Collective states of even Xe isotopes in IBM+MQRPA

Abstract

Abstract. A modification of the Quasiparticle Random Phase Approximation (QRPA) with small ground state correlations is suggested. The lowest energy phonon is used as the image of d-boson of the Interacting Boson Model 1 (IBM1) and applied to microscopical calculations of the IBM1 parameters. Results are compared with experimental data for Xe isotopes.The Quasiparticle Random Phase Approximation (QRPA) is one of the widely used methods for description of semimagic and deformed nuclei [1]. Application of this approximation is quite correct in those cases when the Ground State Correlations (GSC) i.e. the distinction between the quasiparticle vacuum (QV) and the RPA-phonon vacuum (PV), exist but are rather small. Quantitatively it means, e.g., that Σψ 2 Σϕ 2 , ψ, ϕ being amplitudes of the RPA D μ -phonons (μ=0, ±1, ±2)Futher, we'll work with the QRPA-phonons composed of the Bogoliubov quasiparticles. In Eq.(1), a + i , a k are creation and annihilation quasiparticle operators, i is a single-particle state in a spherical mean field,ī is a timeconjugated state.Direct application of QRPA is not justified in the region where the transition takes place from spherical nuclei to deformed ones that is revealed in lowering the energies of the first 2 + -states (e.g., from 1.2 MeV in Sn isotopes up to 0.32 MeV in 120 Xe) and at the same time in increasing B(E2, 2). Applying the standard QRPA yields the values Σ ϕ 2 smaller then but comparable with Σ ψ 2 that necessitates to modify QRPA conformably.Several modification of RPA, included the particlehole RPA and QRPA, have been suggested which take into account GSC more consistently [2][3][4][5][6][7][8]. The main idea of our modification of QRPA (MQRPA) was formulated many years ago [9,10] and was developed further in [11,12]. We construct special equations like RPA for amplitudes ψ and ϕ of the collective quadrupole phonon D μ , Eq. (1), which give very small values of Σ ϕ 2 , i.e. with small GSC in the fermion space. However, after mapping the D-phonons and PV onto the boson space the boson Hamiltonian proves to be such that its diagonalization a e-mail: efimov98@mail.ru leads to a rather complicated ground state function comprising apart from the boson vacuum (BV) two, three and more quadrupole bosons. Thus, if one returned from the boson space to the fermion one the ground state in this space would turn out to be strongly correlated.Transition to the boson description is implemented following the Interacting Boson Model (IBM) in its first variant (IBM1 or SU (6) wherêIn Eqs. (2) Article available at