1. In addition, even tenth-value layers TVLs that are derived from broad beam measurements, such as those pro- 0 „Shielding ability of a material is determined by the thickness of the material required to absorb half of the radiation „This thickness of the material is called the half-thickness „Radiation that has passed through one half-thickness will be reduced by half again if it passes through another half-thickness (HT) Thickness of material required to reduce the intensity of radiation to one half of its original intensity (50% attenuation). Furthermore, we calculated the half value layer and tenth value layer concerning the greatly attenuated wide X-ray beam. Half Value Layer The half value layer (HVL) is the thickness of a shielding material required to reduce the intensity of radiation at a point to one half of its original intensity. 5. 0000000556 00000 n In radiography, technologists use the half value layer (HVL) to measure the quality or intensity of the beam. b. Half-Value Thickness c. Tenth-Value Thickness 4. In a shielding calculation, such as illustrated to the right, it can be seen that if the thickness of one HVL is known, it is possible to quickly determine how much material is needed to reduce the intensity to less than 1%. Shielding calculation Rules of thumb Primary barrier Secondary barrier Shielding material Gamma shielding Point source shielding Half-value layer Half-value thickness HVL Tenth-value layer TVL Tenth-value thickness Extended source shielding Point-kernel method Scattered radiation Albedo Commercial software X-ray shielding Occupancy factors Shielding from beta emitters Shielding from … Solve total dose problems given dose rate or curie content values for various types of radiation. Quarter-value layer is the amount of specified material that reduces the air kerma rate (or exposure rate, exposure, air kerma, … :R��o����p�H+�ؔnjG���-�08��^U;8�uU��k۱�C����J_k�~p�����xA��+��U���U�C�7�V���]ݙ_U{&7O�������R,�H���T���E���4�E6_t1���#A!�q���6ۼ�`18�R��]�F���+O����h�����'�N��(��C/�P̅��� The evaluated lead-free board, used in this examination, is useful as the shielding material for the diagnosis X-ray and, moreover, the partition wall materials are hard enough, with a board that is even heavier than the usual plaster board. 5. 8. To reduce the dose rate by half, the half value layer (HVL) is used [39] and to reduce it to the tenth part, the tenth value layer (TVL) was used. 147 on Structural Shielding Design for Medical X-Ray Imaging Facilities, and in line with the recommendations set out by the International Atomic Energy Agency Safety Series Reports No. 0000003269 00000 n See also calculator: Gamma activity to dose rate (with/without shield) See also XCOM – photon cross-section DB: XCOM: Photon Cross Sections Database. Introduction History Present State Future Direction, Physics of Radiography Nature of Penetrating Radiation X-rays Gamma Rays Activity Decay Rate   -Carbon 14 Dating Ionization Inverse Square Law Interaction of RT/Matter Attenuation Coefficient Half-Value Layer Sources of Attenuation   -Compton Scattering Geometric Unsharpness Filters in Radiography Scatter/Radiation Control Radiation Safety, Equipment & Materials X-ray Generators Radio Isotope Sources Radiographic Film Exposure Vaults, Techniques & Calibrations Imaging Consideration Contrast Definition Radiographic Density Characteristic Curves Exposure Calculations Controlling Quality Film Processing Viewing Radiographs Radiograph Interp-Welds Radiograph Interp - Castings, Advanced Techniques Real-time Radiography Computed Tomography XRSIM. The HVL is expressed in units of distance (mm or cm). Like the attenuation coefficient, it is photon energy dependant. The half value layer for 500 keV gamma rays in water is 7.15 cm and the linear attenuation coefficient for 500 keV gamma rays in water is 0.097 cm-1. Therefore, the HVL and m are related as follows: The HVL is often used in radiography simply because it is easier to remember values and perform simple calculations. Tenth Value Layer (TVL). It can be seen that HVL decreases with R value suggesting that with increase in R value the shielding properties are improved. trailer [�3�#[T��q��r�����ƟQ���t� !��$����i�Gؒ�3h�8Ϲ_-������}���� x4�w3 v�Xp�+]����r��8 Ch��n���q� ����R N|��p*�k�l$+�\E��>�?�q�G���v���3���� ����v`��=�7v��nӔͥ�{�"���n�?�i8�����+�isa懸ÿ:�Vq��]G���?i=�^����nr�)��yk�Y ���o\VRJ�q ϓ�3�! %%EOF Increasing the penetrating energy of a stream of photons will result in an increase in a material's HVL. Measurement of half-value layer Types of spectral distribution • Fluence or energy fluence as a function of energy • Exposure distribution MV spectra • Bremsstrahlung spectra • Labeled by the energy of electron beam striking the target • HVL is not typically used except for shielding calculations Half Value Layer (HVL) is the thickness of a shield or an absorber that reduces the radiation level by a factor of 2 that is to half the initial level and is calculated by the following equation: (7) HVL = ln 2 μ = 0.693 μ where μ (cm −1) is the linear attenuation coefficient of the absorber. Air Monitoring Calculations 42 - 44 Surface Area Calculations 45 Volume Calculations 46 Gamma & Neutron Half-Value Layers 47 Shielding Calculations 48 - 50 Shielding Materials 51 Calculating Transmission Factor (X-ray) 51 Density of Various Materials 52 Radioactive Decay Graphs 53 - 54 Table 1 of DOE 5400.5 55 Appendix D of 10CFR835 56 It also helps to determine the type and thickness of shielding required in the facility. Like the attenuation coefficient, it is photon energy dependant. S���;��?�2���hL�w��gZ��'O�l�:��n�2���k��JL�E;�@gC��y������q�a�;��8��$ͤ-�ar�9�s�t0lVc����Xf�սZ-�CEj���~+d�5�.���"Xӳ����`w�zZBL���� S*���B7�+�?���.��:���.�~b1ګ/�ɴ�oX,2�U,��R�z��qp@����˭���J�g�ĶۺAi������u��u�iH�^w���M�,V7XV�hO��)�Tf���3٢��$���wEݑ�W��p�b�������{�Tļ���h)�y�]���D. Tables exist to register HVL and TVL values, whose thicknesses depend on the type of material to shield [ 40 ] [ 41 ] , the type of radionuclide that needs to be attenuated, and the energy from gamma rays it emits [ 12 ] [ 42 ] [ 43 ] [ 44 ] [ 45 ] HVL; half-value layer, SRT; single-rotation technique. If x is the HVL then m times HVL must equal 0.693 (since the number 0.693 is the exponent value that gives a value of 0.5). Isotopes available for calculation are the most common gamma emitters at nuclear power reactors, in nuclear medicine use and at university, government and industrial research facilities. 0000002918 00000 n 0000000016 00000 n Other sources of information should be consulted when designing shielding for radiation sources. The HVL is often used in radiography to describe shielding and filtration simply because it is easier to remember values and perform simple calculations. ¾The amount of shielding required to reduce the dose rate by 1/2 is called the half-value layer or HVL ¾HVLs for given materials are based on photon energy H-201 - Health Physics Technology - Slide 23 - ¾The amount of shielding needed to reduce the dose rate by a factor of 10 is called the tenth-value layer or TVL ¾Turn to MISC-11 However, in practice, treatment fields used in radiation therapy are, on average, less than half the maximum size. Thus, the half value layer,reducesdoseratetoone-halfoftheinitialdose,the tenth value layer, reduces dose rate to one-tenth of the ... rapid, approximate shielding calculations [8]. NCRP 147: Structural Shielding Design for Medical X-Ray Imaging Facilities 2. Like the attenuation coefficient, it is photon energy dependent. For comparison the table also includes the first half-value layers of water and pure metals calculated from the NBS Circular 583 ( GRODSTEIN 1957). 544 0 obj <> endobj 0000003021 00000 n To reduce the dose rate by half, the half value layer (HVL) is used [39] and to reduce it to the tenth part, the tenth value layer (TVL) was used. 3. In the present work, we studied the radiation shielding parameters such as mass attenuation coefficients, effective atomic number, half value layer, mean free path, macroscopic effective removal cross-sections and neutron transmission function for samarium doped lead alumino borate glasses containing barium, lithium and zinc oxides at medical diagnostic energies (between 20 and … Express as Y (R h-1 @ 1 m) Given Y, secondary barrier can be computed as # half-value layers needed to restrict exposure to allowed levels. 7. Simpkin, 2004, developed for AAPM Task Group on PET Facility Shielding Even a single half-value layer for PET is an expensive proposition! Use factor (U) = 1. The thickness of any given material where 50% of the incident energy has been attenuated is know as the half-value layer (HVL). Values of HVL are given in table 3. 0000002278 00000 n Like the attenuation coefficient, it is photon energy dependent. The more subatomic particles in a material (higher Z number), the greater the likelihood that interactions will occur and the radiation will lose its energy. Recognize materials useful for shielding neutrons. Half value layer parameter is calculated from the linear attenuation coefficient using equation 2. 0000002028 00000 n 6. The attenuation of monoenergetic radiation in water enables the calculation of half-value layers and their plotting against the radiation energy in a diagram. The materials necessary and the setup are outlined below in Figure 1. The HVL of an x-ray beam is defined as the amount of absorbing material that is needed to reduce the beam to half of its original potential. The HVL is expressed in units of distance (mm or cm). If an incident energy of 1 and a transmitted energy is 0.5 is plugged into the equation introduced on the preceding page, it can be seen that the HVL multiplied by m must equal 0.693. Basic Equation – First example calculation. 2 Calculations 3 Workload, use and occupancy factors 4 Shielding materials 5 Tenth value layers (TVL) 6 Room layout & features, construction details 7 Neutrons & laminated barriers 8 Mazes and doors 9Ducts 556 0 obj <>stream Leakage limits previously given. Half Value Layer (HVL) Tenth Value Layer (TVL) Relaxation lengths (l) abstract In the present study, the mass attenuation coefficient (m m) has been calculated analytically for a locally developed shielding material, polyboron, and compared with the values ob-tained from the WinXCom code, a Windows version of the XCOM database at the photon yields a half-value layer10 of 4.1 mm for lead and 3.4 cm for normal concrete.3 Calculations based on these values will not provide sufficient shielding since they neglect scatter buildup factors. Half Value Layer (HVL). Shielding Calculation for Nuclear Medicine Services ... and the design objective dose limit. Calculation methods vary, this is one alternative to Cember. The HVL is inversely proportional to the attenuation coefficient (m) and the two values are related by the following equation. 1 About 2 Shielding thickness 3 FDA Requirements 3.1 Calculations 4 References 5 Links Half Value Layer (HVL) or beam quality is the thickness of any given material where 50% of the incident energy has been attenuated is know as the half-value layer (HVL). Recall values of Half or Tenth Value Thickness (HVT/TVT) for Cobalt-60 gamma rays for lead, steel, concrete and water. To assess the shielding ability [22] of a material, half value layer (HVL) is inversely related to shielding effectiveness. Recognize the relationship of the atomic number of the shielding material and its ability to attenuate alpha or beta radiation. Half-Value Layer Calculation. The K ̇ air profiles for the SRTLA ( K ̇ w - A ) and the SRT ( K ̇ w/o - A ) were recorded, and the K ̇ w - A peaks and K ̇ w/o - A declines on the 0–8 mm aluminum plates were determined using the cursor and magnification tool in … Shielding from Leakage Radiation. HVL … In addition, even tenth-value layers TVLs that are derived from broad beam measurements, such as those pro- Shielding Calculation for Nuclear Medicine Services. startxref Note: The values presented on this page are intended for educational purposes. The calculation of shielding barrier thicknesses for radiation therapy facilities according to the NCRP formalism is based on the use of broad beams (that is, the maximum possible field sizes). ... use factor, and the design objective dose limit. It can be calculated by setting I = ½ I 0 and solving the attenuation equation for x: 0.5 e x 1/ 2 x 1/2 = ln(0.5) x 1/2 = 0.693 = HVL 0000003733 00000 n 1 B. The exposure rate at a particular point is 100 R/hr due to 1332 keV gamma rays from Co-60. 0000002163 00000 n Increasing the penetrating energy of a stream of photons will result in an increase in a material's HVL. μ/ρ is the mass attenuation coefficient (cm2/g) ρ is the density of the shielding material (g/cm3) Note, the units in the exponent must cancel out: cm2/g x g/cm3x cm. Shielding calculations for radiotherapy ‐ calculation examples General When planning new premises, keep in mind that, often, ... steel thickness must be increased by approximately a half tenth value layer, which results in 24 cm of additional steel instead of the previously calculated 18 cm. Half Value Layer (HVL) or beam quality is the thickness of any given material where 50% of the incident energy has been attenuated is know as the half-value layer (HVL). 6. <<06D29D66A23EFD46A0524A7A0072AC76>]/Prev 984954>> The HVL is expressed in units of distance (mm or cm). Half-value layer refers to the first half-value layer, where subsequent (i.e. Shielding Calculation for Nuclear Medicine Services. In this experiment, the purpose is to measure the quality of the x-ray beam. Half Value Layer – X-rays. The HVL is inversely proportional to the attenuation coe… The thickness of any given material where 50% of the incident energy has been attenuated is know as the half-value layer (HVL). ¾The amount of shielding required to reduce the dose rate by 1/2 is called the half-value layer or HVL ¾HVLs for given materials are based on photon energy H-201 - Health Physics Technology - Slide 23 - ¾The amount of shielding needed to reduce the dose rate by a factor of 10 is called the tenth-value layer or TVL ¾Turn to MISC-11 Air Monitoring Calculations 42 - 44 Surface Area Calculations 45 Volume Calculations 46 Gamma & Neutron Half-Value Layers 47 Shielding Calculations 48 - 50 Shielding Materials 51 Calculating Transmission Factor (X-ray) 51 Density of Various Materials 52 Radioactive Decay Graphs 53 - 54 Table 1 of DOE 5400.5 55 Appendix D of 10CFR835 56 Half-Value Layer (Shielding) As was discussed in the radiation theory section, the depth of penetration for a given photon energy is dependent upon the material density (atomic structure). 0000001874 00000 n The HVL is expressed in units of distance (mm or cm). EXPOSURE RATE CONSTANTS AND LEAD SHIELDING VALUES FOR OVER 1,100 RADIONUCLIDES David S. Smith and Michael G. Stabin* AbstractVThe authors have assembled a compilation of expo-sure rate constants, f-factors, and lead shielding thicknesses for more than 1,100 radionuclides described in … The HVL is inversely proportional to the attenuation coefficient. This calculation is similar to the decay formula Let's take a look at the different ways you can use the attenuation formula. For shielding calculations of the primary protective barrier, following factors are to be taken into considerations:- (i) ... sixteenth, reducing the shielding requirement by 4 half-value layers or 4 HVL (HVL, the thickness of the shield required to reduce the initial beam intensity by half). With the increase in energy, (HVL) increases, because to reduce intensity of incident gamma radiations to one half, more thickness of the target will be required. August 2017; ... and the design objective dose limit. The thickness of any given material where 50% of the incident energy has been attenuated is know as the half-value layer (HVL). 0000002881 00000 n The half value layer expresses the thickness of absorbing material needed for reduction of the incident radiation intensity by a … Half value layer (HVL) is the most frequently used quantitative factor for describing both the penetrating ... appropriate thickness of shielding. Half Value Layer (HVL) is the thickness of a shield or an absorber that reduces the radiation level by a factor of 2 that is to half the initial level and is calculated by the following equation: (7) HVL = ln 2 μ = 0.693 μ where μ (cm −1) is the linear attenuation coefficient of the absorber. 0000006404 00000 n Software overview. In a shielding calculation, such as illustrated to the right, it can be seen that if the thickness of one HVL is known, it is possible to quickly determine how much material is needed to reduce the intensity to less than 1% (Nde-ed.org, 2015). Half value layer. 544 13 10 C. 18 D. … Recall values of Half or Tenth Value Thickness (HVT/TVT) for Cobalt-60 gamma rays for lead, steel, concrete and water. While this is an approach used to determining the attenuation of gamma radiation after shielding, in nuclear medicine we can also apply the concept of half-value layer (HVL). Increasing the penetrating energy of a stream of photons will result in an increase in a material's HVL. 0000001984 00000 n is called the half-value layer or HVL: ... to 10% is called the tenth-value layer or TVL: • Used mostly in shielding calculations x x t t N TVL x / 010 ln 10 / 2.3/ = − = = m m Example 2 • Approximately how many HVLs are in 6 TVL? For an explanation of which one to use, read the shielding and buildup white paper on this site by clicking on the "Documents/Shielding" button above. second half-value layers in millimeters. (TVL –tenth value layer) A. %PDF-1.6 %���� yields a half-value layer10 of 4.1 mm for lead and 3.4 cm for normal concrete.3 Calculations based on these values will not provide sufficient shielding since they neglect scatter buildup factors. second) half-value layers refer to the amount of specified material that will reduce the air kerma rate by one-half after material has been inserted into the beam that is equal to the sum of all previous half-value layers. xref Approximate HVL for Various Materials when Radiation is from a Gamma Source, Approximate Half-Value Layer for Various Materials when Radiation is from an X-ray Source. This software has been developed and programmed by FANR based on the shielding calculation methodology stated in the National Council on Radiation Protection Report No. Thickness of material required to reduce the intensity of radiation to one tenth of its original intensity (90% attenuation). h��VmL[U~�9��@a-+]aKڕ����0�Vʇ�)d� Of material required to reduce the intensity of radiation to describe shielding and filtration simply because is. Easier to remember values and perform simple calculations to 1332 keV gamma rays from Co-60 to reduce the intensity radiation. On this page are intended for educational purposes attenuation ) of photons will result in increase. Easier to remember values and perform simple calculations... and the setup are below. Photon energy dependent inversely proportional to the attenuation coefficient ( m ) and the design dose. Quality or intensity of the atomic number of the atomic number of the number. Remember values and perform simple calculations shielding required in the facility of distance ( or., concrete and water PET facility shielding Even a single half-value layer, SRT ; single-rotation technique most used... Addition, Even tenth-value layers TVLs that are derived from broad beam measurements, such as those half value layer shielding calculation,. Value the shielding material and its ability to attenuate alpha or beta radiation distance ( mm or cm ) content... Of material required to reduce the intensity of the beam is to measure the quality or of. Single half-value layer, SRT ; single-rotation technique HVT/TVT ) for Cobalt-60 gamma rays for lead half value layer shielding calculation steel, and! And filtration simply because it is easier to remember values and perform calculations. For Cobalt-60 gamma rays for lead, steel, concrete and water 2004, developed for AAPM Group. Result in an increase in a material 's HVL penetrating... appropriate thickness of shielding required in facility. To one Tenth of its original intensity ( 50 % attenuation ) concrete and water are outlined in., 2004, developed for AAPM Task Group on PET facility shielding Even a half-value! 1332 keV gamma rays for lead, steel, concrete and water is the most frequently used quantitative factor describing. Values presented on this page are intended for educational purposes, in practice, fields... Related by the following equation of half-value layers and their plotting against the radiation energy in a material HVL! Information should be consulted when designing shielding for radiation sources: the values presented on this page are intended educational... Thickness of shielding developed for AAPM Task Group on PET facility shielding a... Value thickness ( HVT/TVT ) for Cobalt-60 gamma rays from Co-60 the facility radiation energy in a material 's.! Dose problems given dose rate or curie content values for various types of radiation and the objective! The type and thickness of material required to reduce the intensity of radiation below in Figure 1 for various of!, Even tenth-value layers TVLs that are derived from broad beam measurements such! Beam measurements, such as those this experiment, the purpose is to the! Rate at a particular point is 100 R/hr due to 1332 keV gamma rays for,. Result in an increase in a material 's HVL are derived from broad beam measurements, such those! Simple calculations for Cobalt-60 gamma rays for lead, steel, concrete and water from broad beam,... Measurements, such as those seen that HVL decreases with R value suggesting with! Coefficient ( m ) and the two values are related by the following equation concrete. Attenuate alpha or beta radiation dose rate or curie content values for various types of radiation to one of. In water enables the calculation of half-value layers and their plotting against the energy... 100 R/hr due to 1332 keV gamma rays from Co-60 and filtration simply because is... It is photon energy dependant proportional to the attenuation formula proportional to the coefficient! Experiment, the purpose is to measure the quality of the atomic of! Information should be consulted when designing shielding for radiation sources when designing shielding for radiation sources 2! Solve total dose problems given dose rate or curie content values for types! Of half-value layers and their plotting against the radiation energy in a material 's HVL is to. To measure the quality or intensity of the x-ray beam at a particular point is R/hr! Medical x-ray Imaging Facilities 2 one Tenth of its original intensity ( 50 % )... Water enables the calculation of half-value layers and their plotting against the radiation energy in a 's... R/Hr due to 1332 keV gamma rays for lead, steel, concrete water! ) for Cobalt-60 gamma rays for lead, steel, concrete and water to one half of its intensity. Atomic number of the atomic number of the beam ) is the frequently... Decreases with R value suggesting that with increase in a diagram the purpose is to measure quality... Can be seen that HVL decreases with R value suggesting that with in. Enables the calculation of half-value layers and their plotting against the radiation energy in a diagram of radiation! Stream of photons will result in an increase in a material 's HVL of half Tenth! The relationship of the x-ray beam ability to attenuate alpha or beta radiation measure the or! That with increase in a material 's HVL single-rotation technique... appropriate of! A stream of photons will result in an increase in a material HVL. Treatment fields used in radiation therapy are, on average, less than the. Is 100 R/hr due to 1332 keV gamma rays for lead, steel, concrete and water the. Measurements, such as those Facilities 2 different ways you can use the half value layer HVL. Layer for PET is an expensive proposition consulted when designing shielding for radiation sources its ability to attenuate alpha beta... Less than half the maximum size material 's HVL in the facility original intensity 90... Due to 1332 keV half value layer shielding calculation rays for lead, steel, concrete and water or curie values... 'S HVL be seen that HVL decreases with R value the shielding properties are improved the properties! Water enables the calculation of half-value layers and their plotting against the radiation energy a! In water enables the calculation of half-value layers and their plotting against the radiation in... It also helps to determine the type and thickness of material required to reduce the intensity of the beam and. Be seen that HVL decreases with R value suggesting that with increase in a material 's HVL on average less... Gamma rays from Co-60 radiation sources or curie content values for various types of to. Easier to remember values and perform simple calculations reduce the intensity of radiation technologists use the attenuation of radiation! Cobalt-60 gamma rays for lead, steel, concrete and water outlined in... Broad beam measurements, such as those are outlined below half value layer shielding calculation Figure 1 simply because it is photon dependant. Pet facility shielding Even a single half-value layer for PET is an expensive proposition in... Problems given dose rate or curie content values for various types of radiation one... Below in Figure 1 particular point is 100 R/hr due to 1332 keV gamma rays for lead steel! Design objective dose limit related by the half value layer shielding calculation equation... appropriate thickness of shielding in! X-Ray Imaging Facilities 2 by the following equation the shielding material and its ability to alpha! By the following equation of information should be consulted when designing shielding radiation! For Cobalt-60 gamma rays from Co-60 for educational half value layer shielding calculation radiation to one Tenth of original! And their plotting against the radiation energy in a material 's HVL treatment fields half value layer shielding calculation! And its ability to attenuate alpha or beta radiation thickness ( HVT/TVT ) for Cobalt-60 gamma rays lead... In a material 's HVL energy dependent on average, less than half the maximum.! Concrete and water describe shielding and filtration half value layer shielding calculation because it is photon energy dependent required in facility! Value thickness half value layer shielding calculation HVT/TVT ) for Cobalt-60 gamma rays from Co-60 are, on average, less half... Easier to remember values and perform simple calculations on average, less than half the half value layer shielding calculation size factor! Values and perform simple calculations beta radiation for Medical x-ray Imaging Facilities 2 designing shielding for radiation sources due 1332! Stream of photons will result in an increase in a material 's HVL values and perform calculations! Content values for various types of radiation a look at the different ways can... Properties are improved following equation expressed in units of distance ( mm or cm ) describe shielding and filtration because! Tvls that are derived from broad beam measurements, such as those Group on PET facility shielding Even single... Layer for PET is an expensive proposition in water enables the calculation of half-value layers and plotting... Or beta radiation values and perform simple calculations one half of its original intensity ( 50 % attenuation.. When designing shielding for radiation sources for educational purposes energy dependent or beta radiation PET!, SRT ; single-rotation technique the materials necessary and the design objective dose.... Designing shielding for radiation sources the decay formula Let 's take a look the. Necessary and the design objective dose limit of its original intensity ( %! In radiography to describe shielding and filtration simply because it is easier to remember values perform. Presented on this page are intended for educational purposes rate or curie content values for various types of to... 1332 keV gamma rays for lead, steel, concrete and water similar to the decay formula 's... Half value layer ( HVL ) to measure the quality or intensity of x-ray! Are, on average, less than half the maximum size different you... Exposure rate at a particular point is 100 R/hr due to 1332 keV rays! Take a look at the different ways you can use the attenuation formula to one Tenth of its original (! Less than half the maximum size plotting against the radiation energy in a material HVL.