Systematics of high-spin isomers produced in nuclear reactions with intermediate-energy protons

Systematics is proposed for determining the isomeric ratios (and, consequently, the production cross sections) for high-spin isomeric states in nuclear reactions induced by intermediate-energy protons. It is based on experimental data obtained by bombarding tantalum targets with protons of energy 100 to 500 MeV. For reactions involving the emission of more than two nucleons, a linear dependence between the spin transfer and the logarithm of the isomeric ratio is observed; i.e., $$\sigma _m /\sigma _g \approx aexp[ - b|J_m - J|]$$ where σg is the cross section for the ground state (perhaps from a calculation within the intranuclear cascade-evaporation model); σm is the cross section for the isomeric state of the nucleus; J m and J t are spin values for, respectively, the product isomeric nucleus and the target nucleus; and a and b are coefficients that are determined from 16 experimental results (a ≈ 1.05, b ≈ 0.47). The systematics is assumed to be valid over a wide range of nuclei, proton energies, and isomeric ratio. An explanation for the observed regularities is given.