Breakup of beryllium 9

In ENDL the breakup of beryllium 9 is listed as an (n, 2n) reaction ( $\tt c\_ID$ = 12), giving ⁹Be (n, 2n) ⁸Be, and endep produces two output files, one for the total average energy of the two neutrons ( $\tt yo$ = 1) and one for the total average energy of the two alphas as residual ( $\tt yo$ = 16). It might make more sense to list this reaction as ⁹Be (n, 2n$\alpha$) ⁴He with the identifier $\tt c\_ID$ = 33.

This is the only ENDL reaction in which the data are joint energy-angle distributions. Specifically, for given energy of the incident neutron E_yi we have the probability distribution p(E_yi,$\mu$) of the direction cosine $\mu$ of the alphas, and for given E_yi and $\mu$ we have the probability distribution P(E_yi,$\mu$, E_yo) of the energy E_yo of the alphas. Therefore, the average alpha energy is obtained by calculating the double integral

$$\langle \rangle \int_{{-1}}^{1} \left(\vphantom{ \int E_{\rm yo}P(E_{\rm yi},\mu, E_{\rm yo}) \, dE_{\rm yo} }\right. \int \mu \left.\vphantom{ \int E_{\rm yo}P(E_{\rm yi},\mu, E_{\rm yo}) \, dE_{\rm yo} }\right) \mu \mu$$ (27)

The ouput file of average alpha energies contains the pairs

(E_yi, 2$$\langle$$E_yo$$\rangle$$).

The average neutron energies are then obtained from energy balance. The ENDL library does contain joint energy-angle distributions for the secondary neutrons. Therefore, endep also calculates the double integrals (27) for this data and checks for consistency of the results.