heprops is a simple python package implementing useful properties of the chemical element helium at low temperature

It includes experimental data and interpolation for the data found in the incredible and useful paper:

• James S. Brooks and Russell J. Donnelly, The calculated thermodynamic properties of superfluid helium-4, J. Phys. Chem. Ref. Data 6 51 (1977).

Most of the data in this paper was available on the late Russel Donnelly's former website http://pages.uoregon.edu/rjd which has since been taken offline but it is still available via a 2015 snapshot on the WayBackMachine.

The library also implements a number of historical and modern intramolecular interaction potentials for helium atoms. Details of these are taken from the following papers:

• R. A. Aziz, V. P. S. Nain, J. S. Carley, W. L. Taylor, and G. T. McConville, An accurate intermolecular potential for helium, J. of Chem. Phys. 70, 4330 (1979).
• R. A. Aziz, F. McCourt, and C. Wong, A new determination of the ground state interatomic potential for He₂, Mol. Phys. 61, 1487 (1987).
• R. A. Aziz, A. R. Janzen, and M. R. Moldover, Ab Initio Calculations for Helium: A Standard for Transport Property Measurements, Phys. Rev. Lett. 74, 1586 (1995).
• M. Przybytek, W. Cencek, J. Komasa, G. Łach, B. Jeziorski, and K. Szalewicz, Relativistic and Quantum Electrodynamics Effects in the Helium Pair Potential, Phys. Rev. Lett. 104, 183003 (2010).
• W. Cencek, M. Przybytek, J. Komasa, J. B. Mehl, B. Jeziorski, and K. Szalewicz, Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium, J. Chem. Phys. 136, 224303 (2012).

Supported Python Versions

Python >= 3.6 (for f-strings)

Installation

To install via pip:

pip install heprops

Or from within a notebook:

import sys
!{sys.executable} -m pip install heprops

Usage

The package implements two modules: helium which contains a number of functions that return the thermodynamics properties of helium and potential which implements the pair-potentials. For example:

from heprops import helium,potential
import numpy as np

T = np.linspace(0.5,2.5,5)

# the superfluid fraction
ρsoρ = helium.superfluid_fraction_SVP(T)
print(f'ρs/ρ(T) = {ρsoρ}')

# the coherence length
ξ = helium.ξ(T)
print(f'ξ(T) = {ξ} Å')

# Interaction Potential
V = potential.szalewicz_2012
r = np.linspace(2.5,5,1000)
rₘ = r[np.argmin(V(r))]
print(f'rₘ = {rₘ:6.3f} Å')

ρs/ρ(T) = [1.    0.993 0.889 0.447 0.   ]
ξ(T) = [4.11100244e-10 5.21483803e-10 7.56156315e-10 1.86293613e-09 1.24228114e-09] Å
rₘ =  2.968 Å 

Examples

A notebook including detailed examples of how to plot and compare the different interaction potentials is included in the examples directory at examples/he_potential_examples.ipynb.

Support

The creation of this software was supported in part by the National Science Foundation under Award Nos. DMR-1808440 and DMR-1809027.