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Papers by Alejandro Frank
Quantum Theory and Symmetries, 2002
An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the anal... more An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the corresponding anharmonic bosons are associated with the SU (2) algebra. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation with the specific heat. A physical interpretation of a quantum deformation associated with the model is given.
Physical Review Letters, 1993
Nuclear resonance fluorescence experiments are reported to search for enhanced M1 scissors mode s... more Nuclear resonance fluorescence experiments are reported to search for enhanced M1 scissors mode states in the deformed odd-mass nucleus ' Dy. A concentration of dipole strengths near 3 MeV excitation energy is found, which fits nicely into the systematics observed for M1 excitations in the neighboring even-even Dy isotopes. The observed strength distribution and the decay branching ratios are discussed in the context of the interacting boson-fermion model.
Physical Review Letters, 2005
Predictions are obtained for T 0 and T 1 deuteron-transfer intensities between self-conjugate N Z... more Predictions are obtained for T 0 and T 1 deuteron-transfer intensities between self-conjugate N Z nuclei on the basis of a simplified interacting boson model which considers bosons without orbital angular momentum but with full spin-isospin structure. These transfer predictions can be correlated with nuclear binding energies in specific regions of the mass table.
Physical Review C, 2006
The phase diagram of models with configuration mixing is investigated in mean-field approximation... more The phase diagram of models with configuration mixing is investigated in mean-field approximation. The configurations correspond to different limits of a dynamical algebra U(n), such as U(n -1) and SO(n), and are allowed to mix. It is shown that this diagram has unusual properties not present in models with a single configuration. Applications to nuclear and molecular physics are discussed.
Physical Review C, 2004
A matrix coherent-state approach is applied to the interacting boson model (IBM) with configurati... more A matrix coherent-state approach is applied to the interacting boson model (IBM) with configuration mixing to describe the evolving geometry of neutron-deficient Pb isotopes. It is found that for small mixing with parameters determined previously, the potential energy surface of 186 Pb has three minima, which correspond to spherical, oblate, and prolate shapes, in agreement with recent measurements and mean-field calculations. Away from midshell, in the heavier Pb isotopes, no deformed minima occur. Our analysis suggests that the configuration-mixing IBM, used in conjunction with a matrix coherent-state method, may be a reliable tool for the study of geometric aspects of shape coexistence in nuclei.
Physical Review C, 2008
The matrix coherent-state approach of the interacting boson model with configuration mixing is us... more The matrix coherent-state approach of the interacting boson model with configuration mixing is used to study the geometry of the platinum isotopes. With a parameter set determined in previous studies, it is found that the absolute minimum of the potential for the Pt isotopes evolves from spherical to oblate and finally to prolate shapes when the neutron number decreases from N = 126 (semi-magic) to N = 104 (mid-shell). Shape coexistence is found in the isotopes 182,184,186,188 Pt. A phase diagram is constructed which shows the coexistence region as a function of the number of bosons and the strength of the mixing parameter.
Physical Review C, 1989
A geometric interpretation of effective interacting boson approximation Hamiltonians describing s... more A geometric interpretation of effective interacting boson approximation Hamiltonians describing series of isotopes is carried out. It is shown that a recently introduced SO{5) dynamical symmetry Hamiltonian, which describes the Ru region with fixed parameters for all isotopes, gives rise to a sharp shape transition from spherical to y-unstable nuclei. Moreover, it is shown that the SO{6), SU{3), and U{5) interacting boson approximation symmetries may display transitional behavior when studied as a function of boson number. A set of constraints in the parameter space are de- rived, in order for the standard geometrical interpretation of these symmetries to hold.
Journal of Physics A: Mathematical and General, 2001
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU (... more A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU (2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or q-boson algebra which is a generalisation of the Heisenberg-Weyl algebra obtained by introducing a deformation parameter q. Further, we present a new algebraic realization of the qbosons, for the case of q being a root of unity, which corresponds to a periodic structure described by a finite-dimensional representation. We show that this structure represents the symmetry of a linear lattice with periodic boundary conditions.
Phase transitions and critical points in rare earth-transition metal ferrimagnets
Journal of Magnetism and Magnetic Materials, 1995
ABSTRACT
An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the anal... more An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the corresponding anharmonic bosons are associated with the SU (2) algebra. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation with the specific heat. A physical interpretation of a quantum deformation associated with the model is given.
The geometry and phase transition behavior of configuration mixing in the interacting boson model
A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2 is studied. The sym... more A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2 is studied. The symmetry is associated with linear canonical transformations of boson operators, or, equivalently, with the existence of different realizations of the symmetry algebras of the models. The relevance of the parameter symmetry to physical observables is discussed.
An algebraic model based on Lie-algebraic techniques is applied to the analysis of thermodynamic ... more An algebraic model based on Lie-algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. The local anharmonic effects are described by a Morse-like potential and corresponding anharmonic bosons associated with the U (2) algebra. A vibrational high temperature partition function and the related thermodynamic functions are derived in terms of the parameters of the model. The thermal expansion operator is defined and obtained using the renormalized frequency of the model.
The stretching and bending vibrations of methane are studied in a local anharmonic model of molec... more The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm -1 (and a r.m.s. deviation of 1.16 cm -1 ).
Physical Review C, 1985
We present a generalization of the O(6) limit of the interacting boson model by considering an F.... more We present a generalization of the O(6) limit of the interacting boson model by considering an F. 2 tran- sition operator which is different from the quadrupole operator used in the Hamiltonian. We analyze, both quantum mechanically and in the classical limit, under which conditions this more general O(6) limit is in- variant under time reversal.
AIP Conference Proceedings, 2002
Nuclear Structure Physics, 2001
Random interactions are used to investigate to what extent the low-lying behavior of even-even nu... more Random interactions are used to investigate to what extent the low-lying behavior of even-even nuclei depend on particular nucleon-nucleon interactions. The surprising results that were obtained for the interacting boson model, i.e. the dominance of ground states with L = 0 and the occurrence of both vibrational and rotational structure, are interpreted and explained in terms of a mean-field analysis.
Nuclear Structure, 2001
The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the inte... more The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the interacting boson model using an ensemble of random one-and twobody interactions. Despite the randomness of the interactions (in sign and size) we find a predominance of L P = 0 + ground states and strong evidence for the occurrence of both vibrational and rotational band structure.
The stretching and bending vibrations of methane are studied in a local anharmonic model of molec... more The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm -1 (and a r.m.s. deviation of 1.16 cm -1 ).
Czechoslovak Journal of Physics, 1998
An algebraic method especially suited to describe strongly anharmonic vibrational spectra in mole... more An algebraic method especially suited to describe strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study vibrational spectra of Na + n clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be4, H + 3 , Be3 and Na + 3 clusters.
Quantum Theory and Symmetries, 2002
An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the anal... more An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the corresponding anharmonic bosons are associated with the SU (2) algebra. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation with the specific heat. A physical interpretation of a quantum deformation associated with the model is given.
Physical Review Letters, 1993
Nuclear resonance fluorescence experiments are reported to search for enhanced M1 scissors mode s... more Nuclear resonance fluorescence experiments are reported to search for enhanced M1 scissors mode states in the deformed odd-mass nucleus ' Dy. A concentration of dipole strengths near 3 MeV excitation energy is found, which fits nicely into the systematics observed for M1 excitations in the neighboring even-even Dy isotopes. The observed strength distribution and the decay branching ratios are discussed in the context of the interacting boson-fermion model.
Physical Review Letters, 2005
Predictions are obtained for T 0 and T 1 deuteron-transfer intensities between self-conjugate N Z... more Predictions are obtained for T 0 and T 1 deuteron-transfer intensities between self-conjugate N Z nuclei on the basis of a simplified interacting boson model which considers bosons without orbital angular momentum but with full spin-isospin structure. These transfer predictions can be correlated with nuclear binding energies in specific regions of the mass table.
Physical Review C, 2006
The phase diagram of models with configuration mixing is investigated in mean-field approximation... more The phase diagram of models with configuration mixing is investigated in mean-field approximation. The configurations correspond to different limits of a dynamical algebra U(n), such as U(n -1) and SO(n), and are allowed to mix. It is shown that this diagram has unusual properties not present in models with a single configuration. Applications to nuclear and molecular physics are discussed.
Physical Review C, 2004
A matrix coherent-state approach is applied to the interacting boson model (IBM) with configurati... more A matrix coherent-state approach is applied to the interacting boson model (IBM) with configuration mixing to describe the evolving geometry of neutron-deficient Pb isotopes. It is found that for small mixing with parameters determined previously, the potential energy surface of 186 Pb has three minima, which correspond to spherical, oblate, and prolate shapes, in agreement with recent measurements and mean-field calculations. Away from midshell, in the heavier Pb isotopes, no deformed minima occur. Our analysis suggests that the configuration-mixing IBM, used in conjunction with a matrix coherent-state method, may be a reliable tool for the study of geometric aspects of shape coexistence in nuclei.
Physical Review C, 2008
The matrix coherent-state approach of the interacting boson model with configuration mixing is us... more The matrix coherent-state approach of the interacting boson model with configuration mixing is used to study the geometry of the platinum isotopes. With a parameter set determined in previous studies, it is found that the absolute minimum of the potential for the Pt isotopes evolves from spherical to oblate and finally to prolate shapes when the neutron number decreases from N = 126 (semi-magic) to N = 104 (mid-shell). Shape coexistence is found in the isotopes 182,184,186,188 Pt. A phase diagram is constructed which shows the coexistence region as a function of the number of bosons and the strength of the mixing parameter.
Physical Review C, 1989
A geometric interpretation of effective interacting boson approximation Hamiltonians describing s... more A geometric interpretation of effective interacting boson approximation Hamiltonians describing series of isotopes is carried out. It is shown that a recently introduced SO{5) dynamical symmetry Hamiltonian, which describes the Ru region with fixed parameters for all isotopes, gives rise to a sharp shape transition from spherical to y-unstable nuclei. Moreover, it is shown that the SO{6), SU{3), and U{5) interacting boson approximation symmetries may display transitional behavior when studied as a function of boson number. A set of constraints in the parameter space are de- rived, in order for the standard geometrical interpretation of these symmetries to hold.
Journal of Physics A: Mathematical and General, 2001
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU (... more A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU (2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or q-boson algebra which is a generalisation of the Heisenberg-Weyl algebra obtained by introducing a deformation parameter q. Further, we present a new algebraic realization of the qbosons, for the case of q being a root of unity, which corresponds to a periodic structure described by a finite-dimensional representation. We show that this structure represents the symmetry of a linear lattice with periodic boundary conditions.
Phase transitions and critical points in rare earth-transition metal ferrimagnets
Journal of Magnetism and Magnetic Materials, 1995
ABSTRACT
An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the anal... more An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the corresponding anharmonic bosons are associated with the SU (2) algebra. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation with the specific heat. A physical interpretation of a quantum deformation associated with the model is given.
The geometry and phase transition behavior of configuration mixing in the interacting boson model
A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2 is studied. The sym... more A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2 is studied. The symmetry is associated with linear canonical transformations of boson operators, or, equivalently, with the existence of different realizations of the symmetry algebras of the models. The relevance of the parameter symmetry to physical observables is discussed.
An algebraic model based on Lie-algebraic techniques is applied to the analysis of thermodynamic ... more An algebraic model based on Lie-algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. The local anharmonic effects are described by a Morse-like potential and corresponding anharmonic bosons associated with the U (2) algebra. A vibrational high temperature partition function and the related thermodynamic functions are derived in terms of the parameters of the model. The thermal expansion operator is defined and obtained using the renormalized frequency of the model.
The stretching and bending vibrations of methane are studied in a local anharmonic model of molec... more The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm -1 (and a r.m.s. deviation of 1.16 cm -1 ).
Physical Review C, 1985
We present a generalization of the O(6) limit of the interacting boson model by considering an F.... more We present a generalization of the O(6) limit of the interacting boson model by considering an F. 2 tran- sition operator which is different from the quadrupole operator used in the Hamiltonian. We analyze, both quantum mechanically and in the classical limit, under which conditions this more general O(6) limit is in- variant under time reversal.
AIP Conference Proceedings, 2002
Nuclear Structure Physics, 2001
Random interactions are used to investigate to what extent the low-lying behavior of even-even nu... more Random interactions are used to investigate to what extent the low-lying behavior of even-even nuclei depend on particular nucleon-nucleon interactions. The surprising results that were obtained for the interacting boson model, i.e. the dominance of ground states with L = 0 and the occurrence of both vibrational and rotational structure, are interpreted and explained in terms of a mean-field analysis.
Nuclear Structure, 2001
The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the inte... more The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the interacting boson model using an ensemble of random one-and twobody interactions. Despite the randomness of the interactions (in sign and size) we find a predominance of L P = 0 + ground states and strong evidence for the occurrence of both vibrational and rotational band structure.
The stretching and bending vibrations of methane are studied in a local anharmonic model of molec... more The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm -1 (and a r.m.s. deviation of 1.16 cm -1 ).
Czechoslovak Journal of Physics, 1998
An algebraic method especially suited to describe strongly anharmonic vibrational spectra in mole... more An algebraic method especially suited to describe strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study vibrational spectra of Na + n clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be4, H + 3 , Be3 and Na + 3 clusters.