Description of low-lying vibrationalK ??0+ states of deformed nuclei in the quasiparticle-phonon nuclear model

Abstract

The QPNM equations are derived taking account of p-h and p-p interactions. The calculated quadrupole, octupole and hexadecapole vibrational states in 168Er, 172yb and tVSHf are found to be in reasonable agreement with experimental data. It is shown that distribution of the E2 strength in some deformed nuclei differs from the standard one. There are cases when for a given K ~ the E2 strength is concentrated not on the first but on higher-lying states. The assertion made earlier about the absence of collective two-phonon states in deformed nuclei is confirmed. PACS: 21.60.Ev; 21.60.Jz

Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

“…Reference [66], using the boson-expansion method, obtained B(E2)↑ = 0.130 e 2 b 2 in 154 Sm, a value somewhat larger than ours. Soloviev et al [67,68] used the quasiparticle-phonon nuclear model, which includes two-phonon couplings, and obtained B(E2) ↑ = 0.127 e 2 b 2 ( 168 Er), 0.042 e 2 b 2 ( 172 Yb), and 0.122 e 2 b 2 ( 178 Hf). Those transition probabilities are close to the experimental data (0.116 e 2 b 2 in 178 Hf [67]), and the fit of the interaction meant that energies were also reproduced well.…”

“…Early work on vibrations in rare-earth nuclei often made use of the pairing-plus-QQ (quadrupolequadrupole) Hamiltonian, both in the (Q)RPA [61][62][63][64][65] and in approximations that went beyond the QRPA order, e. g. [66][67][68]. Single-particle energies were usually obtained from the Nilsson potential, with slight shifts to improve phenomenology, and the strength of the QQ interactions was modified slightly from the self-consistent value so as to reproduce the energies of the γ-vibrational states.…”

Skyrme RPA description ofγ-vibrational states in rare-earth nuclei

“…Following early schematic QRPA studies [12,13], the PBE noticeably affects K π = 2 + γ -energies in even-even axial nuclei. Indeed, 2qp states form the QRPA configuration space.…”

“…So the accurate (with PBE) treatment of the first 2qp states is important for a correct description of the lowest QRPA solutions. Since PBE mainly affects the 2qp energies [12,13], one may correct only them and keep unchanged the g.s. set of Bogoliubov coefficients.…”

“…This force has a large isoscalar effective mass m 0 /m = 1 and so should generate the mean field similar to the phenomenological WoodsSaxon one [11]. Numerous early studies of K π = 2 + γ states were performed within schematic QRPA with the WoodsSaxon single-particle (s-p) scheme [12,13]. In this connection, it would be interesting to see how well the simia e-mail: nester@theor.jinr.ru …”