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N. Minkov

Publications and source records attributed to N. Minkov.

At least 73 records · Page 4Linked to original sources
arXiv2011

Bohr Hamiltonian with deformation-dependent mass term for the Davidson potential

Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the beta variable, in the cases of gamma-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the Deformation Dependent Mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, reduces the rate of increase of the moment of inertia with deformation, removing a main drawback of the model.

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arXiv2009

Bohr Hamiltonian with deformation-dependent mass term

The Bohr Hamiltonian describing the collective motion of atomic nuclei is modified by allowing the mass to depend on the nuclear deformation. Exact analytical expressions are derived for spectra and wave functions in the case of a gamma-unstable Davidson potential, using techniques of supersymmetric quantum mechanics. Numerical results in the Xe-Ba region are discussed.

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arXiv2008

Exactly separable version of the Bohr Hamiltonian with the Davidson potential

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum) and a stiff harmonic oscillator for u(gamma) centered at gamma=0. In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, gamma band and 0_2^+ band are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare earth and actinide nuclei using two parameters (beta_0, gamma stiffness). Insights regarding the recently found correlation between gamma stiffness and the gamma-bandhead energy, as well as the long standing problem of producing a level scheme with Interacting Boson Approximation SU(3) degeneracies from the Bohr Hamiltonian, are also obtained.

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arXiv2007

sp(4,R)-systematics of atomic nuclei. F-multiplets and nuclear structure

A systematics of the atomic nuclei in the frame of the nucleon number $A = Z + N$ and the proton-neutron difference $F = Z - N$ is considered. The classification scheme is provided by means of the non-compact algebra $sp(4,R)$. In this scheme the nuclei are ordered into isobaric multiplets, for which $A={fix}$, as well as in F-multiplets, for which $F={fix}$. The dependence of the mass excess $Δ$, the first exited states $E_{2^+}$ and the ratio $R_2=E_{4^+}/E_{2^+}$ on the nucleon number $A$ is empirically investigated within the $F$-multiplets. Appropriate filters are used to study the properties of the mass excess. Many structural effects are observed. The mirror symmetry is clearly indicated for the energy levels of the nuclei with the same value of $A$ and opposite $F$-values.

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arXiv2006

Parity shift and beat staggering structure of octupole bands in a collective model for quadrupole-octupole deformed nuclei

We propose a collective model formalism which describes the strong parity shift observed in low-lying spectra of nuclei with octupole deformations together with the fine rotational band structure developed at higher angular momenta. The parity effect is obtained by the Schroedinger equation for oscillations of the reflection asymmetric (octupole) shape between two opposite orientations in an angular momentum dependent double-well potential. The rotational structure is obtained by a collective quadrupole-octupole rotation Hamiltonian. The model scheme reproduces the complicated beat staggering patterns observed in the octupole bands of light actinide nuclei. It explains the angular momentum evolution of octupole spectra as the interplay between the octupole shape oscillation (parity shift) mode and the stable quadrupole-octupole rotation mode.

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arXiv2006

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

A collective Hamiltonian for the rotation-vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the two deformation variables $β_2$ and $β_3$. The system is considered to oscillate between positive and negative $β_3$-values, by rounding an infinite potential core in the $(β_2,β_3)$-plane with $β_2>0$. By assuming a coherent contribution of the quadrupole and octupole oscillation modes in the collective motion, the energy spectrum is derived in an explicit analytic form, providing specific parity shift effects. On this basis several possible ways in the evolution of quadrupole-octupole collectivity are outlined. A particular application of the model to the energy levels and electric transition probabilities in alternating parity spectra of the nuclei $^{150}$Nd, $^{152}$Sm, $^{154}$Gd and $^{156}$Dy is presented.

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arXiv2005

Analytic Description of Critical Point Actinides in a Transition from Octupole Deformation to Octupole Vibrations

An analytic collective model in which the relative presence of the quadrupole and octupole deformations is determined by a parameter (phi_0), while axial symmetry is obeyed, is developed. The model [to be called the analytic quadrupole octupole axially symmetric model (AQOA)] involves an infinite well potential, provides predictions for energy and B(EL) ratios which depend only on phi_0, draws the border between the regions of octupole deformation and octupole vibrations in an essentially parameter-independent way, and describes well 226-Th and 226-Ra, for which experimental energy data are shown to suggest that they lie close to this border. The similarity of the AQOA results with phi_0=45 degrees for ground state band spectra and B(E2) transition rates to the predictions of the X(5) model is pointed out. Analytic solutions are also obtained for Davidson potentials, leading to the AQOA spectrum through a variational procedure.

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arXiv2004

Ground-gamma band mixing and evolution of collectivity in even-even neutron-rich nuclei with 40<Z<50

We propose an extended band mixing formalism capable of describing the ground-gamma band interaction in a wide range of collective spectra beyond the regions of well deformed nuclei. On this basis we explain the staggering effects observed in the gamma bands of Mo, Ru and Pd nuclei providing a consistent interpretation of new experimental data in the neutron rich region. As a result the systematic behavior of the odd-even staggering effect and some general characteristics of the spectrum such as the mutual disposition of the bands, the interaction strength and the band structures is explained as the manifestation of respective changes in collective dynamics of the system.

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arXiv2004

E(5) and X(5) critical point symmetries obtained from Davidson potentials through a variational procedure

Davidson potentials of the form $β^2 +β_0^4/β^2$, when used in the E(5) framework, bridge the U(5) and O(6) symmetries, while they bridge the U(5) and SU(3) symmetries when used in the X(5) framework. Using a variational procedure, we determine for each value of angular momentum $L$ thevalue of $β_0$ at which the rate of change of various physical quantities (energy ratios, intraband B(E2) ratios, quadrupole moment ratios) has a maximum, the collection of the values of the physical quantity formed in this way being a candidate for describing its behavior at the relevant critical point. Energy ratios lead to the E(5) and X(5) results (whice correspond to an infinite well potential in $β$), while intraband B(E2) ratios and quadrupole moments lead to the E(5)-$β^4$ and X(5)-$β^4$ results, which correspond to the use of a $β^4$ potential in the relevant framework. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

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arXiv2003

Ground State Bands of the E(5) and X(5) Critical Symmetries Obtained from Davidson Potentials through a Variational Procedure

Davidson potentials of the form $β^2 +β_0^4/β^2$, when used in the original Bohr Hamiltonian for $γ$-independent potentials bridge the U(5) and O(6) symmetries. Using a variational procedure, we determine for each value of angular momentum $L$ the value of $β_0$ at which the derivative of the energy ratio $R_L=E(L)/E(2)$ with respect to $β_0$ has a sharp maximum, the collection of $R_L$ values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to O(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

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arXiv2003

Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries

It is proved that the potentials of the form $β^{2n}$ (with $n$ being integer) provide a ``bridge'' between the U(5) symmetry of the Bohr Hamiltonian with a harmonic oscillator potential (occuring for $n=1$) and the E(5) model of Iachello (Bohr Hamiltonian with an infinite well potential, materialized for infinite $n$). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $β^4$, $β^6$, $β^8$, corresponding to $R_4=E(4)/E(2)$ ratios of 2.093, 2.135, 2.157 respectively, compared to the $R_4$ ratios 2.000 of U(5) and 2.199 of E(5). Hints about nuclei showing this behaviour, as well as about potentials ``bridging'' the E(5) symmetry with O(6) are briefly discussed. A note about the appearance of Bessel functions in the framework of E(n) symmetries is given as a by-product.

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arXiv2003

Sequence of Potentials Lying Between the U(5) and X(5) Symmetries

Starting from the original collective Hamiltonian of Bohr and separating the beta and gamma variables as in the X(5) model of Iachello, an exactly soluble model corresponding to a harmonic oscillator potential in the beta-variable (to be called X(5)-$β^2$) is constructed. Furthermore, it is proved that the potentials of the form $β^{2n}$ (with n being integer) provide a ``bridge'' between this new X(5)-$β^2$ model (occuring for n=1) and the X(5) model (corresponding to an infinite well potential in the beta-variable, materialized for n going to infinity. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $β^2$, $β^4$, $β^6$, $β^8$, corresponding to E(4)/E(2) ratios of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the E(4)/E(2) ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this behaviour, as well as about potentials ``bridging'' the X(5) symmetry with SU(3) are briefly discussed.

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arXiv2001

Staggering behavior of the low lying excited states of even-even nuclei in a Sp(4,R) classification scheme

We implement a high order discrete derivative analysis of the low lying collective energies of even-even nuclei with respect to the total number of valence nucleon pairs N in the framework of F- spin multiplets appearing in a symplectic sp(4,R) classification scheme. We find that for the nuclei of any given F- multiplet the respective experimental energies exhibit a Delta N=2 staggering behavior and for the nuclei of two united neighboring F- multiplets well pronounced Delta N=1 staggering patterns are observed. Those effects have been reproduced successfully through a generalized sp(4,R) model energy expression and explained in terms of the step-like changes in collective modes within the F- multiplets and the alternation of the F-spin projection in the united neighboring multiplets. On this basis we suggest that the observed Delta N=2 and Delta N=1 staggering effects carry detailed information about the respective systematic manifestation of both high order alpha - particle like quartetting of nucleons and proton (neutron) pairing interaction in nuclei.PACS number(s):21.10.Re, 21.60.Fw

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arXiv2001

Odd-Even Staggering in Octupole Bands of Actinides and Rare Earths: Systematics of "Beat" Patterns

``Beat'' patterns are shown to appear in the octupole bands of several actinides and rare earths, their appearance being independent from the formula used in order to isolate and demonstrate them. It is shown that the recent formalism, making use of discrete approximations to derivatives of the transition energies (or of the energy levels) gives results consistent with the traditional formulae. In both regions it is seen that the first vanishing of the staggering occurs at higher values of the angular momentum I in nuclei exhibiting higher staggering at low I. Since these nuclei happen to be good rotators, the observed slow decrease of the amplitude of the staggering with increasing I is in good agreement with the parameter independent predictions of the su(3) (rotational) limit of several algebraic models. In the actinides it has been found that within each series of isotopes the odd-even staggering exhibits minima at N=134 and N=146, while a local maximum is shown at N=142, these findings being in agreement with the recent suggestion of a secondary maximum of octupole deformation around N=146.

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arXiv2001

Staggering effects in nuclear and molecular spectra

It is shown that the recently observed Delta J = 2 staggering effect (i.e. the relative displacement of the levels with angular momenta J, J+4, J+8, ..., relatively to the levels with angular momenta J+2, J+6, J+10, ...) seen in superdeformed nuclear bands is also occurring in certain electronically excited rotational bands of diatomic molecules (YD, CrD, CrH, CoH), in which it is attributed to interband interactions (bandcrossings). In addition, the Delta J = 1 staggering effect (i.e. the relative displacement of the levels with even angular momentum J with respect to the levels of the same band with odd J) is studied in molecular bands free from Delta J = 2 staggering (i.e. free from interband interactions/bandcrossings). Bands of YD offer evidence for the absence of any Delta J = 1 staggering effect due to the disparity of nuclear masses, while bands of sextet electronic states of CrD demonstrate that Delta J = 1 staggering is a sensitive probe of deviations from rotational behaviour, due in this particular case to the spin-rotation and spin-spin interactions.

physics.chem-ph↗
arXiv2001

"Beat" patterns for the odd-even staggering in octupole bands from a quadrupole-octupole Hamiltonian

We propose a collective Hamiltonian which incorporates the standard quadrupole terms, octupole terms classified according to the irreducible representations of the octahedron group, a quadrupole-octupole interaction, as well as a term for the bandhead energy linear in K (the projection of angular momentum on the body-fixed z-axis). The energy is subsequently minimized with respect to K for each given value of the angular momentum I, resulting in K values increasing with I within each band, even in the case in which K is restricted to a set of microscopically plausible values. We demonstrate that this Hamiltonian is able to reproduce a variety of ``beat'' patterns observed recently for the odd-even staggering in octupole bands of light actinides.

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arXiv2001

Rotations of nuclei with reflection asymmetry correlations

We propose a collective Hamiltonian which incorporates interactions capable to generate rotations in nuclei with simultaneous presence of octupole and quadrupole deformations. It is demonstrated that the model formalism could be applied to reproduce the staggering effects observed in nuclear octupole bands. On this basis we propose that the interactions involved would provide a relevant handle in the study of collective phenomena in nuclei and other quantum mechanical systems with reflection asymmetry correlations.

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