add Hartrees as unit def'n

[librasteve]

from @kjpye

3. Some of the constants have a value expressed in Hartrees (part of the Hartree atomic units system). A reasonable response is probably to just ignore those constants. Especially considering the usual symbol for the unit is U_h with a subscript h which is rather difficult to type, although the alternative Ha is given which might be made to work.

[librasteve]

wikipedia info is very useful on this - https://en.wikipedia.org/wiki/Hartree_atomic_units

some thoughts:

• there is potential for confusion here - CODATA lists constants such as atomic mass unit-hartree relationship ... my emphasis because this is a constant as conversion factor / as unit definition but presented as a Constant
• if we want to put Hartree base units in this module (which we do), then we can write them as unit definitions as usual which embed the relationship back to SI ... so we need to be wary of then defining constants in terms of units that are defined in terms of (slightly different) constants
• so ideally we would have one version of the truth of the definition - but the units want to be defined in terms of the constants!

a proposal:

• short term, we update Physics::Unit with just the definition of Hartree-energy, since that is needed as a Unit name in Math::Constants
• but, we recognise that CODATA has a very large set of relationship type constants (not just for Hartree) and that where Physics::Unit just has one conversion factor (thence a path to SI Base Units), CODATA may have separate forward and backward conversion factors that are not mutually inverse and also specifies uncertainty
• so long term, we rebuild Physics::Unit and Physics::Constants so that unit definitions can be based on the CODATA numbers (both forward and backwards) and that Physics::Unit can also employ Physics::Error for the application of uncertainties [new project needed here]

[librasteve]

a raku snippet that

• encapsulates the circularity
• shows how to localise use statements to blocks to help avoid use conflicts
• shows how a custom unit can be defined and then used in one script NB. in line 'my $He-mea' the raku type Energy must be specified (and not Measure)

  
  #!/usr/bin/env raku

constant \hartree-energy = %( name => 'Hartree energy', value => 4.3597447222071e-18, uncertainty => 0.0000000000085e-18, units => 'J' ); my \c-he := hartree-energy;

my $He-unit; { use Physics::Unit;

$He-unit = Unit.new( defn => "{c-he<value> ~ ' ' ~ c-he<units>}", names => <Eₕ E_h Ha> );

dd $He-unit;

} { use Physics::Measure;

my $He-mea = Energy.new(value => 1, units => $He-unit );

say $He-mea;             #1Eₕ
say $He-mea.in('J');     #4.3597447222071e-18J

}

[librasteve]

closing for now (added to https://github.com/p6steve/raku-Physics-Unit/issues/12 instead )