New collective modes for a many-body system with proton-neutron pairing interaction

Abstract

A solvable Hamiltonian is treated within a time-dependent variational approach using four different variational states. One description is equivalent to the pnQRPA approach, while another one describes a new proton-neutron collective mode which is associated with a new phase of the nuclear system. The transition from one solution to the other is achieved through a Goldstone mode. For the quantized ground and first excited states the quasi-particle correlations, the Fermi β- and β+ transition amplitude and the Ikeda sum rule have been calculated. Two of the variational states are similar to the standard pnQRPA vacuum and are used to calculate the second excited states.

New results for 2νββ decay with large particle–particle two-body proton–neutron interaction

“…Since the coherent state for SU (2) and for the Weyl group are formally identical with the difference that in the first case the operators A † , A satisfy exact commutation relations, while in the later case they are considered as quasibosons, we complete our study with a fourth wave function which is similar to the SU(1,1) coherent state but the operators involved satisfy exact commutation relations. Concluding, the following trial functions have been alternatively considered for the variational state [26,27]:…”

Quasiparticle random-phase approximation with an optimal ground state

“…Recently, it has been shown that the QRPA does not develop any collapse and is in good agreement with exact results, if the Pauli exclusion principle (PEP) is consistently implemented in this approach [1]. However, there is another group of studies saying that the collapse of the QRPA indicates a phase transition, i.e., a rearrangement of the nuclear ground state [2,3,5,15]. In Ref.…”

“…It is a common practice to investigate the validity of different approximation schemes within exactly solvable models, which describe the gross properties of the fermion many-body systems [1][2][3][4][5]7,8,14,15]. Recently, it has been shown that the QRPA does not develop any collapse and is in good agreement with exact results, if the Pauli exclusion principle (PEP) is consistently implemented in this approach [1].…”

“…It is worth to note that the functions describing the limiting cases (ρ, φ) = (0, 0) and (r, θ) = (0, 0) were earlier considered [2] as trial states in a time dependent formalism:…”

New features of some proton–neutron collective states

“…Since we are not going to describe realistically some experimental data but to stress on some specific features of a heterogeneous many nucleon system with proton-neutron interaction, we consider a schematic Hamiltonian which is very often [11,12] used to study the single and double beta Fermi transitions:…”