Whether the σ − meson (f 0 (600)) exists as a real particle is a longstanding problem in both particle physics and nuclear physics. In this work, we analyze the deuteron binding energy in the linear σ model and by fitting the data, we are able to determine the range of m σ and also investigate applicability of the linear σ model for the interaction between hadrons in the energy region of MeV's. Our result shows that the best fit to the data of the deuteron binding energy and other experimental data about deuteron advocates a narrow range for the σ−meson mass as 520 ≤ m σ ≤ 580 MeV and the concrete values depend on the input parameters such as the couplings. Inversely fitting the experimental data, our results set constraints on the couplings. The other relevant phenomenological parameters in the model are simultaneously obtained. reasonable models express certain aspects of the real physical world, but not complete. There is a limited range for each model, beyond the limit, application of the model is not legitimate. On other side, for a certain range, all possible models are equivalent for describing the concerned physics. Therefore, in some sense, various models are parallel. This is understood as we use the Cornell potential, the Richardson potential or even the logarithmic potential to describe the bound states of heavy quarks such as J/ψ, Υ etc. and obtain close results with specific parameters. Of course, it by no means manifests that they are real physics, but just serve as an effective model and are applicable to the some concerned processes.For the quark-bound states, i.e. hadrons, to deal with the non-perturbative QCD effects, we can use, for example, the QCD sum rules, potential models, the bag model, as well as the lattice calculations to evaluate the spectra and other properties. It is believed that even though α s is large the quark-gluon picture is still valid. By contrast, for the nucleon-nucleon interaction (or hadron-hadron interactions when both of them are in color singlet), even though it is in principle due to QCD, there is no single-gluon exchange between the nucleons because they reside in color-singlet. Instead, just as the familiar Van der Waals force between moleculas in classical physics, which is induced by the electric and magnetic multipoles, the strong interaction between nucleons is the interaction between the chromo-electric and magnetic multipoles of nucleons. So far, there is no a successful way to derive an effective form of such strong interaction at the hadron level from the fundamental QCD theory yet, but on other side, it is also believed that the chiral Lagrangian is consistent with the general principles of QCD and could serve as an effective theory of strong interaction at hadron level [1]. An alternative version of the chiral Lagrangian is the linear sigma model where the σ−particle stands as an independent resonance. Recently, many theorists and experimentalists are searching for σ which may play an important role in nuclear physics, because the σ meson can provide re...