Exact numerical diagonalization of the Bohr Hamiltonian by SU(1,1)xSO(5) methods is used to obtain detailed quantitative predictions for single-phonon and multi-phonon excitations in well-deformed rotor nuclei. Dynamical gamma deformation is found to significantly influence the predictions through its coupling to the rotational motion. Basic signatures for the onset of rigid triaxial deformation are obtained.
Detailed quantitative predictions are obtained for phonon and multiphonon excitations in well-deformed rotor nuclei within the geometric framework, by exact numerical diagonalization of the Bohr Hamiltonian in an SO(5) basis. Dynamical gamma deformation is found to significantly influence the predictions through its coupling to the rotational motion. Basic signatures for the onset of rigid triaxial deformation are also obtained.
In a recent work (Phys.Rev.C84, 044321, 2011) M.J. Ermamatov and P.R. Fraser have studied rotational and vibrational excited states of axially symmetric nuclei within the Bohr Hamiltonian with different mass parameters. However, the energy formula that the authors have used contains some inaccuracies. So, the numerical results they obtained seem to be controversial. In this paper, we revisit all calculations related to this problem and determine the appropriate formula for the energy spectrum. Moreover, in order to improve such calculations, we reconsider this problem within the framework of t…
Analytical solutions of the Bohr Hamiltonian are obtained in the $γ$-unstable case, as well as in an exactly separable rotational case with $γ\approx 0$, called the exactly separable Morse (ES-M) solution. Closed expressions for the energy eigenvalues are obtained through the Asymptotic Iteration Method (AIM), the effectiveness of which is demonstrated by solving the relevant Bohr equations for the Davidson and Kratzer potentials. All medium mass and heavy nuclei with known $β_1$ and $γ_1$ bandheads have been fitted by using the two-parameter $γ$-unstable solution for transitional nuclei and t…
In the present work, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning-Rosen potential for γ-unstable nuclei as well as exactly separable rotational ones with γ=0. Some heavy nuclei with known \b{eta} and γ bandheads have been fitted by using two parameters in the ν-unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.
Eigenfunctions of the collective Bohr Hamiltonian with the Morse potential have been obtained by using the Asymptotic Iteration Method (AIM) for both gamma-unstable and rotational structures. B(E2) transition rates have been calculated and compared to experimental data. Overall good agreement is obtained for transitions within the ground state band, while some interband transitions appear to be systematically underpredicted in gamma-unstable nuclei and overpredicted in rotational nuclei.
From Bohr-Mottelson model, a three parametric simple expression for the ground state rotational band of deformed even-even nuclei is deduced by incorporating the variable moment of inertia and the softness parameter. Our obtained results show good agreement with data in comparison with other existing models.
Analytical expressions of the wave functions are derived for a Bohr Hamiltonian with the Manning{Rosen potential in the cases of γ-unstable nuclei and axially symmetric prolate deformed ones with γ=0. By exploiting the results we have obtained in a recent work on the same theme Ref. [1], we have calculated the B(E2) transition rates for 34 γ-unstable and 38 rotational nuclei and compared to experimental data, revealing a qualitative agreement with the experiment and phase transitions within the ground state band and showing also that the Manning-Rosen potential is more appropriate for such cal…
From the semi-empirical formalisms of Bohr-Mottelson, a new model, based on the effect of beta- and gamma- head energies and the variable moment of inertia, was developed to calculate the ground state rotational band of almost all deformed e-e nuclei. The model can be tuned for nuclei with experimentally available beta- and gamma-vibrational energies as well as for those with unmeasured beta- and gamma-vibrations.
Embedding of the 5-dimensional (5D) space of the Bohr Hamiltonian with a deformation-dependent mass (DDM) into a 6-dimensional (6D) space shows that the free parameter in the dependence of the mass on the deformation is connected to the curvature of the 5D space, with the special case of constant mass corresponding to a flat 5D space. Comparison of the DDM Bohr Hamiltonian to the 5D classical limit of Hamiltonians of the 6D interacting boson model (IBM), shows that the DDM parameter is proportional to the strength of the pairing interaction in the U(5) (vibrational) symmetry limit, while it is…
Damping of rotational motion in superdeformed Hg and Dy-region nuclei is studied by means of cranked shell model diagonalization. It is shown that a shell oscillation in single-particle alignments affects significantly properties of rotational damping. Onset properties of damping and damping width for Hg are quite different from those for Dy-region superdeformed nuclei.
Exact diagonalizations with a realistic interaction show that configurations with four neutrons in a major shell and four protons in another -or the same- major shell, behave systematically as backbending rotors. The dominance of the $q\cdot q$ component of the interaction is explained by an approximate form of SU3 symmetry. It is suggested that these configurations are associated with the onset of rotational motion in medium and heavy nuclei.
The triaxial nature of low-lying rotational bands of $^{166}$Er is presented from the viewpoint of the Bohr Hamiltonian and from that of many-fermion calculations by the Monte Carlo shell model and the constrained Hartree-Fock method with projections. A recently proposed novel picture of those bands suggests definite triaxial shapes of those bands, in contrast to the traditional view with the prolate ground-state band and the $γ$-vibrational excited band. Excitation level energies and E2 transitions can be described well by the Bohr Hamiltonian and by the many-fermion approaches, where rather …
Exact numerical diagonalization is carried out for the Bohr Hamiltonian with a beta-soft, axially stabilized potential. Wave function and observable properties are found to be dominated by strong beta-gamma coupling effects. The validity of the approximate separation of variables introduced with the X(5) model, extensively applied in recent analyses of axially stabilized transitional nuclei, is examined, and the reasons for its breakdown are analyzed.
The essential point of Bohr-Mottelson theory is to assume a irrotational flow. As was already suggested by Marumori and Watanabe, the internal rotational motion, i.e., the vortex motion, however, may exist also in nuclei. So, we have a necessity of taking the vortex motion into consideration. In a classical fluid dynamics, there are various ways to treat the internal rotational velocity. The Clebsch representation, v(x) = -\nabla ϕ(x) + λ(x) \nabla ψ(x) (ϕ; velocity potential, λand ψ: Clebsch parameters) is very powerful and has an advantage deriving equations of fluid motion from a Lagransian…
The spectral and statistical properties of nuclei $^{46}$V and $^{48}$Cr are studied in the framework of nuclear shell model. A microscopical effective Hamiltonian derived from the CD-Bonn \textit{NN} potential is employed. The calculations are preliminary results of a newly developed parallel shell-model code. Calculations with the realistic \textit{NN} interaction reproduce well the ground-state rotational band and backbending phenomenon in $^{48}$Cr. A sudden alignment of all particles is seen above the backbend. The nearest-neighbour spacing distribution in $^{46}$V is presented and compar…
We construct a microscopic model of thermally excited superdeformed states that describes both the barrier penetration mechanism, leading to the decay-out transitions to normal deformed states, and the rotational damping causing fragmentation of rotational E2 transitions. We describe the barrier penetration by means of a tunneling path in the two-dimensional deformation energy surface, which is calculated with the cranked Nilsson-Strutinsky model. The individual excited superdeformed states and associated E2 transition strengths are calculated by the shell model diagonalization of the many-par…
Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form which can be diagonalized for large number of bosons. We present results for the low energy spectrum and the transition probabilities for systems up to 10000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a $β^4$ potential.
Within the collective Bohr Hamiltonian, the adoption of a mass tensor as a function of collective coordinates has demonstrated its importance for describing the structure of nuclei. On the other hand, for odd-mass nuclei, the Coriolis interaction between the rotational and single-particle motions affects significantly the structure of nuclear excited states. In the framework of a recently developed extended Bohr Hamiltonian, by considering the Deformation-Dependent Mass Formalism whith different mass parameters for the rotation and the two \betha and γvibrations and taking into account the Cor…
We extend an effective field theory developed to describe rotational bands in even-even nuclei to the odd-mass case. This organizes Bohr and Mottelson's treatment of a particle coupled to a rotor as a model-independent expansion in powers of the angular velocity of the overall system. We carry out this expansion up to fourth order in the angular velocity and present results for $^{99}$Tc, ${}^{159}$Dy, ${}^{167, 169}$Er, ${}^{167, 169}$Tm, ${}^{183}$W, ${}^{235}$U and ${}^{239}$Pu. In each case, the accuracy and breakdown scale of the effective field theory can be understood based on the singl…
The influence of quadrupole and hexadecapole residual interactions on rotational bands is investigated in a single-j shell model. An exact shell-model diagonalization of quadrupole-plus-hexadecapole interaction can sometimes produce a staggering of energy levels in the yrast bands.
Eight pairs of rare earth normally deformed nuclei around the isobaric nuclei with A = 164 and have identical values of F-spin have been studied. These pairs of identical bands cover 16 mass units and are classified. We suggested a theoretical collective rotational formula containing three parameters (CRF3) as an extended version of Bohr-Mottelson model to calculate the ground state positive parity excitation energies. Also, the sd-version of the interacting boson model (IBM) has been used to describe the nuclear shapes by using the intrinsic coherent-state. The optimized models parameters for…
Exact diagonalizations with a minimally modified realistic force lead to detailed agreement with measured level schemes and electromagnetic transitions in $^{48}$Ca, $^{48}$Sc, $^{48}$Ti, $^{48}$V, $^{48}$Cr and $^{48}$Mn. Gamow-Teller strength functions are systematically calculated and reproduce the data to within the standard quenching factor. Their fine structure indicates that fragmentation makes much strength unobservable. As a by-product, the calculations suggest a microscopic description of the onset of rotational motion. The spectroscopic quality of the results provides strong argumen…
The rapid transition between spherical and $γ$-soft shapes in Ba and Xe nuclei in the mass region $A \geq 130$ is analyzed using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The results reproduce the characteristic evolution of excitation spectra and E2 transition probabilities and, in general, a good agreement with available data is obtained. The calcul…
The Hamiltonian for a small number, N <= 11, of bosons in a rapidly rotating harmonic trap, interacting via a short range (contact potential) or a long range (Coulomb) interaction, is studied via an exact diagonalization in the lowest Landau level. Our analysis shows that, for both low and high fractional fillings, the bosons localize and form rotating boson molecules (RBMs) consisting of concentric polygonal rings. Focusing on systems with the number of trapped atoms sufficiently large to form multi-ring bosonic molecules, we find that, as a function of the rotational frequency and regardless…
Based on Bohr model, we have presented a general formalism describing the collective motion for any deformed system, in which the collective Hamiltonian is expressed as vibrations in the body-fixed frame, rotation of whole system around the laboratory frame, and coupling between vibrations and rotation. Under the condition of decoupling approximation, we have derived the quantized Hamiltonian operator. Based on the operator, we have calculated the rotational spectra for some special octupole and hexadecapole deformed systems, and shown their dependencies on deformation. The result indicates th…
The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treate…
Exact diagonalization results are reported for the lowest rotational band of N=6 electrons in strong magnetic fields in the range of high angular momenta 70 <= L <= 140 (covering the corresponding range of fractional filling factors 1/5 >= nu >= 1/9). A detailed comparison of energetic, spectral, and transport properties (specifically, magic angular momenta, radial electron densities, occupation number distributions, overlaps and total energies, and exponents of current-voltage power law) shows that the recently discovered rotating-electron-molecule wave functions [Phys. Rev. B 66, 115315 (200…
