A new renormalization procedure of the quasiparticle random phase approximation

The ground state of a many body Hamiltonian considered in the quasiparticle representation is redefined by accounting for the quasiparticle quadrupole pairing interaction. The residual interaction of the newly defined quasiparticles is treated by the QRPA. Solutions of the resulting equations exhibit specific features. In particular, there is no interaction strength where the first root is vanishing. A comparison with other renormalization methods is presented.Comment: 16 pages, 4 figure

Interplay of classical and quantal features within the coherent state model

The classical and quantal features of a quadrupole coherent state and its projections over angular momentum and boson number are quantitatively analyzed in terms of the departure of the Heisenberg uncertainty relations from the classical limit. This study is performed alternatively for two choices of the pairs of conjugate coordinates. The role of deformation as mediator of classical and quantal behaviors is also commented. Although restoring the rotational and gauge symmetries makes the quantal features manifest dominantly for small deformation, these are blurred by increasing the deformation which pushes the system toward a classical limit.Comment: 11 pages, 5 figure

Description of the chiral bands in 188,190Os^{188,190}Os

To a phenomenological core described by the Generalized Coherent State Model a set of interacting particles are coupled. Among the particle-core states one identifies a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles respectively, are mutually orthogonal. The magnetic properties of such states are studied. All terms of the model Hamiltonian satisfy the chiral symmetry except for the spin-spin interaction. There are four bands of two quasiparticle-core dipole states type, which exhibit properties which are specific for magnetic twin bands. Application is made for the isotopes $^{188, 190}$Os.Comment: 13pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1401.469

Semi-phenomenological description of the chiral bands in 188,190Os^{188,190}Os

A set of interacting particles are coupled to a phenomenological core described using the generalized coherent state model. Among the particle-core states a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles, separately, are mutually orthogonal are identified. The magnetic properties of such states are studied. All terms of the model Hamiltonian exhibit chiral symmetry except the spin-spin interaction. There are four bands of the type with two-quasiparticle-core dipole states, exhibiting properties which are specific for magnetic twin bands. An application is presented, for the isotopes $^{188, 190}$Os.Comment: 20 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1407.505

Description of the 2ννββ2\nu\nu\beta\beta decay within a fully renormalized pnQRPA approach with a restored gauge symmetry

A many body Hamiltonian involving the mean field for a projected spherical single particle basis, the pairing interactions for alike nucleons and the dipole-dipole proton-neutron interactions in the particle-hole ($ph$) and particle-particle ($pp$) channels is treated by the projected gauge fully renormalized proton-neutron quasiparticle random phase approximation (PGFRpnQRPA) approach. The resulting wave functions and energies for the mother and the daughter nuclei are used to calculate the $2\nu\beta\beta$ decay rate and the process half life. For illustration, the formalism is applied for the decay $^{100}$Mo$\to$ $^{100}$Ru. The results are in good agreement with the corresponding experimental data. The Ikeda sum rule ($ISR$) is obeyed. The gauge projection makes the $pp$ interaction inefficient.Comment: 11 pages, 1 figur

A new picture for the chiral symmetry properties within a particle-core framework

The Generalized Coherent State Model, proposed previously for a unified description of magnetic and electric collective properties of nuclear systems, is extended to account for the chiral like properties of nuclear systems. To a phenomenological core described by the GCSM a set of interacting particles are coupled. Among the particle-core states one identifies a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles respectively, are mutually orthogonal. All terms of the model Hamiltonian satisfy the chiral symmetry except for the spin-spin interaction. The magnetic properties of the particle-core states, where the three mentioned angular momenta are orthogonal, are studied. A quantitative comparison of these features with the similar properties of states, where the three angular momenta belong to the same plane, is performed.Comment: 35 pages, 14 figures, to appear in Journal of Physics G: Nucl. Part. Phy

The CSM extension for description of the positive and negative parity bands in even-odd nuclei

A particle-core Hamiltonian is used to describe the lowest parity partner bands $K^{\pi}=1/2^{\pm}$ in $^{219}$Ra, $^{237}$U and $^{239}$Pu, and three parity partner bands, $K^{\pi}=1/2^{\pm}, 3/2^{\pm}, 5/2^{\pm}$, in $^{227}$Ra. The core is described by a quadrupole and octupole boson Hamiltonian which was previously used for the description of four positive and four negative parity bands in the neighboring even-even isotopes. The particle-core Hamiltonian consists of four terms: a quadrupole-quadrupole, an octupole-octupole, a spin-spin and a rotational $\hat{I}^2$ interaction, with $\hat {I}$ denoting the total angular momentum. The single particle space for the odd nucleon consists of three spherical shell model states, two of positive and one of negative parity. The product of these states with a collective deformed ground state and the intrinsic gamma band state generate, through angular momentum projection, the bands with $K^{\pi}=1/2^{\pm},3/2^{\pm},5/2^{\pm}$, respectively. In the space of projected states one calculates the energies of the considered bands. The resulting excitation energies are compared with the corresponding experimental data as well as with those obtained with other approaches. Also, we searched for some signatures for a static octupole deformation in the considered odd isotopes. The calculated branching ratios in $^{219}$Ra agree quite well with the corresponding experimental data.Comment: 26 pages, r figure

Specific features and symmetries for magnetic and chiral bands in nuclei

Magnetic and chiral bands have been a hot subject for more than twenty years. Therefore, quite large volumes of experimental data as well as theoretical descriptions have been accumulated. Although some of the formalisms are not so easy to handle, the results agree impressively well with the data. The objective of this paper is to review the actual status of both experimental and theoretical investigations. Aiming at making this material accessible to a large variety of readers, including young students and researchers, I gave some details on the schematic models which are able to unveil the main features of chirality in nuclei. Also, since most formalisms use a rigid triaxial rotor for the nuclear system's core, I devoted some space to the semi-classical description of the rigid triaxial as well as of the tilted triaxial rotor. In order to answer the question whether the chiral phenomenon is spread over the whole nuclear chart and whether it is specific only to a certain type of nuclei, odd-odd, odd-even or even-even, the current results in the mass regions of $A\sim 60,80,100,130,180,200$ are briefly described for all kinds of odd/even-odd/even systems. The chiral geometry is a sufficient condition for a system of proton-particle, neutron-hole and a triaxial rotor to have the electromagnetic properties of chiral bands. In order to prove that such geometry is not unique for generating magnetic bands with chiral features, I presented a mechanism for a new type of chiral bands. One tries to underline the fact that this rapidly developing field is very successful in pushing forward nuclear structure studies.Comment: 80 pages, 22 figure

Wobbling motion in 165,167^{165,167}Lu within a semi-classical framework

The results obtained for $^{165,167}$Lu with a semi-classical formalism are presented. Properties like excitation energies for the super-deformed bands TSD1, TSD2, TSD3, in $^{165}$Lu, and TSD1 and TSD2 for $^{167}$Lu, inter- and intra-band B(E2) and B(M1), the mixing ratios, transition quadrupole moments are compared either with the corresponding experimental data or with those obtained for $^{163}$Lu. Also alignments, dynamic moments of inertia, relative energy to a reference energy of a rigid symmetric rotor with an effective moment of inertia and the angle between the angular momenta of the core and odd nucleon were quantitatively studied. One concludes that the semi-classical formalism provides a realistic description of all known wobbling features in $^{165, 167}$Lu.Comment: 29 pages, 14 figure

Possible chiral symmetry in 138^{138}Nd

The pheomenological 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 paring, as well as with a particle-core interaction involving a quadrupole-quadrupole and a hexadecapole-hexdecapole force and a spin-spin interaction. The model Hamiltonian is treated in a restricted space consisting of the core projected states associated to the bands ground, $\beta, \gamma,\widetilde{\gamma}, 1^+$ and $\widetilde{1^+}$ and two proton aligned quasiparticles coupled to the states of the ground 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 trihedral $({\bf J_F}, {\bf J_p}, {\bf J_n})$ and the left handed ones $(-{\bf J_F}, {\bf J_p}, {\bf J_n})$, $({\bf J_F}, -{\bf J_p}, {\bf J_n})$, $({\bf J_F}, {\bf J_p}, -{\bf J_n})$ where ${\bf J_F}, {\bf J_p}, {\bf J_n}$ are the angular momenta carried by fermions, proton and neutron bosons, respectively. The energies defined with the particle-core states form four chiral bands, two of them being degenerate. Electromagnetic properties of the chiral bands are investigated. Results are compared with the experimental data on $^{138}$Nd.Comment: 22 pages, 15 figures. arXiv admin note: text overlap with arXiv:1407.5059, arXiv:1505.0091