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Register a new userComparaison between Coulomb and Hulth`en potentials within Bohr Hamiltonian for $gamma$-rigid nuclei in the presence of minimal length
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In this work we solve the Schrodinger equation for Bohr Hamiltonian with Coulomb and Hulthen potentials within the formalism of minimal length in order to obtain analytical expressions for the energy eigenvalues and eigenfunctions by means of asymptotic iteration method. The obtained formulas of the energy spectrum and wave functions, are used to calculate excitation energies and transition rates of $gamma$-rigid nuclei and compared with the experimental data at the shape phase critical point X(3) in nuclei.
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We introduce the package SWANLOP to calculate scattering waves and corresponding observables for nucleon elastic collisions off spin-zero nuclei. The code is capable of handling local and nonlocal optical potentials superposed to long-range Coulomb interaction. Solutions to the implied Schrodinger integro-differential equation are obtained by solving an integral equation of Lippmann-Schwinger type for the scattering wavefunctions, $psi=phi_{C} + {G}_{C} {U}_{S}psi$, providing and exact treatment to the Coulomb force [Phys. Lett. B 789, 256 (2019)]. The package has been developed to handle potentials either in momentum or coordinate representations, providing flexible options under each of them. The code is fully self-contained, being dimensioned to handle any $A!geq!4$ target for nucleon beam energies of up to 1.1 GeV. Accuracy and benchmark applications are presented and discussed.
The optical potential of halo and weakly bound nuclei has a long range part due to the coupling to breakup that damps the elastic scattering angular distributions. In order to describe correctly the breakup channel in the case of scattering on a heavy target, core recoil effects have to be taken into account. We show here that core recoil and nuclear breakup of the valence nucleon can be consistently taken into account. A microscopic absorptive potential is obtained within a semiclassical approach and its characteristics can be understood in terms of the properties of the halo wave function and of the reaction mechanism. Results for the case of medium to high energy reactions are presented.
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.
We discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes. We consider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as well as axially symmetric and asymmetric shape fluctuations. Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinates and collective momenta, we microscopically derive the collective Hamiltonian of Bohr and Mottelson, which describes low-frequency quadrupole dynamics. We show that the five-dimensional collective Schrodinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We summarize the modern concepts of microscopic theory of large-amplitude collective motion, which is underlying the microscopic derivation of the Bohr-Mottelson collective Hamiltonian.
An exact solution for the scattering wavefunction from a nonlocal potential in the presence of Coulomb interaction is presented. The approach is based on the construction of a Coulomb Greens function in coordinate space whose associated kernel involves any nonlocal optical potential superposed to the Coulomb-screened interaction. The scattering wavefunction, exact solution of the integro-differential Schrodingers equation, poses no restrictions on the type of nonlocality of the interaction nor on the beam energy.
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