Phase shift effective range expansion from supersymmetric quantum mechanics

Supersymmetric or Darboux transformations are used to construct local phase equivalent deep and shallow potentials for $\ell \neq 0$ partial waves. We associate the value of the orbital angular momentum with the asymptotic form of the potential at infinity which allows us to introduce adequate long-distance transformations. The approach is shown to be effective in getting the correct phase shift effective range expansion. Applications are considered for the $^1P_1$ and $^1D_2$ partial waves of the neutron-proton scattering.Comment: 6 pages, 3 figures, Revtex4, version to be publised in Physical Review

Reconstructing the nucleon-nucleon potential by a new coupled-channel inversion method

A second-order supersymmetric transformation is presented, for the two-channel Schr\"odinger equation with equal thresholds. It adds a Breit-Wigner term to the mixing parameter, without modifying the eigenphase shifts, and modifies the potential matrix analytically. The iteration of a few such transformations allows a precise fit of realistic mixing parameters in terms of a Pade expansion of both the scattering matrix and the effective-range function. The method is applied to build an exactly-solvable potential for the neutron-proton $^3S_1$-$^3D_1$ case.Comment: 4 pages, 4 figure

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

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

Cross-sectional TEM preparation of hybrid inorganic/organic materials systems by ultramicrotomy

Preparation of hybrid inorganic-organic systems (HIOS) for transmission electron microscopy (TEM) in cross sectional view is the key for understanding the interfacial structure. Strikingly different materials properties like hardness, cleavability and heat sensitivity limit the number of applicable preparation strategies. Successful preparation of a HIOS system combining ZnO and para-sexiphenyl (6P) is realized by ultramicrotomy. It is shown that the alignment of the cutting plane with respect to the (0001) cleavage plane of ZnO plays a decisive role for successful preparation of extended TEM lamellae and the preservation of the HIOS structure. In particular, for (0001) oriented ZnO substrates the optimum cut direction is parallel to the HIOS interface. In cross-sectional high-resolution TEM images (100) lattice planes of 6P are observed proving the appropriate preparation strategy.Peer Reviewe

Many-body approach to proton emission and the role of spectroscopic factors

The process of proton emission from nuclei is studied by utilizing the two-potential approach of Gurvitz and Kalbermann in the context of the full many-body problem. A time-dependent approach is used for calculating the decay width. Starting from an initial many-body quasi-stationary state, we employ the Feshbach projection operator approach and reduce the formalism to an effective one-body problem. We show that the decay width can be expressed in terms of a one-body matrix element multiplied by a normalization factor. We demonstrate that the traditional interpretation of this normalization as the square root of a spectroscopic factor is only valid for one particular choice of projection operator. This causes no problem for the calculation of the decay width in a consistent microscopic approach, but it leads to ambiguities in the interpretation of experimental results. In particular, spectroscopic factors extracted from a comparison of the measured decay width with a calculated single-particle width may be affected.Comment: 17 pages, Revte

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