Coexistence of chiral symmetry and pseudospin symmetry in one nucleus: triplet bands in ${}^{105}$Ag

The nearly degenerate triplet bands with the $\pi g_{9/2}^{-1}\otimes \nu h_{11/2} (g_{7/2},d_{5/2})$configurationin$^{105}$Ag are studied via the relativistic mean-field (RMF) theory and the multiparticle plus rotor model (MPRM), which indicates that these bands are associated with chiral symmetry and pseudospin symmetry. The configuration-fixed constrained triaxial RMF calculations exhibit the pseudospin symmetry in single particle spectra and the triaxial shape coexistence. The experimental excitation energies and the electromagnetic transition probabilities for the triplet bands are reproduced very well by the MPRM calculaitons. The chiral doublet bands show the same phase in the $B(M1)\mathrm{/}B(E2)$ staggering, while the pseudospin doublet bands hold the opposite phase. The coexistence of chiral symmetry and pseudospin symmetry in one nucleus and its corresponding characteristic of the rotational structure are discussed for the first time.