Attenuation coefficients of gamma and X-rays passing through six materials

The aim of this study was to determine the attenuation of gamma and X-rays with different energies caused by passage through different materials.To this end,different materials with a range of atomic numbers were chosen to measure gamma and X-ray attenuation coefficients and to explore the mechanisms of interaction of gamma and X-rays with matter of various kinds.It is shown that the attenuation coefficients first decrease and then increase with increase in the radiation(photon)energy.The attenuation of gamma and X-rays passing through materials with high atomic number is greater than that in materials with low atomic number.The attenuation minimum is related to the atomic number of the irradiated materials.The larger the atomic number is,the lower the energy corresponding to attenuation minimum is.Photoelectric and Compton effects are the main processes when gamma rays pass through individual materials with high and low atomic numbers,respectively.Therefore,for radiotherapy and radiation protection,different methods should be considered and selected for the use of gamma and X-rays of different energies for use in different materials.

Variation in downwelling diffuse attenuation coefficient in the northern South China Sea

The diffuse attenuation coefficient for downwelling irradiance(Kd(λ)) is an important parameter for ocean studies.Based on the optical profile data measured during three cruises in the northern South China Sea in autumn from 2003 to 2005,variations in the Kd(λ) spectra were analyzed.The variability of Kd(λ) shows much distinct features in both magnitude and spectra pattern,it is much higher in coastal waters than that of open oceanic waters;and the blue-to-green(443/555) ratio of Kd(λ) tends to increase with chlorophyll a concentration([Chl-a]) from open ocean to coastal waters.These characteristics can be explained most by the increase of aw+p(443)/aw+p(555) with [Chl-a].In short waveband,the relation between Kd(λ)-Kw(λ) and [Chl-a] can be well described by a power law function,indicating the large contribution of phytoplankton to the variations in Kd(λ).As for the spectral model of the diffuse attenuation coefficient,there are good linear relationships between Kd(490) and Kd(λ) in other wavelengths with own slope and intercept of a linear functions in the spectral range 412-555 nm.Kd(490) is well correlated with the spectral ratio of remote sensing reflectance;and should enough measurement data are given,this empirical algorithm would be used in the Kd(λ) retrieval from ocean color satellite data.The variation in Kd(λ) provides much useful information for us to study the bio-optical property in the northern South China Sea.

Variation of diffuse attenuation coefficient of downwelling irradiance in the Arctic Ocean

The diffuse attenuation coefficient （Kd） for downwelling irradiance is calculated from solar irradiance data measured in the Arctic Ocean during 3rd and 4th Chinese National Arctic Research Expedition （CHINARE）, including 18 stations and nine stations selected for irradiance profiles in seawater respectively. In this study, the variation of attenuation coefficient in the Arctic Ocean was studied, and the following results were obtained. First, the relationship between attenuation coefficient and chlorophyll concentration in the Arctic Ocean has the form of a power function. The best fit is at 443 nm, and its determination coefficient is more than 0.7. With increasing wavelength, the determination coefficient decreases abruptly. At 550 nm, it even reaches a value lower than 0.2. However, the exponent fitted is only half of that adapted in low-latitude ocean because of the lower chlorophyll-specific absorption in the Arctic Ocean. The upshot was that, in the case of the same chlorophyll concentration, the attenuation caused by phytoplankton chlorophyll in the Arctic Ocean is lower than in low-latitude ocean. Second, the spectral model, which exhibits the relationship of attenuation coefficients between 490 nm and other wavelength, was built and provided a new method to estimate the attenuation coefficient at other wavelength, if the attenuation coefficient at 490 nm was known. Third, the impact factors on attenuation coefficient, including sea ice and sea water mass, were discussed. The influence of sea ice on attenuation coefficient is indirect and is determined through the control of enter- ing solar radiation. The linear relationship between averaging sea ice concentration （ASIC, from 158 Julian day to observation day） and the depth of maximum chlorophyll is fitted by a simple linear equation. In addition, the sea water mass, such as the ACW （Alaskan Coastal Water）, directly affects the amount of chlo- rophyll through taking more nutrient, and results in the higher attenuation coefficient in the layer of 30-60 m. Consequently, the spectral model of diffuse attenuation coefficient, the relationship between attenuation coefficient and chlorophyll and the linear relationship between the ASIC and the depth of maximum chlorophyll, together provide probability for simulating the process of diffuse attenuation coefficient during summer in the Arctic Ocean.

A generalized method of converting CT image to PET linear attenuation coefficient distribution in PET/CT imaging

The accuracy of attenuation correction in positron emission tomography scanners depends mainly on deriving the reliable 511-keV linear attenuation coefficient distribution in the scanned objects. In the PET/CT system, the linear attenu- ation distribution is usually obtained from the intensities of the CT image. However, the intensities of the CT image relate to the attenuation of photons in an energy range of 40 keV-140 keV. Before implementing PET attenuation correction, the intensities of CT images must be transformed into the PET 511-keV linear attenuation coefficients. However, the CT scan parameters can affect the effective energy of CT X-ray photons and thus affect the intensities of the CT image. Therefore, for PET/CT attenuation correction, it is crucial to determine the conversion curve with a given set of CT scan parameters and convert the CT image into a PET linear attenuation coefficient distribution. A generalized method is proposed for con- verting a CT image into a PET linear attenuation coefficient distribution. Instead of some parameter-dependent phantom calibration experiments, the conversion curve is calculated directly by employing the consistency conditions to yield the most consistent attenuation map with the measured PET data. The method is evaluated with phantom experiments and small animal experiments. In phantom studies, the estimated conversion curve fits the true attenuation coefficients accurately, and accurate PET attenuation maps are obtained by the estimated conversion curves and provide nearly the same correction results as the true attenuation map. In small animal studies, a more complicated attenuation distribution of the mouse is obtained successfully to remove the attenuation artifact and improve the PET image contrast efficiently.

Studies on mass attenuation coefficients for some body tissues with different medical sources and their validation using Monte Carlo codes

The mass attenuation coefficients of the breasts,lungs,kidneys,pancreas,liver,eye lenses,thyroid,brain,ovary,heart,large intestines,blood,skin,spleen,muscle,and cortical bone were measured at different sources(i.e.,0.021,0.029,0.03,0.14,0.218,0.38,0.412,0.663,0.83,and 1.25 MeV)using various methods including the Monte Carlo N-particle transport code(MCNP),the geometry and tracking code(GEANT4),and theoretical approach described in this study.Mass attenuation coefficients were also compared with the values from the national institute of standards and technology(NIST-XCOM).The values obtained were similar to those obtained using NISTXCOM.Our results show that the theoretical method is quite convenient in comparison with GEANT4 and MCNP in the calculation of the mass attenuation coefficients of the human body samples applied when compared with the NIST values and demonstrated an acceptable difference.

Study the Attenuation Coefficient of Granite to Use It as Shields against Gamma Ray

The present work investigates the linear and mass attenuation coefficients for gamma rays practically and theoretically by using spectroscopy gamma ray (UCS-20) and program (XCOM)) for various types of common use granite, and compares them with the lead because of its high blocking ability for this type of radiation. This paper concluded through linear and mass attenuation coefficients measurements that these coefficients decrease with increasing incident photons energy. Measurements also showed that the linear attenuation coefficients appropriate linearly with density while mass attenuation coefficients do not get affected.

Direct Analytical Method to Calculate Photopeak Efficiency and Photopeak Attenuation Coefficient of NaI(Tl) Well-Type Detector

In this paper full-energy peak (photopeak) efficiency and photopeak attenuation coefficient of 3'' × 3'' NaI(Tl) well-type scintillation detector were calculated using gamma-rayisotropic radiating point sources (with photon energy: 0.245, 0.344, 0.662, 0.779, 0.964, 1.1732, 1.333 and 1.408 MeV) placed outside the detector well. These energies were obtained from 152Eu, 137Cs and 60Co. The relations between the full energy peak efficiency and photopeak attenuation coefficients, were plotted vs. photon energy at different sources to detector distance, and it found that the full energy peak efficiency decreased by increasing the distance between the source and the detector.

Determination of gamma ray spectrometry efficiency for the attenuation coefficients of some bismuth borate glasses by MCNP and(ISOCS)techniques

Background Radiation detection has been a main interest for researchers as all kind of produced particles in atomic and subatomic physics based on the measurement systems so-called detector.Detection efficiency is one of the main parameters in detection system besides many other different parameters of the detector.The detector in experimental physics is an instrument that converts radiation energy into an electrical signal,and this is achieved basically by either ionization or excitation.The choice for any type of a detector(gas-filled,scintillation or semiconductor)for any application depends upon the X-ray of gamma energy range of interest.A working model is therefore developed which is capable of describing the overall NaI(Tl)detection efficiency as a function of several known parameters.Purpose The attenuation coefficients for the bismuth borate glasses with different concentrations were measured using gamma spectroscopy technique.The numerical absolute efficiency calibration of a detector can be determined by In-Situ Object Calibration Software(ISOCS)and Monte Carlo Neutral Particle version 5(MCNP5)techniques which does not require any calibration standards or reference materials.Methods By using the ISOCS and MCNP5 methodologies,the full energy peak efficiency of a scintillator detector(3“X3”NaI(Tl))exposed to Co-60 and Cs-137 gamma ray sources with average accuracy range 0.126–1.224%for the used samples can be detected.The used materials are ternary and are located between the detector and the source to determine the attenuation coefficients for these samples by using the calculated full energy peak efficiencies of a detector.Results The average accuracy ranged from−1.808 to 1.960%for linear attenuation coefficient(μ),while it ranged from−1.999 to 1.888%and from−1.924 to 1.960%for half value layer(HVL)and mass linear attenuation coefficient(μm),respectively.Conclusion The calculated values of the absolute full energy peak efficiency have been used to determine the attenuation coefficients of materials with different concentrations and different densities.The results proved the validation of ISOCS and MCNP to determine the absolute full energy peak efficiency of the detector which can be used to determine the attenuation coefficients for the simulated samples and it is a good tool to be used when experimental methods are not available.

Dual Energy CT Imaging in Cone-Beam Micro-CT for Improved Attenuation Coefficient Measurement

In order to improve micro-CT＇s capability of accurate quantification of linear attenuation coefficient μ, a dual energy method was developed to correct beam hardening artifacts caused by the polychromatic spectra of X-ray tubes. In this method, two sets of scans, taken at different energy levels, were combined to create a synthetic monochromatic image. A physical polychromatic model of μ in dual energy imaging was developed with an iterative method to solve the model for a few selected pixels. To find a high-speed and effective computing approach, the physics model was approximated by a polynomial function of the measured intensities. The method was tested on a PMMA-aluminum phantom and CaCI2 admixtures. The results show that streak and cupping artifacts are completely eliminated and that the measurement of the reconstructed attenuation coefficient μ is observed to be over 95% accurate.

Optimal Dual-Channel Dynamic Pricing of Perishable Items under Different Attenuation Coefficients of Demands

This paper discusses optimal dual-channel dynamic pricing of a retailer who sells perishable products in a finite horizon.The type of product which is equipped with different attenuation coefficients of demands on different sales channels is considered.Novel demand functions for the two channels are proposed according to attenuation coefficients of demands,and then a decision model is constructed,which can be handled stage-by-stage.It is shown that the sales price and the sales quantity of the channel which possesses more market shares are both higher than the ones of the other channel at each sales stage.More importantly,by analyzing the reasonability of the obtained solution,a necessary and sufficient condition is proposed to guarantee that both of the two channels will not stop selling through the entire period.We also propose an approach by the elimination method to deal with cases in which some channel stops selling.Further,we demonstrate that the channel which possesses more market shares is the optimal option when only one channel runs.Finally,numerical examples are presented to investigate the change of sales prices of the two channels under different market potential demands.

Observation and simulation of the diffuse attenuation coefficient of downwelling irradiance in the Polar Ocean

The three-stream radiation transfer model is used to investigate the fluctuation in the underwater diffuse attenuation coefficient of downwelling irradiance in the polar ocean with a high solar zenith angle and different direct radiation proportions.First,the applicability of the three-stream radiation model in the polar region is validated by using 18 in situ observation data from September to October 2009 in the Beaufort Sea.Statistics show that in the absence of sea ice,the average relative errors between the simulation and observation values for 490 nm downwelling irradiance (E_(d)(490)) and its diffuse attenuation coefficient (K_(d)(490)) are 7.04%and 9.88%,respectively.At the stations surrounded by sea ice,the radiation is relatively small due to ice blocking,and the average relative errors simulated by the model reach 15.89%and 15.55%,respectively.Second,simulations with different chlorophyll concentrations and different proportions of direct radiation reveal that a high solar zenith angle has a greater impact on K_(d)(490) in the surface water.K_(d)(490) is less affected by the light field (affected by the solar zenith angle and the proportion of direct radiation) at depths greater than 30 m,and meets the linear relationship with the inherent optical parameters(the sum of the absorption coefficient and backscattering coefficient).The surface K_(d)(490) is still consistent with that at a depth of more than 50 meters under a high solar zenith angle,implying that the surface K_(d)(490) can also be considered as an inherent optical parameter at a high solar zenith angle (greater than 60 degrees).The relative error of obtaining surface K_(d)(490) by using the linear relationship at the 50 m layer is found to be less than 8%in the seawater with chlorophyll concentration greater than0.05 mg m^(-3).The effect of the solar zenith angle and proportion of direct radiation can be ignored when measuring the diffuse attenuation coefficient in the polar region.Finally,the model can correct the ice-induced fluctuation in downward irradiance,allowing for optical research of seawater beneath the ice in the polar ocean.

Extraction of mode attenuation coefficient from low frequency reverberation signal

A method of extracting normal mode attenuation coefficient from low frequency reverberation signal has been proposed.Pseudo-inverse normal mode filtering method is implemented to get single mode reverberation field firstly.Based on the assumption of separability of modal back-scattering matrix,effective back-scattering matrix element can be calculated using single mode average reverberation intensity.Finally,mode attenuation coefficient is extracted by comparing effective back-scattering matrix elements at different ranges.The extracted mode attenuation coefficients are used to predict sound transmission loss at the same experiment area. Results show that the predicted transmission loss agrees well with the measured data.This method avoids the difficult of treating the coupling between bottom scattering attenuation and normal mode propagation attenuation.Research on extraction of mode attenuation coefficient from low frequency reverberation signal is useful for both geoacoustic inversion and rapid underwater environment assessment.

Ultrasonic characterization of modified Cr_2O_3 coatings by reflection coefficient spectroscopy

Pores,microcracks and density of plasma sprayed Cr2O3 coatings before and after high-intensity pulsed ion beam(HIPIB) irradiation were investigated using the ultrasonic reflection coefficient spectroscopy(URCS).The URCS was analyzed based on an acoustic transmission model for the multi-layered structure.The longitudinal velocity in the coatings was calculated from the experimental URCS,and the attenuation coefficient expression was deduced by comparing the experimental and numerical fitting amplitude spectral lines.The longitudinal velocity of as-sprayed Cr2O3 coating is 2 002 m/s,and increases to 2 099 and 2 148 m/s after being irradiated by HIPIB with 1 and 5 shots.Correspondingly,the factor A changes from 0.046 to 0.026 and 0.020 and n from 1.702 to 1.658 and 1.649 in the attenuation coefficient expression of α=Af n.It is observed that the surface morphology of Cr2O3 coatings changes from rough and porous to smooth and uniform with the increase of shot number,which accords with the ultrasonic analyses reasonably.The URCS seems to provide a convenient and nondestructive method to characterize surface modification of the plasma sprayed coatings.

Measurement of Attenuation of Ultrasonic Propagating through the Thin Layer Media with Time Delay Spectrum

The ultrasonic attenuation coefficient is one of the most important acoustic parameters to character the performance of a thin layer media, but it can not be measured due to mutual superposition of multiple reflected waves at the same interface in ultrasonic testing. Ultrasonic pulse echo and lamb wave to evaluate the thin layer media can not obtain attenuation coefficient at present. In this paper, analytical method was used to study the acoustics characteristic of thin layer media with the ultrasonic echo testing. Meanwhile, the process of ultrasonic attenuation measurement was presented. Simulation and experimental investigation is focused on a thin layer of rubber. Attenuation coefficient was introduced and evaluation mathematics model was established by the two echoes cross-correlation with and without the thin layer media based on the time delay spectrum. It involved the parameters related to the acoustic properties of the thin layer media. Through calculating the sound velocity and acoustic impedance with the evaluation model, it can deduce the relation between the attenuation coefficient and the frequency. Through analyzing the simulation results, it indicated that the attenuation coefficients were invariable with the varying of the frequency. However, the attenuation coefficients increased with the frequency increasing by ultrasonic testing the thin layer of rubber. The reason was that the attenuation factor was not taken into account during the simulation. This method overcomes shortcomings that the traditional ultrasonic testing can not evaluate the thin layer media whose thickness is less than motivation wavelength. It is a new solution to study the attenuation characteristic and on-line nondestructive evaluation in the thin layer media.

The vertical attenuation of irradiance as a function of turbidity: a case of the Huanghai (Yellow) Sea in spring

The planar photosynthetically available radiation （PAR）, turbidity and concentration of chlorophyll a （chl a）, were measured at 26 stations in the Huanghai （Yellow） Sea during a cruise of China SOLAS from 19 to 27 March 2005. Due to low chl a （〈0.35 mg · m^-3 ） in upper layers （above 5 m）, suspended particulate matter became the major factor that influenced the turbidity in early spring. The calculated vertical diffuse attenuation coefficient of PAR, K PAR , varied with water depths with a maximum value in the upper 5 m layer. The mean K PAR in survey area was 0.277 ± 0.07 m^-1 that is considerably higher than most of the other case 2 waters. Within the survey area, K PAR also showed distinct regional characteristics, corresponding to the distribution of turbidity. Based on measurements, the relationship between K PAR and turbidity as well as chl a was established. It was suggested that suspended particulate matter plays an important role in light attenuation in the Huanghai （Yellow） Sea in spring.

Wave Attenuation Properties of Double Trapezoidal Submerged Breakwaters on Flat-Bed

This paper investigates the wave attenuation properties of the double trapezoidal submerged breakwaters on the flat-bed by conducting physical experiments subjected to linear and cnoidal incident waves.The method of Goda's two points is used to separate the heights of incident,reflected and transmitted waves based on the experimental data.The possible factors affecting the wave attenuation properties of the double trapezoidal submerged breakwaters(i.e.,the relative submerged water depth,relative breakwater spacing,wave steepness and relative wave height) are investigated with respect to the reflection and transmission coefficients.The results show that there is a range,within which the breakwater spacing has little impact on the reflection coefficient,and the transmission coefficient tends to be a constant.The influence of the wave steepness is reduced while the breakwater spacing is too large or too small.Within the range of the relative wave height tested in this study,the reflection and transmission coefficients increase and decrease with the relative wave height,respectively.The double trapezoidal submerged breakwaters model indicates a good attenuation effect for larger wave steepness,big relative wave height and within the range of the relative breakwater spacing between 12.5 and 14 according to linear and cnoidal waves.The changes of wave energy spectra between the double submerged breakwaters on the flat-bed are investigated by the fast Fourier transform(FFT) method,showing that wave energy dissipation can be reached more effectively when the relative breakwater spacing is 12.5.

Study on gamma-ray attenuation characteristics of some amino acids for 133Ba,137Cs, and 60Co sources

Amino acids are the building blocks of proteins,which are the most abundant macromolecules in living cells.From the standpoint of the photon interaction cross sections of amino acids,the mass attenuation coefficients,half and tenth value layers,mean free path,effective atomic and electronic cross sections,effective atomic number,and effective electron density of fifteen essential amino acids have been determined for 133Ba,137Cs,and 60Co gamma-ray sources.The MCNP-4C code and the XCOM program have been used to calculate these parameters.The results have been compared to the available experimental and theoretical data.The theoretical results agreed with the experimental data,with RD values of ≤±7%.In the energy region of 81-1332.5 keV,it was found that the μm,σa,and revalues of the amino acids decreased as the photon energy increased,and the increasing density of amino acids had no steady effect on these quantities.Additionally,results demonstrated that the HVL,TVL,and MFP values increased with the increase in photon energy.The μm,σa,and Zeff values of aspartic acid were the highest among those of all amino acids,and they were the lowest for isoleucine.The Zeff value of each sample containing H,C,N,and O atoms was nearly constant in the studied energy region.The Neffvalues of the studied amino acids varied in the range of 3.14×10^23-3.44×10^23 electron/g.Furthermore,the Neffvalues were approximately independent of the amino acid type in this energy region.

An analytical validation for the attenuation of lateral propagating light in sea ice

The attenuation of lateral propagating light （LPL） in sea ice was measured using an artificial light source in the Canadian Arctic during the 2007/2008 winter. The apparent attenuation coefficientμ（λ）for lateral prop-agating light was obtained from the measured logarithmic relative variation rate. In this study an analytical solution based on the strict optical theories is developed to validate the measured result. There is a good consistency between theoretical solution and measured data, by which a quite simple but very rigorous relationship among the light source, measurement geometry, and measured irradiance is established. The attenuation coefficients acquired by measurement and theory are the diffusion attenuation as an apparent optical property of ice, independent of the light source and shining condition. The attenuation ability of sea ice should be caused by the microstructure of sea ice, such as crystal size, ice density, brine volume, air inclusion, etc. It also includes the leak from both interfaces by directional scattering. It is verified that the measuring approach is operational and accurate to measure the attenuation of the LPL. The solution from this study did not tell the connection among the extinction and the inclusions of sea ice theoretically be-cause of insufficient understanding.

BISQ model based on a Kelvin-Voigt viscoelastic frame in a partially saturated porous medium

Taking into account three important porous media mechanisms during wave propagation （the Biot-flow, squirt-flow, and solid-skeleton viscoelastic mechanisms）, we introduce water saturation into the dynamic governing equations of wave propagation by analyzing the effective medium theory and then providing a viscoelastic Biot/squirt （BISQ） model which can analyze the wave propagation problems in a partially viscous pore fluid saturated porous media. In this model, the effects of pore fluid distribution patterns on the effective bulk modulus at different frequencies are considered. Then we derive the wave dynamic equations in the time-space domain. The phase velocity and the attenuation coefficient equations of the viscoelatic BISQ model in the frequency-wavenumber domain are deduced through a set of plane harmonic solution assumptions. Finally, by means of numerical simulations, we investigate the effects of water saturation, permeability, and frequency on compressional wave velocity and attenuation. Based on tight sandstone and carbonate experimental observed data, the compressional wave velocities of partially saturated reservoir rocks are calculated. The compressional wave velocity in carbonate reservoirs is more sensitive to gas saturation than in sandstone reservoirs.

Experimental Study on Damage Properties of Rocks Under Dynamic Loading

The damage properties of two types of rocks under dynamic loading are studied. The shock induced experiments are done using planar impact technique on the one? stage light gas gun, and the ultrasonic tests on the damaged rocks have been made by use of the ultrasonic pulse? transmission method. The shock induced damage of rock is related to the shock speed and the attenuation coefficient of sonic wave, and the latter reflects the damage degree in rock fairly well. The attenuation coefficient α can be used as main damage parameter for constructing damage model of rock under dynamic loading.