Violation of the Ikeda sum rule and the self-consistency in the renormalized quasiparticle random phase approximation and the nuclear double-beta decay

The effect of the inclusion of ground state correlations into the QRPA equation of motion for the two-neutrino double beta ($\beta\beta_{2\nu}$) decay is carefully analyzed. The resulting model, called renormalized QRPA (RQRPA), does not collapse near the physical value of the nuclear force strength in the particle-particle channel, as happens with the ordinary QRPA. Still, the $\beta\beta_{2\nu}$ transition amplitude is only slightly less sensitive on this parameter in the RQRPA than that in the plain QRPA. It is argued that this fact reveals once more that the characteristic behaviour of the $\beta\beta_{2\nu}$ transition amplitude within the QRPA is not an artifact of the model, but a consequence of the partial restoration of the spin-isospin $SU(4)$ symmetry. It is shown that the price paid for bypassing the collapse in the RQRPA is the violation of the Ikeda sum rule.Comment: 16 pages, latex, 3 postscript figure

Quantum entanglement of bound particles under free center of mass dispersion

On the basis of the full analytical solution of the overall unitary dynamics, the time evolution of entanglement is studied in a simple bipartite model system evolving unitarily from a pure initial state. The system consists of two particles in one spacial dimension bound by harmonic forces and having its free center of mass initially localized in space in a minimum uncertainty wave packet. The existence of such initial states in which the bound particles are not entangled is pointed out. The entanglement of the two particles is shown to be independent of the wavepacket mean momentum, and to increase monotonically in a time scale distinct from that of the spreading of the center of mass wavepacket.Comment: 17 pages, 5 figure

Self Consistent and Renormalized particle-particle RPA in a Schematic Model

The dynamical effects of ground state correlations for excitation energies and transition strengths near the superfluid phase transition are studied in the soluble two level pairing model, in the context of the particle-particle self consistent Random Phase Approximation (SCRPA). Exact results are well reproduced across the transition region, beyond the collapse of the standard particle-particle Random Phase Approximation. The effects of two-body correlation in the SCRPA are displayed explicitly.Comment: 11 pages, revtex, 3ps figures, to appear in Phys. Rev.

Population Dynamics in the Penna Model

We build upon the recent steady-state Penna model solution, Phys.Rev.Lett. 89, 288103 (2002), to study the population dynamics within the Penna model. We show, that any perturbation to the population can be broken into a collection of modes each of which decay exponentially with its respective time constant. The long time behaviour of population is therefore likely to be dominated by the modes with the largest time constants. We confirm our analytical approach with simulation data.Comment: 6 figure

Kvazičestična aproksimacija nasumnih faza bez urušavanja za dvojni beta raspad

We show how the longstanding problem of the collapse of the charge–exchange QRPA near the physical value of the force strength can be circumvented. This is done by including the effect of ground state correlations into the QRPA equations of motion. The corresponding formalism, called renormalized QRPA, is briefly outlined and its consequences are discussed in the framework of a schematic model for the two-neutrino double beta decay in the 100Mo → 100Ru system. The question of the conservation of the Ikeda sum rule is also addressed within the new formalism.Pokazuje se kako se može izbjeći tvrdokorni problem urušavanja kvazičestične aproksimacije nasumnih faza (QRPA) s nabojskom izmjenom za realne vrijednosti jakosti sila. To se postiže uključivanjem korelacije u osnovnom stanju u jednadžbe stanja QRPA. Raspravljaju se rezultati za shematski model dvoneutrinskog dvojnog beta raspada 100Mo → 100Ru. U okviru ovog formalizma također se raspravlja pitanje Ikedinog zbrojnog pravila