This study proposes an improvement of the general formalism for calculating gamma-ray buildup factors in multilayer shields developed by Assad et al. The main modification concerns the treatment of the double-layer shield formed by the two first layers of a multilayer shield. Instead of replacing the double-layer shield with an equivalent thickness of the layer of the second material, the improved general formalism replaces it with a single-layer shield made of an appropriate material. The determination of the appropriate material is implemented into MERCURE-6.1 thanks to neural networks trained on a large set of various configurations.

One-dimensional comparisons with the TWODANT transport Sn code shows the accuracy of the new formalism for shields composed of three and five layers. Indeed, for three-layer shields with an infinitesimal second layer and for multilayer shields composed of numerous thin layers (more than 15), MERCURE-6.1 matches the reference data quite well. The MERCURE-6.1 ability to solve three-dimensional realistic cases is highlighted by comparisons to the TRIPOLI-4 and MCNP-4C Monte Carlo codes.