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Coulomb and nuclear polarization of the nucleon density in the dinuclear configuration of the Ca40+Pb208 system

Bakhodir Kayumov*

  • *Contact author: b.kayumov@newuu.uz
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Phys. Rev. C 114, 044624 – Published 28 October, 2026

DOI: https://doi.org/10.1103/d6vs-ppv1

Abstract

The change of the nucleon density distribution of a heavy nucleus caused by the presence of a second nucleus at a fixed center-to-center distance is studied in the framework of the deformed Woods–Saxon mean field. The single-particle problem of one nucleus has been solved by diagonalization in a cylindrical harmonic-oscillator basis with the external field of the partner nucleus included in the Hamiltonian before diagonalization. The external field consists of the Coulomb potential of the partner charge distribution and of the nuclear part obtained by double folding of the Migdal density-dependent effective nucleon-nucleon interaction, in the same form as used in the dinuclear system approach. The induced density change δρ(r;R) and the corresponding changes of the quadrupole moment, of the mean-square radius and of the interaction energy have been calculated for the Ca40+Pb208 system at separations R=15.5–20 fm. The results are compared with the first-order (linear-response) treatment of the same external field. Because the mean field is anchored at the origin, the multipole moments are shown to require a translationally invariant definition: a displaced but undeformed distribution acquires a quadrupole moment second order in the displacement, and in this problem that kinematic term is comparable with the induced moment itself. Once it is removed, the intrinsic quadrupole response of Pb208 agrees with the first-order one to better than half a percent, and remains so over the full range of the switching parameter for the Coulomb field at R=20 fm, while that of Ca40 retains a genuine higher-order contribution of 12% to 16%. The polarization of both partners is dominated by the repulsive Coulomb tidal field, which produces an oblate deformation of the density, while the attractive nuclear field acts in the opposite sense and partially cancels the Coulomb contribution at the smallest separations. At the larger separations the induced octupole deformation is close to 40% of the quadrupole one for Pb208 and to 50% for Ca40, and it is the more sensitive indicator of the breakdown of the one-center picture. The polarization energy is a dipole quantity, the induced quadrupole deformation contributing only a few percent of it; it is verified by coupling-constant integration and is quoted under several correction prescriptions for the spurious translational component and for the absence of the residual interaction. The sensitivity to the geometry of the folding densities and the limits of validity of the one-center description are established quantitatively.

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Phys. Rev. C 114, 044624– Published 28 October, 2026
  • Received 30 July 2026
  • Revised 12 September 2026
  • Accepted 14 October 2026
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