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(Abridged) In our previous work we found a statistically significant offsetDelta V = 27 m/s between the radial velocities of the HC3N(2-1) and NH3(1,1)transitions observed in molecular cores from the Milky Way. This may indicatethat the electron-to-proton mass ratio, mu = m_e/m_p, increases by 3x10^{-8}when measured under interstellar conditions with matter densities of more than10 orders of magnitude lower as compared with laboratory (terrestrial)environments. We now map four molecular cores L1498, L1512, L1517, and L1400Kselected from our previous sample in order to estimate systematic effects inDelta V due to possible velocity gradients. We find that in two cores L1498 andL1512 the NH3(1,1) and HC3N(2-1) transitions closely trace the same materialand show an offset of Delta V = 26.9 +/- 1.2_stat +/- 3.0_sys m/s throughoutthe entire clouds. The measured velocity offset, being expressed in terms ofDelta mu = (mu_obs - mu_lab)/mu_lab, gives Delta mu = (26 +/- 1_stat +/-3_sys)x10^{-9}.

Searching for chameleon-like scalar fields with the ammonia method. II. Mapping of cold molecular cores in NH3 and HC3N lines