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In polymer melts, the interaction between segments are considered to be screened and the ideal Gaussian chain statistics is recovered. The experimental fact that linear viscoelasticity of unentangled polymers can be well described by the Rouse model is naively considered as due to this screening effect. Although various theoretical models are based on the screening effect and the screening effect is believed to be reasonable, the screening effect cannot be fully justified on a solid theoretical basis. In this work, we study the screening effect by utilizing a simple dumbbell type model. We perform simulations for dumbbell systems in which particles interact via the Gaussian soft-core potential. We show that, if the density of dumbbells is high, the Gaussian soft-core interaction is actually screened and the static structures are well described by the ideal model without Gaussian soft-core interaction. We also show that the relaxation moduli of interacting dumbbell systems approximately coincide to those of the non-interacting dumbbell systems. In the low density systems, we observe the deviations from the ideal non-interacting systems. For example, the relaxation moduli become relatively broad. However, the relaxation moduli of such systems can be decomposed into the relaxation modes by the Gaussian soft-core interaction and the bond. The bond relaxation mode can be successfully described by a single Maxwell relaxation with effective relaxation strength and time. Our results support a naive use of the Rouse model to analyze unentangled polymer melts.