K X-ray emission and kinetic energy-nuclear charge relationship of ²⁵²Cf spontaneous fission

Abstract

Experimental study of physical quantities after fission provides crucial insights into the fission process, which is an indispensable way to test the fission theory. The characteristics of primary fission products before beta decay are of great value in unraveling fission kinematics and nuclear energy applications. However, the measurement of the fragment charge has always been challenging. Multi-parameter studies related to nuclear charge remain relatively scarce. The deexcitation of the primary fission products may undergo internal conversion and is often accompanied by characteristic X-ray emissions. Therefore, the correlated measurement of fragment kinetic energy and K X-rays for ²⁵²Cf spontaneous fission is conducted. A silicon surface barrier detector is used to measure the fragment kinetic energy, while two low-energy high-pure germanium detectors are utilized for K X-ray measurement. Identification of fission fragments with <i>Z</i> = 39–62 is realized through characteristic K X-rays with a charge resolution of Δ<i>Z</i> ≈ 0.7. Fission fragment K X-ray yields exhibit a strong charge correlation, with an odd-even effect factor of about 13%. Based on K X-rays, the post-neutron-emission average kinetic energy, average total kinetic energy <inline-formula><tex-math id="Z-20240630205303">\begin{document}$(\langle \rm TKE\rangle) $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20240563_Z-20240630205303.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20240563_Z-20240630205303.png"/></alternatives></inline-formula>, and its dispersion (<inline-formula><tex-math id="M1">\begin{document}$ {\sigma }_{{\mathrm{T}}{\mathrm{K}}{\mathrm{E}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20240563_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20240563_M1.png"/></alternatives></inline-formula>) of fission fragments are determined each as a function of nuclear charge. The kinetic energy distribution of light fragments shows a pronounced odd-even effect, with even-Z elements exhibiting kinetic energy enhanced by about 0.48 MeV compared with odd-Z fragments. The peak of the <inline-formula><tex-math id="Z-20240630205332">\begin{document}$(\langle\rm TKE\rangle) $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20240563_Z-20240630205332.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20240563_Z-20240630205332.png"/></alternatives></inline-formula> distribution is nearly <i>Z</i> = 52–53, while the minimum of the <inline-formula><tex-math id="M2">\begin{document}$ {\sigma }_{{\mathrm{T}}{\mathrm{K}}{\mathrm{E}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20240563_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20240563_M2.png"/></alternatives></inline-formula> appears near <i>Z</i> = 56, indicating the significant influence of deformed shells in the highly asymmetric fission region. The post-neutron kinetic energy distribution of fission fragments from ²⁵²Cf (sf) is calculated by using the GEF model and CGMF model. The CGMF model effectively reproduces the overall trend of kinetic energy as a function of charge number, while the results of the GEF calculation are systematically higher than the experimental values. Nonetheless, these two phenomenological models make it difficult to quantitatively describe the kinetic energy distribution of fission fragments accurately. In this study, the insights into K X-ray emissions and kinetic energy-nuclear charge relationships provide valuable reference data for independently measuring the fission yields and verifying the theoretical models of fission.