Optimizing phonon space in the phonon-coupling model

Abstract

We present a new scheme to select the most relevant phonons in the phonon-coupling model, named here time-blocking approximation (TBA). The new criterion, based on the phonon-nucleon coupling strengths rather than on B(EL) values, is more selective and thus produces much smaller phonon spaces in TBA. This is beneficial in two respects: first, it curbs down the computational cost, and second, it reduces the danger of double counting in the expansion basis of TBA. We use here TBA in a form where the coupling strength is regularized to keep the given Hartree-Fock ground state stable. The scheme is implemented in an RPA and TBA code based on the Skyrme energy functional. We first explore carefully the cutoff dependence with the new criterion and can work out a natural (optimal) cutoff parameter. Then we use the freshly developed and tested scheme to a survey of giant resonances and low-lying collective states in six doubly magic nuclei looking also on the dependence of the results when varying the Skyrme parametrization.

Microscopic theory of pygmy- and giant resonances: accounting for complex 1p1h$$\otimes $$phonon configurations

“…( 32) and Eq. (34), which correspond to the ω-dependent two-quasiparticle amplitude Φ(ω) in [18,32]. The difference is due to the use of a special factorization procedure for Φ(ω) in [18,32].…”

“…6, they were realized numerically without the TBA prescription in articles [20,21] for fine structure characteristics of isovector M1 resonances in magic nuclei. With the use of the TBA prescription and within the strongly improved TBA version, they were realized for the M1 resonance in 208 P b recently in articles [33,34] (see modifications of the TBA model there). In all these calculations there were no full explanation of the fine structure of the M1 resonance in 208 P b.…”

Low-energy M1 excitations in Pb208 and the spin channel of the Skyrme energy-density functional

“…It is known that the parameters C s T , C s,α T , and C ∆s T in most cases have little influence on the characteristics of the natural parity excitations, but in some cases can lead to the spin instability in the self-consistent RPA and extended RPA calculations. In particular for this reason sometimes (including our recent papers [32,33,[49][50][51]) they are set to be equal to zero, while the other C-constants are determined by the Skyrme-force parameters according to Eqs. (B1).…”

“…Inappropriate strengths of spin-orbit coupling were identified as one major source of the problem [21,22]. We had applied a recently optimized phonon-coupling model on top of self-consistent RPA [32,33] to M1 modes and, unfortunately, did not find any improvement concerning spectral separation of low and upper mode nor sufficiently strong fragmentation. The problem has first to be cleared at RPA level be-fore invoking more advanced approaches.…”

Estimation of a 2p2h effect on Gamow-Teller transitions within the second Tamm-Dancoff approximation

“…It is recently pointed out that the downward shift obtained in the higher-order RPA is substantially attributed to the double counting between the residual interaction and the static response of the ground state [52,53]. To overcome this problem, a subtraction method is suggested [52]. Gambacurta et al applied it to SRPA and calculated monopole and quadrupole responses.…”