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C. M. Raduta

Publications and source records attributed to C. M. Raduta.

At least 19 recordsLinked to original sources
arXiv2025

Semi-classical and boson descriptions of scissors states

A two interacting rotors Hamiltonian is alternatively treated semi-classically and by a Dyson boson expansion method. The linearized equations of motion lead to dispersion equation for the wobbling frequency. One defined a ground band with energies consisting in a rotational part and one half of the vibrational wobbling energy. Adding to each state energy the corresponding wobbling quanta one obtains the first excited band. Phonon amplitudes are used to calculate the reduced probability for the inter-band M1 transitions. The states exhibit a shears character. One points out a chiral symmetry which is broken by the interaction term, leading to a pair of twin chiral bands. Applications are made for $^{156}$Gd. One outlines the ability of the two rotor model to account for the wobbling and chiral motion in nuclei. Although the chosen trial function has not a definite total angular momentum, for two particular ansatz of the pairs $I_p,I_n$ the average value of the total angular momentum approximates, to a certain accuracy, the partial angular momentum $I_p$ In this context, the rotational bands defined throughout this present paper could be labeled by the total I.

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arXiv2022

Simultaneous description of wobbling and chiral properties in even-odd triaxial nuclei

A particle-triaxial rigid core Hamiltonian is semi-classically treated. The coupling term corresponds to a particle rigidly coupled to the triaxial core, along a direction that does not belong to any principal plane of the inertia ellipsoid.The equations of motion for the angular momentum components provide a sixth-order algebraic equation for one component and subsequently equations for the other two. Linearizing the equations of motion, a dispersion equation for the wobbling frequency is obtained. The equations of motion are also considered in the reduced space of generalized phase space coordinates. Choosing successively the three axes as quantization axis will lead to analytical solutions for the wobbling frequency, respectively. The same analysis is performed for the chirally transformed Hamiltonian. With an illustrative example one identified wobbling states whose frequencies are mirror image to one another. Changing the total angular momentum I, a pair of twin bands emerged. Note that the present formalism conciliates between the two signatures of triaxial nuclei, i.e., they could coexist for a single nucleus.

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arXiv2020

New results about the canonical transformation for boson operators

The Bogoliubov transformation for a monopole boson induces an unitary transformation connecting the Fock spaces of initial and correlated boson-s. Here we provide a very simple method for deriving the analytical expression for the overlap matrix of the basis states generating the two boson spaces.

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arXiv2020

A new boson approach for the wobbling motion in even-odd nuclei

A triaxial core rotating around the middle axis, i.e. 2-axis, is cranked around the 1-axis, due to the coupling of an odd proton from a high j orbital. Using the Bargmann representation of a new and complex boson expansion of the angular momentum components, the eigenvalue equation of the model Hamiltonian acquires a Schrödinger form with a fully separated kinetic energy. From a critical angular momentum, the potential energy term exhibits three minima, two of them being degenerate. Spectra of the deepest wells reflects a chiral-like structure. Energies corresponding to the deepest and local minima respectively, are analytically expressed within a harmonic approximation. Based on a classical analysis, a phase diagram is constructed. It is also shown that the transverse wobbling mode is unstable. The wobbling frequencies corresponding to the deepest minimum are used to quantitatively describe the wobbling properties in $^{135}$Pr. Both energies and e.m. transition probabilities are described.

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arXiv2019

A new approach for the wobbling motion in the even-odd isotopes $^{161,163,165,167}$Lu

A new interpretation for the wobbling bands in the even-odd Lu isotopes is given within a particle-triaxial rotor semi-classical formalism. While in the previous papers the bands TSD1, TSD2, TSD3 and TSD4 are viewed as the ground, one, two and three phonon wobbling bands, here the corresponding experimental results are described as the ground band with spin equal to I=R+j, for R=0,2,4,...(TSD1), the ground band with I=R+j and R=1,3,5,...(TSD2), the one phonon excitations of TSD2 (TSD3), with the odd proton moving in the orbit $j=i_{13/2}$, and the ground band of I=R+j, with R=1,3,5,... and $j=h_{9/2}$ (TSD4). The moments of inertia (MoI) of the core for the first three bands are the same, and considered to be free parameters. Due to the core polarization effect caused by the particle-core coupling, the MoI's for TSD4 are different. The energies and the e.m. transitions are quantitatively well described. Also, the phase diagram of the odd system is drawn. In the parameter space, one indicates where the points associated with the fitted parameters are located, which is the region where the transversal wobbling mode might be possible, as well as where the wobbling motion is forbidden.

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arXiv2019

Towards a new semi-classical interpretation of the wobbling motion in $^{163}$Lu

A new interpretation for the wobbling bands in $^{163}$Lu is given within a particle-triaxial rotor semi-classical formalism. While in the previous papers the bands TSD1, TSD2, TSD3 and TSD4 are viewed as the ground, one, two and three phonon wobbling bands, here the corresponding experimental results are described as the ground band with spin equal to I=R+j, for R=0,2,4,...(TSD1), the ground band with I=R+j and R=1,3,5,...(TSD2), the one phonon excitations of TSD2 (TSD3), with the odd proton moving in the orbit $j=i_{13/2}$, and the ground band of I=R+j, with R=1,3,5,... and $j=h_{9/2}$ (TSD4). The moments of inertia (MoI) of the core for the first three bands are the same, and considered to be free parameters. Due to the core polarization effect caused by the particle-core coupling, the MoI's for TSD4 are different. The energies and the e.m. transitions are quantitatively well described. Also, the phase diagram of the odd system is drawn. In the parameter space one indicates where the point associated with the fitted parameters is located and also which is the region of transversal wobbling mode as well as where the wobbling motion is forbidden.

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arXiv2015

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.

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arXiv2015

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

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.

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arXiv2014

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

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.

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arXiv2014

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.

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arXiv2013

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.

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arXiv2010

Description of the $2ννββ$ 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 $2νββ$ 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.

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arXiv2009

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 $K^π=1/2^{\pm}$ in $^{219}$Ra, $^{237}$U and $^{239}$Pu, and three parity partner bands, $K^π=1/2^{\pm}, 3/2^{\pm}, 5/2^{\pm}$, 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 $K^π=1/2^{\pm},3/2^{\pm},5/2^{\pm}$, 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.

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arXiv2009

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

A particle-core Hamiltonian is used to describe the lowest parity partner bands $K^π=1/2^{\pm}$ in $^{237}$U and $^{239}$Pu. The quadrupole and octupole boson Hamiltonian associated to the core is identical to the one previously used for the description of four positive and four negative parity bands in the neighboring even-even isotopes. The single particle space for the odd nucleon consists of three spherical shell model states, two of positive and one of negative parity. 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 parameters involved in the particle-core coupling Hamiltonian were fixed by fitting four particular energies in the two bands. The calculated 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.

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arXiv2008

Remarks on monopole charge properties within the Generalized Coherent State Model

The Generalized Coherent State Model, proposed previously for a unified description of magnetic and electric collective properties of nuclear systems, is used to study the ground state band charge density as well as the E0 transitions from $0^+_β$ to $0^+_g$. The influence of the nuclear deformation and of angular momentum projection on the charge density is investigated. The monopole transition amplitude has been calculated for ten nuclei. The results are compared with some previous theoretical studies and with the available experimental data. Our results concerning angular momentum projection are consistent with those of previous microscopic calculations for the ground state density. The calculations for the E0 transitions agree quite well with the experimental data. Issues like how the shape transitions or shape coexistence are reflected in the $ρ(E0)$ behavior are also addressed.

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arXiv2006

Double beta decay to the first $2^+$ 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 $2νββ$ 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.

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arXiv2006

Simultaneous description of four positive and four negative parity bands

The extended coherent state model is further extended in order 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 $K^π=1^+$ band acquires a magnetic character, while the electric properties prevail for the other band. Signatures for a static octupole deformation in some states of the dipole bands are pointed out. Some properties which distinguish between the dipole band states and states of the same parity but belonging to other bands are mentioned. Interesting features concerning the decay properties of the two bands are found. Numerical applications are made for $^{158}$Gd, $^{172}$Yb, $^{228,232}$Th, $^{226}$Ra, $^{238}$U and $^{238}$Pu, and the results are compared with the available data.

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