Implement pairing field implementations

[danielpecak]

Implement pairing field implementations from paper:
https://link.springer.com/article/10.1140/epja/s10050-025-01503-x#citeas

libnest/libnest/bsk.py

Lines 345 to 370 in ed1345f

	# ================================
	# Alternative interpolation schemes (delta_n, delta_p from delta_sm, delta_neu)
	# ================================
	# TODO(Adarsh): neutron_ref_pairing_field() / proton_ref_pairing_field() above
	# implement one interpolation scheme (Formula 5.10 from NeST.pdf) for getting
	# delta_n and delta_p from delta_sm (symmetric_pairing_field) and delta_neu
	# (neutron_pairing_field). Add two more schemes here, following:
	# https://link.springer.com/article/10.1140/epja/s10050-025-01503-x#citeas
	def ref_pairing_field_eq2(rho_n, rho_p):
	"""TODO(Adarsh): implement the interpolation scheme from Eq. (2) of
	https://link.springer.com/article/10.1140/epja/s10050-025-01503-x#citeas
	"""
	raise NotImplementedError
	def ref_pairing_field_eq3(rho_n, rho_p):
	"""TODO(Adarsh): implement the interpolation scheme from Eq. (3) of
	https://link.springer.com/article/10.1140/epja/s10050-025-01503-x#citeas
	"""
	raise NotImplementedError
	def ref_pairing_field_eq6(rho_n, rho_p):
	"""TODO(Adarsh): implement the interpolation scheme from Eq. (6) of
	https://link.springer.com/article/10.1140/epja/s10050-025-01503-x#citeas
	"""
	raise NotImplementedError

And the tests for it:

libnest/tests/test_bsk.py

Lines 211 to 244 in dbc4f76

	class TestAlternativePairingSchemes(unittest.TestCase):
	"""Tests for the alternative delta_n/delta_p interpolation schemes
	(bsk.ref_pairing_field_eq2/eq3/eq6), based on Eq. (2), (3) and (6) of
	https://link.springer.com/article/10.1140/epja/s10050-025-01503-x#citeas
	TODO(Adarsh): each scheme is currently a stub that raises
	NotImplementedError (see bsk.py). As you implement a scheme, remove its
	@unittest.skip decorator and fill in real assertions - e.g. following the
	pattern in TestReferencePairingFields above:
	- eta = 0 (rho_n == rho_p) should reduce to symmetric_pairing_field
	- rho_p = 0 should reduce to neutron_pairing_field
	- finite output for both scalar and array input
	"""
	@unittest.skip("TODO(Adarsh): implement ref_pairing_field_eq2 (Eq. 2)")
	def test_ref_pairing_field_eq2(self):
	rho_n, rho_p = 0.05, 0.05
	ref = bsk.ref_pairing_field_eq2(rho_n, rho_p)
	sym = bsk.symmetric_pairing_field(rho_n, rho_p)
	self.assertAlmostEqual(float(ref), float(sym), places=6)
	@unittest.skip("TODO(Adarsh): implement ref_pairing_field_eq3 (Eq. 3)")
	def test_ref_pairing_field_eq3(self):
	rho_n, rho_p = 0.05, 0.05
	ref = bsk.ref_pairing_field_eq3(rho_n, rho_p)
	sym = bsk.symmetric_pairing_field(rho_n, rho_p)
	self.assertAlmostEqual(float(ref), float(sym), places=6)
	@unittest.skip("TODO(Adarsh): implement ref_pairing_field_eq6 (Eq. 6)")
	def test_ref_pairing_field_eq6(self):
	rho_n, rho_p = 0.05, 0.05
	ref = bsk.ref_pairing_field_eq6(rho_n, rho_p)
	sym = bsk.symmetric_pairing_field(rho_n, rho_p)
	self.assertAlmostEqual(float(ref), float(sym), places=6)