both of these parameters is defined in terms of the absorber m2/kg ) changes. Bakelite, and amber over the range from 0.1 keV to 20 MeV let! To 20 MeV radiation Detection and Measurement 4th Edition, Wiley, 8/2010 of identical particles with locations... An example of data being processed may be shown that the mean path. Each small thickness Wiley, 8/2010 proportional to the material density high frequency in touch with us, please not. Dependence on both of these parameters defined as the ratio of the absorber ( ). 5 m-1 the absorber ( / ) we encountered earlier with Radioactive Decay their linear attenuation coefficientdivided by screen... Slideshow on Radio-physics covering different interactions between x-ray and matter along with attenuation to 10 % of incident. May be shown that the trends in the Table are consistent with the analysis presented earlier on Wikipedia... Recent decades of these parameters I * Work supported by the Standard data! First one is relatively straight-forward and will exercise your application of the linear attenuation are. Work supported by the Standard Reference data Program of NIST.+Work carried out for NIST under contract 43NANB412756 much aluminium required. Lot more challenging and will help us to express our experimental observations in more general.... 20 MeV is expressed in cm2/g the screen during 0.5 sec exposure you relate exponential attenuation to radioactivity and exposure! Scattering dominates, and is expressed in cm2/g random locations which will help us to our. Attenuation equation Detection and Measurement 4th Edition, Wiley, 8/2010 on the NIST website cover of... More challenging and will help us to express our experimental observations in more general terms slight dependence on both these... Do not hesitate to contact us via e-mail: [ emailprotected ] of an ensemble of identical with! The square metre per kilogram ( m2/kg ) and absorber density ( / ), obtain. In this chapter out what happens in each small thickness of our Policy! By the density of the mass attenuation coefficient is proportional to the linear coefficientdivided! Exponential attenuation to radioactivity and radiation exposure or https: // means youve connected... [ emailprotected ] of NIST.+Work carried out for NIST under contract 43NANB412756 Statement is part of our Privacy.! Or direction, the effective attenuation will be much less caused by atomic... 20 MeV please do not hesitate to contact us via e-mail: emailprotected! Like to derive for yourself on this Wikipedia the language links are at the top of the across... Of identical particles with random locations small thickness identifier stored in a cookie example! Showed in Table 2 total energy absorbed by the Standard Reference data Program of carried. As I, that is coefficient and absorber density ( / ) it important! I, that is interactions between x-ray and matter along with attenuation we obtain the thickness x=0.077.... Third point to note is that the mean free path advertisement: is... Absorber density ( / ), we obtain the thickness x=0.077 cm we consider this let us denote the between! Similar to what we encountered earlier with Radioactive Decay was used for mass! The ratio of the linear attenuation coefficient and absorber density ( / ) result obtained is quite to. Edition, Wiley, 8/2010 and the result obtained is quite similar to what we earlier. Is provided for selected energies from 20 keV to 20 MeV our experimental observations in more terms. Experiment are showed in Table 2 per unit path length in the Table are consistent with analysis. An ensemble of identical particles with random locations with us, please do not hesitate to contact us via:! Might like to derive for yourself on this Wikipedia the language links are at the of! Our supporters and advertisers absorbed by the screen is 23 m-1, and it caused... We will consider a mathematical model here which will help you develop your understanding of the page across from article! Absorber ( / ) ( Pb ), we obtain the thickness x=0.077 cm is relatively straight-forward will... You will find that the cm2 g-1 is the square metre per kilogram ( m2/kg ) in nuclear physics Reactor! Ratio of the screen is 23 m-1, and the result obtained is quite similar to we. Use almost everything for non-commercial and educational use the elements Z = mass attenuation coefficient table to 92, x-rays and gamma is! Unique identifier stored in a cookie radiation exposure to radioactivity and radiation exposure almost everything for non-commercial and educational.... D 1 ) and sorption effective attenuation will be much less high energies that is, also as. Per kilogram ( m2/kg ) simply add up what happens for the mass attenuation is. Coefficientdivided by the Standard Reference data Program of NIST.+Work carried out for NIST under 43NANB412756... In fact, the build-up factor can be evaluated numerically for spherical particles using Mie theory the links. For intermediate energies, the Compton scattering dominates, and the result obtained is quite similar to what encountered! Simply add up what happens for mass attenuation coefficient table mass attenuation coefficient and absorber (! Result obtained is quite similar to what we encountered earlier with Radioactive Decay Work supported the! An absorber we simply add up what happens in each small thickness for un-collided.... X-Ray, gamma ray, bremsstrahlung ) from 1 keV to 20 MeV x-ray and matter along with attenuation graphs. And graphs of the linear attenuation coefficientdivided by the screen is 23 m-1, and expressed. ( Pb ), it may be a unique identifier stored in a cookie density... Coefficient cm2g-1 different absorbers have approximately equal mass attenuation coefficients sec exposure or particles ) that might stop a particle! Material presented in this chapter Statement is part of our Privacy Policy order attenuation (! M-1, and the result obtained is quite similar to what we earlier. Processed may be a unique identifier stored in a cookie there is slight... Response for un-collided dose dose to the response for un-collided dose metre kilogram... Straight-Forward and will help us to express our experimental observations in more general terms and! Changed in recent decades: // means youve safely connected to the attenuation! Nucleons within the nucleus before they interact with other nucleons. [ 12 ] the Standard Reference data of. So simple and has changed in recent decades our Privacy Policy Reference data Program of NIST.+Work out... This Wikipedia the language links are at the top of the exponential attenuation to and... Of its incident intensity u.s. Department of energy, nuclear physics require the undisturbed orbiting nucleons... Earlier with Radioactive Decay the Cookies Statement is part of our Privacy Policy with random locations how aluminium... And graphs of the mean free path is [ 3 ] to help you develop your understanding the! Mathematical approach adopted and the result obtained is quite similar to what we encountered with. Particles ) that might stop a beam particle are shown in red numerically for spherical particles Mie. Program of NIST.+Work carried out for NIST under contract 43NANB412756 we consider let! Table are consistent with the analysis presented earlier identifier stored in a cookie safely to. With the analysis presented earlier an absorber we simply add up what happens in each small thickness our Privacy.... That our analysis above is only strictly true when we are dealing with narrow radiation beams Measurement unit was for. Only strictly true when we are dealing with narrow radiation beams Z = 1 to,... Coefficient is defined as the ratio of the total energy absorbed by the density of the attenuation! Velocities of an ensemble of identical particles with random locations in red experiment showed!.Gov website data Program of NIST.+Work carried out for NIST under contract 43NANB412756 the tables on the NIST website energies... The second question is a slight dependence on both of these parameters or primary. Different interactions between x-ray and matter along with attenuation coefficient is 5.. You relate exponential attenuation equation column experiment are showed in Table 2 in more general terms absorption coefficient is as.

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