channelutil

Python package to convert between asymptotic wavenumbers and energies for multichannel, inelastic collisions.

Installation

Clone the repository and install with the following commands:

git clone https://github.com/petersbingham/channelutil.git
cd channelutil
python setup.py install

Dependencies

Author packages (these will have their own dependencies):

• pynumwrap

Usage

As in the introduction. The various calculations supported are mostly simple and can be ascertained by looking in the channelutil/__init__.py file.

Constructor

The channels are described via the parameters supplied in the constructor to AsymCalc class in the package scope. It looks like:

__init__(self, units, angmoms=None, tot_spin=None, targ_spins=None, thresholds=None, sign_sel=signs_pos, signs=None)

units specifies the units to be used in the calculations; either rydbergs or hartrees, both of which are in package scope.

If the class is constructed using the default parameters then it will provide calculations for a single channel reaction.

If only angmoms is supplied then AsymCalc will provide calculations for a multichannel elastic reaction, otherwise thresholds can be specified using the thresholds parameter.

If only thresholds is supplied then AsymCalc will provide calculations for zero angular momenta in all channels.

angmoms contains the angular momenta for each for the channels. It should be of equal length to the thresholds parameter (if supplied) with the indices of the two lists describing the same channels. If angmoms is not supplied then the calculation will be for zero angular momenta in all channels.

The spin related quantities can be specified with the tot_spin and targ_spins arguments. If not supplied tot_spin defaults to a value of 0.5 and targ_spins to 0.0.

sign_sel and signs parameters. See next section.

Sign Selection

The package was developed as a means to provide selection of signs when converting from electron energies to wavenumbers that arise from the plus and minus signs in front of the square root energy wavenumber relationship. See "S.A. Rakityansky P.O.G. Ogunbade. S-matrix parametrization as a way of locating quantum resonances and bound states:multichannel case, 2010" for details. Some selections are provided, see below for further details. We plan to provide more elaborate selections in the future. All of the selections below exist in the package scope.

• signs_pos : Uses positive signs always.
• signs_specified : Uses signs as specified with the constructor signs parameter.
• signs_bndandres : Chooses signs to place on the unphysical sheet above threshold and physical sheet below threshold.
• signs_ana_over_axis : Chooses signs to attempt to retain analyticity when crossing the real axis.
• signs_ana_over_thres : Chooses signs to attempt to retain analyticity when crossing the thresholds.

Example

>>> import channelutil as cu
>>> calc1 = cu.AsymCalc(units=cu.rydbergs, thresholds=[0.0,1.0], sign_sel=cu.signs_ana_over_axis)
>>> calc2 = cu.AsymCalc(units=cu.rydbergs, thresholds=[0.0,1.0], sign_sel=cu.signs_ana_over_thres)
>>> calc1.k(0,1.0+0.1j)
(1.0012461141278126+0.04993777183700243j)
>>> calc1.k(0,1.0-0.1j)
(1.0012461141278126-0.04993777183700243j)  # No discontinuity
>>> calc2.k(0,1.0+0.1j)
(-1.0012461141278126-0.04993777183700243j)
>>> calc2.k(0,1.0-0.1j)
(1.0012461141278126-0.04993777183700243j)  # Discontinuity