Integer ratios ofSn/EninCa40+nresonances suggesting two-oscillator excitations in the target nucleus

Abstract

In s-wave neutron resonances of $^{40}\mathrm{Ca}$ at ${E}_{n}\ensuremath{\leqslant}2.5 \mathrm{MeV}$, ${S}_{n}/{E}_{n}$ for many levels is found to be of the form $17(n/m)$ where $n$, $m$ are small integers. Statistical tests show small probabilities for the observed dispositions of many levels at ${E}_{n}=(j/k)(1/70)G$ ($j$, $k$; small integers). To meet the requirement of time periodicity of the compound nucleus at resonance, a breathing model is developed, where the excitation energies ${E}_{x}$ are written as a sum of inverse integers; ${E}_{x}={S}_{n}+{E}_{n}=G\ensuremath{\sum}(1/k)$ ($k$: integer). In $^{40}\mathrm{Ca}+n$, the separation energy ${S}_{n}=8362 \mathrm{keV}$ is written as ${S}_{n}=(17/70)G=(1/7+1/10)G$, where $G=34.4$ MeV. $G$ is almost equal to the Fermi energy of the nucleus. It is suggested that two oscillators of energy $(1/7)G$ and $(1/10)G$ are excited in $^{40}\mathrm{Ca}$ by neutron incidence, in which the recurrence energy $(1/70)G$ is resonat with neutrons of energies at $(j/k)(1/70)G$, forming a simple compound nucleus.