Constraints on the effective mass splitting by the isoscalar giant quadrupole resonance

Background: Previous theoretical work has found that the effective mass of the nucleon influences the excitation energy of the isoscalar giant quadrupole resonance (ISGQR). Purpose: The present paper presents an attempt to constrain the effective mass splitting by using the isospin dependence of the ISGQR energies. Methods: Using the macroscopic Langevin equation (LE), the ISGQR energies are calculated from the particle density and kinetic energy density of the nucleus in the ground state, obtained from either the Thomas-Fermi (TF) approach or the Skyrme Hartree-Fock-Bogolyubov (SHFB) model. Results: It is found that the calculations of the ISGQR energies by the SHFB+LE model agree with, or are even better than, the results by other approaches when applying the Skyrme functional Sly4. The values of the isoscalar and isovector effective masses are optimized by fitting the data for the ISGQR energies for a mass region from 28 to 238. The root-mean-squared deviation of the best fit to the data measured after the year 2000 is 0.22 MeV by the TF+LE model and 0.30 MeV by the SHFB+LE model. The extracted isoscalar effective mass is 0.70 < m(s)*/m < 0.73. With respect to the isovector effective mass m(v)*, the constrained value is about half of the isoscalar effective mass m(s)*. Conclusions: The present work supports the statement that, in neutron-rich matter, the effective mass of the neutron is definitely larger than that of the proton.