New features of some proton–neutron collective states

Abstract

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.PACS number(s): 23.40. Hc, 23.40.Bw, Typeset using REVT E X

Description of the2ννββdecay within a fully renormalized proton-neutron quasiparticle random-phase approximation approach with a restored gauge symmetry

“…Interesting properties for these equations and their solutions are discussed in our previous publications [11,12]. Here we mention one of these features.…”

Description of the 2ννββ decay within a gauge restored of a fully renormalized pnQRPA approach

“…Interesting properties for these equations and their solutions are discussed in our previous publications [12,13].…”

“…Such a renormalization is inconsistently achieved since the scattering operators are not renormalized. This lack of consistency was removed in [12,13] where a fully renormalized pnQRPA (FRpnQRPA) is proposed.…”

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

“…The latter solutions have been separately studied in Ref. [13]. It has been proven that such solutions describe a wobbling motion of the isospin degrees of freedom.…”

“…It was shown that for charge conserving excitations these modes are spurious [12]. In a later publication we treated the scattering terms semi-classically and the harmonic mode defined there describes the wobbling motion of the isospin degrees of freedom [13].…”