We investigate electric quadrupole hyperfine-structure constant (B) results in 135 Ba + and 137 Ba + and compare their ratios with the reported measurements of the ratio between the nuclear quadrupole moment (Q) values of these isotopes. We carry out confidence tests for the reported experimental B values and calculations of B/Q from the present work. Inconsistencies in the experimental B values are observed in both the isotopes from different experiments performed using the same techniques. The present calculations are carried out using an all order relativistic many-body theory considering only single and double excitations in the coupled-cluster ansatz. After a detailed analysis of the results, the values of Q we obtain for 135 Ba and 137 Ba are 0.153(2)b and 0.236(3)b, respectively, which differ by about 4% from the currently referred precise values.The effective ellipsoidal nuclear charge distribution of an isotope in the nuclear ground state is generally quantified by the nuclear electric-quadrupole moment (Q). The nuclear shell model assumes that the charge distribution is spherically symmetric for a doubly magic closed-shell nucleus, and therefore its quadrupole moment vanishes; otherwise it will have an intrinsic nonzero Q value. Thus, accurate evaluations of Q for different isotopes could probe the shell theory (e.g., see [1]) and therefore the investigation of this quantity has been of considerable interest to nuclear, atomic, and molecular physicists for the last six decades [2][3][4][5][6][7].Although the value of Q for nuclear ground states cannot be measured directly, it is possible to measure their ratios for different isotopes [8][9][10][11]. Also, for an atomic state of a particular isotope, Q can be determined by combining the measured electric-quadrupole hyperfine-structure constant (B) with a calculation of B/Q for that isotope. To obtain an accurate value of Q by this procedure, both the measurement and the calculation have to be performed to high precision. Experimental results are generally considered to be more reliable than the calculated results for many-electron atoms owing to the fact that ab initio evaluation of various physical quantities using many-body methods involve a number of approximations at different stages of the calculations. However, measurements from different experiments are not always in agreement and, in certain cases, large discrepancies between measurements and accurate calculations have been noted [12,13]. It is therefore essential to scrutinize the accuracies of both the experimental B and calculated B/Q results when determining values of Q from them.Studies of hyperfine-structure constants in singly ionized barium (Ba + ) can provide valuable information about the wave functions in the nuclear region and the role of the electron correlation effects whose knowledge are relevant for the proposed parity nonconservation experiments [14]. It is also important for the extraction of higher-order nuclear * bijaya@prl.res.in moments [15]. Furthermore, studies of the hype...