positronium
python tools pertaining to positronium
Dependencies
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, attrs
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 containes 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 values.
The package only contains a few very simple modules.
constants
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", lifetime_oPs)
The mean lifetime of ortho-Ps is 142.037 ± 0.036 ns
>>> print("The ground-state hyperfine splitting is", frequency_hfs)
The ground-state hyperfine splitting is 203.38910 ± 0.00074 GHzWhere appropriate constants are stored in a class called MeasuredValue, which is a subclass of float, with extra attributes [uncertainty, unit, source, url]. For example
>>> lifetime_oPs
1.4203738423953184e-07
>>> lifetime_oPs.uncertainty
3.631431333889514e-11The value and uncertainty are in SI units. When calling print(MeasuredValue), the class attempts to format the result using a suitable metric prefix.
>>> print(lifetime_oPs)
142.037 ± 0.036 nsTo see the value's source,
>>> 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
Estimate the principle energy levels of positronium using the Rydberg formula.
For instance, the UV wavelength (in nm) needed to excite the Lyman-alpha transition can be found by:
>>> from positronium.Bohr import energy
>>> energy(1, 2, unit='nm')
243.00454681426382This 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, 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 attrs class can be used to represent a particular atomic state of positronium using the quantum numbers
| n | principal |
| l | orbital angular momentum |
| S | total spin |
| J | total angular momentum |
And can be used to estimate the energy of the state,
>>> from positronium import Ps
>>> x1 = Ps(n=2, l=1, S=1, J=2)
>>> x1.energy(unit='eV')
-1.7007156831792944It uses an equation described in
Richard A. Ferrell (1951) Phys. Rev. 84, 858 http://dx.doi.org/10.1103/PhysRev.84.858
which 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
