Time-dependent response calculations of nuclear resonances

A new alternative method for evaluating linear response theory is formally developed, and results are presented. This method involves the time evolution of the system using the time-dependent Hartree-Fock calculation and is constructed directly on top of a static Hartree-Fock calculation. By Fourier transforming the time-dependent result, the method extracts the response function and the total probability amplitude. This method allows for a coherent description of static properties of nuclei, such as binding energies and deformations, while also providing a method for calculating collective modes and reaction rates. A full three-dimensional cartesian basis-spline collocation representation is used with several Skyrme interactions. Sample results are presented for the giant multipole resonances of ${}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca}$, and ${}^{32}\mathrm{S}$ and compared to other calculations.

Figure 1

Fluctuations in the isoscalar axial quadrupole moment as a function of time for ${}^{16}\mathrm{O}$, ${}^{32}\mathrm{S}$, and ${}^{40}\mathrm{Ca}$ using the SkM${}^{*}$ interaction. The size of the time step is $0.4$ fm/c. A grid of ${24}^3$ with a cartesian box dimensioned $(-12,+12\hspace{1em}\mathrm{fm}){}^3$ is used.

Figure 2

Imaginary part of the response function corresponding to the isoscalar quadrupole moment shown for ${}^{16}\mathrm{O}$ using three different Skyrme force parametrizations. The experimentally measured giant quadrupole resonance is around 20.7 MeV.

Figure 3

FFT results for ${}^{16}\mathrm{O}$ using three different numbers of time steps. The case when the number of time steps equals an exact power of two (32 768) is clearly the better converged result, showing almost no positive values.

Figure 4

Imaginary part of the response function corresponding to the isoscalar quadrupole moment shown for ${}^{40}\mathrm{Ca}$ using two different Skyrme force parametrizations, SkM${}^{*}$ and SgII.

Figure 5

Imaginary part of the response function corresponding to the isoscalar quadrupole moment shown for ${}^{32}\mathrm{S}$ using the SkM${}^{*}$ force.

Figure 6

Imaginary part of the response function corresponding to the isoscalar and isovector octupole and the isovector dipole shown for ${}^{16}\mathrm{O}$ using the SkM${}^{*}$ force.

Figure 7

Imaginary part of the response function corresponding to the isoscalar and isovector octupole and isovector dipole shown for ${}^{16}\mathrm{O}$ using the SgII force.