Double beta decay to the first 2+2^+ state within a boson expansion formalism with a projected spherical single particle basis

The Gamow-Teller transition operator is written as a polynomial in the dipole proton-neutron and quadrupole charge conserving QRPA boson operators, using the prescription of the boson expansion technique of Belyaev-Zelevinski type. Then, the $2\nu\beta\beta$ process ending on the first $2^+$ state in the daughter nucleus is allowed via one, two and three boson states describing the odd-odd intermediate nucleus. The approach uses a single particle basis which is obtained by projecting out the good angular momentum from an orthogonal set of deformed functions. The basis for mother and daughter nuclei have different deformations. The GT transition amplitude as well as the half lives were calculated for ten transitions. Results are compared with the available data as well as with some predictions obtained with other methods.Comment: 12 page

New results for the fully renormalized proton-neutron quasiparticle random phase approximation

A many-body Hamiltonian describing a system of Z protons and N neutrons moving in spherical shell model mean field and interacting among themselves through proton-proton and neutron-neutron pairing and a dipole-dipole proton-neutron interaction of both particle-hole and particle-particle type, is treated within a fully renormalized (FR) pnQRPA approach. Two decoupling schemes are formulated. One of them decouples the equations of motion of particle total number conserving and non-conserving operators. One ends up with two very simple dispersion equations for phonon operators which are formally of Tamm-Dancoff types. For excitations in the (N-1,Z+1) system, Ikeda sum rule is fully satisfied provided the BCS equations are renormalized as well and therefore solved at a time with the FRpnQRPA equations. Next, one constructs two operators ${\cal R}^{\dagger}_{1\mu}$, ${\cal R}_{1,-\mu}(-)^{1-\mu}$ which commutes with the particle total number conserving operators, ${\cal A}^{\dagger}_{1\mu}$ and ${\cal A}_{1,-\mu}(-)^{1-\mu}$, and moreover could be renormalized so that they become bosons. Then, a phonon operator is built up as a linear combination of these four operators. The FRpnQRPA equations are written down for this complex phonon operator and the ISR is calculated analytically. This formalism allows for an unified description of the dipole excitations in four neighboring nuclei (N-1,Z+1),(N+1,Z-1),(N-1,Z-1),(N+1,Z+1). The phonon vacuum describes the (N,Z) system ground state.Comment: 24 page

New features of some proton-neutron collective states

Using a schematic solvable many-body Hamiltonian, one studies a new type of proton-neutron excitations within a time dependent variational approach. Classical equations of motion are linearized and subsequently solved analytically. The harmonic state energy is compared with the energy of the first excited state provided by diagonalization as well as with the energies obtained by a renormalized RPA and a boson expansion procedure. The new collective mode describes a wobbling motion, in the space of isospin, and collapses for a particle-particle interaction strength which is much larger than the physical value. A suggestion for the description of the system in the second nuclear phase is made. We identified the transition operators which might excite the new mode from the ground state.Comment: 28 pages and 3 figure

Description of positive and negative parity dipole bands within the extended coherent state model

AbstractThe extended coherent state model is further extended as to describe two dipole bands of different parities. The formalism provides a consistent description of eight rotational bands. A unified description for spherical, transitional and deformed nuclei is possible. Projecting out the angular momentum and parity from a sole state, the Kπ=1+ band acquires a magnetic character, while the electric properties prevail for the other band. New signatures for a static octupole deformation are pointed out. Interesting features concerning the decay properties of the two bands are found. For illustration the formalism was applied to 172Yb and results are compared with the available data

FRpnQRPA approach with the gauge symmetry restored. Application for the 2

A many body Hamiltonian involving the mean field for a projected spherical single particle basis, the pairing interactions for alike nucleons, a repulsive dipole-dipole proton-neutron interaction in the particle-hole (ph) channel and an attractive dipole-pairing interaction is treated by a gauge restored and fully renormalized proton-neutron quasiparticle random phase approximation formalism. Application to the 2νββ decay rate show a good agreement with the corresponding data. The Ikeda sum rule is obeyed

New type of chiral motion in even–even nuclei: the 138^{138}Nd case

International audienceThe phenomenological generalized coherent state model Hamiltonian is amended with a many body term describing a set of nucleons moving in a shell model mean-field and interacting among themselves with pairing, as well as with a particle–core interaction of spin–spin type. The model Hamiltonian is treated in a restricted space consisting of the core projected states associated to the band ground, $\beta ,\gamma ,\widetilde{\gamma },{1}^{+}$ and $\widetilde{{1}^{+}}$ and two proton aligned quasiparticles coupled to the states of the collective dipole band. The chirally transformed particle–core states are also included. The Hamiltonian contains two terms which are not invariant to the chiral transformations relating the right-handed frame $({{\bf{J}}}_{{\bf{F}}},{{\bf{J}}}_{{\bf{p}}},{{\bf{J}}}_{{\bf{n}}})$ and the left-handed ones $(-{{\bf{J}}}_{{\bf{F}}},{{\bf{J}}}_{{\bf{p}}},{{\bf{J}}}_{{\bf{n}}})$, $({{\bf{J}}}_{{\bf{F}}},-{{\bf{J}}}_{{\bf{p}}},{{\bf{J}}}_{{\bf{n}}})$, $({{\bf{J}}}_{{\bf{F}}},{{\bf{J}}}_{{\bf{p}}},-{{\bf{J}}}_{{\bf{n}}})$ where ${{\bf{J}}}_{{\bf{F}}},{{\bf{J}}}_{{\bf{p}}},{{\bf{J}}}_{{\bf{n}}}$ are the angular momenta carried by fermions, proton and neutron bosons, respectively. The energies defined with the particle–core states form four bands, two of them being degenerate in the present formalism, while the other two exhibit chiral properties reflected by energies, electromagnetic properties and the energy staggering function. A numerical application for (138)Nd shows a good agreement between results and the corresponding experimental data

FRpnQRPA approach with the gauge symmetry restored. Application for the 2 νββ

A many body Hamiltonian involving the mean field for a projected spherical single particle basis, the pairing interactions for alike nucleons, a repulsive dipole-dipole proton-neutron interaction in the particle-hole (ph) channel and an attractive dipole-pairing interaction is treated by a gauge restored and fully renormalized proton-neutron quasiparticle random phase approximation formalism. Application to the 2νββ decay rate show a good agreement with the corresponding data. The Ikeda sum rule is obeyed