Range-energy Relation Research Articles

Depth-intensity relation for large depths in sea water derived from the primary-cosmic-ray energy spectrum.

Using the energy-loss parameters in water for muons according to Bezrukov and Bugaev the range-energy relation in sea water was derived and compared with previous results. For the first time the depth-intensity relation was derived dynamically from the latest primary spectrum in the range 1000--6000 hg ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ by considering the depth-energy relation and also accounting for the loss of muon intensity due to range fluctuations. The calculated result is in accordance with the latest depth-intensity measurements of the Soviet group in the Caribbean Sea.

Range-energy relationship for a scanning beam electron linear accelerator

In a scientific note of the same title (Anderson and St George, ibid., vol.30, p.461-5, 1985) investigations concerning a known empirical range-energy relation (ICRU, 1972) are reported. Based on their measurements with a scanned electron beam of a medical linear accelerator, Anderson and St George find some divergences from and raise some objections to the formula. Because of the far reaching importance of a stable system of electron energy determination in radiotherapy, any uncertainty should be removed as soon as possible, and because the formula discussed is sometimes connected with the present author's name, detailed comments are offered. From the considerations given, the base seems to be insufficiently broad for the conclusions drawn by Anderson and St George. In particular the equation rho Pp(Z/A)eff=0.285E0-0.137 may be the best available method to derive the most probable electron energy at the surface from a few MeV up to approximately 30 MeV without further energy loss corrections, and this for both scanned or scattered electron beams.

Derivation of muon range spectrum at different polar angles in deep underground from primary nucleon spectrum

The energy spectra of sea-level muons at different zenith angles have been estimated from the latest JACEE primary spectrum using ISR results modified for p-nucleus interactions. The theoretical results have been compared with the experimental results. Using the recent modified range-energy relation after Kobayakawa along with the fluctuation correction procedure after Kiraly, Kiraly and Osborne, the muon range spectra in deep underground at different polar angles have been calculated. The derived results are well in agreement with the latest Mont Blanc data after Bergamascoet al., Battistoniet al. and Utah experiments after Bergessonet al.

Calculation of muon range spectrum under sea-water from the latest JACEE primary spectrum using the modified energy loss formulation after Kobayakawa

The muon range spectrum under sea-water has been estimated from the latest primary nucleon spectrum based on JACEE measurements. The hadronic-energy moments for p-nucleus collisions have been used for the calculation of meson production spectrum. The latest modified range-energy relation after Kobayakawa has been applied for the conversion of muon energy spectrum at sea-level to depth-intensity spectrum under sea. The calculated result has been compared with the measured data after Higashiet al., Davitaevet al. and Rogers and Tristam.

Calibration of CR-39 (DOP) detector module for indian cosmic ray experiment using accelerated beams

We are using CR-39 (DOP) detectors to study cosmic rays in the charge region Z = 2–26 in our Spacelab-3 experiment. We have exposed the detector samples to different accelerated beams He, C, N, O, Ne 20 , Ne 22 , Si, Cr, Fe, Ni and U of various energies. These exposed samples are etched in 6.25 N NaOH at 70°C for different etching times. Different etched track parameters are measured to obtain minimum error in calculated V t /V b ratio. The obtained values of V t /V b are plotted against dE/dX as well as (Z∗/β) 2 . A non-linear curve of the form V t /V b = 1 + a(dE/dX) + b(dE/dX) c + d(dE/dX) e which has linear as well as power terms, is fitted using least square method. The possible charge resolution is calculated from the measured standard deviation. The curves between particle energy and V t /V b are drawn for different ions using suitable range energy relations for low energy region. The possible isotopic resolution is also discussed.

Derivation of muon range spectrum under rock from the recent primary spectrum

The muon range spectra under Mont Blanc Tunnel and Kolar Gold Field rocks have been calculated from the recently measured primary cosmic ray spectrum. The scaling hypothesis of Feynman has been used for the calculation of pion and kaon spectra in the atmosphere. The meson atmospheric diffusion equation has been solved by following the method of Bugaev et al. The derived muon energy spectrum has been found to be in good agreement with the measured data of the Kiel, Durham, DEIS, and Moscow University groups. The calculated muon energy spectra at large polar angles have been compared with the different experimental results. The integral muon spectrum up to 20 TeV supports the MARS burst data favourably. Using the procedure of Kobayakawa, the muon energy loss in rock due to ionization, pair production, and bremsstrahlung and nuclear interactions from Bezrukov and Bugaev, we have constructed the range–energy relation in Mont Blanc and Kolar Gold Field rocks. The estimated range spectra have been corrected for range fluctuations and have been compared with the Mont Blanc Tunnel data of Castagnoli et al., Bergamasco et al., and Sheldon et al. and the Kolar Gold Field data compilation by Krishnaswamy et al.

Range energy relationship for a scanning beam electron linear accelerator

The absolute energies for electron beams from a newly installed clinical accelerator should be established prior to starting treatments and periodically thereafter (AAPM 1966, ICRU 1972). Several methods for energy calibration of high energy accelerators have been suggested. A method which is widely used involves the measurement of the electron beam practical range Rp and deduction of the energy from that information. The problem of relating the measured practical range to the electron energy has been approached in several ways. Calculations of the electron range under the continuous slowing down approximation (CSDA) for a variety of incident energies and absorbers have been made and tabulated. A widely used empirical approximation was given by B. Markus (1961, 1964) and refined by the ICRU for the practical electron range in water as a function of energy and density. In the light of differences between the Markus-ICRU values,, and calculated CSDA range values and the differences in scattering media and operable energies, the authors investigate the range of electron beams in water produced by a scanning beam linear accelerator.

Amplitude Distribution of Cosmic Ray Events in Extrinsic IR Detectors

A method of calculating the amplitude distribution of cosmic ray events in IR detectors utilizing known range-energy relationships for the various cosmic particles (mostly protons and helium nuclei) and published cosmic ray energy spectra is described. Good agreement is obtained between the calculated amplitude distribution and the spurious events observed in an extrinsic detector during a flight test.

The absolute depth-intensity curve for cosmic-ray muons underwater and the integral sea-level momentum spectrum in the range 1-100 GeV/c

A portable scintillation counter telescope has been used to measure the absolute intensities of cosmic-ray muons underwater at 11 depths in the range 10-175 m. Over this depth range the depth-intensity curve is found to be well represented by the Miyake relationship I=A0h- alpha e- beta h/(h+h1) with A0, alpha , beta and h1 being 29.5, 1.32, 1.6*10-3 and 123.0, respectively. Using a calculated range-energy relationship for muons in water, the integral sea-level momentum spectrum was obtained from the depth-intensity curve for the momentum range 1-100 GeV/c. This spectrum has been compared with spectra reported by workers using both magnet and range spectrographs, and it is found that the present spectrum differs from these in both the absolute intensity values (intensity at >1 GeV/c=(6.29+or-0.40)*10-3 cm-2 s-1 sr-1 compared with 7.22*10-3 cm-2 s-1 sr-1 quoted by Allkofer et al.) and in the spectral shape. It is concluded that the differences result from the use of a simple muon propagation model to derive spectra from spectrograph data since this model leads to a distorted spectrum.

Experimental and Calculated Response of a Radiochromic Dye Film Dosimeter to High-LET Radiations

Dose-response characteristics were measured for the FWT 60 nylon-base radiochromic dye film dosimeter irradiated with ion beams of 3- and 16-MeV protons, 10-MeV a particles, and 21-MeV 7Li, 42-MeV '4N, and 64-MeV 160 ions. These characteristics were compared with the response to reference low-LET radiations, i.e., 6Co y rays and 10-MeV electrons. The ion beams covered an initial LET range of 28-5430 MeV cm2 g-' corresponding to an average LET in the detector of 28-6740 MeV cm2 g-'. The experimental relative effectiveness (RE) decreased monotonically with zf2f2 from 1.00 for 16-MeV protons to 0.81, 0.55, 0.47, 0.36, and 0.28 for 3MeV protons, a particles, and 7Li, 160, and '4N ions, respectively. The radial dose distribution around the ion path was calculated using two different range-energy relations for the 6 rays: a linear relation r = k, wo and a power-law relation r = k2 . w, where r is the range and o the energy of the 6 rays. Calculations of theoretical RE values, based on the track structure theory of Katz and co-workers, were in good agreement with experimental results. The best agreement (-6.2 to +14.3%) was obtained by using a power-law range-energy relation.

Derivation of Muon Intensities in Sea-water Depths up to 1400 M.W.E. from a Recent Primary Cosmic Ray Spectrum

The muon intensities in sea-water depths up to 1400 M.W.E. have been derived from a recent primary cosmic ray spectrum. The scaling hypothesis of Feynman has been used in the calculation of meson spectra in the atmosphere. The range-energy relation for muons in sea water, used in the present work, accounts for the muon energy loss in sea water due to collisions, pair production, bremsstrahlung and nuclear interactions. The calculated muon range spectrum in sea water is well in accord with the experimental data obtained by Higashi et al. (1966), Davitaev et al. (1969), and Rogers and Tristam (1981, 1983

Particle identification by measurements of track-etch rate as a function of residual range of heavy ions in biotite mica

A response curve of track-etch rate V T versus primary ionization was obtained for biotite mica, from the measurement of V T as a function of residual range of heavy ions of 10⪕Z⪕54 and energy E⪕9.6 MeV/nucleon. The data were found to be best fit by using a value of 10.1 for the fitting constant K in the primary ionization equation. The response curve of biotite reaches a plateau at J-values of about 30. It was found that the etch-rate data for Ar and S ions do not fit with the data of other ions, showing an enhancement in the track-etch rate for values of J⪕24. Profiles of track-etch rate as a function of residual range for use in particle identification studies can be constructed from these data along with a suitable range-energy relationship.

Stopping powers and extrapolated ranges for electrons (1-10 keV) in metals

A thin film quasiadiabatic calorimeter has been applied to the measurement of the stopping power for electrons, under conditions of small angle scattering, in Al, Ni, Cu, Ag and Au in the energy region 1 keV to 10 keV. Results are presented with an estimated precision of 15%. Corrections are included for the multiple scattering enhancement of the apparent path length of electrons in the film; thermal leakage during the irradiation of the calorimeter and the effective primary electron energy in the film. Good agreement is found with available theory. Fractional transmission curves are presented for monoenergetic electrons incident on the metal films. From these, extrapolated ranges are deduced and expressed as empirical range-energy relationships. A clear Z dependence is observed.

The Interaction of Low-Energy Negative Pions with Nuclear Emulsion

ET6B emulsions 200 µm thick were exposed to 65 MeV and 379 MeVπ- beams, and the range-energy relations of π- in emulsion for the energy region from 50 MeV to 10 MeV were obtained. The multiplicity and energy spectra of charged particles from pion absorption in emulsion were measured with a 65 MeVπ- beam. The multiplicity of charged particles was also measured with a 379 MeVπ- beam. The experimental results were compared with calculations by the evaporation and cascade theory. The experimental setup and the conditions for the processing of the emulsion to study the pion-nucleus interaction are reported.

π<sup>-</sup>中間子による癌治療の可能性 I.高分子物質による捕捉・吸収の測定

A future application of negative pions to radiotherapy has arrived at a promising stage. Negative pions, in addition to their good localization characteristics, offer an advantage of favorably influencing biological factors because of differences in the quality of radiation given to a) the treatment volume and b) the intervening normal tissue. By utilizing dose fractionation, the low dose to intervening normal tissue with its low LET allows these tissues to recover better than cells in the treatment volume. In this study the lucite phantom was bombarded with 150 MeV/c and 173 MeV/c negative pions and 173 MeV/c positive pions, respectively, by using the 12 GeV proton synchrotron of the National Laboratory for High Energy Physics (KEK). Range-energy relations in the lucite and the remaining curves of pions were observed. The observed range of pions in lucite agreed well with the theoretical prediction. The remaining curves show the different structures for pi+ and pi- mesons. Peak to plateau ratio is ten times.

Production of Fast Switching Power Thyristors by Proton Irradiation

There are several techniques currently employed by various manufacturers in the fabrication of fast switching power thyristors. Gold doping and irradiation by electron beams are among the more common ones. In all cases, the fast switching capability results from a reduction of the minority carrier lifetime of the host material by the introduction of carrier traps or recombination centers. However, accompanying this beneficial reduction in switching speed is a deleterious increase in forward voltage drop which also results from the introduction of carrier traps. Methods which minimize the voltage drop increase as the switching speed is reduced are highly desirable. One such method would achieve this by introducing the traps or recombination centers into well defined narrow regions where they will be more effective in reducing the switching speed than in increasing the forward voltage drop. Because the proton range-energy relationship in materials is relatively well defined and the lifetime reducing displacements occur near the end of their ranges, the lifetime in silicon can be reduced where desired by the precise control of proton energy. Dual energy proton beams from a tandem Van de Graaff accelerator were used in the experiments to determine whether proton beam irradiations offer advantages over other techniques. This was the subject of the present work. The results indicate that this is the preferred technique for reproducibly and rapidly processing fast switching thyristors with superior characteristics. The experimental procedure is discussed and comparisons are made with electron and neutron irradiated thyristors.

A double time-of-flight ( E− ΔE) mass spectrometer

A correlated ( E− ΔE) double time-of-flight mass spectrometer was designed and used in the dE dx measurements of 235U fission fragments in nickel as a function of mass and energy. The system has a time resolution of 1 ns, a mass resolution of ΔM L = 2.24 amu, ΔM H = 1.54 amu, and energy resolution of ΔE L = 1.56 MeV, ΔE H = 1.08 MeV for the median light and median heavy fission fragments, respectively. A simple Range-Energy relation of the form R = KE α was fitted to the data points. K was found to be mass dependent and decreases with the increase of the ion mass. For α = 0.75, best range-energy results were obtained for K = 0.176 mg cm 2/MeV 0.75. K was determined from the values of the ranges and kinetic energies of the median light and median heavy fragments and then extrapolated to other masses.

Computation and measurement of differential ranges of low-energy alpha particles in matter

The stopping power formula of Bethe (1953) is discussed and is used to compute differential ranges of low-energy alpha particles in air argon, aluminium and copper. A single radioactive source containing three active elements is used in experiments to measure the differential ranges in these materials. A range-energy relationship for the alpha particles in air is deduced.

Modified energy-deposition model, for the computation of the stopping-power ratio for small cavity sizes

This paper presents a modification to the Spencer-Attix theory, which allows application of the theory to larger cavity sizes. The modified theory is in better agreement with the actual process of energy deposition by delta rays. In the first part of the paper it is recalled how the Spencer-Attix theory can be derived from basic principles, which allows a physical interpretation of the theory in terms of a function describing the space and direction average of the deposited energy. A realistic model for the computation of this function is described and the resulting expression for the stopping-power ratio is calculated. For the comparison between the Spencer-Attix theory and this modified expression a correction factor to the ''Bragg-Gray inhomogeneous term'' has been defined. This factor has been computed as a function of cavity size for different source energies and mean excitation energies; thus, general properties of this factor have been elucidated. The computations have been extended to include the density effect. It has been shown that the computation of the inhomogeneous term can be performed for any expression describing the energy loss per unit distance of the electrons as a function of their energy. Thus an expression has been calculated whichmore » is in agreement with a quadratic range-energy relationship. In conclusion, the concrete procedure for computing the stopping-power ratio is reviewed.« less

The kinetic energy deficit in the symmetric fission of 259Md

Abstract