Simple function forms and nucleon-nucleus total cross sections

Total cross sections for neutron scattering with energies between 10 and $600\mathrm{MeV}$ and from nine nuclei spanning the mass range from ${}^6\mathrm{Li}\text{to}{}^{238}\mathrm{U}$ have been analyzed using a simple function of three parameters. The values of those parameters with which neutron total cross-section data are replicated vary smoothly with energy and target mass and may themselves be represented by functions of energy and mass.

Figure 1

The partial total cross sections for scattering of neutrons from ${}^{208}\mathrm{Pb}$ with the set of energies between 10 and $600\mathrm{MeV}$ specified in the text. The largest energy has the broadest spread of values.

Figure 2

The values of $l_0$ that fit neutron total scattering cross-section data from the nine nuclei considered and for energies between 10 and $600\mathrm{MeV}$. The curves portray the best fits found by taking a function form for $l_0\left(E\right)$.

Figure 3

The values of $l_0$ depicted in Fig. 2 as they vary with mass for all of the energies considered. Some of those energies are indicated in the diagram and the curves are splines linking best fit values for each mass assuming a function form for $l_0\left(A\right)$.

Figure 4

Total cross sections for neutrons scattered from ${}^6\mathrm{Li}$, ${}^{12}\mathrm{C}$, ${}^{19}\mathrm{F}$, and ${}^{40}\mathrm{Ca}$. The results have been scaled as described in the text to provide clarity.

Figure 5

Total cross sections for neutrons scattered from ${}^{89}\mathrm{Y}$, ${}^{184}\mathrm{W}$, ${}^{197}\mathrm{Au}$, and ${}^{238}\mathrm{U}$. The results have been scaled as described in the text to provide clarity.

Figure 6

Total cross section for neutrons scattered from ${}^{208}\mathrm{Pb}$.

Figure 7

The coefficients of $l_0^{\text{th}}\left(E\right)$ for each nucleus. The separate results are identified in the text.

Figure 8

The percentage differences between actual total cross-section values and those generates using the three-parameter prescription with parameter values set by the energy function forms for $l_0\left(E\right)$, $a$, and $ϵ$. Those differences for ${}^{40}\mathrm{Ca}$ and heavier nuclei are depicted in the top segment, while those for ${}^6\mathrm{Li}$, ${}^{12}\mathrm{C}$, and ${}^{19}\mathrm{F}$ are given in the middle segment. In the bottom segment are the differences between the optimal data fit values of $l_0\left(E\right)$ and those specified by using Eq. (8) for ${}^{40}\mathrm{Ca}$ and heavier nuclei.

Figure 9

Parameter values of $l_0\left(A\right)$ that give best fits to total cross-section data. Details are specified in the text.