grasp_rciqed_qed_flambaum Module Reference

Functions/Subroutines
real(real64) function	qedse_flambaum (k1, k2, phi_l, phi_f, phi_g)
	Estimates the QED self-energy of the kth orbital using potentials presented in [Flambaum & Ginges, 2005]. More...
real(real64) function	phi_f_inner (t, r)
	Calculate the integral-kernel for the radiative \(\Phi_f\) potential. More...
real(real64) function	phi_g1_inner (t, r)
	Calculate the first part of the integral-kernel for the radiative \(\Phi_g\) potential. More...
real(real64) function	phi_g2_inner (t, r)
	Calculate the second part of the integral-kernel for the radiative \(\Phi_g\) potential. More...
subroutine	quad_t_us2 (f, t, ntmax, nt, result)
	Uses the Simpson's rule for a non-uniform grid t to evaluate the integral of f. More...
subroutine	se_t_grid (f, t, ntmax, nt, r, nterm)
	Populates the t and f arrays (of length ntmax) with grid (t) and integrand (f) values to prepare for the inner integrations of the radiative potentials. More...

Function/Subroutine Documentation

phi_f_inner()

real(real64) function grasp_rciqed_qed_flambaum::phi_f_inner	(	real(real64)	t,
		real(real64)	r
	)

Calculate the integral-kernel for the radiative \(\Phi_f\) potential.

Equation 10 in [Flambaum & Ginges, 2005].

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phi_g1_inner()

real(real64) function grasp_rciqed_qed_flambaum::phi_g1_inner	(	real(real64)	t,
		real(real64)	r
	)

Calculate the first part of the integral-kernel for the radiative \(\Phi_g\) potential.

This is the first term from the product rule in equation (7) of [Flambaum & Ginges, 2005].

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phi_g2_inner()

real(real64) function grasp_rciqed_qed_flambaum::phi_g2_inner	(	real(real64)	t,
		real(real64)	r
	)

Calculate the second part of the integral-kernel for the radiative \(\Phi_g\) potential.

This is the second term from the product rule in equation (7) of [Flambaum & Ginges, 2005].

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qedse_flambaum()

real(real64) function grasp_rciqed_qed_flambaum::qedse_flambaum	(	integer, intent(in)	k1,
		integer, intent(in)	k2,
		real(real64), intent(out)	phi_l,
		real(real64), intent(out)	phi_f,
		real(real64), intent(out)	phi_g
	)

Estimates the QED self-energy of the kth orbital using potentials presented in [Flambaum & Ginges, 2005].

Returns the self-energy estimate for the orbital k. Additional output will stored in the phi_l, phi_f, phi_g variables, which will contain the corresponding parts of the self-energy estimate.

In the article the self-energy is assumed to be a spherically symmetric scalar potential, which has further been split up into three terms must be summed up. I.e. we're calculating equation (11), but without the Uehling a WC bits:

\[ \Phi_{\textrm{rad}}(r) = \Phi_l(r) + \Phi_f(r) + \Phi_g(r) \]

The code is based on the implementation in GRASP92 by Christian Thierfelder, Peter Schwerdtfeger and Lukáš Félix Pašteka.

References

[Flambaum & Ginges, 2005] Flambaum and Ginges, Phys.Rev.A 72, 052115 (2005) [Thierfelder & Schwerdtfeger, 2010] Thierfelder and Schwerdtfeger, Phys.Rev.A 82, 062503 (2010)

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quad_t_us2()

subroutine grasp_rciqed_qed_flambaum::quad_t_us2	(	real(real64), dimension(ntmax)	f,
		real(real64), dimension(ntmax)	t,
		integer	ntmax,
		integer	nt,
		real(real64)	result
	)

Uses the Simpson's rule for a non-uniform grid t to evaluate the integral of f.

t must be an array of length ntmax and will contain the gridpoints. f is an array of the same lengt, containing the values of the integrand for each t(i). The integral is then evaluated between t(1) and t(nt) and stored in result.

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se_t_grid()

subroutine grasp_rciqed_qed_flambaum::se_t_grid	(	real(real64), dimension(ntmax)	f,
		real(real64), dimension(ntmax)	t,
		integer	ntmax,
		integer	nt,
		real(real64)	r,
		character*2	nterm
	)

Populates the t and f arrays (of length ntmax) with grid (t) and integrand (f) values to prepare for the inner integrations of the radiative potentials.

• nt will contain the largest array index which still contain non-neglible integrand values.
• r is the radius for which the integral kernels will be integrated.
• nterm is is a string that determines which integrand will be used to populate f (possible values are F, G1 or G2).

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