Toward a Spin- and Parity-Independent Nucleon-Nucleon Potential

A supersymmetric inversion method is applied to the singlet $^1S_0$ and $^1P_1$ neutron-proton elastic phase shifts. The resulting central potential has a one-pion-exchange (OPE) long-range behavior and a parity-independent short-range part; it fits inverted data well. Adding a regularized OPE tensor term also allows the reproduction of the triplet $^3P_0$, $^3P_1$ and $^3S_1$ phase shifts as well as of the deuteron binding energy. The potential is thus also spin-independent (except for the OPE part) and contains no spin-orbit term. These important simplifications of the neutron-proton interaction are shown to be possible only if the potential possesses Pauli forbidden bound states, as proposed in the Moscow nucleon-nucleon model.Comment: 9 pages, RevTeX, 5 ps figure

Supersymmetric transformations for coupled channels with threshold differences

The asymptotic behaviour of the superpotential of general SUSY transformations for a coupled-channel Hamiltonian with different thresholds is analyzed. It is shown that asymptotically the superpotential can tend to a diagonal matrix with an arbitrary number of positive and negative entries depending on the choice of the factorization solution. The transformation of the Jost matrix is generalized to "non-conservative" SUSY transformations introduced in Sparenberg et al (2006 J. Phys. A: Math. Gen. 39 L639). Applied to the zero initial potential the method permits to construct superpartners with a nontrivially coupled Jost-matrix. Illustrations are given for two- and three-channel cases.Comment: 17 pages, 3 explicit examples and figures adde

Microscopic description of the beta delayed deuteron emission from \bbox{^6}He

The beta delayed deuteron emission from $^6$He is studied in a dynamical microscopic cluster model. This model gives a reasonably good description for all the subsystems of $^6$He and $^6$Li in a coherent way, without any free parameter. The beta decay transition probability to the $^6$Li ground state is underestimated by a few percents. The theoretical beta delayed deuteron spectrum is close to experiment but it is also underestimated by about a factor 1.7. We argue that, in spite of their different magnitudes, both underestimations might have a common origin. The model confirms that the neutron halo part of the $^6$He wave function plays a crucial role in quenching the beta decay toward the $\alpha$ + d channel.Comment: LATEX with REVTEX, Submitted to Phys. Rev. C, 11 pages, 3 figures (not included) are available upon request. ATOMKI-93/

Eigenphase preserving two-channel SUSY transformations

We propose a new kind of supersymmetric (SUSY) transformation in the case of the two-channel scattering problem with equal thresholds, for partial waves of the same parity. This two-fold transformation is based on two imaginary factorization energies with opposite signs and with mutually conjugated factorization solutions. We call it an eigenphase preserving SUSY transformation as it relates two Hamiltonians, the scattering matrices of which have identical eigenphase shifts. In contrast to known phase-equivalent transformations, the mixing parameter is modified by the eigenphase preserving transformation.Comment: 16 pages, 1 figur

Canonical-basis solution of the Hartree-Fock-Bogoliubov equation on three-dimensional Cartesian mesh

A method is presented to obtain the canonical-form solutions of the HFB equation for atomic nuclei with zero-range interactions like the Skyrme force. It is appropriate to describe pairing correlations in the continuum in coordinate-space representations. An improved gradient method is used for faster convergences under constraint of orthogonality between orbitals. To prevent high-lying orbitals to shrink into a spatial point, a repulsive momentum dependent force is introduced, which turns out to unveil the nature of high-lying canonical-basis orbitals. The asymptotic properties at large radius and the relation with quasiparticle states are discussed for the obtained canonical basis.Comment: 23 pages including 17 figures, REVTeX4, revised version, scheduled to appear in Phys. Rev. C, Vol.69, No.

Clarification of the relationship between bound and scattering states in quantum mechanics: Application to 12C + alpha

Using phase-equivalent supersymmetric partner potentials, a general result from the inverse problem in quantum scattering theory is illustrated, i.e., that bound-state properties cannot be extracted from the phase shifts of a single partial wave, as a matter of principle. In particular, recent R-matrix analyses of the 12C + alpha system, extracting the asymptotic normalization constant of the 2+ subthreshold state, C12, from the l=2 elastic-scattering phase shifts and bound-state energy, are shown to be unreliable. In contrast, this important constant in nuclear astrophysics can be deduced from the simultaneous analysis of the l=0, 2, 4, 6 partial waves in a simplified potential model. A new supersymmetric inversion potential and existing models give C12=144500+-8500 fm-1/2.Comment: Expanded version (50% larger); three errors corrected (conversion of published reduced widths to ANCs); nine references added, one remove

Breakup reaction models for two- and three-cluster projectiles

Breakup reactions are one of the main tools for the study of exotic nuclei, and in particular of their continuum. In order to get valuable information from measurements, a precise reaction model coupled to a fair description of the projectile is needed. We assume that the projectile initially possesses a cluster structure, which is revealed by the dissociation process. This structure is described by a few-body Hamiltonian involving effective forces between the clusters. Within this assumption, we review various reaction models. In semiclassical models, the projectile-target relative motion is described by a classical trajectory and the reaction properties are deduced by solving a time-dependent Schroedinger equation. We then describe the principle and variants of the eikonal approximation: the dynamical eikonal approximation, the standard eikonal approximation, and a corrected version avoiding Coulomb divergence. Finally, we present the continuum-discretized coupled-channel method (CDCC), in which the Schroedinger equation is solved with the projectile continuum approximated by square-integrable states. These models are first illustrated by applications to two-cluster projectiles for studies of nuclei far from stability and of reactions useful in astrophysics. Recent extensions to three-cluster projectiles, like two-neutron halo nuclei, are then presented and discussed. We end this review with some views of the future in breakup-reaction theory.Comment: Will constitute a chapter of "Clusters in Nuclei - Vol.2." to be published as a volume of "Lecture Notes in Physics" (Springer

Vortex line in a neutral finite-temperature superfluid Fermi gas

The structure of an isolated vortex in a dilute two-component neutral superfluid Fermi gas is studied within the context of self-consistent Bogoliubov-de Gennes theory. Various thermodynamic properties are calculated and the shift in the critical temperature due to the presence of the vortex is analyzed. The gapless excitations inside the vortex core are studied and a scheme to detect these states and thus the presence of the vortex is examined. The numerical results are compared with various analytical expressions when appropriate.Comment: 8 pages, 6 embedded figure

On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms

The energy spectra of two different quantum systems are paired through supersymmetric algorithms. One of the systems is Hermitian and the other is characterized by a complex-valued potential, both of them with only real eigenvalues in their spectrum. The superpotential that links these systems is complex-valued, parameterized by the solutions of the Ermakov equation, and may be expressed either in nonlinear form or as the logarithmic derivative of a properly chosen complex-valued function. The non-Hermitian systems can be constructed to be either parity-time-symmetric or non-parity-time-symmetric.Comment: 9 pages, 2 figures (affiliation institution corrected