A method for discretizing the continuum by using a transformed harmonic oscillator basis has rece... more A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented ͓Phys. Rev. A 63, 052111 ͑2001͔͒. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional Morse, Pöschl-Teller, and square well potentials. We show how the method can deal with potentials having several bound states, and for the square well case we present a comparison of the discretized and exact continuum wave functions.
Symmetries in Nuclear Structure: an Occasion to Celebrate the 60th Birthday of Francesco Iachello, 2004
The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to... more The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.
The structure of the Borromean nucleus 9 Be (α+α+n) is addressed within a three-body approach usi... more The structure of the Borromean nucleus 9 Be (α+α+n) is addressed within a three-body approach using the analytical transformed harmonic oscillator method. The three-body formalism provides an accurate description of the radiative capture reaction rate for the entire temperature range relevant in Astrophysics. At high temperatures, results match the calculations based on two-step sequential processes. At low temperatures, where the particles have no access to intermediate twobody resonances, the three-body direct capture leads to reaction rates larger than the sequential processes. These results support the reliability of the method for systems with several charged particles.
Beauty in Physics: Theory and Experiment: in Honor of Francesco Lachello on the Occasion of His 70th Birthday, 2012
ABSTRACT The validity of the stabilization method in core+valence systems including the possibili... more ABSTRACT The validity of the stabilization method in core+valence systems including the possibility of exciting the core is studied. A pseudostate method, based on the transformed harmonic oscillator basis, is extended to include the core degrees of freedom. The method is applied to the case of 11Be structure considering the 0+ ground state and the 2+ first excited state of the 10Be core. The stabilization method is defined in terms of one parameter that can be chosen either discrete or continuous. In the application to 11Be, both cases are analyzed.
An extension of the Interacting Boson Model that includes the cubic (Q ×Q ×Q) (0) term is propose... more An extension of the Interacting Boson Model that includes the cubic (Q ×Q ×Q) (0) term is proposed. The potential energy surface for the cubic quadrupole interaction is explicitly calculated within the coherent state formalism using the complete (χ −dependent) expression for the quadrupole operator. The Q-cubic term is found to depend on the asymmetry deformation parameter γ as a linear combination of cos (3γ) and cos 2 (3γ) terms, thereby allowing for triaxiality. The phase diagram of the model in the large N limit is explored: The orders of the phase transition surfaces that define the phase diagram are described, and the possible nuclear equilibrium shapes are established. It is found that for this particular Hamiltonian, contrary to expectations, there is only a very tiny region of triaxiality, and that the transition from prolate to oblate shapes is so fast that, in most cases, the onset of triaxiality might go unnoticed.
One-neutron halo nuclei, composed of a weakly bound particle coupled to a core nucleus, are studi... more One-neutron halo nuclei, composed of a weakly bound particle coupled to a core nucleus, are studied within a particle-plus-core model. A semi-microscopic method to generate the two-body Hamiltonian of such a system, including core excitation, is proposed. The method consists of generating the spin-independent part of the valencecore interaction using a single-folding procedure, convoluting a realistic nucleon-nucleon (NN) interaction with the core transition densities. The latter are calculated with the antisymetrized molecular dynamics (AMD) method. The prescription is applied to the well known halo nucleus, 11 Be, as a test case. The results show an important predictive power that opens a door to the understanding of other lesser known halo nuclei. In order to show the potential usefulness of the method, it is applied to analyze the structure of 19 C.
We introduce a simple two-level boson model with the same energy surface as the Q-consistent Inte... more We introduce a simple two-level boson model with the same energy surface as the Q-consistent Interacting Boson Model Hamiltonian. The model can be diagonalized for large number of bosons and the results used to check analytical finite-size corrections to the energy gap and the order parameter in the critical region.
The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), i... more The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.
Exact numerical results of the interacting boson model Hamiltonian along the integrable line from... more 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.
The application of a recently proposed procedure for discretizing the continuum to collision proc... more The application of a recently proposed procedure for discretizing the continuum to collision processes involving weakly bound nuclei is studied. In particular, the coupling to breakup states in the collision of d ϩ 208 Pb at 50 MeV is discussed. For illustrative purposes, only the s-wave component of the bound state of the deuteron is considered, and the study is restricted to the case of nuclear s-wave breakup. The continuum discretization procedure provides a basis of transformed harmonic oscillator wave functions to accomplish the necessary calculations. Appropriate convergence of the elastic and breakup cross sections with increasing dimension of the basis is reported. In addition, it is shown that the results obtained converge to those of a standard continuum discretized coupled channels calculation, with the advantage that the convergence of the method is determined by only one parameter, namely the dimension of the basis.
Within the neutron-proton interacting boson model we study the population of mixed-symmetry state... more Within the neutron-proton interacting boson model we study the population of mixed-symmetry states via α transfer processes. Closed expressions are deduced in the case of the limiting U π +ν (5) and SU π +ν (3). We find that the population of the lowest mixed-symmetry 2 + state, vanishing along the N π = N ν line, depends on the number of active bosons and is normally smaller than that of the lowest full symmetric 2 + state. In particular, for deformed nuclei where the number of bosons is normally large, the relative population of the mixed-symmetry 2 + state is of the order of a few percent. More favorable cases can be found near shell closures, as in the case of α transfer leading to 140 Ba.
The boson-conserving one-nucleon transfer operator in the interacting boson model (IBA) is reanal... more The boson-conserving one-nucleon transfer operator in the interacting boson model (IBA) is reanalyzed. Extra terms are added to the usual form used for that operator. These new terms change generalized seniority by one unit, as the ones considered up to now. The results obtained using the new form for the transfer operator are compared with those obtained with the traditional form in a simple case involving the pseudo-spin Bose-Fermi symmetry U B (6)⊗ U F (12) in its U BF (5) ⊗ U F (2) limit. Sizeable differences are found. These results are of relevance in the study of transfer reactions to check nuclear supersymmetry and in the description of β-decay within IBA.
The problem of describing resonances when the continuum is represented by a discrete set of norma... more The problem of describing resonances when the continuum is represented by a discrete set of normalizable states is addressed. In particular, here the description of resonances in a transformed harmonic oscillator basis is presented. A method to disentangle the resonances from the nonresonant continuum is proposed. The Ginocchio potential is used to model a case in which resonances appear in the continuum and a reference case in which only nonresonant continuum appears.
A method for discretizing the continuum by using a transformed harmonic oscillator basis has rece... more A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented ͓Phys. Rev. A 63, 052111 ͑2001͔͒. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional Morse, Pöschl-Teller, and square well potentials. We show how the method can deal with potentials having several bound states, and for the square well case we present a comparison of the discretized and exact continuum wave functions.
We present the results of a study of the properties of both negative-and positive-parity states i... more We present the results of a study of the properties of both negative-and positive-parity states in odd-proton Cs and odd-neutron Xe isotopes within the framework of the proton-neutron interacting boson-fermion model (IBFA-2). We show that within IBFA-2 a unified description of long odd-A isotopic chains, including isospin effects, can be given.
The vibrational excitations of ozone, including both bending and stretching vibrations, are studi... more The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U (2) algebra and the one-dimensional Morse oscillator, and the introduction of point group symmetry techniques. The use of symmetry-adapted interactions, which in the harmonic limit have a clear physical interpretation, makes it possible to systematically include higher order terms and anharmonicities. A least-square fit to all published experimental levels (up to ten quanta) of 16 O 3 and 18 O 3 yields a r.m.s. deviation of 2.5 and 1.0 cm −1 , respectively.
A method for discretizing the continuum by using a transformed harmonic oscillator basis has rece... more A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented ͓Phys. Rev. A 63, 052111 ͑2001͔͒. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional Morse, Pöschl-Teller, and square well potentials. We show how the method can deal with potentials having several bound states, and for the square well case we present a comparison of the discretized and exact continuum wave functions.
Symmetries in Nuclear Structure: an Occasion to Celebrate the 60th Birthday of Francesco Iachello, 2004
The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to... more The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.
The structure of the Borromean nucleus 9 Be (α+α+n) is addressed within a three-body approach usi... more The structure of the Borromean nucleus 9 Be (α+α+n) is addressed within a three-body approach using the analytical transformed harmonic oscillator method. The three-body formalism provides an accurate description of the radiative capture reaction rate for the entire temperature range relevant in Astrophysics. At high temperatures, results match the calculations based on two-step sequential processes. At low temperatures, where the particles have no access to intermediate twobody resonances, the three-body direct capture leads to reaction rates larger than the sequential processes. These results support the reliability of the method for systems with several charged particles.
Beauty in Physics: Theory and Experiment: in Honor of Francesco Lachello on the Occasion of His 70th Birthday, 2012
ABSTRACT The validity of the stabilization method in core+valence systems including the possibili... more ABSTRACT The validity of the stabilization method in core+valence systems including the possibility of exciting the core is studied. A pseudostate method, based on the transformed harmonic oscillator basis, is extended to include the core degrees of freedom. The method is applied to the case of 11Be structure considering the 0+ ground state and the 2+ first excited state of the 10Be core. The stabilization method is defined in terms of one parameter that can be chosen either discrete or continuous. In the application to 11Be, both cases are analyzed.
An extension of the Interacting Boson Model that includes the cubic (Q ×Q ×Q) (0) term is propose... more An extension of the Interacting Boson Model that includes the cubic (Q ×Q ×Q) (0) term is proposed. The potential energy surface for the cubic quadrupole interaction is explicitly calculated within the coherent state formalism using the complete (χ −dependent) expression for the quadrupole operator. The Q-cubic term is found to depend on the asymmetry deformation parameter γ as a linear combination of cos (3γ) and cos 2 (3γ) terms, thereby allowing for triaxiality. The phase diagram of the model in the large N limit is explored: The orders of the phase transition surfaces that define the phase diagram are described, and the possible nuclear equilibrium shapes are established. It is found that for this particular Hamiltonian, contrary to expectations, there is only a very tiny region of triaxiality, and that the transition from prolate to oblate shapes is so fast that, in most cases, the onset of triaxiality might go unnoticed.
One-neutron halo nuclei, composed of a weakly bound particle coupled to a core nucleus, are studi... more One-neutron halo nuclei, composed of a weakly bound particle coupled to a core nucleus, are studied within a particle-plus-core model. A semi-microscopic method to generate the two-body Hamiltonian of such a system, including core excitation, is proposed. The method consists of generating the spin-independent part of the valencecore interaction using a single-folding procedure, convoluting a realistic nucleon-nucleon (NN) interaction with the core transition densities. The latter are calculated with the antisymetrized molecular dynamics (AMD) method. The prescription is applied to the well known halo nucleus, 11 Be, as a test case. The results show an important predictive power that opens a door to the understanding of other lesser known halo nuclei. In order to show the potential usefulness of the method, it is applied to analyze the structure of 19 C.
We introduce a simple two-level boson model with the same energy surface as the Q-consistent Inte... more We introduce a simple two-level boson model with the same energy surface as the Q-consistent Interacting Boson Model Hamiltonian. The model can be diagonalized for large number of bosons and the results used to check analytical finite-size corrections to the energy gap and the order parameter in the critical region.
The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), i... more The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.
Exact numerical results of the interacting boson model Hamiltonian along the integrable line from... more 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.
The application of a recently proposed procedure for discretizing the continuum to collision proc... more The application of a recently proposed procedure for discretizing the continuum to collision processes involving weakly bound nuclei is studied. In particular, the coupling to breakup states in the collision of d ϩ 208 Pb at 50 MeV is discussed. For illustrative purposes, only the s-wave component of the bound state of the deuteron is considered, and the study is restricted to the case of nuclear s-wave breakup. The continuum discretization procedure provides a basis of transformed harmonic oscillator wave functions to accomplish the necessary calculations. Appropriate convergence of the elastic and breakup cross sections with increasing dimension of the basis is reported. In addition, it is shown that the results obtained converge to those of a standard continuum discretized coupled channels calculation, with the advantage that the convergence of the method is determined by only one parameter, namely the dimension of the basis.
Within the neutron-proton interacting boson model we study the population of mixed-symmetry state... more Within the neutron-proton interacting boson model we study the population of mixed-symmetry states via α transfer processes. Closed expressions are deduced in the case of the limiting U π +ν (5) and SU π +ν (3). We find that the population of the lowest mixed-symmetry 2 + state, vanishing along the N π = N ν line, depends on the number of active bosons and is normally smaller than that of the lowest full symmetric 2 + state. In particular, for deformed nuclei where the number of bosons is normally large, the relative population of the mixed-symmetry 2 + state is of the order of a few percent. More favorable cases can be found near shell closures, as in the case of α transfer leading to 140 Ba.
The boson-conserving one-nucleon transfer operator in the interacting boson model (IBA) is reanal... more The boson-conserving one-nucleon transfer operator in the interacting boson model (IBA) is reanalyzed. Extra terms are added to the usual form used for that operator. These new terms change generalized seniority by one unit, as the ones considered up to now. The results obtained using the new form for the transfer operator are compared with those obtained with the traditional form in a simple case involving the pseudo-spin Bose-Fermi symmetry U B (6)⊗ U F (12) in its U BF (5) ⊗ U F (2) limit. Sizeable differences are found. These results are of relevance in the study of transfer reactions to check nuclear supersymmetry and in the description of β-decay within IBA.
The problem of describing resonances when the continuum is represented by a discrete set of norma... more The problem of describing resonances when the continuum is represented by a discrete set of normalizable states is addressed. In particular, here the description of resonances in a transformed harmonic oscillator basis is presented. A method to disentangle the resonances from the nonresonant continuum is proposed. The Ginocchio potential is used to model a case in which resonances appear in the continuum and a reference case in which only nonresonant continuum appears.
A method for discretizing the continuum by using a transformed harmonic oscillator basis has rece... more A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented ͓Phys. Rev. A 63, 052111 ͑2001͔͒. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional Morse, Pöschl-Teller, and square well potentials. We show how the method can deal with potentials having several bound states, and for the square well case we present a comparison of the discretized and exact continuum wave functions.
We present the results of a study of the properties of both negative-and positive-parity states i... more We present the results of a study of the properties of both negative-and positive-parity states in odd-proton Cs and odd-neutron Xe isotopes within the framework of the proton-neutron interacting boson-fermion model (IBFA-2). We show that within IBFA-2 a unified description of long odd-A isotopic chains, including isospin effects, can be given.
The vibrational excitations of ozone, including both bending and stretching vibrations, are studi... more The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U (2) algebra and the one-dimensional Morse oscillator, and the introduction of point group symmetry techniques. The use of symmetry-adapted interactions, which in the harmonic limit have a clear physical interpretation, makes it possible to systematically include higher order terms and anharmonicities. A least-square fit to all published experimental levels (up to ten quanta) of 16 O 3 and 18 O 3 yields a r.m.s. deviation of 2.5 and 1.0 cm −1 , respectively.
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Papers by José Arias