Universal curve of Gth – Formulae

Universal curves of Gres and Gth

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[1] O. Shcherbakov and H. Harada, *Resonance self-shielding corrections for activation cross section measurements*. Journal of Nuclear Science and Technology **39** (5) (May 2002) 548-553.

[2] E. Martinho, I.F. Gonçalves, J. Salgado, *Universal curve of epithermal neutron resonance self-shielding factors in foils, wires and spheres*. Applied Radiation and Isotopes **58** (3) (March 2003) 371-375.

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The introduction of an appropriate dimensionless variable, which takes into account, simultaneously, the material absorbing and scattering properties, can express the thermal neutron self-shielding factor of spherical samples by a unique curve. It is shown that the differences between the values calculated by Blaauw and those of the proposed curve are < 1.5%.

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The interpretation of the sample activation in a nuclear reactor requires the knowledge of two corrective parameters: the thermal neutron self-shielding factor, Gth, and the resonance neutron self-shielding factor, Gres. The authors established a universal curve of Gres for isolated resonances and various geometries. The present paper deals with the description of Gth in foils, wires, spheres and cylinders by means of a universal curve on the basis of a dimensionless variable which includes the physical, nuclear and geometrical properties of the sample. The universal curve is in good agreement with the experimental and calculated values obtained from the literature.

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The presence of a sample in the neutron field of a nuclear reactor creates a perturbation of the local neutron fluxes. In general, the interpretation of the sample activation due to thermal and epithermal neutrons requires the knowledge of two parameters: the thermal neutron self-shielding factor, Gth, and the resonance neutron self-shielding factor, Gres. In recent works, the authors established an universal curve of Gres for isolated resonances and various geometries. The present paper deals with the description of Gth in foils by means of an universal curve on the basis of a dimensionless variable which includes the physical, nuclear and geometrical properties of the sample. The universal curve is in very good agreement with experimental and calculated values obtained from the literature. The study of other geometries (spheres, wires and cylinders) is in progress.

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An epithermal neutron self-shielding factor must be introduced to take into account the absorption of a neutron beam crossing a sample. This factor depends on the geometry and dimension of the sample, as well as on the physical and nuclear properties of the nuclides. On the basis of a dimensionless variable, which includes the relevant characteristics of the sample, universal curves for monoenergetic and 1/E collimated neutron beams are proposed, which enable the determination of the self-shielding factor for isolated resonances of high absorber nuclides.

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The resonance neutron self-shielding factor, Gres, is required in neutron metrology and activation data analysis. In a previous paper, the authors have shown that a dimensionless variable can be introduced which converts the dependence of Gres on the physical and nuclear properties of the material samples into an universal curve, valid for the isolated resonances of any nuclide. This work presents a methodology based on the universal curve, which enables to calculate Gres for a group of isolated resonances by weighting its individual contributions. A good agreement was reached with results calculated by the MCNP code and with experimental values for Mo foils and wires.

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Resonance neutron self-shielding factors for cylindrical samples of nuclides used as activation detectors or as targets for radionuclide production have been calculated using the MCNP code. These factors depend on the sample dimensions, as well as on the physical and nuclear properties of the nuclides. However, defining a dimensionless variable, which includes the relevant characteristics of the samples, it is possible to extend to cylinders a previously deduced universal curve for isolated resonances of any nuclide and samples of other geometries (foils, wires and spheres).

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The presence of a nuclide sample in an epithermal neutron field of a nuclear reactor creates a perturbation of the local neutron flux. This effect can be very important, especially if the nuclide cross-section exhibits a prominent resonance peak. To take into account the effect of the neutron flux perturbation in the sample activation, a resonance neutron self-shielding factor (Gres) must be considered. This factor depends on the geometry and dimension of the sample, as well as on the physical and nuclear properties of the nuclide. On the basis of a dimensionless variable which includes the relevant characteristics of the sample, an universal curve is proposed, which enables the determination of the factor Gres for isolated resonances of any nuclide and samples of various geometries (foils, wires and spheres). The proposed universal curve is in very good agreement with experimental and calculated values obtained from the literature.

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