positronium 0.1.8

Description:

positronium 0.1.8

python tools pertaining to positronium

Prerequisites
Tested using Anaconda (Continuum Analytics) with Python 2.7 and 3.5.
Examples written using IPython 4.0.1 (python 3.5.1 kernel).
Package dependencies:

scipy, numpy

IPython examples dependencies:

matplotlib



Installation
via pip (recommended):
pip install positronium
alternatively, try the development version
git clone https://github.com/PositroniumSpectroscopy/positronium
and then run
python setup.py install


About
This package is designed to collate useful bits of code relating to the
positronium atom (an electron bound to its antiparticle, the positron).
The functions are generally simple approximations that give roughly the
right answers, rather than rigorous quantum mechanical calculations.
The package currently only contains a few very simple modules.

constants
is intended to collect useful constants in SI units, including:


const
description



m_Ps
2 * mass_electron

Rydberg_Ps
Rydberg value for Ps

a_Ps
Bohr radius for Ps

decay_pPs
decay rate of para-Ps (S=0)

decay_oPs
decay rate of ortho-Ps (S=1)

lifetime_pPs
lifetime of para-Ps (S=0)

lifetime_oPs
lifetime of ortho-Ps (S=1)

frequency_hfs
frequency of the ground-state hyperfine splitting

energy_hfs
energy interval of the ground-state hyperfine splitting

frequency_1s2s
frequency of the 1s2s transition

energy_1s2s
energy interval of the 1s2s transition



Example usage,
>>> from positronium.constants import lifetime_oPs, frequency_hfs
>>> print("The mean lifetime of ortho-Ps is", "%.1f ns."%(lifetime_oPs * 1e9))
The mean lifetime of ortho-Ps is 142.0 ns.

>>> print("The ground-state hyperfine splitting is", "%.1f GHz."%(frequency_hfs * 1e-9))
The ground-state hyperfine splitting is 203.4 GHz.
Where appropriate constants are stored in a subclass of float called
MeasuredValue, which has a few extra attributes [uncertainty, unit,
source, url], for example
>>> lifetime_oPs
1.4203738423953184e-07

>>> lifetime_oPs.uncertainty
3.631431333889514e-11

>>> print(lifetime_oPs.source)
R. S. Vallery, P. W. Zitzewitz, and D. W. Gidley (2003) Phys. Rev. Lett. 90, 203402

>>> lifetime_oPs.article()
The final line opens a url to the source journal.


Bohr
contains an adaptation of the Rydberg formula, which is used to
calculate the principle energy levels of positronium, or the interval
between two levels. The default unit is ‘eV’, however, this can be
changed using the keyword argument ‘unit’.
For instance, the UV wavelength (in nm) needed to excite the Lyman-alpha
transition can be found by:
>>> from positronium import Bohr
>>> Bohr.energy(1, 2, unit='nm')
243.00454681357735
This accepts numpy arrays for the initial (n1) and/ or final (n2) energy
level, e.g.,
>>> import numpy as np
>>> n1 = np.arange(1, 10)
>>> np.array([n1, Bohr.energy(n1, unit='eV')]).T
array([[ 1. , 6.8028465 ],
[ 2. , 1.70071163],
[ 3. , 0.75587183],
[ 4. , 0.42517791],
[ 5. , 0.27211386],
[ 6. , 0.18896796],
[ 7. , 0.1388336 ],
[ 8. , 0.10629448],
[ 9. , 0.08398576]])


Ps
This package contains a class called Ps, which can be used to represent a
particular atomic state of positronium using the quantum numbers


n
principle

l
orbital angular momentum

m
magnetic quantum number

S
total spin

J
total angular momentum



This can be used to return estimates of, e.g., the energy
level,
>>> from positronium import Ps
>>> x1 = Ps(n=2, l=1, S=1, J=2)
>>> x1.energy(unit='eV')
-1.7007156827724967
which uses an equation described in

Richard A. Ferrell (1951) Phys. Rev. 84, 858
http://dx.doi.org/10.1103/PhysRev.84.858

This includes fine structure but not radiative corrections.
A representation of the state using Latex code can be made using,
>>> x1.tex()
'$2^{3}P_{2}$'
For further examples see the IPython/ Jupyter notebooks,
https://github.com/PositroniumSpectroscopy/positronium/tree/master/examples

License

For personal and professional use. You cannot resell or redistribute these repositories in their original state.

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