Transformed Harmonic Oscillator Research Articles

Axially-deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (IV) hfbtho (v4.0): A new version of the program

We describe the new version 4.0 of the code hfbtho that solves the nuclear Hartree-Fock-Bogoliubov problem by using the deformed harmonic oscillator basis in cylindrical coordinates. In the new version, we have implemented the restoration of rotational, particle number, and reflection symmetry for even-even nuclei. The restoration of rotational symmetry does not require using bases closed under rotation. Furthermore, we added the SeaLL1 functional and improved the calculation of the Coulomb potential. Finally, we refactored the code to facilitate maintenance and future developments. New version program summaryProgram title:hfbtho v4.0CPC Library link to program files:https://doi.org/10.17632/c5g2f92by3.2Code Ocean capsule:https://codeocean.com/capsule/5389629Licensing provisions: GPLv3Programming language: Fortran 2003Journal reference of previous version: R.N. Pérez, N. Schunck, R.-D. Lasseri, C. Zhang and J. Sarich, Comput. Phys. Commun. 220 (2017) 363Does the new version supersede the previous version: YesReasons for the new version: This version adds new capabilities to restore broken symmetries and determine corresponding quantum numbers of even-even nucleiSummary of revisions:1.Angular momentum projection for even-even nuclei in a deformed basis;2.Particle number projection for even-even nuclei in the quasiparticle basis;3.Implementation of the SeaLL1 functional;4.Expansion of the Coulomb potential onto Gaussians;5.MPI-parallelization of a single hfbtho execution;6.Code refactoring.Nature of problem:hfbtho is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of hfbtho, the energy density is derived either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear superfluidity is treated at the Hartree-Fock-Bogoliubov (HFB) approximation. Constraints on the nuclear shape allow probing the potential energy surface of the nucleus as needed, e.g., for the description of shape isomers or fission. A local scale transformation of the single-particle basis in which the HFB solutions are expanded provides a tool to properly compute the structure of weakly-bound nuclei. Restoration of the rotational, particle number, and reflection symmetry for even-even nuclei enables recovering the quantum numbers that are lost at the HFB approximation.Solution method: The program uses the axial harmonic oscillator (HO) or the transformed harmonic oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the HFB Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. Lagrange parameters are used to impose constraints on HFB solutions, and their value is updated at each iteration from an approximation of the quasiparticle random phase approximation (QRPA) matrix. Symmetry restoration is implemented through standard projection techniques. Previous versions of the program were presented in [1-3].Additional comments including restrictions and unusual features: Axial and time-reversal symmetries are assumed in HFB calculations; y-simplex symmetry and even particle numbers are assumed in angular momentum projection.

Global study of Be9 + p at 2.72A MeV

Background: In our recent experiment, $^9$Be+p at 5.67A MeV, the breakup decay rates to the 3 configurations, $\alpha$+$\alpha$+n, $^8$Be$^*$+n and $^5$He+$^4$He of $^9$Be, were observed and quantified, in a full kinematics approach. Unfolding step by step the accessibility to the above configurations, it will require similar studies at lower and higher energies as well as the interpretation of the data in a theoretical framework. Purpose: Investigate the breakup decay rate of $^9$Be+p at 2.72A MeV, where the $\alpha$+$\alpha$+n configuration is mainly accessible. Compare and interpret data at 2.72A MeV and 5.67A MeV into a 4-body CDCC formalism; Point out and discuss couplings to continuum. Methods: Our experimental method includes an exclusive breakup measurement in a full kinematic approach of $^9$Be incident on a proton target at 2.72A MeV, together with elastic scattering and other reaction channels measurements under the same experimental conditions. The interpretation of the data at 2.72A MeV and 5.67A MeV is considered in a 4-body CDCC approach, using the Transformed Harmonic Oscillator method for the 3-body projectile. Results: An elastic scattering angular distribution at 2.72A MeV is measured, which compares very well with CDCC calculations, indicating a strong coupling to continuum. At the same energy, the measured breakup and total reaction cross sections present good agreement with the calculated values. Further on, the elastic scattering and breakup cross section data at 5.67A MeV are found in very good agreement with the CDCC calculations. The present results support further our 3-body model for the structure of $^9$Be, validating relevant radiative reaction rates obtained previously.

Study of nuclear structure for carbon isotopes using local scale transformation technique in shell model

This work is devoted to study the properties of the ground states such as the root-mean square ( ) proton, charge, neutron and matter radii, nuclear density distributions and elastic electron scattering charge form factors for Carbon Isotopes (9C, 12C, 13C, 15C, 16C, 17C, 19C and 22C). The calculations are based on two approaches; the first is by applying the transformed harmonic-oscillator (THO) wavefunctions in local scale transformation (LST) to all nuclear subshells for only 9C, 12C, 13C and 22C. In the second approach, the 9C, 15C, 16C, 17C and 19C isotopes are studied by dividing the whole nuclear system into two parts; the first is the compact core part and the second is the halo part. The core and halo parts are studied using the radial wave functions of HO and THO radial wavefunctions, respectively. For 9C, 12C and 13C isotopes, the no-core shell model (NCSM) are studied using the Warburton-Brown interaction. Very good agreements are obtained for the calculated density distributions and form factors in comparison with experimental data.

Calculation of orbital fractional parentage coefficients for five particles in translationally invariant basis

In this work we present an independent scheme of the O(4) group transformation suitable for the calculation of orbital fractional parentage coefficients (OFPC) for N particle systems composed of N−1 and 1 particle subsystems or N−2 and 2 particle subsystems, where the presented subsystems have their own intrinsic clusterization. Simple expressions for the corresponding five-particle harmonic oscillator transformation brackets (5HOB) used for the OFPC calculation are presented. The method does not require the calculation of the full expression of the 5HOB matrix. Instead of the full 5HOB matrix calculation, it is enough to calculate the 5HOB eigenvector matrix M and the diagonal eigenvalue matrix F. Examples of few body fermion systems, where this technique can be applied, are shown. Calculations of the 5HOB are fast and produce results with small numerical uncertainties.

A study of nuclear structure properties of even and odd 103–140Sb, 105–143Te, 107–145I, 109–148Xe and 112–151Cs nuclei in the axial deformation

We investigated ground-state nuclear structure properties of even and odd [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] nuclei via the axially deformed solution of Skyrme Hartree–Fock Bogoliubov (HFB) based on the transformed harmonic oscillator (THO) and the harmonic oscillator. In the calculations, different Skyrme force parameters were used to obtain wide nuclear data of the nuclei. The calculated results were compared with the results of the experimental data and theoretical models, i.e., the finite-range liquid-drop model (FRDM) and relativistic mean-field theory (RMFT). Additionally, the deformation regions of neutron rich Sb, Te, I, Xe and Cs nuclei have also been discussed. Moreover, in addition to the binding energy per particle, charge, proton and neutron density radii, one-neutron [Formula: see text], and two-neutron separation energies [Formula: see text], the quadropule deformation parameter [Formula: see text], the neutron skin thicknesses (NST), the quadrupole moments [Formula: see text] and the pairing gap energies of the nuclei were determined by HFBTHO 2.00 code.

Alpha and cluster decay half-lives in Tungsten isotopes: A microscopic analysis

Alpha and cluster decay half-lives of Tungsten (W) isotopes in the range between 2p drip line and beta stability line are studied. The sensitivity of different Skyrme parametrizations in predicting the alpha decay and probable cluster decay modes from W isotopes have been analysed. The half-lives are calculated using Universal Decay Law (UDL). Predicted half-lives are compared with Effective Liquid Drop Model (ELDM) and also with available experimental values. The use of harmonic oscillator (HO) and transformed harmonic oscillator (THO) basis do not produce much differences in the results. The study also revealed the role of neutron shell closure in cluster decay process.

Two-nucleon emitters within a pseudostate method: The case of Be6 and Be16

Background: Since the first experimental observation, two-nucleon radioactivity has gained renewed attention over the past fifteen years. The $^6$Be system is the lightest two-proton ground-state emitter, while $^{16}$Be has been recently proposed to be the first two-neutron ground-state emitter ever observed. A proper understanding of their properties and decay modes requires a reasonable description of the three-body continuum. Purpose: Study the ground-state properties of $^6$Be and $^{16}$Be within a general three-body model and investigate their nucleon-nucleon correlations in the continuum. Method: The pseudostate (PS) method in hyperspherical coordinates, using the analytical transformed harmonic oscillator (THO) basis for three-body systems, is used to construct the $^6$Be and $^{16}$Be ground-state wave functions. These resonances are approximated as a stable PS around the known two-nucleon separation energy. Effective core-$N$ potentials, constrained by the available experimental information on the binary subsystems $^5$Li and $^{15}$Be, are employed in the calculations. Results: The ground state of $^{16}$Be is found to present a strong dineutron configuration, with the valence neutrons occupying mostly an $l=2$ state relative to the core. The results are consistent with previous $R$-matrix calculations for the actual continuum. The case of $^6$Be shows a clear symmetry with respect to its mirror partner, the two-neutron halo $^6$He: The diproton configuration is dominant, and the valence protons occupy an $l=1$ orbit. Conclusions: The PS method is found to be a suitable tool in describing the properties of unbound $\text{core}+N+N$ ground states. For both $^{16}$Be and $^6$Be, the results are consistent with previous theoretical studies and confirm the dominant dinucleon configuration. This favors the picture of a correlated two-nucleon emission.

Axially deformed solution of the Skyrme–Hartree–Fock–Bogolyubov equations using the transformed harmonic oscillator basis (III) hfbtho (v3.00): A new version of the program

We describe the new version 3.00 of the code hfbtho that solves the nuclear Hartree–Fock (HF) or Hartree–Fock–Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle–hole and particle–particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. PROGRAM SUMMARYProgram title:hfbtho v3.00Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1Licensing provisions: GPL v3Programming language: FORTRAN-95Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013).Does the new version supersede the previous one: YesSummary of revisions:1. the Gogny force in both particle–hole and particle–particle channels was implemented;2. the nuclear collective inertia at the perturbative cranking approximation was implemented;3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments;4. the regularization method of zero-range pairing forces was implemented;5. the localization functions of the HFB solution were implemented;6. a MPI interface for large-scale mass table calculations was implemented.Nature of problem:hfbtho is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of hfbtho, the energy density derives either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated at the Hartree–Fock–Bogolyubov (HFB) approximation. Constraints on the nuclear shape allows probing the potential energy surface of the nucleus as needed e.g., for the description of shape isomers or fission. The implementation of a local scale transformation of the single-particle basis in which the HFB solutions are expanded provide a tool to properly compute the structure of weakly-bound nuclei.Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree–Fock–Bogolyubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. A previous version of the program was presented in M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013) 1592–1604 with much of the formalism presented in the original paper M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43–63.Additional comments: The user must have access to (i) the LAPACK subroutines dsyeevr, dsyevd, dsytrf and dsytri, and their dependencies, which compute eigenvalues and eigenfunctions of real symmetric matrices, (ii) the LAPACK subroutines dgetri and dgetrf, which invert arbitrary real matrices, and (iii) the BLAS routines dcopy, dscal, dgemm and dgemv for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/.

HOTB update: Parallel code for calculation of three- and four-particle harmonic oscillator transformation brackets and their matrices using OpenMP

This is a new version of the HOTB code designed to calculate three and four particle harmonic oscillator (HO) transformation brackets and their matrices. The new version uses the OpenMP parallel communication standard for calculations of harmonic oscillator transformation brackets. A package of Fortran code is presented. Calculation time of large matrices, orthogonality conditions and array of coefficients can be significantly reduced using effective parallel code. Other functionalities of the original code (for example calculation of single harmonic oscillator brackets) have not been modified.

9Be scattering within a four-body continuum-discretized coupled-channels framework

The scattering of $^9$Be on $^{208}$Pb is addressed within a four-body Continuum-Discretized Coupled-Channels (CDCC) framework, considering a three-body $\alpha + \alpha + n$ projectile plus a structureless target. The projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Both the elastic and breakup channels are described on the same footing. We find a good agreement between our calculations and the experimental data at beam energies around and below the Coulomb barrier.

Importance of the single-particle continuum in BCS pairing with a pseudostate basis

In a recent work [arXiv:1510.03185] the use of the Transformed Harmonic Oscillator (THO) basis for the discretization of the singleparticle continuum into a Generalized Bardeen-Cooper-Schrieffer (BCS) formalism was proposed for the description of weakly bound nuclei. We make use of the flexibility of this formalism to study the evolution of the pairing when the nucleus becomes more and more weakly bound. Specifically we focus on the evolution of the occupation of the different partial waves in 22 O when the Fermi level approaches zero.

Be9elastic scattering onPb208andAl27within a four-body reaction framework

We investigate the low-energy $^9$Be elastic scattering on two different targets (heavy, light) within a four-body framework using the Continuum-Discretized Coupled-Channels (CDCC) method. The $^9$Be projectile is described in a $\alpha + \alpha + n$ three-body model using the analytical transformed harmonic oscillator (THO) basis in hyperspherical coordinates. We show that continuum couplings are important to describe the elastic cross section, especially at low energies and on heavy targets. The dipolar contribution to the elastic cross section at energies around the Coulomb barrier is important but small compared to the case of halo nuclei. The effect of the projectile low-energy resonances is also relevant. The agreement with the available experimental data supports the reliability of the method to describe reactions induced by three-body projectiles including more than one charged particle.

HOTB: High precision parallel code for calculation of four-particle harmonic oscillator transformation brackets

HOTB: High precision parallel code for calculation of four-particle harmonic oscillator transformation brackets

Continuum-discretized coupled-channels calculations with core excitation

The effect of core excitation in the elastic scattering and breakup of a two-body halo nucleus on a stable target nucleus is studied. The structure of the weakly-bound projectile is described in the weak-coupling limit, assuming a particle-rotor model. The eigenfunctions and the associated eigenvalues are obtained by diagonalizing this Hamiltonian in a square-integrable basis (pseudo-states). For the radial coordinate between the particle and the core, a transformed harmonic oscillator (THO) basis is used. For the reaction dynamics, an extension of the Continuum-Discretized Coupled-Channels (CDCC) method, which takes into account dynamic core excitation and deexcitation due to the presence of non-central parts in the core-target interaction, is adapted to be used along with a pseudo-states (PS) basis.

Core excitations in the structure and reactions of halo nuclei

We analyse the resonant break-up of halo nuclei including possible excita- tions of the core both in the structure of the halo nucleus and in the reaction dynamics. The structure of the halo nucleus is treated in the weak-coupling limit, assuming a parti- cle+core model with core excitations. The bound and resonant states of this system are calculated as an expansion in a pseudo-state basis, for which we use a recent generaliza- tion of the Transformed Harmonic Oscillator basis. This basis is used within a distorted wave Born approximation reaction framework which includes possible excitations and deexcitations of the core during the collision. We apply this scheme to describe the res- onant break-up of 11 Be on 12 C at 67 MeV/u. Comparing with the available experimental data from RIKEN (N. Fukuda et al., PRC 70, 054606 (2004)) we discuss the possibil- ity of extracting spectroscopic information of 11 Be resonances from the analysis of the break-up angular distributions.

Axially deformed solution of the Skyrme-Hartree–Fock–Bogoliubov equations using the transformed harmonic oscillator basis (II) hfbtho v2.00d: A new version of the program

We describe the new version 2.00d of the code hfbtho that solves the nuclear Skyrme-Hartree–Fock (HF) or Skyrme-Hartree–Fock–Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00dCatalog identifier: ADUI_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License version 3No. of lines in distributed program, including test data, etc.: 167228No. of bytes in distributed program, including test data, etc.: 2672156Distribution format: tar.gzProgramming language: FORTRAN-95.Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6.Operating system: UNIX, LINUX, WindowsXP.RAM: 200 MwordsWord size: 8 bitsClassification: 17.22.Does the new version supercede the previous version?: YesCatalog identifier of previous version: ADUI_v1_0Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43Nature of problem:The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the transformed harmonic oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines.Solution method:The program uses the axial Transformed Harmonic Oscillator (THO) single- particle basis to expand quasi-particle wave functions. It iteratively diagonalizes the Hartree–Fock–Bogoliubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions until a self-consistent solution is found. A previous version of the program was presented in: M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43–63.Reasons for new version:Version 2.00d of HFBTHO provides a number of new options such as the optional breaking of reflection symmetry, the calculation of axial multipole moments, the finite temperature formalism for the HFB method, optimized multi-constraint calculations, the treatment of odd–even and odd–odd nuclei in the blocking approximation, and the framework for generalized energy density with arbitrary density-dependences. It is also the first version of HFBTHO to contain threading capabilities.Summary of revisions:1.The modified Broyden method has been implemented,2.Optional breaking of reflection symmetry has been implemented,3.The calculation of all axial multipole moments up to λ=8 has been implemented,4.The finite temperature formalism for the HFB method has been implemented,5.The linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations has been implemented,6.The blocking of quasi-particles in the Equal Filling Approximation (EFA) has been implemented,7.The framework for generalized energy density functionals with arbitrary density-dependence has been implemented,8.Shared memory parallelism via OpenMP pragmas has been implemented.Restrictions:Axial- and time-reversal symmetries are assumed.Unusual features:The user must have access to (i)the LAPACK subroutines DSYEVD, DSYTRF and DSYTRI, and their dependences, which compute eigenvalues and eigenfunctions of real symmetric matrices,(ii)the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and(iii)the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/.Running time:Highly variable, as it depends on the nucleus, size of the basis, requested accuracy, requested configuration, compiler and libraries, and hardware architecture. An order of magnitude would be a few seconds for ground-state configurations in small bases Nmax≈8−12, to a few minutes in very deformed configuration of a heavy nucleus with a large basis Nmax>20.

Particle motion in a deformed potential using a transformed oscillator basis

The quantum description of a particle moving in a deformed potential is investigated. A pseudostate (PS) basis is used to represent the states of the composite system. This PS basis is obtained by diagonalizing the system Hamiltonian in a family of square integrable functions. In this work the Transformed Harmonic Oscillator (THO) functions, obtained from the solutions of the Harmonic Oscillator using a Local Scale Transformation (LST), are used. The proposed method is applied to the 11Be nucleus, treated in a two-body model (10Be+n). Both structure and reaction observables have been studied. Wavefunctions and energies obtained for the bound states and some low-lying resonances are compared with those obtained by direct integration of the Schroedinger equation. The dipole and quadrupole electric transition probabilities for the low-energy continuum have been calculated in the THO basis, and compared with the exact distributions obtained with the scattering states. Finally, the method is applied to describe the 11Be states in the Coulomb breakup of 11Be+208Pb at 69 MeV/nucleon. The energy and angular distributions of the exclusive breakup have been calculated using the Equivalent Photon Method, including both E1 and E2 contributions. The calculated distributions are found to be in good agreement with the available experimental data from RIKEN [Phys. Rev. C70, 054606]. At the very forward angles, the cross section is completely dominated by the dipole couplings.

FOUR-BODY CONTINUUM-DISCRETIZED COUPLED-CHANNEL CALCULATIONS APPLIED TO 6He REACTIONS AROUND THE COULOMB BARRIER

The scattering of a weakly bound three-body system by a target is studied within the four-body continuum-discretized coupled-channels (4b-CDCC) framework. Two different methods, the transformed harmonic oscillator (THO) method and the binning procedure, are used for discretizing the three-body continuum. The formalism is applied to different reactions induced by the Borromean nucleus 6 He at energies around the Coulomb barrier: 6 He +64 Zn at 13.6 MeV, 6 He +120 Sn at 17.4 MeV, and 6 He +208 Pb at 22 MeV. Elastic cross section distributions are presented for these reactions comparing both discretization methods, THO and binning, as the mass of the target increases.

Continuum effects: Structure and reactions of 6He

A description of three-body weakly bound systems using the Transformed Harmonic Oscillator (THO) method is presented and applied to the study of the Borromean nucleus 6He. First, relevant structure observables are studied. Then, the THO method is applied to the study of 6He scattering within the Continuum-Discretized Coupled Channels (CDCC) framework.

Coulomb breakup in a transformed harmonic oscillator basis

The problem of Coulomb breakup in the scattering of a two-body loosely bound projectile by a heavy target is addressed. A basis of transformed harmonic oscillator (THO) wave functions is used to discretize the projectile continuum and to diagonalize the Hamiltonian of the two-body system. Results for the reaction $^{8}$B+$^{58}$Ni at subcoulomb energies are presented. Comparison of different observables with those obtained with the standard Continuum Discretized Coupled-Channels (CDCC) method shows good agreement between both approaches.