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R. Budaca

Publications and source records attributed to R. Budaca.

At least 19 recordsLinked to original sources

Interplay of quadrupole and octupole degrees of freedom in the Gd isotopes

A systematic theoretical investigation of the quadrupole and octupole collective properties across the Gd isotopic chain is performed employing a quadrupole-octupole axially symmetric model. These nuclei have recently attracted significant attention following the revelation that the maximum octupole collectivity in this region is located at $^{150}$Gd. The model parameters are optimized by fitting to the low-lying positive and negative-parity energy levels, as well as to known $E0$, $E1$, $E2$, and $E3$ transition strengths. Our primary objective is a simultaneous and unified description of quadrupole and octupole collectivity across the even-even Gd nuclei in the $84\leqslant N \leqslant96$ range, a region that includes the transition from spherical to rotational nuclear shapes. The results show a smooth evolution of the quadrupole deformation, highlighted by a distinct jump at the well-known $N=90$ critical point. The enhancement of quadrupole deformation is also correlated with the loss of non-zero octupole deformation, which is reported only for the lightest $^{148,150}$Gd nuclei. This translates into a fair agreement with the measured $E3$ strength, predicting a maximum $B(E3)$ value for the $^{152}$Gd isotope.

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Study of the shape coexistence in the 96Zr, 96Mo, 96Ru isobars

Three stable isobars, $^{96}_{40}$Zr$_{56}$, $^{96}_{42}$Mo$_{54}$ and $^{96}_{44}$Ru$_{52}$, which are in the vicinity of the harmonic oscillator proton shell closure Z=40 and the spin-orbit neutron shell closure N=50, are investigated for the presence of the shape coexistence and mixing phenomena. The ground state deformation of these isobars is extracted from the potential energy surface determined with the Covariant Density Functional Theory using a density-dependent point-coupling interaction, while the excited states are described involving the Bohr-Mottelson Hamiltonian with octic potential for both axially symmetric and $\gamma$-unstable quadrupole deformations. Within the broader view of the two approaches, the obtained results clearly highlight the significant contribution of these phenomena to the structure of the states of these nuclei.

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Shape phase transition, coexistence and mixing in the $^{98-106}$Ru isotopes

The deformation properties within the $^{98-106}$Ru even-even isotopic chain, are investigated by means of the Covariant Density Functional Theory with a Density-Dependent Point-Coupling X parametrization. The considered nuclei are found to exhibit very shallow prolate and triaxial ground state deformation. This information is used to ascertain their dynamical behavior within prolate $\gamma$-stable and $\gamma$-unstable instances of a phenomenological Bohr-Mottelson Hamiltonian with an octic potential in the axial deformation variable. The comparative study of the low-lying collective states, revealed the presence of a shape phase transition from low to high deformation, as well as evidence of shape coexistence and mixing between spherical vibrator, $\gamma$-unstable or prolate configurations in ground and excited states. It is also shown that the effect of shape coexistence and mixing on the $\gamma$-band states can account to some extent for the typical $\gamma$-unstable staggering even in prolate $\gamma$-stable conditions.

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Bohr-Mottelson Hamiltonian with octic potential applied to the $^{106-116}$Cd isotopes

The Bohr-Mottelson Hamiltonian, with an octic potential in the $\beta$-deformation variable, is numerically solved for a $\gamma$-unstable symmetry of the nuclear system. The analytical structure of the model allows the description of multiple phenomena of great interest for the nuclear structure such as ground-state shape phase transitions and their critical points, dynamical shape phase transitions, shape coexistence with and without mixing, anomalous in-band $E2$ transitions, large $E2$ intra-band transitions and large monopole transition between the first excited $0^+$ state and the ground state, respectively. As a first application of the present model is selected the $^{106-116}$Cd isotope chain known in literature to manifest shape phase transition, respectively shape coexistence and mixing.

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Harmonic chiral vibration in triaxial nuclei

The low spin states of chiral partner bands are described by means of harmonic oscillations of the total angular momentum vector. The validity of the adopted approximation is established in terms of triaxiality, quasiparticle alignments and the maximal total angular momentum. The spectral properties of the model are described in detail with experimental realizations presented for nuclei with large resultant quasiparticle alignments. The model provides a simple phenomenological way for the determination of the triaxial deformation from the experimental data and easily discernable observable signatures.

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Shape Coexistence in 74Ge, 74Se and 74Kr Investigated by Phenomenological and Microscopic Models

The deformation properties of 74Ge, 74Se and 74Kr are studied within the phenomenological Bohr-Mottelson model, having as input the experimental collective energy states, as well with Covariant Density Functional theories based on microscopic structural information. The results of these approaches are shown to be compatible in what concerns the presence of coexisting shapes in the considered nuclei, while the emergence of shape mixing is deduced from the phenomenological calculated collective states.

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Semiclassical description of chiral geometry in triaxial nuclei

A triaxial particle-rotor Hamiltonian for three mutually perpendicular angular momentum vectors corresponding to two high-$j$ quasiparticles and the rotation of a triaxial collective core, is treated within a time-dependent variational principle. The resulting classical energy function is used to investigate the rotational dynamics of the system. It is found that the classical energy function exhibits two minima starting from a critical angular momentum value which depends on the single-particle configuration and the asymmetry measure $γ$. The emergence of the two minima is attributed to the breaking of the chiral symmetry. Quantizing the energy function for a given angular momentum, one obtains a Schrödinger equation with a coordinate dependent mass term for a symmetrical potential which changes from a single to a double well shape as the angular momentum pass the critical value. The energies of the chiral partner bands for a given angular momentum are then given by the lowest two eigenvalues. The procedure is exemplified for maximal triaxiality and two $h_{11/2}$ quasiparticles, with the results used for the description of the chiral doublet bands in $^{134}$Pr.

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Tilted-axis wobbling in odd-mass nuclei

A triaxial rotor Hamiltonian with a rigidly aligned high-$j$ quasiparticle is treated by a time-dependent variational principle, using angular momentum coherent states. The resulting classical energy function have three unique critical points in a space of generalized conjugate coordinates, which can minimize the energy for specific ordering of the inertial parameters and a fixed angular momentum state. Due to the symmetry of the problem, there are only two unique solutions, corresponding to wobbling motion around a principal axis and respectively a tilted-axis. The wobbling frequencies are obtained after a quantization procedure and then used to calculate $E2$ and $M1$ transition probabilities. The analytical results are employed in the study of the wobbling excitations of $^{135}$Pr nucleus, which is found to undergo a transition from low angular momentum transverse wobbling around a principal axis toward a tilted-axis wobbling at higher angular momentum.

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Proton emission with a screened electrostatic barrier

Half-lives of proton emission for Z$\ge$51 nuclei are calculated within a simple analytical model based on the WKB approximation for the barrier penetration probability which includes the centrifugal and overlapping effects besides the electrostatic repulsion. The model has a single free parameter associated to a Hulthen potential which emulates a Coulomb electrostatic interaction only at short distance. The agreement with experimental data is very good for most of the considered nuclei. Theoretical predictions are made for few cases with uncertain emitting state configuration or incomplete decay information. The model's assignment of the proton orbital momentum is in agreement with the differentiation of the experimental data by orbital momentum values realized with a newly introduced correlation formula.

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Shape phase mixing in critical point nuclei

Spectral properties of nuclei near the critical point of the quantum phase transition between spherical and axially symmetric shapes are studied in a hybrid collective model which combines the $γ$-stable and $γ$-rigid collective conditions through a rigidity parameter. The model in the lower and upper limits of the rigidity parameter recovers the X(5) and X(3) solutions respectively, while in the equally mixed case it corresponds to the X(4) critical point symmetry. Numerical applications of the model on nuclei from regions known for critical behavior reveal a sizable shape phase mixing and its evolution with neutron or proton numbers. The model also enables a better description of energy spectra and electromagnetic transitions for these nuclei.

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Bohr Hamiltonian with an energy dependent $γ$-unstable Coulomb-like potential

An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like $γ$-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in the asymptotic limit of the slope parameter resembles the spectral structure of the spherical vibrator, however with a different state degeneracy. The parameter free energy spectrum as well as the transition rates for this case are given in closed form and duly compared with those of the harmonic $U(5)$ dynamical symmetry. The model wave functions are found to exhibit properties that can be associated to shape coexistence. A possible experimental realization of the model is found in few medium nuclei with a very low second $0^{+}$ state known to exhibit competing prolate, oblate and spherical shapes.

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Extended systematics of alpha decay half lives for exotic superheavy nuclei

The experimentally available data on the alpha decay half lives and Q? values for 96 superheavy nuclei are used to fix the parameters for a modified version of the Brown empirical formula through two fitting procedures which enables its comparison with similar fits using Viola-Seaborg and Royer formulas. The new expressions provide very good agreement with experimental data having fewer or the same number of parameters. All formulas with the obtained parameters are then extrapolated to generate half lives predictions for 125 unknown superheavy alpha emitters. The nuclei where the employed empirical formulas maximally or minimally diverge are pointed out and a selection of 36 nuclei with exceptional superposition of predictions was made for experimental reference.

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Competing $γ$-rigid and $γ$-stable vibrations in neutron rich Gd and Dy isotopes

An exactly separable version of the Bohr Hamiltonian which combines the $γ$-stable and $γ$-rigid axial vibration-rotation is used to describe the collective properties of few neutron rich transitional nuclei. The coupling between the two types of collective motion is managed through a rigidity parameter which also influences the geometry of the shape-phase space. While the $γ$-angular part of the problem associated to axially symmetric shapes is treated within the small angles approximation and the stiff $γ$ oscillation hypothesis, the $β$ vibration is described by means of a Davidson potential. The resulting model have three free parameters not counting the scale and was successfully applied for the description of the collective spectra for few heavier isotopes of Gd and Dy. In both cases a critical nucleus was identified through a discontinuous behavior in respect to the rigidity parameter and relevant experimental observables.

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Sextic potential for $γ$-rigid prolate nuclei

The equation of the Bohr-Mottelson Hamiltonian with a sextic oscillator potential is solved for $γ$-rigid prolate nuclei. The associated shape phase space is reduced to three variables which are exactly separated. The angular equation has the spherical harmonic functions as solutions, while the $β$ equation is brought to the quasi-exactly solvable case of the sextic oscillator potential with a centrifugal barrier. The energies and the corresponding wave functions are given in closed form and depend, up to a scaling factor, on a single parameter. The $0^{+}$ and $2^{+}$ states are exactly determined, having an important role in the assignment of some ambiguous states for the experimental $β$ bands. Due to the special properties of the sextic potential, the model can simulate, by varying the free parameter, a shape phase transition from a harmonic to an anharmonic prolate $β$-soft rotor crossing through a critical point. Numerical applications are performed for 39 nuclei: $^{98-108}$Ru, $^{100,102}$Mo, $^{116-130}$Xe, $^{132,134}$Ce, $^{146-150}$Nd, $^{150,152}$Sm, $^{152,154}$Gd, $^{154,156}$Dy, $^{172}$Os, $^{180-196}$Pt, $^{190}$Hg and $^{222}$Ra. The best candidates for the critical point are found to be $^{104}$Ru and $^{120,126}$Xe, followed closely by $^{128}$Xe, $^{172}$Os, $^{196}$Pt and $^{148}$Nd.

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Conjunction of $γ$-rigid and $γ$-stable collective motion in the critical point of the phase transition from spherical to deformed nuclear shapes

Based on the competition between $γ$-stable and $γ$-rigid collective motions mediated by a rigidity parameter, a two-parameter exactly separable version of the Bohr Hamiltonian is proposed. The $γ$-stable part of the Hamiltonian is restricted to stiff oscillations around the $γ$ value of the rigid motion. The separated potential for $β$ and $γ$ shape variables is chosen such that in the lower limit of this parameter, the model recovers exactly the ES-$X(5)$ model, while in the upper limit it tends to the prolate $γ$-rigid solution $X(3)$. The combined effect of the rigidity and stiffness parameters on the energy spectrum and wave function is duly investigated. Numerical results are given for few nuclei showing such ambiguous behaviour.

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Analytical solution for the Davydov-Chaban Hamiltonian with sextic potential for $γ=30^{\circ}$

An analytical solution for the Davydov-Chaban Hamiltonian with a sextic oscillator potential for the variable $β$ and $γ$ fixed to $30^{\circ}$, is proposed. The model is conventionally called Z(4)-Sextic. For the considered potential shapes the solution is exact for the ground and $β$ bands, while for the $γ$ band an approximation is adopted. Due to the scaling property of the problem the energy and $B(E2)$ transition ratios depend on a single parameter apart from an integer number which limits the number of allowed states. For certain constraints imposed on the free parameter, which lead to simpler special potentials, the energy and $B(E2)$ transition ratios are parameter independent. The energy spectra of the ground and first $β$ and $γ$ bands as well as the corresponding $B(E2)$ transitions, determined with Z(4)-Sextic, are studied as function of the free parameter and presented in detail for the special cases. Numerical applications are done for the $^{128,130,132}$Xe and $^{192,194,196}$Pt isotopes, revealing a qualitative agreement with experiment and a phase transition in Xe isotopes.

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Quartic oscillator potential in the γ-rigid regime of the collective geometrical model

A prolate $γ$-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in $β$ collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the exact separation between the two Euler angles and the $β$ variable, one arrives to a differential Schrödinger equation with a quartic anharmonic oscillator potential and a centrifugal-like barrier. The corresponding eigenvalue is approximated by an analytical formula depending only on a single parameter up to an overall scaling factor. The applicability of the model is discussed in connection to the existence interval of the free parameter which is limited by the accuracy of the approximation and by comparison to the predictions of the related $X(3)$ and $X(3)$-$β^{2}$ models. The model is applied to qualitatively describe the spectra for nine nuclei which exhibit near vibrational features.

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Semi-microscopic description of the double backbending in some deformed even-even rare earth nuclei

A semi-microscopic model to study the neutron and proton induced backbending phenomena in some deformed even-even nuclei from the rare earth region, is proposed. The space of particle-core states is defined by the angular momentum projection of a quadrupole deformed product state. The backbending phenomena are described by mixing four rotational bands, defined by a set of angular momentum projected states, and a model Hamiltonian describing a set of paired particles moving in a deformed mean field and interacting with a phenomenological deformed core. The ground band corresponds to the configuration where all particles are paired while the other rotational bands are built on one neutron or/and one proton broken pair. Four rare earth even-even nuclei which present the second anomaly in the observed moments of inertia are successfully treated within the proposed model.

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