lengthy formulas. Since it is very small in comparison to the dominant uncertainties in $V_K$ it is dropped, leading to a significant simplification of the variational approach.

As the next step, equation (\[s17\]) is solved with an S-wave interaction based on the more realistic NN potential of Argonne [@ARG95]. This solution is also compared to another, variational solution with the intention of checking the variational method used in heavier systems. The actual interaction used, in the notation of Ref. [@ARG95], has the form $$v(NN)=v^{EM}(NN)+v^{\pi}(NN)+v^{R}(NN),
\label{Wir1}$$ where the electromagnetic part $v^{EM}$ only includes the dominant term proportional to $F_C(r)$ in Eq. (4) of Ref. [@ARG95], the OPE term $v^{\pi}$ is given by Eq. (18) of Ref. [@ARG95] and the phenomenological short range term $v^{R}$ from Eq. (20) with the parameters in Table II - again all from Ref. [@ARG95]. This gives directly the S-wave T=1, S=0 interaction $v(\rm{S-wave, \
T=1, \ S=0})$. However, in the T=0, S=1 deuteron channel, the effect of the tensor interaction $\upsilon_t(T=0, \ S=1)$ on the central component $
 \upsilon_c(\rm{T=0, \ S=1})$ is incorporated by the closure approximation to give $$V(\rm{S-wave, \ Deuteron})= \upsilon_c(\rm{T=0, \ S=1})-
\frac{8\upsilon_t(\rm{T=0, \ S=1})^2}{\rm{Den}}, \label{Wir2}$$ where the energy denominator was adjusted to 