Heisenberg’s uncertainty principle in the PTOLEMY project: A theory update
Alice Apponi, Maria Grazia Betti, M. Borghesi, Alexey Boyarsky, N. Canci, G. Cavoto, C. L. Chang, Vadim Cheianov, Yevheniia Cheipesh, Wonyong Chung, A.G. Cocco, A. P. Colijn, N. D’Ambrosio, N. De Groot, Angelo Esposito, M. Faverzani, A. D. Ferella, E. Ferri, L. Ficcadenti, T. Frederico, Stefano Gariazzo, F. Gatti, Carmelo Gentile, A. Giachero, Yonit Hochberg, Yonatan Kahn, Mariangela Lisanti, G. Mangano, L. E. Marcucci, Carlo Mariani, Marcelo Marques, Guido Menichetti, M. Messina, Oleksii Mikulenko, E. Monticone, A. Nucciotti, D. Orlandi, F. Pandolfi, S. Parlati, Carlo Pepe, C. Pérez de los Heros, O. Pisanti, Marco Polini, A. D. Polosa, A. Puiu, Ilaria Rago, Yevgeny Raitses, M. Rajteri, N. Rossi, K. Rozwadowska, Isabel Rucandio, A. Ruocco, C. F. Strid, Andi Tan, L. K. Teles, Valentina Tozzini, C. G. Tully, M. Viviani, U. Zeitler, Fang Zhao
Abstract
We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the $\ensuremath{\beta}$-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue recently raised by Cheipesh, Cheianov, and Boyarsky [Phys. Rev. D 104, 116004 (2021)], and discuss the relevant timescales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty.