Beta Gamma Decays

The routine MCG_SET_BETA_GAMMAS prepares the generation of beta gamma decays. It selects a decay channel according to the relative channel weights. The energy of the positron or electron is determined by the routine EN_BETA (see below) but the other attributes (position, direction and time) are controlled by the MCPI bank in the same way as for ``Start a Particle" interaction. The gammas are given the same position and time as the electron or positron, but with isotropic directions. Note: to speed up the event simulations, there is a minimum kinetic energy threshold for the generation of betas and for gammas, respectively (see the documentation on "id_en_types"). The user can set these to stop the production of particles that are unlikely to produce Cerenkov light.

It should be noted that for the decays of $^212$Bi and $^214$Bi, each of which have both a beta-gamma and an alpha decay mode, only the beta-gamma mode is modelled. This means that setting off 1000 $^212$Bi decays gives you 1000 $^212$Bi beta-gamma decays and not 640 as might be expected from the branching ratio.

The energy of the positron or electron is determined in EN_BETA (together with FERMI_F, L_BETA and SHAPE_F*) and models the following effects:-

• A simple correction for screening by the atomic electrons, using a simple Thomas-Fermi model approximation.

• The exact Fermi function for a point source nucleus. Nuclear finite-size effects such as the de Broglie wavelength of the electron and the spatial distribution of the nuclear charge are not included since the shape of the spectrum is not strongly affected by these (see the article by C.P. Bhalla and M.E. Rose, Phys. Rev 128 (1962) p.774. They calculate that, for Z=96 and a beta endpoint energy of 3 MeV, the shape of the allowed spectrum will deviate by $<$5%. The deviation gets smaller for higher orders of angular momentum, or smaller values of Z). Hence, in all calculations, the nucleus is treated as a point charge.

• Type of decay. Shape factors for first, second and third unique forbidden decays are calculated (including the effects of the Coulomb field). Shape factors for first and second parity forbidden decays are included, but the user must provide the coefficients for the shape factor in the titles bank for the decay. These are small in most cases, so can be set to zero if unknown for the decay. Decays to broad states, such as 8Li or 8B, are approximated using many narrow states with the proper branching ratios. This means that such decays can be incorporated in SNOMAN without any changes to the code.

Hence, to properly calculate the beta energy, EN_BETA requires the following information: (Z,A) for the daughter nucleus, as well as the beta end-point energy, decay type and shape factor coefficients for each decay channel. The routine MCG_SET_BETA_GAMMAS prepares this data by reading it from the MCDS bank pointed to by the interaction code. Alternatively, the data for a decay with a single channel can be set using the energy parameters in the MCPI bank (see the documentation on "id_en_types"). The interaction code for starting an electron or positron should then be used, to avoid calling the routine MCG_SET_BETA_GAMMAS (which expects an MCDS bank). However, this latter scheme has the disadvantage that gamma rays have to be added by hand using other MCPI banks.