Energy-dependent Correction Factor Research Articles

Detailed Monte-Carlo characterization of a Faraday cup for proton therapy.

Experiments with ultra-high dose rates in proton therapy are of increasing interest for potential treatment benefits. The Faraday Cup (FC) is an important detector for the dosimetry of such ultra-high dose rate beams. So far, there is no consensus on the optimal design of a FC, or on the influence of beam properties and magnetic fields on shielding of the FC from secondary charged particles. To perform detailed Monte Carlo simulations of a Faraday cup to identify and quantify all the charge contributions from primary protons and secondary particles that modify the efficiency of the FC response as a function of a magnetic field employed to improve the detector's reading. In this paper, a Monte Carlo (MC) approach was used to investigate the Paul Scherrer Institute (PSI) FC and quantify contributions of charged particles to its signal for beam energies of 70, 150, and 228 MeV and magnetic fields between 0 and 25 mT. Finally, we compared our MC simulations to measurements of the response of the PSI FC. For maximum magnetic fields, the efficiency (signal of the FC normalized to charged delivered by protons) of the PSI FC varied between 99.97% and 100.22% for the lowest and highest beam energy. We have shown that this beam energy-dependence is mainly caused by contributions of secondary charged particles, which cannot be fully suppressed by the magnetic field. Additionally, it has been demonstrated that these contributions persist, making the FC efficiency beam energy dependent for fields up to 250 mT, posing inevitable limits on the accuracy of FC measurements if not corrected. In particular, we have identified a so far unreported loss of electrons via the outer surfaces of the absorber block and show the energy distributions of secondary electrons ejected from the vacuum window (VW) (up to several hundred keV), together with electrons ejected from the absorber block (up to several MeV). Even though, in general, simulations and measurements were well in agreement, the limitation of the current MC calculations to produce secondary electrons below 990eV posed a limit in the efficiency simulations in the absence of a magnetic field as compared to the experimental data. TOPAS-based MC simulations allowed to identify various and previously unreported contributions to the FC signal, which are likely to be present in other FC designs. Estimating the beam energy dependence of the PSI FC for additional beam energies could allow for the implementation of an energy-dependent correction factor to the signal. Dose estimates, based on accurate measurements of the number of delivered protons, provided a valid instrument to challenge the dose determined by reference ionization chambers, not only at ultra-high dose rates but also at conventional dose rates.

Spectral analysis of Monte Carlo calculated fluence correction and cema conversion factors for high-energy photon beams at different depths

Purpose: The aim of this study is to investigate the depth-dependent detector response of detailed thimble air-filled ionization chambers by calculating spectral charged particle fluence correction factors at different depths in water. Those spectral correction factors will help to understand, how the detector response varies at different depths and what kind of influences disparate effects have on the spectral detector response.Methods: The cema-approach can be used to obtain spectral charged particle fluence-based correction factors for various measurement conditions by substituting the commonly well-known dose conversion factor with a conversion factor based on the dosimetric quantity cema (“converted-energy per unit mass”). The resulting spectral fluence correction factors were calculated with the EGSnrc software toolkit and analyzed for two air-filled cylindrical ionization chambers (PTW type 31021 Semiflex 3D, SNC125c™) at different depths in a water phantom irradiated with a 6 MV linear accelerator x-ray spectrum. The ionization chamber models have been stepwise decomposed to investigate the perturbation caused by internal and external effects on the fluence distribution within the detector.Results: Monte Carlo calculated fluence-based perturbation correction factors revealed that for all investigated detectors, considerable fluence disturbances occur, especially in the build-up region of depth-dose curves. Our results have shown that even slight variations in depth can have major consequences on the differential charged particle fluence within the ionization chamber, mainly due to internal cavity-specific effects. Furthermore, the results showed that in the case of relative dose measurements, the depth-depending detector response can significantly differ from unity in a range of 1.4%–2.8% depending on the ionization chamber design.Conclusion: The complexity of different effects on the fluence disturbance could be broken down with regard to their influence on the spectral fluence distribution in the sensitive volume of the investigated detectors. It could be demonstrated, that the displacement of water is a depth-depending effect, which can not be compensated or corrected ideally for each investigated water depth by the shift of the effective point of measurement. Generally, the spectral analysis of those energy-dependent correction factors serves to a deeper understanding of the detector response under various conditions.

Beam Monitor Calibration for Radiobiological Experiments With Scanned High Energy Heavy Ion Beams at FAIR

Precise and reliable monitoring of the particle rate is of great importance at accelerator facilities worldwide. In this article we describe the standard beam monitor calibration currently employed at the multi-purpose experimental sites Cave A and Cave M at GSI, where intense highly energetic ion beams are routinely used for a wide variety of experiments. An absolute dose-to-water measurement is performed with an air-filled ionization chamber and transferred into a calibration per primary particle. This is necessary for the raster scanning system used to enable the irradiation of extended fields, required for biophysical experiments in the research fields of particle therapy or space radiation protection. The main focus of this work is to understand through Monte Carlo simulations whether the currently used dosimetry procedure is valid for all the ion species and energies that are provided at GSI Cave A by the SIS18 synchrotron and that will be provided by the SIS100 at FAIR. With this aim the detailed geometry of the 30013 Farmer ionization chamber currently used in the cave was implemented in the transport code FLUKA and the beam quality correction factor kQ for different energies and ion species was calculated. Further details about the robustness of the calibration are investigated as well, e.g. appropriate irradiation depth of biological samples. Evidence is presented that for ions above 1 GeV/u the kQ factor decreases due to the density effect, which modifies the water-to-air stopping power ratio at relativistic energies. These findings are of particular importance for future biophysics experiments with ion beams from the SIS100 in the framework of the FAIR project. For energies in the regime of several GeV/u the constant kQ value as used in common practice should be replaced with the energy-dependent correction factor provided in this work.

Potentials and phase shifts for nucleon–light nuclei systems

Two simple models based on the Coulomb-distorted phase function and supersymmetry-inspired factorisation methods are adapted to deal with the nucleon–light nuclei elastic scattering at low energies. The first one is associated with the derivation of a closed-form expression of the scattering phase shift for motion in Coulomb-distorted separable non-local potentials. The second one deals with the development of an energy-dependent phase equivalent local potential to the non-local one for s-wave and its subsequent generation of higher partial wave interactions through the formalism of supersymmetric quantum mechanics. The usefulness of our models is demonstrated through the computation of $$\upalpha $$ –nucleon scattering phase shifts at low energies up to partial waves $$\ell = 2$$ . Certain energy-dependent correction factors are also incorporated into energy-dependent higher partial wave potentials to achieve an excellent agreement with the standard data.

Dosimetry in a mammography phantom using TLD-300 dosimeters.

The purpose of this study was to evaluate the photon field effective energy (Eeff ) distribution and percentage depth-dose (PDD) within a mammography phantom by the analysis of the CaF2 :Tm (TLD-300) thermoluminescent (TL) glow curve. The experimental procedure involves the use of TLD-300 to determine with single dosimeter exposures both the relative dose and the beam quality. TLD-300 chips were exposed to x rays from a GE Senographe 2000D mammography unit at the surface and different depths within a BR12 phantom. X-ray beams were generated with Mo/Mo, Mo/Rh, and Rh/Rh anode/filter combinations and voltages between 25 and 34kV. Glow curves were deconvoluted into component peaks and the high- to low-temperature ratio (HLTR) was evaluated. The photon field Eeff was obtained from the HLTR values using a calibration curve determined previously. PDD was established from the peak 5 TL signal (TLSP5 ) at depths between 0.0 and 3.5cm inside the phantom. Taking into account the differences in density and composition between CaF2 :Tm and breast tissue, an energy-dependent correction factor (β(E)) was applied to TLSP5 . Measurements were compared with radiation transport Monte Carlo (MC) simulations performed with PENELOPE-2008. A typical 5% change in the HLTR from the phantom top surface to 3.5cm depth was measured, which corresponds to a 2.2keV increase in photon field Eeff . Values of the β(E) correction factor were 0.33 and 0.13 for Eeff equal to 15.1 and 22.5keV, respectively. This strong energy dependence of β(E) is mostly due to the differences in fluence attenuation between CaF2 and breast tissue. According to PDD measurements, dose decreased to half the surface value at depths between 0.7 and 1.0cm for Mo/Mo/25 and Rh/Rh/34 beams, respectively. Values of PDD, less than 10% at 3.5cm depth, would have been overestimated by about 3.5% (a large relative error) if an energy-independent correction factor had been assumed. Mean differences between experiments and MC simulations were 0.8keV and 1.2% in the determination of Eeff and PDD, respectively. The TLD-300 glow curve was used to accurately measure the photon field Eeff and PDD within a mammographic phantom. This work has demonstrated that Eeff and dose can be established simultaneously by using solely TLD-300.

Parameterization of Nuclear Hulthén Potential for Nucleus-Nucleus Elastic Scattering

In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthén type interaction is considered to describe the α-α, α-3He and α-3H systems. By exploiting the phase function method, scattering phase shifts are computed up to ELab = 100 MeV for the α-α system and ELab = 15 MeV for α-3He and α-3H systems. The S-wave phase shift δ0 for the α-α system tends to 2π and δ3/2− for the α-3He system tends to π, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2− states of α-3He and α-3H systems. With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2− states. We have also compared our results with the convenient Born approximations.

Supersymmetry-inspired low-energy α–p elastic scattering phases

We consider an effective potential model consisting of an electromagnetic part plus a nuclear part as the ground state interaction for an α–p system. The next few higher partial wave interactions are generated using the formalism of supersymmetric quantum mechanics. We adapt the phase function method to compute α–p elastic scattering phases up to 12 MeV, including the effect of the electromagnetic interaction quite rigorously in our phase shift calculation. With the further incorporation of some energy-dependent correction factors to our interactions, we obtain a good agreement with the experimental data.

A systematic characterization of the low-energy photon response of plastic scintillation detectors

To characterize the low energy behavior of scintillating materials used in plastic scintillation detectors (PSDs), 3 PSDs were developed using polystyrene-based scintillating materials emitting in different wavelengths. These detectors were exposed to National Institute of Standards and Technology (NIST)-matched low-energy beams ranging from 20 kVp to 250 kVp, and to 137Cs and 60Co beams. The dose in polystyrene was compared to the dose in air measured by NIST-calibrated ionization chambers at the same location. Analysis of every beam quality spectrum was used to extract the beam parameters and the effective mass energy-absorption coefficient. Monte Carlo simulations were also performed to calculate the energy absorbed in the scintillators’ volume. The scintillators’ expected response was then compared to the experimental measurements and an energy-dependent correction factor was identified to account for low-energy quenching in the scintillators. The empirical Birks model was then compared to these values to verify its validity for low-energy electrons. The clear optical fiber response was below 0.2% of the scintillator’s light for x-ray beams, indicating that a negligible amount of fluorescence contamination was produced. However, for higher-energy beams (137Cs and 60Co), the scintillators’ response was corrected for the Cerenkov stem effect. The scintillators’ response increased by a factor of approximately 4 from a 20 kVp to a 60Co beam. The decrease in sensitivity from ionization quenching reached a local minimum of about between 40 keV and 60 keV x-ray beam mean energy, but dropped by 20% for very low-energy (13 keV) beams. The Birks model may be used to fit the experimental data, but it must take into account the energy dependence of the kB quenching parameter. A detailed comprehension of intrinsic scintillator response is essential for proper calibration of PSD dosimeters for radiology.

Characterization of the energy response and backscatter contribution for two electronic personal dosimeter models.

We characterized the energy response of personal dose equivalent (Hp(10) in mrem) and the contribution of backscatter to the readings of two electronic personal dosimeter (EPD) models with radionuclides commonly used in a nuclear medicine clinic. The EPD models characterized were the RADOS RAD‐60R, and the SAIC PD‐10i. The experimental setup and calculation of EPD energy response was based on ANSI/HPS N13.11‐2009. Fifteen RAD‐60R and 2 PD‐10i units were irradiated using 99mTc, 131I, and 131I radionuclides with emission energies at 140 keV, 364 keV, and 511 keV, respectively. At each energy, the EPDs output in Hp(10) [mrem] were recorded with 15 inch thick PMMA to simulate backscatter form the torso. Simultaneous free‐in‐air exposure rate measurements were also performed using two Victoreen ionization survey meters to calculate the expected EPD Hp(10) values per ANSI/HPS N13.11‐2009. The energy response was calculated by taking the ratio of the EPD Hp(10) readings with the expected Hp(10) readings and a two‐tailed z‐test was used to determine the significance of the ratio deviating away from unity. The contribution from backscatter was calculated by taking the ratio of the EPD Hp(10) readings with and without backscatter material. A paired, two‐tailed t‐test was used to determine the significance of change in EPD Hp(10) readings. The RAD‐60R mean energy response at 140 keV was 0.85, and agreed to within 5% and 11% at 364 and 511 keV, respectively. The PD‐10i mean energy response at 140 keV was 1.20, and agreed to within 5% at 364 and 511 keV, respectively. On average, in the presence of acrylic, RAD‐60R values increased by 32%, 12%, and 14%, at 140, 364, and 511 keV, respectively; all increases were statistically significant. The PD‐10i increased by 25%, 19%, and 10% at 140 keV, 364 keV, and 511 keV, respectively; however, only the 140 keV measurement was statistically significant. Although both EPD models performed within the manufacturers' specifications of ±25% in the energy ranges used, they fell outside of our criteria of 10% at lower energies, suggesting the need to calculate energy‐dependent correction factors, depending on the intended EPD use.PACS numbers: 87.53.Bn, 87.55.N‐, 87.57.U‐

TH-AB-201-11: A Systematic Characterization of the Low Energy Response of Plastic Scintillation Detectors

Purpose: To characterize the low energy behavior of scintillating material used in plastic scintillation detectors. Methods: Four plastic scintillation detectors (PSDs) were developed using three different scintillating material (BCF-10, BCF-12, BCF-60) and one scintillator-free fiber. The scintillators were 1 mm in diameter and 10 mm-long, coupled to a 15 meter long clear PMMA optical fiber. A photomultiplier tube was connected to this fiber to collect the scintillator’s light signal. All fibers were covered by a light-tight polyethylene jacket. The PSDs were exposed to AAPM accredited low energy beam qualities ranging from 20 kVp to 250 kVp. Their response described the dose in polystyrene and was compared to the dose in air measured by a primary calibration chamber located at the beam exit. The mean energy and the spectral method were used to extract the effective mass energy-absorption coefficient using NIST database for each beam quality reference spectrum. Attenuation in air and in the fiber jacket were also considered. The scintillators expected response was compared to the experimental measurements and an energy-dependent correction factor was identified to account for low energy quenching occurring within the scintillators. Results: The clear optical fiber response was below 0.5% of the scintillator’s light, which indicated that a negligible amount of fluorescence contamination was produced. The scintillators response increased by a factor 3.65 ± 0.07 between a 20 kVp and a 250 kVp beam. The correction factor varied with beam energy and remained above 84% for beam qualities of 30 kVp and above, but drops for very low energy (20 kVp) to about 77%. Conclusion: This work describes the PSD energy dependence to low energy beam qualities and identifies a correction factor related to low energy quenching. A detailed comprehension of intrinsic scintillator response is essential when designing accurate PSD dosimeters for radiology purposes. This work was supported in part by a NIH/NCI SBIR grant R44CA153824 and by grant # 435510 from the NSERC. JB is supported by a FQRNT doctoral research scholarchip and acknowledges partial support by the NSERC CREATE Medical Physics Research Training Network grant # 432290.

SU-E-T-69: Energy Response Characterization and Calibration of Electronic Personal Dosimeters

Purpose: To characterize the personal dose equivalent energy response, Hp(10), for electronic personal dosimeters (EPDs) with commonly used radionuclides in nuclear medicine. Methods: Rados-60R with an energy compensated PIN diode and the SAIC Pd-10i with a miniature energy compensated Geiger-Muller tube EPDs were characterized. The experimental setup and calculation of EPD energy responses were based on ANSI/HPS N13.11-2009. 15 Rados-60R and 2 SAIC Pd-10i units were irradiated using 99mTc, 131I, and 18F radionuclides corresponding to emission energies at 140 keV, 364 keV, and 511 keV, respectively. EPDs output in Hp(10) [mrem] were recorded for free-in-air and with 15-in. thick PMMA to simulate backscatter form the torso. Simultaneous exposure rate measurements were also performed using 2 Victoreen 451-B ionization survey meters to serve as gold standard measurements. The expected EPD Hp(10) values were calculated from exposure (from the Victoreen 451-B survey meters) to Hp(10) as specified in ANSI/HPS N13.11-2009 and ICRU Report 57. These measurements were repeated for both setups at all energies. Results: On average, in the presence of acrylic, the reported Rados-60R values increased by 27%, 12%, and 13% and those reported by the SAIC Pd-10i increased by 23%, 19%, and 12% at 140 keV, 364 keV, and 511 keV, respectively. The Rados-60R EPDs were observed to under-respond at 140 keV by ∼16%, and agreed to within 5% and 10% of the expected values at 364 and 511 keV, respectively. The SAIC Pd-10i EPDs were observed to over-respond at 140 keV by ∼20%, and agreed to within 5% of the expected values 364 and 511 keV. Conclusion: Both Rados-60R and SAICPD-10i EPDs displayed Hp(10) values that were accurate to within 10% at energies above 364 keV. However, their accuracies degraded to 15–20% at lower energies (140 keV) suggesting the need to calculate energy dependent correction factors.

Technical Note: Precision and accuracy of a commercially available CT optically stimulated luminescent dosimetry system for the measurement of CT dose index

To determine the precision and accuracy of CTDI(100) measurements made using commercially available optically stimulated luminescent (OSL) dosimeters (Landaur, Inc.) as beam width, tube potential, and attenuating material were varied. One hundred forty OSL dosimeters were individually exposed to a single axial CT scan, either in air, a 16-cm (head), or 32-cm (body) CTDI phantom at both center and peripheral positions. Scans were performed using nominal total beam widths of 3.6, 6, 19.2, and 28.8 mm at 120 kV and 28.8 mm at 80 kV. Five measurements were made for each of 28 parameter combinations. Measurements were made under the same conditions using a 100-mm long CTDI ion chamber. Exposed OSL dosimeters were returned to the manufacturer, who reported dose to air (in mGy) as a function of distance along the probe, integrated dose, and CTDI(100). The mean precision averaged over 28 datasets containing five measurements each was 1.4% ± 0.6%, range = 0.6%-2.7% for OSL and 0.08% ± 0.06%, range = 0.02%-0.3% for ion chamber. The root mean square (RMS) percent differences between OSL and ion chamber CTDI(100) values were 13.8%, 6.4%, and 8.7% for in-air, head, and body measurements, respectively, with an overall RMS percent difference of 10.1%. OSL underestimated CTDI(100) relative to the ion chamber 21∕28 times (75%). After manual correction of the 80 kV measurements, the RMS percent differences between OSL and ion chamber measurements were 9.9% and 10.0% for 80 and 120 kV, respectively. Measurements of CTDI(100) with commercially available CT OSL dosimeters had a percent standard deviation of 1.4%. After energy-dependent correction factors were applied, the RMS percent difference in the measured CTDI(100) values was about 10%, with a tendency of OSL to underestimate CTDI relative to the ion chamber. Unlike ion chamber methods, however, OSL dosimeters allow measurement of the radiation dose profile.

SU-E-T-313: Probe-Type Experimental Dosimetry in Terms of Absorbed Dose to Water in Photon-Brachytherapy a Proposal for a Radiation-Quality Index.

In photon-brachytherapy (BT), all data for clinical dosimetry (e.g., the dose-rate constant) are not measured in water, but calculated, based on MC-simulation. To enable the measurement of absorbed dose to water, DW, in the vicinity of a source, the complex energy-dependence and other influence quantities must be considered. The detectors response, R=M/D, is understood as product of a detector-material dependent 'absorbed dose response', Ren, and Rin, the 'intrinsic response'. Ren is described by the Burlin-theory and because of dissimilarities between the detector-material and water, will have energy dependent correction factors which convert Ren into the clinically relevant DW,Qo=MQo × ND,W,Qo. To characterize BT- source-types, we propose a new 'radiation-quality index' QBT=Dprim(2cm)/Dprim(1cm), the ratio of the primary-dose to water at r=2cm to that at the reference distance r=1cm, similar to external beam dosimetry. Although QBT cannot be measured directly, it can be derived from primary and scatter separated dose-data, published as consensus data e.g., in the Carlton AAPM-TG-43-database. Mean QBT-values are: for nine HDR and four PDR 192Ir-sources: 0.2258±0.5%; one 169Yb- source: 0.2142; and one 125I-source: 0.1544. The main benefit of this new QBT-concept is that a type of BT-dosimetry-detector needs to be calibrated only for one reference radiation-quality, e.g., for Q0=192Ir. To measure the dose for different source-types, DW can be determined using calculated radiation-quality conversion factors kQ,QoBT, to be included in the AAPM-database and to be provided by the manufacturer for each detector-type. Typical BT-dosimetry-detectors are plastic scintillation detectors, radiochromic film, thermoluminescence detectors, optically stimulated detectors, and small volume ionization chambers. Recently, different DW(1cm)-primary standards have been developed in several European NMIs, enabling to calibrate BT-radiation- sources and BT-dosimetry-detectors and allowing to verify MC-calculated dose-rate constant values. The proposed definition of QBT has to be discussed internationally to find broad consensus.

Determination of the quality index for photon beams at arbitrary field sizes

A commonly used beam quality index (Q) for high-energy photon beams is the tissue phantom ratio (TPR20,10) for a square field of 10 x 10 cm2 and SDD of 100 cm. On some specialized radiotherapy treatment equipment such a reference collimator setting is not achievable. Likewise a flat beam profile, not explicitly required in dosimetry protocols, but certainly influences the measurement of Q, is not always produced. In this work, a method was developed in order to determine Q at any field size, especially for small and nonflattened beams. An analytical relationship was derived between TPR20,10 for arbitrary field sizes and Q [the TPR20,10 (10 x 10 cm2)] as quality index. The proposed model equation was fitted to the measured and published data in order to achieve three general fit parameters. The procedure was then tested with published data from TomoTherapy and CyperKnife treatment devices. For standard flattened photon fields, the uncertainty in Q measured at any field size using the parameters derived from this study is better than 1%. In flattening-filter free beams, the proposed procedure results in a reliable Q for any field size setting. A method is introduced and successfully tested in order to measure the beam quality under nonstandard conditions. It can be used, e.g., to get energy dependent correction factors as tabulated in dosimetry codes of practice even if standard conditions are not adjustable.

SU‐FF‐T‐321: Megavoltage Electron Beam Energy Estimation Using Thermoluminescent Dosimeters

Purpose: To explore the possibility of using a combination of thermoluminescent (TL) materials to estimate electron beam energy from a range of TL materials which exhibit energy dependent TL response to electrons. Method and Materials: Five different types of thermoluminescence dosimeters (TLD100, TLD100H, TLD200, TLD400 and TLD500) were irradiated with five electron energies available from a Siemens Primus linear accelerator. All types of TLDs were irradiated at depth of maximum dose to a dose of 1 Gy and the process was repeated three times. TL Response per Gy dose delivered was calculated for all the materials. Ratios of TL sensitivity of different combinations of TL materials for all five electron beams were determined. Results: All TL materials showed different magnitudes of variation in electron beam energy dependent response. The reproducibility of each type of TLD was; TLD100 2%, TLD200 3%, TLD400 1%, TLD500 5% and TLD100H 2%. The sensitivity ratios of combination TLD400‐TLD100 and TLD400H‐TLD100H showed the highest variation with electron energy. Conclusion: Lithium Fluoride (LiF) based TL materials are commonly employed in dosimetry audits conducted by IAEA/WHO. In electron dosimetry intercomparison and audits where the beam energy may not be accurately known, error in dose estimation can occur where LiF based materials are employed. However, if a combination of two TL materials is employed, the energy of the electron beam can be estimated. The present study has demonstrated that the combination of TLD100 and TLD 400 has the highest sensitivity to variation in electron energy in the nominal electron energy (E0) range of 5–14 MeV. In IAEA/WHO dosimetry audits when a combination of these two TL dosimeters (instead of a single TL dosimeter) is used, it has the potential to improve the accuracy of electron dosimetry by providing an energy dependent correction factor.

Calorimetric determination of kQ factors for NE 2561 and NE 2571 ionization chambers in 5 cm × 5 cm and 10 cm × 10 cm radiotherapy beams of 8 MV and 16 MV photons

The relative uncertainty of the ionometric determination of the absorbed dose to water, Dw, in the reference dosimetry of high-energy photon beams is in the order of 1.5% and is dominated by the uncertainty of the calculated chamber- and energy-dependent correction factors kQ. In the present investigation, kQ values were determined experimentally in 5 cm × 5 cm and 10 cm × 10 cm radiotherapy beams of 8 MV and 16 MV bremsstrahlung by means of a water calorimeter operated at 4 °C. Ionization chambers of the types NE 2561 and NE 2571 were calibrated directly in the water phantom of the calorimeter. The measurements were carried out at the linear accelerator of the Physikalisch-Technische Bundesanstalt. It is shown that the kQ factor of a single ionization chamber can be measured with a standard uncertainty of less than 0.3%. No significant variations of kQ were found for the different lateral sizes of the radiation fields used in this investigation.

A simple method for the approximate calculation of electron ranges in media

Abstract A method is described for calculating approximate electron ranges. The method uses a simple but less accurate analytic expression for electron range derived in calculations of cascade showers. An energy dependent correction factor is then applied to give reasonable agreement with calculations using the more rigorous theoretical treatment employing the continuous slowing down approximation. It is shown that, if energy dependent correction factors are derived for one element (e.g. aluminium), then these same correction factors can be used to compute electron ranges in other materials that are not too different in atomic weight.

Lifetime Measurements in La II with the Beam-Laser Method

Cascade-free lifetime measurements of the y 3F2 3 40, the z 1D20 and the z 3D1 2 30 levels in La II have been made with the beam-laser technique. Our results, together with other recent lifetime measurements in La II, are compared with lifetimes inferred from transition probabilities measured by Corliss and Bozman (CB). An energy-dependent correction factor to the CB lifetimes is found, indicating a misjudgement of the effective temperature in Corliss' and Bozman's arc. A new value of the La solar photosphere abundance based on six transitions in La II, is presented.

The solar radial gradient of galactic cosmic rays

The radial gradient of cosmic rays in the interplanetary region has been investigated taking into account convection, diffusion, energy losses, and differential streaming S. At high energies the analysis given here shows that S can be neglected and the radial gradient written C(r, T)Gs(r, T), where Gs(r, T) is the gradient given by the convection–diffusion theory and C(r, T) is an energy-dependent correction factor which can be computed from the observed differential intensity spectrum. During 1964–65 this result can probably be used for protons and helium nuclei down to a few hundred MeV/nucleon, with, at that time, [Formula: see text]. At lower energies Gs will be quite inaccurate as an estimate of the radial gradient unless changes in C are offset by streaming. Combining observations with this analysis it is shown that the radial anisotropy of protons (ξ) is: (i) positive but small (< 0.02%) at kinetic energies [Formula: see text]; (ii) negative in the range 40–600 MeV with ξmax = −0.75% (which should be observable); (iii) positive for energies less than about 40 MeV.