Fine structure in the stopping powers and ranges of fission fragments in matter

doi:10.1016/0375-9474(83)90162-8

Nuclear Physics A

Volume 394, Issues 1–2, 14–21 February 1983, Pages 77-86

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Abstract

Accurate energy loss measurements of ²⁵²Cf fission fragments for 9 gases are presented. Analysis of these results, together with additional energy loss data from the literature and previous range results of ²⁵²Cf fission fragments, indicates the existence of Z₂ oscillations of the electronic stopping cross sections for fragment energies up to about 0.5 MeV/amu. The local maxima and minima are roughly at the same Z₂ values found for light particles. The amplitude of the oscillations decreases with increasing energy. These osculations set a limit to the accuracy that can be achieved from a smooth dependent stopping theory. For ²⁵²Cf fission fragment ranges the fluctuations are up to 15 % from the average values.

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Accurate simultaneous lead stopping power and charge-state measurements in gases and solids: Benchmark data for basic atomic theory and nuclear applications
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We have measured for the first time simultaneously both the mean charge states and stopping powers of (35–280) MeV/u ²⁰⁸Pb ions in gases and solids with an accuracy of 1%. The existence at lower energies and disappearance at higher of density effects in the charge-state distribution and the corresponding stopping power are directly confirmed and comparisons with widely used theories and simulations for heavy ions demonstrate strong deviations of up to 27%. However, an unprecedented prediction power of better than 3% has been achieved for the energy loss when the measured mean charge-states are implemented in the Lindhard-Sørensen theory. Our present benchmark data contribute to an improved understanding of the basic atomic collision processes and to numerous applications in nuclear physics. Extending the GANIL data [1] to higher accuracy and energies, we can now answer at which velocities the Bohr-Lindhard density effect in stopping will vanish.
12C, 15N and 16O stopping powers between 0.5 and 3.4 MeV in solid targets
1993, Nuclear Inst. and Methods in Physics Research, B
Stopping powers for ¹²C, ¹⁵N and ¹⁶O ions in Al, Cu, Ag and Au targets in the energy range from 0.5 to 3.4 MeV have been measured using transmission and backscattering techniques. The results are compared to available experimental data and to values in Ziegler's compilation. To avoid the limitation due to the magnitude of the kinematic factor, a procedure is described for extracting the stopping power from a backscattering spectrum. The stopping power measurements are compared to LSS predictions and fitted to the power function $S_{e} = η(ν ν_{0})^{μ}$ .
Fission fragment escape from bare fission foils: Measurement and comparison with calculations based on the use of the LSS-theory for fission fragment range determination
1990, Nuclear Inst. and Methods in Physics Research, A
The fission fragment escape fraction from bare ²³⁵U, 10% ²³⁹Pu/Al and 10% ²³⁷Np/Al foils were measured for four selected fission products, relevant for reactor neutron dosimetry, using the absolute radiometric technique. The escape fraction for the foils studied amounts up to 4% for the light fission fragments measured, a non-negligible correction in neutron dosimetry.
Attempts for prediction of the fission fragment escape fraction, based on fission fragment range calculations using the LSS-theory accounting for Z₂-oscillations, were performed and compared to the measurements. Agreement ranging from 2 to 16% could be achieved.
Furthermore, the experimental fission fragment escape fraction measurements were interpreted in terms of fission fragment range determination.
A semiempirical method based on the LSS formalism for estimating electronic energy loss
1986, Nuclear Inst. and Methods in Physics Research, B
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1986, Nuclear Inst. and Methods in Physics Research, B
The initial energies associated with fission fragments relate them to the medium velocity region of the order of $v_{0} Z_{1}^{23}$ in which most of the fragment energy is lost by “electronic” stopping. Theoretical models for electronic stopping in this velocity region are based on a statistical treatment of the atoms. Thus effects due to the electronic shell structure of the stopping medium cannot be reproduced and the resulting stopping parameters are monotonically dependent of Z₂. Range and energy loss determinations offission fragments reveal a pronounced non-monotonic dependence on Z₂. Based on these results an attempt is made to determine the systematics of the Z₂-oscillations in the stopping process of fission fragments. Systematic analysis of a large number of experimental results pointed out the dependence of the stopping process on several parameters characterizing both the fragment and the target. A spectral analysis was performed and typical periodicities in the Z₂-oscillations determined. After performing a sensitivity analysis a semiempirical modified LSS-expression for the calculation of fission fragment ranges was developed which includes the Z₂-oscillations. This expression has been evaluated and compared to the original LSS-theory by means of the Theory of Information.
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Analysis of extensive experimental range and energy loss data of ²⁵²Cf fission fragments in gases and solids reveals large discrepancies between the ranges calculated according to LSS theory and the experimental data. The same applies also to experimental energy loss data. A modified LSS expression which is based on these results enables the prediction of range and energy loss data for ²⁵²Cf fragments in any substance. Both the original LSS expressions and the modified expressions used to involve an interpolation procedure and iterative processes.
Based on extensive experimental range and energy loss data a direct method for calculating the LSS parameters is introduced, eliminating the need for the interpolation procedure and the iterative process.

^∗: Present address: Nuclear Research Center, Negev, POB 9001, Beer Sheva, Israel.

^∗∗: Charles Wolfson Chair in Nuclear Engineering.

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Abstract

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Cited by (6)

Accurate simultaneous lead stopping power and charge-state measurements in gases and solids: Benchmark data for basic atomic theory and nuclear applications

<sup>12</sup>C, <sup>15</sup>N and <sup>16</sup>O stopping powers between 0.5 and 3.4 MeV in solid targets

Fission fragment escape from bare fission foils: Measurement and comparison with calculations based on the use of the LSS-theory for fission fragment range determination

A semiempirical method based on the LSS formalism for estimating electronic energy loss

Z<inf>2</inf>-oscillation systematics in the stopping of fission fragments

Direct computation of lss parameters for the prediction of fission-fragment ranges and energy-loss in any substance