text:
\section{Introduction}

The theoretical description of electromagnetic processes is based, like most nuclear physics formalisms, on a partial wave decomposition of relevant operators. This restricts theoretical methods to systems where a relatively small number of partial waves is important. Recently, several formalisms for the three dimensional description of few-body systems and processes have been developed.
In this paper we fill a gap in the development of the three dimensional framework and present an approach that allows for a simple implementation of three dimensional electromagnetic currents. Our final expressions can be translated to a numerical implementation via direct substitutions of $16$ dimensional square matrices representing operators in the 2N isospin - spin space. Finding the matrix representation of relevant operators is greatly simplified by using symbolic programming in the Mathematica $^{\mbox{\textregistered}}$ \cite{math} software package. Our approach allows us to use a very general operator form of current operators and can therefore be used for a wide class of processes.

In this paper we apply it to the case of electron induced deuteron disintegration and compare the results with traditional partial wave calculations. It is worth noting that the methods presented in the following sections can be applied to the description of other processes, where electroweak probes interact with the 2N system.
Electromagnetic currents can be replaced by any operators acting on the same degrees of freedom; this makes our implementations also useful for calculations involving for example muon capture or neutrino induced deuteron disintegration, performed recently still with the use partial wave expansion \cite{Marcucci:2010ts,Shen:2012xz}.

\section{Formalism and notation}

We adopt a notation in which capital letters describe the total momentum of a two particle system ($\mathbf{P} = \mathbf{p}_{1} + \mathbf{p}_{2}$), lower-case letters describe the relative momentum ($\mathbf{p} = \frac{1}{2} \left(\mathbf{p}_{1} - \mathbf{p}_{2}\right)$). Subscripts
denote individual particles and superscripts
assign a momentum to a particular quantum eigenstate. The two particle momentum eigenstates are normalized such that:
\begin{eqnarray}
\langle \mathbf{p}^{\prime} \mathbf{P}^{\prime} \mid \mathbf{p} \mathbf{P} \rangle = \delta^{3}(\mathbf{p}^{\prime} - \mathbf{p}) \delta^{3}(\mathbf{P}^{\prime} - \mathbf{P}) \label{norm1}, \\
 \int \,d^{3}\mathbf{p} \,d^{3}\mathbf{P} \mid \mathbf{p} \mathbf{P} \rangle \langle \mathbf{p} \mathbf{P} \mid = {\rm 1 \hspace{-0.6ex} I}
 \label{norm2}
\end{eqnarray}
and the transition from the total and relative to the individual momenta can be achieved using:
\begin{eqnarray}
\mathbf{p}_{1} = \mathbf{p} + \frac{1}{2} \mathbf{P} \nonumber \\
\mathbf{p}_{2} = \frac{1}{2} \mathbf{P} - \mathbf{p} \label{trans2},
\end{eqnarray}
where in (\ref{trans2}) and in the following we assume that the difference between the proton and neutron mass is negligible.

We examine the case of deuteron disintegration ($e + ^{2}\!\mathrm{H} \rightarrow e + p + n$) where the 2N system is treated in the non-relativistic approximation. In the initial state the deuteron is at rest ($\mathbf{P} = 0$) and the electron has a momentum magnitude of $q_{e}$. We assume that the rest mass of the electron is negligible in comparison to its kinetic energy therefore the initial electron energy $E_{e} \approx q_{e}$.
The final electron momentum magnitude is $q_{e}^{\prime}$, the final energy $E_{e}^{\prime} \approx q_{e}^{\prime}$ and the electron scattering angle is $\theta_{e}$
The magnitude of the three momentum transferred to the 2N system is
\begin{equation}
Q = \sqrt{q_{e}^{2} + q_{e}^{\prime 2} - 2 q_{e} q_{e}^{\prime} \cos{\theta_{e}}} \approx \sqrt{E_{e}^{2} + E_{e}^{\prime 2} - 2 E_{e} E_{e}^{\prime} \cos{\theta_{e}}}.
\label{momentumQ}
\end{equation}
We work in a reference frame, where the momentum transfer is parallel to $\hat{\mathbf{z}}$. In this frame momentum conservation leads to the expression for the total momentum of the proton and the neutron in the final state:
\begin{equation}
	\mathbf{P^{\mathrm{f}}} = \mathbf{p}_{\mathrm{1}} + \mathbf{p}_{\mathrm{2}} = (0 , 0 , Q).
\end{equation}
The magnitude of the final relative momentum can be calculated from the energy conservation:
\begin{equation}
	|\mathbf{p^{\mathrm{f}}}| = |\frac{1}{2}(\mathbf{p}_{\mathrm{1}} - \mathbf{p}_{\mathrm{2}})| = \frac{1}{2} \sqrt{4 m (E_{d} + E_{e} - E_{e}^{\prime}) - Q^{2}},
	\label{relmom}
\end{equation}
where $E_{d}$ is the (negative) deuteron binding energy and the direction of $\mathbf{p^{\mathrm{f}}}$ can be
arbitrary. The crucial nuclear matrix element $\mathbf{M}^{\mu}$ between the initial deuteron state (where the total momentum $\mathbf{P} = 0$ and the two particle total angular momentum has a $\hat{z}$ projection $m_{d}$) and the final 2N scattering state can be expressed in terms of the full 2N current operator ($j^{\mu}_{2N}$) and the $t$ operator:
\begin{eqnarray}
\mathbf{M}^{\mu}\left(\mathbf{p}^{\mathrm{f}} , \mathbf{P}^{\mathrm{f}}\right) \nonumber \\
\equiv _{a}\langle  \mathbf{p}^{\mathrm{f}} \mathbf{P}^{\mathrm{f}} , m_{1} \nu_{1} , m_{2} \nu_{2} \mid ({\rm 1 \hspace{-0.6ex} I} + t(E) G_{0}(E)) j^{\mu}_{2N} \mid \phi_{d} \, m_{d} \, \mathbf{P}=0 \rangle   \nonumber \\
= _{a}\langle  \mathbf{p}^{\mathrm{f}} \mathbf{P}^{\mathrm{f}} , m_{1} \nu_{1} , m_{2} \nu_{2} \mid ({\rm 1 \hspace{-0.6ex} I} + t(E) G_{0}(E))\nonumber \\
 (j^{\mu}(1) + j^{\mu}(2) + j^{\mu}(1 , 2)) \mid \phi_{d} \, m_{d} \, \mathbf{P}=0 \rangle   \nonumber \\
= 2 _{a}\langle  \mathbf{p}^{\mathrm{f}} \mathbf{P}^{\mathrm{f}} , m_{1} \nu_{1} , m_{2} \nu_{2} \mid  j^{\mu}(2) \mid \phi_{d} \, m_{d} \, \mathbf{P}=0 \rangle   \nonumber \\
+ _{a}\langle  \mathbf{p}^{\mathrm{f}} \mathbf{P}^{\mathrm{f}}  , m_{1} \nu_{1} , m_{2} \nu_{2} \mid  j^{\mu}(1,2) \mid \phi_{d} \, m_{d} \, \mathbf{P}=0 \rangle   \nonumber \\
+ _{a}\langle  \mathbf{p}^{\mathrm{f}} \mathbf{P}^{\mathrm{f}}  , m_{1} \nu_{1} , m_{2} \nu_{2} \mid t G_{0} j^{\mu}_{2N} \mid \phi_{d} \, m_{d} \, \mathbf{P}=0 \rangle   \label{tG0j2} \label{tG0j12}.
\end{eqnarray}
In this equation the final state is anti-symmetrized:
\begin{equation}
_{a}\langle \mathbf{p} \mathbf{P} , m_{1} \nu_{1} , m_{2} \nu_{2} \mid \equiv \frac{1}{2} \left( \langle \mathbf{p} \mathbf{P} , m_{1} \nu_{1} , m_{2} \nu_{2} \mid - \langle -\mathbf{p} \mathbf{P} , m_{2} \nu_{2} , m_{1} \nu_{1} \mid \right) \label{anti}.
\end{equation}
In the first term on the right hand side of (\ref{anti}) particle $1$ has a spin (isospin) $\hat{\mathbf{z}}$ projection $m_{1}$ ($\nu_{1}$), particle $2$ has a spin (isospin) $\hat{\mathbf{z}}$ projection $m_{2}$ ($\nu_{2}$) and in the second term on the right hand side of (\ref{anti}) the particles are exchanged. The $j(1)$ $\left(j(2)\right)$ operator is a single nucleon current acting on the degrees of freedom of the first (second) nucleon. The $j(1 , 2)$ operator accounts for processes where two nucleons are involved, $t$ is the 2N transition operator and $G_{0}$ is the free 2N propagator. The energy argument of the transition operator and the propagator is
$E = (\mathbf{p}^{\mathrm{f}})^{2}/m$.
Finally, the $\mu$ index denotes the component of the current operator. In particular $\mu = 0$ stands for charge density operators while $\mu = 1,2,3$ stand for spatial components. In the  following sections the way we calculate the individual parts of $\mathbf{M}^{\mu}$ in (\ref{tG0j12}) will be discussed separately for a specific choice of the coordinate system and value of $\mu$; we will drop $\mu$ for brevity.

\section{Deuteron bound state}

The structure of the deuteron wave function can be written in the operator form, following \cite{deuteronspin1,fach01,deuteronscalar}:
\begin{flalign}
	& \mid \phi_{d} \, m_{d} \, \mathbf{P}=0 \rangle    \nonumber = & \\
	& =\int d^{3}\mathbf{p} \mid \mathbf{p} \mathbf{P}=0 \rangle\sum_{l = 1}^{2} \phi_{l}(|\mathbf{p}|) \left[{\rm 1 \hspace{-0.6ex} I}^{\mathrm{isospin}} \otimes b_{l}(\mathbf{p})^{\mathrm{spin}} \right] \left[\mid 0 \, 0 \rangle \otimes \chi(m_{d}) \right] \nonumber & \\
	& \equiv \int d^{3}\mathbf{p} \mid \mathbf{p} \mathbf{P}=0 \rangle\sum_{l = 1}^{2} \phi_{l}(|\mathbf{p}|) \left[B_{l}(\mathbf{p}) \right] \left[\mid 0 \, 0 \rangle \otimes \chi(m_{d}) \right]	. &\label{deuteron}
\end{flalign}
where
\[
	b_{1} = {\rm 1 \hspace{-0.6ex} I}
\]
\[
	b_{2} = \left( \boldsymbol{\sigma}(1) \cdot \mathbf{p} \boldsymbol{\sigma}(2) \cdot \mathbf{p}  - \frac{1}{3} \mathbf{p} \cdot \mathbf{p} {\rm 1 \hspace{-0.6ex} I} \right).
\]
In equation (\ref{deuteron}) $\mid \chi(m_{d})\rangle$ is a state in which the spins of the two spin $\frac{1}{2}$ particles are coupled to a total spin $1$ with a $\hat{\mathbf{z}}$ projection $m_{d}$. The isospins of the two nucleons are coupled to the total isospin $0$ state $\mid 0 \, 0 \rangle$. $\phi_{l}$ are scalar functions of the relative momentum and $\boldsymbol{\sigma}(1)$, $\boldsymbol{\sigma}(2)$ are doubled spin operators in the spin space of one nucleon and identity operators in the spin space of the other nucleon, respectively:
\begin{equation}
	\boldsymbol{\sigma}(1) = \left( \sigma^{x} \otimes {\rm 1 \hspace{-0.6ex} I} , \sigma^{y} \otimes {\rm 1 \hspace{-0.6ex} I} , \sigma^{z} \otimes {\rm 1 \hspace{-0.6ex} I} \right) ,
\label{sigma1}
\end{equation}
\begin{equation}
	\boldsymbol{\sigma}(2) = \left( {\rm 1 \hspace{-0.6ex} I} \otimes \sigma^{x} , {\rm 1 \hspace{-0.6ex} I} \otimes \sigma^{y} , {\rm 1 \hspace{-0.6ex} I} \otimes \sigma^{z} \right).
\label{sigma2}
\end{equation}
Vector components in (\ref{sigma1}) and (\ref{sigma2}) are operators written in terms of the tensor product $\otimes$. They act in the $4$ dimensional spin space of the two nucleon system and can be represented by $4 \times 4$ matrices - tensor products of identity operators and Pauli matrices.

Note that in equation (\ref{deuteron}) states and operators in the 2N isospin - spin space are placed inside the $\left[ \dots \right]$ brackets; in Sec. \ref{sec:representation} we will introduce a simple way to implement these expressions as $16$ dimensional vectors and $16 \times 16$ matrices for use in our numerical treatment.

Scalar functions $\phi_{l}$ in expansion (\ref{deuteron}) can be calculated using three dimensional formalism, see for example \cite{deuteronscalar}. Nowadays deuteron bound state calculations can use any 2N potentials given in the operator form and do not require substantial computational resources.

\section{Single nucleon currents in three dimensions.}

Single nucleon (1N) currents act on the degrees of freedom of one particle. Their matrix elements in the momentum space depend only on the initial and final momenta
and are operators in the isospin - spin space. For example the matrix element for the second nucleon, $j(2)$, reads:
\begin{equation}
\left[ \langle \mathbf{p}_{1}^{\prime} \mathbf{p}_{2}^{\prime} \mid j(2) \mid \mathbf{p}_{1} \mathbf{p}_{2} \rangle \right]= \delta \left( \mathbf{p}^{\prime}_{1} - \mathbf{p}_{1} \right) \left[j(2 , \mathbf{p}^{\prime}_{2} - \mathbf{p}_{2} , \mathbf{p}^{\prime}_{2} + \mathbf{p}_{2})\right]
\end{equation}
where in view of the standard nonrelativistic current, the dependence on the difference and sum of the initial and final momenta is used. Implementing the transition from the individual particle momenta to the relative momenta leads to
\begin{eqnarray}
\left[ \langle \mathbf{p}^{\prime} \mathbf{P}^{\prime} \mid j(2) \mid \mathbf{p} \mathbf{P} \rangle \right] = \delta \left( \frac{1}{2} \mathbf{P}^{\prime} - \frac{1}{2} \mathbf{P} + \mathbf{p}^{\prime} - \mathbf{p} \right) \nonumber \\
\left[j(2 ,  \frac{1}{2} \mathbf{P}^{\prime} - \frac{1}{2} \mathbf{P} - \mathbf{p}^{\prime} + \mathbf{p} ,  \frac{1}{2} \mathbf{P}^{\prime} + \frac{1}{2} \mathbf{P} - \mathbf{p}^{\prime} - \mathbf{p})\right].
\end{eqnarray}
Again, the expressions inside the square brackets $\left[ \dots \right]$ can be easily represented using the notion of the Kronecker product, see
Sec. \ref{sec:representation}. The action of $j(2)$ on the deuteron state at rest can be worked out:
\begin{flalign}
&\left[ \langle \mathbf{p}^{\prime} \mathbf{P}^{\prime} \mid j(2)\mid \phi_{d} \, m_{d} \, \mathbf{P}=0  \rangle \right] = \nonumber & \\
&= \sum_{l = 1}^{2} \phi_{l}(|\mathbf{p}^{\prime} + \frac{1}{2} \mathbf{P}^{\prime}|) \left[j(2 , \mathbf{P}^{\prime} , -2 \mathbf{p}^{\prime})\right] \left[ B_{l}(\mathbf{p}^{\prime} + \frac{1}{2} \mathbf{P}^{\prime}) \right] \left[\mid 0 \, 0 \rangle \otimes \chi(m_{d}) \right] \nonumber &\\
&\equiv \left[ O^{\mathrm{1N}}(2 , \mathbf{p}^{\prime} , \mathbf{P}^{\prime}) \right] \left[\mid 0 \, 0 \rangle \otimes \chi(m_{d}) \right] , &\label{j1N}
\end{flalign}
where we used
$\mathbf{P} = 0$ and the normalization of momentum eigenstates (\ref{norm1})-(\ref{norm2}) so $O^{\mathrm{1N}}$ is the resulting single particle operator. Equation (\ref{j1N}) gives the full isospin - spin state for the final
$\mathbf{p}^{\prime}$, $\mathbf{P}^{\prime}$ momenta.

\section{2N currents in three dimensions.}

For a wide class of 2N current operators, their matrix elements in the momentum space (operators in isospin - spin space) are given in the form:
\begin{equation}
\left[ \langle \mathbf{p}_{1}^{\prime} \mathbf{p}_{2}^{\prime} \mid j(1,2) \mid \mathbf{p}_{1} \mathbf{p}_{2} \rangle \right] = \left[j(1 , 2 , \mathbf{p}^{\prime}_{1} - \mathbf{p}_{1} , \mathbf{p}^{\prime}_{2} - \mathbf{p}_{2})\right] ,
\label{2Nform}
\end{equation}
see for example \cite{PSC31471,PRC402294,PRC41309}. The right hand side of (\ref{2Nform}) is as a linear combination of scalar functions ($f_{i}^{jS}$ , $f_{i}^{j}$) and products of spin space operators ($O_{jS}$ , $\mathbf{O}_{j}$) and isospin space operators ($T_{i}$):
\begin{eqnarray}
\left[ j^{0}(1,2) \right] = \sum_{i = 1}^{5} \sum_{j = 1}^{8} f_{i}^{jS}(\mathbf{p}^{\prime}_{1} - \mathbf{p}_{1} , \mathbf{p}^{\prime}_{2} - \mathbf{p}_{2}) \left[ T_{i} O_{jS} \right].
\label{2Ndecomp2} \\
\left[ \vec{j}(1,2) \right] = \sum_{i = 1}^{5} \sum_{j = 1}^{24} f_{i}^{j}(\mathbf{p}^{\prime}_{1} - \mathbf{p}_{1} , \mathbf{p}^{\prime}_{2} - \mathbf{p}_{2}) \left[ T_{i} \mathbf{O}_{j} \right], \label{2Ndecomp1}
\end{eqnarray}
where the subscript S distinguishes density and current components. In Ref. \cite{2Ncurrents1} a general operator basis for the local 2N current operator was introduced.
In Sec. \ref{sec:representation} some examples of operators from (\ref{2Ndecomp2}), (\ref{2Ndecomp1}) will be used to demonstrate our matrix representation of expressions inside $\left[ \dots \right]$.

Again, using (\ref{trans2}), current matrix elements become:
\begin{equation}
\left[ \langle \mathbf{p}^{\prime} \mathbf{P}^{\prime} \mid j(1,2) \mid \mathbf{p} \mathbf{P} \rangle \right] = \left[j(1 , 2 , \frac{1}{2} \mathbf{P}^{\prime} - \frac{1}{2} \mathbf{P} + \mathbf{p}^{\prime} - \mathbf{p} , \frac{1}{2} \mathbf{P}^{\prime} - \frac{1}{2} \mathbf{P} - \mathbf{p}^{\prime} + \mathbf{p})\right]
\end{equation}
In the following we restrict ourselves
to this class of momentum dependences. Our approach can, however, be generalized to include any type of momentum dependence. The action of $j(1 , 2)$ on the deuteron state can be worked out using (\ref{norm1}),(\ref{norm2}), (\ref{trans2}) and
$\mathbf{P} = 0$. In the laboratory frame it yields:
\begin{eqnarray}
\left[ \langle \mathbf{p}^{\prime} \mathbf{P}^{\prime} \mid j(1 , 2) \mid \phi_{d} \, m_{d} \, \mathbf{P}=0 \rangle \right]  \nonumber \\
= \int \,d^{3}\mathbf{p}^{\prime\prime} \sum_{l = 1}^{2} \phi_{l}(|\mathbf{p}^{\prime\prime}|) \left[j(1 , 2 , \frac{1}{2} \mathbf{P}^{\prime} + \mathbf{p}^{\prime} - \mathbf{p}^{\prime\prime} , \frac{1}{2} \mathbf{P}^{\prime} - \mathbf{p}^{\prime} + \mathbf{p}^{\prime\prime})\right] \nonumber \\ \left[ B_{l}(\mathbf{p}^{\prime\prime}) \right] \left[\mid 0 \, 0 \rangle \otimes \chi(m_{d}) \right] \nonumber \\
 \equiv \left[ O^{\mathrm{2N}}(1 , 2 , \mathbf{p}^{\prime} , \mathbf{P}^{\prime}) \right] \left[\mid 0 \, 0 \rangle \otimes \chi(m_{d}) \right]
 \label{j2N} ,
\end{eqnarray}
where $O^{\mathrm{2N}}$ is the resulting two-particle operator.
Equation (\ref{j2N}) gives the full isospin - spin state for the final
$\mathbf{p}^{\prime}$, $\mathbf{P}^{\prime}$ momenta.

\section{$t$ operator in three dimensions}

The $t$ operator satisfies the Lippmann - Schwinger equation:
\begin{equation}
t(E) = V + t(E) G_{0}(E) V
\label{LSEleft}
\end{equation}
or equivalently
\begin{equation}
t(E) = V + V G_{0}(E) t(E)
\label{LSEright}
\end{equation}
where $G_{0}(E)$ is the free propagator depending on the energy $E$
and $V$ is a 2N potential. It follows that, as shown in \cite{decomp} also $t$ can be written as a linear combination of scalar functions ($t_{\gamma , i}$) and operators ($\mathbf{W}_{\gamma , i}$) in the isospin - spin space:
\begin{equation}
\left[ \langle \mathbf{p}^{\prime} \mid t(E) \mid \mathbf{p} \rangle \right] = \sum_{\gamma} \sum_{i = 1}^{6} t_{\gamma , i}(|\mathbf{p}^{\prime}| , |\mathbf{p}| , \hat{\mathbf{p}}^{\prime} \cdot \hat{\mathbf{p}} , E) \left[\mathbf{W}_{\gamma , i}(\hat{\mathbf{p}}^{\prime} , \hat{\mathbf{p}}) \right].
\label{decomp1}
\end{equation}
Here
\begin{equation}
\left[\mathbf{W}_{\gamma , i}(\hat{\mathbf{p}}^{\prime} , \hat{\mathbf{p}}) \right] = \left[\mathbf{C}_{\gamma}^{\mathrm{isospin}} \otimes \mathbf{w}_{i}^{\mathrm{spin}}(\mathbf{p}^{\prime} , \mathbf{p})\right] \nonumber
\end{equation}
are again operators in the isospin - spin space (matrix elements between momentum states), with $\mathbf{w}_{i}$ ($i = 1,2,...,6$) acting in the $4$ dimensional spin space of the 2N system.
The decomposition (\ref{decomp1})
is not unique; our choice of the six $\mathbf{w}_{i}$ operators is consistent with \cite{deuteronscalar}
. Scalar functions arising in the decomposition of $t$ can be calculated in the three dimensional formalism. Calculations can be performed for any type of the NN potential satisfying a similar expansion (\ref{decomp1}).
For details see Ref. \cite{deuteronscalar}.
\begin{eqnarray}
\mathbf{w}_{1}(\mathbf{p}^{\prime} , \mathbf{p}) = {\rm 1 \hspace{-0.6ex} I} ,\\
\mathbf{w}_{2}(\mathbf{p}^{\prime} , \mathbf{p}) = \boldsymbol{\sigma}(1) \cdot \boldsymbol{\sigma}(2) ,\\
\mathbf{w}_{3}(\mathbf{p}^{\prime} , \mathbf{p}) = i (\boldsymbol{\sigma}(1) + \boldsymbol{\sigma}(2)) \cdot (\hat{\mathbf{p}} \times \hat{\mathbf{p}}^{\prime}) ,\\
\mathbf{w}_{4}(\mathbf{p}^{\prime} , \mathbf{p}) = \boldsymbol{\sigma}(1) \cdot (\hat{\mathbf{p}} \times \hat{\mathbf{p}}^{\prime}) \, \boldsymbol{\sigma}(2) \cdot (\hat{\mathbf{p}} \times \hat{\mathbf{p}}^{\prime}) ,\\
\mathbf{w}_{5}(\mathbf{p}^{\prime} , \mathbf{p}) = \boldsymbol{\sigma}(1) \cdot (\hat{\mathbf{p}}^{\prime} + \hat{\mathbf{p}}) \, \boldsymbol{\sigma}(2) \cdot (\hat{\mathbf{p}}^{\prime} + \hat{\mathbf{p}}) ,\\
\mathbf{w}_{6}(\mathbf{p}^{\prime} , \mathbf{p}) = \boldsymbol{\sigma}(1) \cdot (\hat{\mathbf{p}}^{\prime} - \hat{\mathbf{p}}) \, \boldsymbol{\sigma}(2) \cdot (\hat{\mathbf{p}}^{\prime} - \hat{\mathbf{p}})
\end{eqnarray}
The $C_{\gamma} = \mid \gamma \rangle \langle \gamma \mid$ isospin operators project onto one of the four 2N isospin states:
\begin{equation}
	\mid \gamma \rangle = \mid \left( \frac{1}{2} \, \frac{1}{2} \right) t=0 , 1 \, m_{t} = -t \dots t \rangle.
\end{equation}
The $\mid \gamma \rangle$ states are chosen in this way, because $t(E)$ conserves the total 2N isospin.

The rescattering part of the matrix element $M$ in (\ref{tG0j12}) can be written as:
\begin{eqnarray}
\left[ \langle \mathbf{p}^{\prime} \mathbf{P}^{\prime} \mid t(E) G_{0} j_{2N} \mid \phi_{d} \, m_{d} \, \mathbf{P}=0 \rangle \right]  \nonumber \\
= \int \,d^{3}\mathbf{p} \left[ \langle \mathbf{p}^{\prime} \mid t(E) \mid \mathbf{p} \rangle \right] \frac{1}{E - \frac{\mathbf{p}^{2}}{m} + i \epsilon} \nonumber \\
\times \left[ O(\mathbf{p} , \mathbf{P}^{\prime}) \right] \left[\mid 0 \, 0 \rangle \otimes \chi(m_{d}) \right] \nonumber\\
=  m \int_{0}^{\bar{p}}  \frac{\mathbf{p}^{2} \left[ \mathbf{f}(|\mathbf{p}|) \right] - \mathbf{p}^{\prime 2} \left[ \mathbf{f}(|\mathbf{p}^{\prime}|) \right]}{\mathbf{p}^{\prime 2} - \mathbf{p}^{2}} \, d|\mathbf{p}| \nonumber \\
+ m \frac{|\mathbf{p}^{\prime}|  \left[ \mathbf{f}(|\mathbf{p}^{\prime}|) \right]}{2} \left( \ln \left( \frac{\bar{p} + |\mathbf{p}^{\prime}|}{\bar{p} - |\mathbf{p}^{\prime}|}\right)  - i \pi \right)  \nonumber \\
\times \left[\mid 0 \, 0 \rangle \otimes \chi(m_{d}) \right]
\label{tG0j}
\end{eqnarray}
where $O$ is either $O^{1N}$ from Eq. (\ref{j1N}) or $O^{2N}$ from Eq. (\ref{j2N}), $E = \mathbf{p}^{\mathrm{\prime 2}}/m$ is the relative energy of the final 2N state and
\begin{equation}
\left[ \mathbf{f}(|\mathbf{p}|) \right] = \int_{0}^{2 \pi} d\phi \int_{-1}^{1} dx \left[ \langle  \mathbf{p}^{\prime} \mid t(E) \mid \mathbf{p} \rangle \right] \left[ O(\mathbf{p} , \mathbf{P}^{\prime}) \right],
\end{equation}
since
\begin{equation}
\mathbf{p} = |\mathbf{p}| (\sqrt{1 - x^{2}} \cos{\phi} , \sqrt{1 - x^{2}} \sin{\phi} , x).
\end{equation}

The integral (\ref{tG0j}) with the cut-off value $\bar{p}$ can be easily calculated numerically. In the next section we show how to prepare its component $\left[ O(\mathbf{p} , \mathbf{P}^{\prime}) \right]$.

\section{Representation of spin-isospin operators}

\label{sec:representation}

Now that the form of expressions in (\ref{tG0j12}) has been established it remains to find a way to represent operators and states inside $\left[ \dots \right]$. Once an appropriate matrix representation is found, numerical calculations can be constructed using equations (\ref{j1N}), (\ref{j2N}) and (\ref{tG0j}) by simple substitutions and matrix multiplications.

Our choice for the $16$ dimensional basis of the two nucleon isospin - spin state space (the deuteron in the initial state, the proton and the neutron in the final state) is the set of vector states $\{ \mid e_{i} \rangle \}$ ($i = 1,2,...,16$):
\begin{equation}
\mid e_{i} \rangle  = \left( \mid m_{1}^{\mathrm{isospin}}(i) \rangle \otimes \mid m_{2}^{\mathrm{isospin}}(i)\rangle \right) \otimes \left( \mid m_{1}^{\mathrm{spin}}(i) \rangle \otimes \mid m_{2}^{\mathrm{spin}}(i) \rangle \right)
\end{equation}
where $m^{\mathrm{spin(isospin)}}_{j}$ are the spin (isospin) projections of nucleon
$j$ and the corresponding quantum numbers are given in Tab. \ref{fullstates}
\begin{center}
\begin{table}\centering
 \setlength{\extrarowheight}{4pt}
 \caption{Reference quantum numbers for our KP states.}
\begin{tabular}{c|cccc}
 $i$ & $m_{1}^{\mathrm{isospin}}(i)$ & $m_{2}^{\mathrm{isospin}}(i)$ & $m_{1}^{\mathrm{spin}}(i)$ & $m_{2}^{\mathrm{spin}}(i)$ \\ \hline
 $1$ & $\frac{1}{2}$ & $\frac{1}{2}$ & $\frac{1}{2}$ & $\frac{1}{2}$  \\
 $2$ & $\frac{1}{2}$ & $\frac{1}{2}$ & $\frac{1}{2}$ & $-\frac{1}{2}$  \\
 $3$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{1}{2}$ & $\frac{1}{2}$  \\
 $4$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{1}{2}$ & $-\frac{1}{2}$  \\
 $5$ & $\frac{1}{2}$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{1}{2}$  \\
 $6$ & $\frac{1}{2}$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $-\frac{1}{2}$  \\
 $7$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{1}{2}$  \\
 $8$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ & $-\frac{1}{2}$  \\
 $9$ & $-\frac{1}{2}$ & $\frac{1}{2}$ & $\frac{1}{2}$ & $\frac{1}{2}$  \\
 $10$ & $-\frac{1}{2}$ & $\frac{1}{2}$ & $\frac{1}{2}$ & $-\frac{1}{2}$  \\
 $11$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{1}{2}$ & $\frac{1}{2}$  \\
 $12$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{1}{2}$ & $-\frac{1}{2}$  \\
 $12$ & $-\frac{1}{2}$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{1}{2}$  \\
 $14$ & $-\frac{1}{2}$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $-\frac{1}{2}$  \\
 $15$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{1}{2}$  \\
 $16$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ & $-\frac{1}{2}$ .
  \label{fullstates}
\end{tabular}
\end{table}
\end{center}
Any operator or state
in this space can be constructed using the notion of the Kronecker product (KP). The Mathematica $^{\mbox{\textregistered}}$ \cite{math} symbolic programming software contains definitions for the KP, which makes translating expressions for isospin - spin operators a simple task. However, it is important to remember that the order of operators in the KP must be preserved. Tab. \ref{fullstates} can serve as a reference to keep consistence with this paper.

The deuteron operators $[B_{1}(\mathbf{p})]$ and $[B_{2}(\mathbf{p})]$ with $\mathbf{p} = \left(p_{x} , p_{y} , p_{z} \right)$ from equation (\ref{deuteron}) have a form simple enough to have their matrix representation written out in full. $[B_{1}]$ is simply a $16 \times 16$ identity matrix. $[B_{2}]$ has a block diagonal form:
\begin{equation}
\left(
\begin{array}{cccc}
 B & 0 & 0 & 0 \\
 0 & B & 0 & 0 \\
 0 & 0 & B & 0 \\
 0 & 0 & 0 & B
\end{array}
\right)\nonumber
\end{equation}
where $B$ is a $4 \times 4$ matrix:
\begin{tiny}
\begin{equation}
\left(
\begin{array}{cccc}
 \frac{1}{3} \left(-p_x^2-p_y^2-p_z^2\right)+p_z^2 & p_z \left(p_x-i p_y\right) & p_z \left(p_x-i p_y\right) & \left(p_x-i p_y\right){}^2 \\
 p_z \left(p_x+i p_y\right) & \frac{1}{3} \left(-p_x^2-p_y^2-p_z^2\right)-p_z^2 & \left(p_x-i p_y\right) \left(p_x+i p_y\right) & p_z \left(-\left(p_x-i p_y\right)\right) \\
 p_z \left(p_x+i p_y\right) & \left(p_x-i p_y\right) \left(p_x+i p_y\right) & \frac{1}{3} \left(-p_x^2-p_y^2-p_z^2\right)-p_z^2 & p_z \left(-\left(p_x-i p_y\right)\right) \\
 \left(p_x+i p_y\right){}^2 & p_z \left(-\left(p_x+i p_y\right)\right) & p_z \left(-\left(p_x+i p_y\right)\right) & \frac{1}{3} \left(-p_x^2-p_y^2-p_z^2\right)+p_z^2
\end{array}
\right)\nonumber.
\end{equation}
\end{tiny}

Operators appearing in (\ref{2Ndecomp2}) and (\ref{2Ndecomp1}) have a more complicated isospin operator form. A simple example of their matrix representation is given below in Fig. \ref{T2O5mu3}.

\begin{figure}[h]\centering
\includegraphics[width=1.0\textwidth,angle=0]{T2O5mu3.eps}
\caption{$\left[ T_{2} O_{5}^{3} \right] \left( \mathbf{p}_{1}^{\prime} - \mathbf{p}_{1} = \left( q_{1x} , q_{1y} , q_{1z} \right) , \mathbf{p}_{2}^{\prime} - \mathbf{p}_{2} = \left( q_{2x} , q_{2y} , q_{2z} \right) \right)$ with $T_{2} = \boldsymbol{\tau}_{1}^{z}-\boldsymbol{\tau}_{2}^{z}$ and $O_{5} = (\mathbf{q}_{1} \times \boldsymbol{\sigma}_{1})+(\mathbf{q}_{2} \times \boldsymbol{\sigma}_{2})$. $ \boldsymbol{\tau}_{i}$ ($ \boldsymbol{\sigma}_{i}$) is the 2N isospin (spin) vector operator acting in the space of nucleon $i$.}
\label{T2O5mu3}
\end{figure}

States can be constructed in a similar manner using the built in Mathematica $^{\mbox{\textregistered}}$ definitions for Clebsch-Gordan coefficients, for example $\left[\mid 0 \, 0 \rangle \otimes \chi(1) \right]$ results in:
\begin{equation}
\left(0,0,0,0,\frac{1}{\sqrt{2}},0,0,0,-\frac{1}{\sqrt{2}},0,0,0,0,0,0,0\right).
\end{equation}

\section{Results}

In the following we will present results obtained using a chiral NNLO potential \cite{Epelbaum:2004fk} with $\Lambda = 550 $ MeV$/$c and $\tilde{\Lambda} = 600$ MeV$/$c.
The operator form of such a potential was briefly described in Appendix~C of Ref.~\cite{deuteronscalar},
where also an example set of necessary parameters was given for its neutron-proton version.
The same parameters will also be used in the present paper.

There are three basic ingredients in our calculations: the deuteron wave function,
the 2N t-matrix and the 2N current operator. Before we show selected observables
for the $ ^2{\rm H} ( e, e' p) n $ reaction, we will describe our numerical performance
and the way we verify the quality of our calculations.

As described in Ref.~\cite{deuteronscalar} and equation (\ref{deuteron}), the deuteron in the operator form
is represented by two functions $\phi_1(p)$ and $\phi_2(p)$.
The corresponding Schr\"odinger equation for $\phi_1(p)$ and $\phi_2(p)$
can be rewritten as an eigenvalue problem,
which is of the same type and dimension as
the one solved for the
deuteron wave function in the standard partial wave representation,
where one deals with the $s$- and $d$-components, $\psi_0(p) $ and $\psi_2(p)$.
The connection between the solutions is very simple \cite{fach01}
\begin{eqnarray}
\psi_0 (p) = \sqrt{4 \pi} \,\phi_1 (p), \, \, \, \,
\psi_2 (p) = \frac{4 \sqrt{2} \pi p^2 } { 3 } \, \phi_2 (p)
\end{eqnarray}
and can be used to check the numerical performance.

In Fig.~\ref{f1} we show directly the $\phi_1(p)$ and $\phi_2(p)$
functions required for the operator expansion of the deuteron.
In Fig.~\ref{f2} the resulting $s$- and $d$-wave components
in momentum space are compared to the
results obtained by firstly decomposing the NN potential into partial
waves and then solving
the resulting Schr\"odinger equation in its standard form.
The agreement for the two wave function
components is perfect for all their significant values.

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{NNLO105_fig.1.eps}
\includegraphics[width=0.45\textwidth,angle=0]{NNLO105_fig.2.eps}
\caption{The $\phi_1(p)$ (left) and $\phi_2(p)$ (right) expansion
function in the operator form of the deuteron
as a function of the magnitude of the relative momentum $p$
for the considered chiral NNLO potential.
}
\label{f1}
\end{figure}

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{NNLO105_figlog.s.eps}
\includegraphics[width=0.45\textwidth,angle=0]{NNLO105_figlog.d.eps}
\caption{The $s$-wave (left) and $d$-wave (right) component of the deuteron
wave function as a function of the magnitude of the relative momentum $p$
for the considered chiral NNLO potential. Crosses
represent results obtained using the
operator approach and solid lines are directly from the standard
partial wave decomposition.}
\label{f2}
\end{figure}

In Ref.~\cite{deuteronscalar} we solved the Lippmann-Schwinger equation (LSE) for the 2N t-matrix
directly in three dimensions. At that time we focused mainly on the on-shell
behavior of the expansion coefficients $t_i (p',p,x; E_{2N} ) $, that is
we were interested in $t_i \left(p_0,p_0,x; E_{2N}=\frac{p_0^2}{m} \right) $, which are sufficient
to calculate the Wolfenstein parameters and the nucleon-nucleon
scattering observables. Furthermore, we solved the LSE in such a form (Eq.~(2.6) from Ref.~\cite{deuteronscalar})
\begin{eqnarray}
\lefteqn{\sum_{j} A_{ kj} ( {\vec p'}, {\vec p}) t_j^{t m_t}({\vec p'}, {\vec p}) =
 \sum_{j} A_{ kj} ( {\vec p'}, {\vec p}) v_j^ { t m_t}( {\vec p'}, {\vec p} )} \cr
&+&  \int d^ 3 p'' \sum_{ j j'} v_j^ { t m_t}( {\vec p'}, {\vec p''}) G_0 ( p'')
t_{ j'}^ { t m_t}( {\vec p''}, {\vec p)} B_{ kjj'} ( {\vec p'}, {\vec p''},  {\vec p}),
\label{lse1}
\end{eqnarray}
that the magnitude of the initial $ {\vec p} $ momentum could be fixed.

Clearly, for the $^2{\rm H} ( e, e' p) n $ reaction we need
a "left" version of Eq.~(\ref{lse1}), which allows us to find the
half-shell t-matrix for a fixed final relative momentum,
$\vec p^{\mathrm{f}}$, given now by the reaction kinematics.
The starting point for this new version is equation (\ref{LSEleft}).
Repeating the algebra outlined in Ref.~\cite{deuteronscalar}, we prepared
a numerical realization of this "left" version of the LSE, leading to
the scalar expansion coefficients
$t_i \left(\vec p^{\mathrm{f}}, \vec p ; E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right)
\equiv t_i \left( p^{\mathrm{f}}, p , x ; E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right) $,
where $ x \equiv {\hat p}^{\mathrm{f}} \cdot {\hat p} $. Our numerical
scheme was again based on matrix inversion and used
the standard LU decomposition of Numerical Recipes \cite{numrec}.
In order to achieve a unique and smooth solution also for
$ p = p^{\mathrm{f}}$, it was sufficient to calculate the average
\begin{flalign}
& t_i \left(p^{\mathrm{f}}, p , x ; E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right) = \nonumber & \\
& =
\frac12 \left(
t_i \left(p^{\mathrm{f}} - \delta_{p^{\mathrm{f}}},  p , x ; E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right)
\, + \,
t_i \left(p^{\mathrm{f}} + \delta_{p^{\mathrm{f}}} , p , x ; E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right)
\right) \, , &
\label{lse3}
\end{flalign}
with $ \delta_{p^{\mathrm{f}}} \approx \, $ 0.01 fm$^{-1}$.

Actually, this effort turned out to be unnecessary and provided
merely an additional check of numerics, since
\begin{eqnarray}
t_i \left(p^{\mathrm{f}}, p , x ; E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right)
=
t_i \left(p , p^{\mathrm{f}} , x ; E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right)
\label{lse4}
\end{eqnarray}
for the most general rotational, parity and time
reversal invariant form of the NN force. That means that
the left coefficients, $ t_i \left(p^{\mathrm{f}} , p , x ; E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right)$,
can be obtained directly from the "right" version of LSE.

In order to further check our t-matrix coefficients,
we used them to calculate the partial wave representation
of the t-matrix:
\[
\langle p^{\mathrm{f}} ( l' s ) j \mid t \left( E_{2N}= \frac{ (\mathbf{p}^{\mathrm{f}})^2 }{m}  \right)
\mid p ( l s ) j \rangle,
\]
where $l$ ($l'$) is the initial (final) angular
momentum of the 2N system, $s$ is the 2N (conserved) spin and
$j$ is the 2N (conserved) total angular momentum.
These matrix elements can be compared
with direct solutions of LSE obtained in the standard partial
wave representation. We performed the projection of the three-dimensional
t-matrix on partial waves, employing the simple method
proposed in Ref.~\cite{newpwd} for NN forces.
In Figs.~\ref{f3}-\ref{f6} we show examples for the uncoupled and coupled
channels, with the 2N isospin $t=0$ and $t=1$.  We chose $p^{\mathrm{f}} \approx$ 1.9 fm$^{-1}$,
which corresponds to a relatively high NN center of mass energy, $E_{2N}$= 150 MeV.
For such an energy many partial waves contribute to the NN scattering observables
and the question arises if the partial contributions are consistent
with the full three-dimensional calculations. From Figs.~\ref{f3}-\ref{f6}
(and many other cases which are not shown here) we infer that this is really
the case. The agreement between results based on the two quite different
approaches is very good.

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{thalf.1s0.P0_1.90.re.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.1s0.P0_1.90.im.eps}
\caption{The real (left) and imaginary (right) parts of the
half-shell $^1S_0$ t-matrix as a function of the
initial momentum $p$ for $p^{\mathrm{f}} \approx$ 1.9 fm$^{-1}$.
Points represent predictions obtained by a projection
from the three-dimensional results. Solid lines represent
direct solutions of LSE in the standard partial wave decomposition.}
\label{f3}
\end{figure}

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h5.P0_1.90.re.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h5.P0_1.90.im.eps}
\caption{The same as in Fig.~\ref{f3}
for the half-shell $^3H_5$ t-matrix.}
\label{f4}
\end{figure}

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3p2.P0_1.90.re.a.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3p2.P0_1.90.im.a.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3p2.P0_1.90.re.b.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3p2.P0_1.90.im.b.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3p2.P0_1.90.re.c.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3p2.P0_1.90.im.c.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3p2.P0_1.90.re.d.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3p2.P0_1.90.im.d.eps}
\caption{The same as in Fig.~\ref{f3}
for the half-shell $^3P_2-^3F_2$ t-matrix. Rows
show different $l$ and $l'$ cases (from top to bottom):
($l=1$, $l'=1$),
($l=3$, $l'=1$),
($l=1$, $l'=3$) and
($l=3$, $l'=3$).
}
\label{f5}
\end{figure}

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h6.P0_1.90.re.a.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h6.P0_1.90.im.a.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h6.P0_1.90.re.b.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h6.P0_1.90.im.b.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h6.P0_1.90.re.c.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h6.P0_1.90.im.c.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h6.P0_1.90.re.d.eps}
\includegraphics[width=0.45\textwidth,angle=0]{thalf.3h6.P0_1.90.im.d.eps}
\caption{The same as in Fig.~\ref{f3}
for the half-shell $^3H_6-^3J_6$ t-matrix. Rows
show different $l$ and $l'$ cases (from top to bottom):
($l=5$, $l'=5$),
($l=7$, $l'=5$),
($l=5$, $l'=7$) and
($l=7$, $l'=7$).
}
\label{f6}
\end{figure}

The final ingredient in our framework is the 2N current operator. It consists
of the single-nucleon and two-nucleon operators. For the purpose
of this paper we assume that its single-nucleon part comprises the standard nonrelativistic
charge density as well as the convection and spin current operators. In the 2N part we take
for simplicity only the leading one-pion-exchange current operator in the chiral
effective field theory representation. In our three-dimensional treatment
of the $ ^2{\rm H} ( e, e' p) n $ reaction, we calculate the spin and isospin
matrix elements of the current operator directly, using simple matrix representations
of the spin and isospin operators and the concept of the Kronecker product to deal
with the two-nucleon spin and isospin spaces. In the traditional calculations,
a partial wave decomposition of the current operator is required.
It is a rather easy task for the single-nucleon part of the current.
For the one-pion-exchange current operator it is known analytically
(see for instance Ref.~\cite{kotlyar}). It can also be obtained using the method
proposed in Refs.~\cite{rozpedzik1,rozpedzik2}, where even more complicated
two-pion-exchange current operators were considered.

To give examples of our results on deuteron electro-disintegration we chose several electron kinematics
given in Table~\ref{6kinematics}. They allowed us to study the reaction
for three different internal nucleon-nucleon energies (corresponding to the
three values of $p^{\mathrm{f}}$) and for five values of the three-momentum transfer
$Q$. The first parameter is the input for the t-matrix calculations
and the second one specifies the properties of the current matrix elements.

\begin{table}[hp]\centering
\caption{\label{6kinematics} The six electron kinematics
considered in the paper for the exclusive
$ ^2{\rm H} ( e, e' p) n $ process.
The initial electron energy ($E_{e}$), the electron
scattering angle ($\theta_e$), the final electron energy ($E_{e}'$),
the final relative nucleon-nucleon momentum ($|\mathbf{p^{\mathrm{f}}}|$), the energy transfer
($\omega$), and the magnitude of the three-momentum transfer ($Q$) are given.
}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 &  $E_{e}$  & $\theta_e$  & $E_{e}'$ &  $p^{\mathrm{f}}$ of Eq. (\ref{relmom})  & $\omega = E_{e} - E_{e}'$ & $Q$ of Eq. (\ref{momentumQ}) \cr
 &  MeV & deg         &  MeV &  MeV/c &  MeV     &  MeV/c \cr
 \hline
$K1$ &  500 &  6.9 &490.3  & 78.1 &  9.7&  60 \cr
$K2$ &  500 & 17.4 &485.3  & 78.1 & 14.7& 150 \cr
$K3$ &  500 &  6.1 &467.0 & 158.7 & 30.0 & 60 \cr
$K4$ &  500 & 36.4 &447.0 & 158.7 & 53.0 &300 \cr
$K5$ &  500 & 16.3 &337.1 & 375.3 &162.9 &200 \cr
$K6$ &  500 & 73.7 &281.2 & 375.3 &218.8 &500 \cr
\hline
\end{tabular}
\end{table}

In addition to the information given in Table~\ref{6kinematics},
we need to label the exclusive kinematics. For the fixed "electron arm",
we deal in fact with a two-body kinematics in the final proton-neutron
system. We restrict ourselves here to the case where the proton is ejected in the electron plane,
where $\theta_p$ would be the angle between the three-momentum transfer $\vec Q$
and the final proton momentum $\vec p_p$.
Since we have to distinguish between the $\phi_p$=0 deg and $\phi_p$=180 deg
cases, we ascribe the negative sign to $\theta_p$ for $\phi_p$=0 deg.
This is shown in Fig.~\ref{f7}.
Note that the six electron kinematics
provide a unique solution for any $\theta_p$ value and that
$\theta_p$ changes from 0 do 180 degrees.

\begin{figure}[hp]\centering
\includegraphics[width=4cm,angle=0]{kinematics_pQ.eps}
\caption{The kinematics for the exclusive $ ^2{\rm H} ( e, e' p) n $ process.
$\vec k$ ($\vec k'$) is the initial (final) electron momentum.
We neglect the electron mass, so $\mid \vec k \mid = E $ and  $\mid \vec k' \mid = E' $.}
\label{f7}
\end{figure}

We are now ready to show our results for several selected observables.
We chose first of all the unpolarized cross section,
$d^5\sigma/( dE_{e'}\; d\Omega_{e'}\; d\Omega_{p}\; )$.
We take also into account
one example of the spin-dependent helicity asymmetry,
\[
 A_\parallel \equiv \frac{ \sigma (h=+1, {\vec J}_d ) - \sigma (h=-1, {\vec J}_d ) }
                         { \sigma (h=+1, {\vec J}_d ) + \sigma (h=-1, {\vec J}_d ) } \,
\]
where $h$ is the initial electron helicity and the projection of the initial deuteron total angular momentum ($\mathbf{J}_{d}$) on $\vec Q$, $ J_{dz}$, is equal 1.
In addition we show our predictions for the deuteron tensor analyzing powers $T_{kq}$. Note that
they are calculated in the system, where $\vec Q \parallel \hat z$.

Our primary goal was to compare results based on the partial wave decomposition for
the t-matrix and the nuclear current operator with new predictions resulting from the
three-dimensional scheme. We observed
a perfect agreement for all the electron kinematics and for all
the considered observables, if a sufficient number
of partial waves in the first type of calculations is included.
The six kinematics can be divided into two groups: ($K1$ , $K3$ , $K5$) and ($K2$ , $K4$ , $K6$). In each group a similar type of convergence of the observables with respect to the number of partial waves is observed.
That is why
in Figs.~\ref{f14}--\ref{f25} we show predictions for two representative
($K3$ and $K6$) kinematics only. In the first case we see a rapid convergence
and partial wave based results with $ j \le 4$ are already very close
to the full three-dimensional prediction. In the second case all partial waves
with $ j \le 9$ are necessary to achieve convergence.

It is interesting to see that slow convergence for the
$K2$, $K4$ and $K6$ kinematics does not result from the higher
$p^{\mathrm{f}}$ values (that is from the t-matrix)
but is related to the $Q$ values and thus to the partial wave decomposition
of the current operator. It is well known (see for example Ref.~\cite{rozpedzik1})
that especially the partial wave decomposition of the single nucleon current
requires many partial waves. However, even if the initial bound state
is given in the partial wave representation, the single nucleon
current can be applied directly in the case of the plane wave amplitudes.
This holds not only for the two- but also for the three-nucleon
system~\cite{report2005}. In order to demonstrate this behaviour,
we showed in Fig.~\ref{f26} observables for the $K6$ kinematics.
In this case the single-nucleon current contribution to
the plane wave amplitude is calculated without partial wave
decomposition. We clearly see that the convergence is significantly
improved, even if the two-nucleon current
contribution to the plane wave part of the nuclear matrix element
and the whole rescattering part of the nuclear matrix element
is calculated with the partial wave decomposition.

\clearpage

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.sigma.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.sigma.3.eps}
\caption{The unpolarized cross section $d^5\sigma/( dE_{e'}\; d\Omega_{e'}\; d\Omega_{p}\; )$
as a function of the proton scattering angle $\theta_p$
for the $K3$ electron kinematics from Table~\ref{6kinematics}.
In the left panel plane wave results (dashed line) are compared
with results of the full calculations (solid line) obtained within
the same three-dimensional scheme.
In the right panel convergence of the full results calculated
with a different number of nucleon-nucleon partial waves
towards the full three-dimensional
prediction (solid line) is shown.
Partial wave based results with
$ j \le 1 $ (dash-dotted line),
$ j \le 2 $ (dotted line) and
$ j \le 4 $ (dashed line) are displayed.}
\label{f14}
\end{figure}

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.asympara.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.asympara.3.eps}
\caption{The same as in Fig.~\ref{f14} for the spin-dependent
helicity asymmetry $A_\parallel$.}
\label{f15}
\end{figure}

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.it11.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.it11.3.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.t20.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.t20.3.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.t21.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.t21.3.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.t22.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_30.0_Q_60.0.t22.3.eps}
\caption{The same as in Fig.~\ref{f14} for the
deuteron analyzing powers $T_{kq}$.}
\label{f16}
\end{figure}

\clearpage

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.sigma.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.sigma.3.eps}
\caption{The same as in Fig.~\ref{f14} for the $K6$ electron
kinematics from Table~\ref{6kinematics}.
In the right panel
partial wave based results with
$ j \le 4 $ (dash-dotted line),
$ j \le 7 $ (dotted line) and
$ j \le 9 $ (dashed line) are compared
with the full three-dimensional
prediction (solid line).}
\label{f23}
\end{figure}

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.asympara.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.asympara.3.eps}
\caption{The same as in Fig.~\ref{f23} for the spin-dependent
helicity asymmetry $A_\parallel$.}
\label{f24}
\end{figure}

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.it11.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.it11.3.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t20.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t20.3.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t21.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t21.3.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t22.4.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t22.3.eps}
\caption{The same as in Fig.~\ref{f23} for the
deuteron analyzing powers $T_{kq}$.}
\label{f25}
\end{figure}

\clearpage

\begin{figure}[hp]\centering
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.sigma.2.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.asympara.2.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.it11.2.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t20.2.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t21.2.eps}
\includegraphics[width=0.45\textwidth,angle=0]{OMEGA_218.8_Q_500.0.t22.2.eps}
\caption{Various observables for the $K6$ electron
kinematics from Table~\ref{6kinematics}. The single-nucleon current contribution
to the plane wave part of the nuclear matrix element is now calculated
without partial wave decomposition. The remaining parts of the nuclear
matrix element are still calculated using
partial waves. Results obtained with
$ j \le 1 $ (dash-dotted line),
$ j \le 2 $ (dotted line) and
$ j \le 3 $ (dashed line) are compared
with the full three-dimensional
prediction (solid line).}
\label{f26}
\end{figure}

\section{Conclusions and outlook}

The presented method to treat several electroweak processes involving 1N and 2N current operators in three dimensions can successfully replace standard partial wave treatment. We showed, for the case of electron induced deuteron disintegration, that results obtained using the new approach agree very well with those obtained using PWD. For all observables considered in this paper, the traditional results converge to the three dimensional predictions when the number of partial waves is sufficiently high (Figs.~\ref{f14}--\ref{f25}).

Our formalism employs the two nucleon bound state,
the 2N $t$ matrix
and the current operators in the joined isospin - spin space of the 2N system using the three dimensional formalism in 2N momentum space. Each element of this framework has been separately tested and compared with the standard PWD approach. Our method seems to be more flexible and can deal with the rich structures of the 2N force and the current operator, especially derived within the higher orders of the chiral effective field theory \cite{Epelbaum:2004fk,2Ncurrents,2Ncurrents1}. We plan to use our framework for other processes such as muon capture or neutrino induced deuteron disintegration. In \cite{Marcucci:2010ts} muon capture on $^{2}$H and $^{3}$He was considered using the PWD approach. It would be interesting to compare those results with three dimensional calculations. A similar convergence to three dimensional results as in Figs.~\ref{f14}--\ref{f25} is expected.

\section*{Acknowledgements}

We acknowledge support by the Foundation for Polish Science - MPD program, co-financed by the European Union within the Regional Development Fund. This work was supported by the Polish National Science Center under Grant No. DEC-2011/01/B/ST2/00578 and partially by the EU HadronPhysics3 project "Exciting Physics Of Strong Interactions".

One of the authors (JG) would like to thank K. Sagara
for the hospitality extended to him during his stay
at the Kyushu University and E. Epelbaum
for the hospitality extended to him during his stay
at the Ruhr-Universit\"at, Bochum.
KT would like to thank Ulf-G. Mei{\ss}ner
for the hospitality extended to him during his stay at the Institut f\"{u}r Kernphysik in the Forschungszentrum J\"{u}lich.
The numerical calculations have been partly performed on the supercomputers of the JSC, J{\"u}lich, Germany.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


text:
Dr. David Gratzer
About Dr. Gratzer
About the Readings of the Week
Further Writings
Reading of the Week: The Best of 2019
Reading of the Week: Lithium Prescribing – Rare, Too Rare (CJP)? Also, Social Media & Medical Research (Nat Med) and Chocolate Survival Time (BMJ)
Reading of the Week: A Century After Osler, Is He Relevant (NEJM)? Also, AI & Diagnosis (CMAJ) and Ketamine & Safety (JAD)
Reading of the Week: Better PTSD Symptom Control, Less Diabetes (JAMA Psych)? Also, Buckley on Cannabis (Quick Takes), and the Life of Kajander (Globe)
Reading of the Week: The Advocates – Beattie on Her Illness (Lexpert), Goldbloom on Progress Made (CBC Radio)
Susan Inman on Reading of the Week: PTSD – More Common in High-Income Countries? The New BJP Open Paper; Also, the Trauma of 911 & Torrey on His Sister
Susan Inman on Reading of the Week: Is Adult Mental Illness More Common? The New Acta Paper; Also, Hill on Cannabis & Neustadter's Med School Experience
Susan Inman on Reading of the Week: Care – At the System Level, At the Individual Level
Susan Inman on Reading of the Week: Who is at Risk for Daily Cannabis Use? What Should Every Physician Know About Global Psychiatry? And Hussein on Her Psychotic Break
Susan Inman on Reading of the Week: Can Psychotherapy Help Inpatients? Why did Michael Wilson Speak Out? Are Patients Experts?
Reading of the Week: Mental Health's Funding Problem – the New Wang Paper; Also, the Life of Jimmie Holland
January 11, 2018 / David Gratzer / Comments Off on Reading of the Week: Mental Health's Funding Problem – the New Wang Paper; Also, the Life of Jimmie Holland
As we start 2018, additional funding for mental health care is widely discussed.
But what are current funding levels? How have they changed over the past decade? Which provinces are funding more and which are funding less? A new paper just published by The Canadian Journal of Psychiatry attempts to answer these questions. While the paper looks at different aspects of funding, it reaches a surprising conclusion: between 2003 and 2013, "the percentage of mental health costs with respect to total provincial public health care expenditures decreased overall…"
In this Reading, we review that paper and consider the broader implications.
In the second selection, we consider the life and contributions of Dr. Jimmie Holland, who recently passed. Dr. Holland has been called the "mother" of psycho-oncology.
Provincial Spending and Mental Health
"Public Expenditures for Mental Health Services in Canadian Provinces"
Jian Wang, Philip Jacobs, Arto Ohinmaa, Anne Dezetter, and Alain Lesage
The Canadian Journal of Psychiatry, 11 December 2017 (Online First)
http://journals.sagepub.com/doi/full/10.1177/0706743717741059
According to the Canadian Community Health Survey–Mental Health component, conducted by Statistics Canada in 2012, 10.1% or approximately 2.8 million Canadians aged 15 and older experienced at least 1 mental or substance use disorder, including depression, bipolar disorder, generalized anxiety disorder, or alcohol, cannabis, or substance abuse or dependence, in the 12 months prior to the survey. Statistics from the Mental Health Commission of Canada (MHCC) revealed that more than 6.7 million people in Canada are currently living with a mental disorder or illness. Even though a number of public services and programs that target this group are provided with funding from a range of health and nonhealth ministries, the magnitude of the expenditures is seldom estimated.
In an article in the Canadian Journal of Psychiatry in 2008, a wide variety of mental health costs per person and mental health expenditures as a percentage of total health expenditures were reported for the provinces. Jacobs et al. reported that total public and private mental health expenditures in Canada in 2003-2004 amounted to $6.6 billion, of which $5.5 billion was from public sources. Furthermore, public mental health expenditures, a widely used indicator of mental health service availability, was about 6% of the total public health expenditures, with wide variations occurring between the provinces. In the interceding years, a great deal of attention was paid to this issue in reports by the Senate of Canada, the Parliament, and the MHCC. Nevertheless, any policies or programs to promote mental health were left to be implemented by each province. In this article, we consider the publicly funded health care costs associated with mental illness a decade after Jacobs et al. (fiscal year [FY] 2003) estimated expenditures for publicly funded mental health services. We consider data for FY 2013, the most recent year for which data are available, and compare the estimates to those of FY 2003.
Jian Wang
So begins a paper by Wang et al.
Here's what they did:
Drawing on national databases (largely through CIHI), they collected data for several types of expenditures: general hospital, psychiatric hospital, total clinical payments to physicians, community mental health centers, and pharmaceutical services. (Drug spending data was from IMS Health Canada.)
Because of uneven provincial reporting, "expenditures for community mental health are missing from our analysis."
Expenditure data was adjusted for inflation using the provincial Consumer Price Index.
Statistical analyses were done, with expenditures for mental health services expressed per capita and as percentages of total provincial health spending.
Here's what they found:
"Total public spending for the included mental health and addiction programs/services was estimated to be $6.75 billion."
"Of the estimated spending on mental health services, the largest costs were in hospitalization ($4.02 billion, 59.6%), clinical payments ($1.69 billion, 25%), and then prescribed psychotherapeutic medications ($1.04 billion, 15.4%)."
"Overall, inflation-adjusted mental health service costs per capita increased from $135.2 to $192.7 over the 10-year period. The increase varied across provinces, with New Brunswick having the largest, due to increases in hospitalization costs."
"From 2003 to 2013, mental health–related hospital inpatient costs in Canada substantially increased from $70.4 to $104.2 per capita… moreover, the proportion of inpatient costs to total public mental health costs increased by $1.335 billion to 58.1% in 2013."
"[M]ental health services amounted to 4.9% of provincial government health expenditures in FY 2013, compared to 5.4% in FY 2003. Only New Brunswick had an increase, owing to its large increase in mental health hospitalizations." See figure below.
They go on to note:
We measured provincial publicly funded mental health care services for FY 2013, including inpatient services provided by general and psychiatric hospitals, costs of consultations provided by psychiatrists under fee-for-service or alternative payment plans, and prescribed psychotherapeutic medications. Our results during FY 2003 and FY 2013 show that the inflation-adjusted dollar value of public mental health services increased from $135.1 to $192.7 per person. Nevertheless, the percentage of mental health costs with respect to total provincial public health care expenditures decreased overall for the same period, as a national average, from 5.4% to 4.9%.
This is a good paper.
The numbers add nicely to our understanding of national health spending.
Of course, there are limitations to the work. First and foremost: the lack of inclusion of community mental health programs.
We also need to consider the broader context. Here are national health expenditures over that period (source: CIHI).
(Note that total health expenditure includes private spending.) Still, the pattern is clear: while all spending is up, public mental health spending is (relatively speaking) down slightly.
There are many unanswered questions. This paper looked at funding – but what about outcomes? Do people in New Brunswick get significantly better care than those in neighbouring Nova Scotia? How does care (in terms of outcomes) compare in Saskatchewan and Manitoba – two prairie provinces with very different funding stories.
The Life and Career of Jimmie Holland
"Founder, 'Mother' of Psycho-Oncology, Jimmie Holland Dies"
Megan Brooks
Medscape, 28 December 2017
Jimmie C. Holland, MD, known internationally as the founder of the subspecialty field of psycho-oncology, died suddenly on December 24 at age 89.
Dr Holland was an attending psychiatrist and Wayne E Chapman Chair in Psychiatric Oncology at Memorial Sloan Kettering Cancer Center (MSK) in New York City. She was the first chair of MSK's Department of Psychiatry & Behavioral Sciences. She was also professor of psychiatry at Weill Medical College of Cornell University in New York City.
"Jimmie was a pioneer in the truest sense," William Breitbart, MD, chairman, Department of Psychiatry & Behavioral Sciences at MSK, told Medscape Medical News.
"With colleagues, she established a full-time psychiatry service at Memorial Sloan Kettering in 1977 — one of the first of its kind in the field of oncology — and served as its chief from then until 1996. She then became chair of the newly formed Department of Psychiatry and served in that role until 2003. In the interim she founded the American Psychosocial Oncology Society, the International Psycho-Oncology Society, and the international journal Psycho-Oncology," noted Dr Breitbart.
"We've lost a remarkable woman; a once-in-a-generation influencer," he added.
Jimmie Holland
So begins a short article by Megan Brooks describing* the life of Dr. Jimmie Holland.
Dr. Holland was born in Nevada, Texas, in 1928. She received her medical degree from Baylor College of Medicine. She served on many national committees for the American Cancer Society and the National Cancer Institute.
The article notes her many contributions:
"She conducted some of the first studies on the psychological impact of cancer on patients and showed that interventions to address cancer-related anxiety and depression are helpful."
"In 2000, she published a book for patients titled The Human Side of Cancer."
"[She] played a key role in development of the NCCN Distress Thermometer and Problem List for Patients, a psychosocial distress-screening tool that measures a patient's distress level and helps identify those who would benefit from referral to a mental healthcare specialist and closer monitoring."
UHN's Dr. Gary Rodin is quoted: "Jimmie was a role model and a hero to generations of women and men in supportive care — and her legacy of compassion, humanity, and evidence-based psychosocial care have forever transformed what is now considered standard in cancer care. I will miss the twinkle in her eye but I will always be guided by her spirit."
A couple of thoughts:
The New York Times ran a nice obituary. You can find it here: https://www.nytimes.com/2018/01/04/obituaries/jimmie-holland-who-cared-for-the-cancer-patients-mind-dies-at-89.html?_r=0.
Dr. Holland is featured on the website Changing the Face of Medicine. Asked her biggest obstacle, she responds: In the small community in rural Texas [where I grew up], I knew of no women who had become doctors." You can find her profile here: https://cfmedicine.nlm.nih.gov/physicians/biography_152.html.
Reading of the Week. Every week I pick articles and papers from the world of Psychiatry.
Categories: Reading of the Week
Tags: Canadian Journal of Psychiatry, Holland, mental health spending, Wang
« Reading of the Week: The Best of 2017	Reading of the Week: More Demand, Less Physician Care? The New Chiu et al. Paper. Also, CAMH's Really Big Donation »
© 2020 Dr. David Gratzer

redpajama_set_name: RedPajamaCommonCrawl


The liver is the largest organ inside the body, and it plays a vital role. In fact, its function is so important that without it, the body would die within a day. The liver serves as a processing plant for the nutrients obtained from food and a detoxification center for medications.
The liver is the first line of defense against toxins that enter the body. It removes them from the bloodstream before they can reach other organs and be harmful.
That doesn't mean the liver is able to process toxins without any ill effects; some substances will do harm to the liver. In only rare cases does the long-term use of medications cause cirrhosis of the liver or chronic liver damage. However, there are medications and supplements that when taken alone, or mixed with other medications or substances, can cause liver damage.
Liver injury from use or overuse of medications or supplements may be a challenge to diagnose. Often the cause of a drug-induced liver disease is quite apparent to physicians, but in some cases, other causes for liver disease, such as hepatitis, cancer, metabolic disease, or vascular disease, may need to be ruled out first. The medication or supplement that is suspected to be the cause of the liver damage will need to be stopped in order to confirm the diagnosis.
This over-the-counter pain reliever (some brand names include Tylenol and Excedrin) is found in many different oral medications as well as creams and ointments for muscle pain relief. The fact that it is contained in so many different products raises the risk of an accidental overdose and subsequent liver damage.
Taking or using more than one over-the-counter or prescription drugs containing acetaminophen without the guidance of a physician is not recommended, because of the risk of toxicity. Drinking alcoholic beverages regularly while taking acetaminophen can also increase the risk of liver damage.
Drugs used to treat epilepsy (including phenytoin, valproate, carbamazepine) have also been associated with causing drug-induced liver injury. However, because these drugs are used to prevent seizures, the risk of liver damage is typically considered to be outweighed by the benefits in controlling the symptoms of epilepsy.
Antibiotics are commonly used to treat infections, which is perhaps why they are a leading cause of drug-induced liver damage. In most cases the damage is mild, and risk factors include being female, older, having other diseases and conditions, and having liver damage from another antibiotic.
Medications used to treat tuberculosis (including isoniazid and rifampin) have also been found to be a cause of drug-induced liver injury. People taking these drugs are often monitored to ensure their liver enzymes are not going out of the normal range.
This medication, which is used to treat high blood pressure (hypertension), is known to cause liver injury in some cases. More effective and safer anti-hypertensives have become available, which has led to a decrease in the use of this drug. It is typically not recommended for use in patients who are already known to have a liver disorder.
These drugs, used to treat high cholesterol, are very commonly prescribed, and have been known to cause elevated liver enzyme levels in some people. Usually, the problem reverses itself when the drug is stopped, and the damage is not permanent.
Even supplements are known to cause liver damage, including vitamin A (acitretin, etretinate, isotretinoin). When used in excess of 100 times the daily recommended allowance, vitamin A can cause liver injury. These drugs are sometimes used to treat psoriasis or severe acne.
This form of vitamin B is used to treat high cholesterol. It could cause raised liver enzyme levels or liver damage in high doses (many times the recommended daily dosage) in some people. This medication is often started at a lower dose and then increased over time so that the liver can be monitored.
It's important to note that other medications or over-the-counter supplements not listed here could also cause higher than normal liver enzyme levels or cause liver damage.
In some cases, liver damage from medications and supplements is avoidable. Take care to understand the potential risks of medication you are taking, even when they are prescribed by a physician. Use these tips to help avoid drug-induced liver damage.
Only take medications and supplements (even those that are "natural") when truly necessary.
Don't take more than the recommended amount of any medication.
Ensure that all your physicians are aware of all medications you are taking, especially those prescribed by other doctors, or supplements and vitamins you take on your own.
Take care to read labels to ensure that you are not taking more than one medication, cream, or ointment containing acetaminophen at a time.
Tell all your physicians if you have, or have had, liver disease or damage. People who have cirrhosis should be treated by a hepatologist (liver specialist).
Amathieu R, Levesque E, Merle JC, et al. "Severe toxic acute liver failure: etiology and treatment." Ann Fr Anesth Reanim. 2013 Jun;32:416-21. doi: 10.1016/j.annfar.2013.03.004. Epub 2013 May 14. 4 Jun 2015.
American Liver Foundation. "Managing Your Medications." LiverFoundation.org. 14 Jan 2015. 05 Jun 2015.
Devarbhavi H. "An Update on Drug-induced Liver Injury." J Clin Exp Hepatol. 2012 Sep; 2: 247–259. Published online 2012 Sep 21. doi: 10.1016/j.jceh.2012.05.002. 05 Jun 2015.
Is IBD Associated With Liver Diseases?
How Long Will I Live After an Alcoholic Liver Disease Diagnosis?


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text:
(-) Carl LaVO (1)
(-) C P O Bartlett Edited by Nick Bartlett (1)
John B Lundstrom (1)
Paul G Halpern (1)
Back from the Deep
The Strange Story of the Sister Subs 'Squalus' and 'Sculpin'
By Carl LaVO
This epic World War II saga follows the USS Squalus and Sculpin as they play out their dramatic destinies in the Pacific. The author, a seasoned journalist, re-creates their entire perilous journey. The i>Squalus sank during a test dive in 1939, but thirty-three trapped crewmen were saved thanks to the revolutionary use of the McCann diving bell. The Sculpin's role ...
In the Teeth of the Wind
Memoir of the Royal Naval Air Service in the First World War
By C. P. O. Bartlett; Edited by Nick Bartlett
The dawning of aerial warfare is fully recounted in this dramatic memoir of the first bomber squadron mission of the Royal Navy Air Service over the Western Front. The author recounts his own extraordinary 101 missions, including the operation that very nearly decided the war.


Gabriele Ganswindt, Dipl. Psych. is and executive-, career- and life coach, a leadership consultant and underground interfaith minister near Boston, MA. She regularly designs and leads workshops and retreats addressing the strategic questions and facilitating the desired results of a leadership team. She is trained in several large systems change technologies as well as the art and science of generative thinking dialogue. She is an adjunct faculty member of the Massachusetts School of Professional Psychology. She is a frequent keynote speaker on topics related to leadership resiliency, resiliency, reinvention and executive coaching in a turbulent world. She is passionate about living a balanced, deeply purposeful life.


text:
1926: Josef Jakubowski, Weimar Germany wrongful execution	1688: James Renwick, to end the Killing Time
1943: Mildred Fish-Harnack, an American in the German Resistance
February 16th, 2016 Headsman
On this date in 1943, the Milwaukee-born translator and historian Mildred Fish-Harnack was beheaded at Plotzensee Prison — the only American woman executed by Hitler's order.
A graduate student at the University of Wisconsin Milwaukee,* she met German jurist Arvid Harnack when the latter was a visiting scholar at the university's sister campus in Madison.
In 1929, the couple moved to Germany where they worked as academics: Mildred, a teacher of language and literature; Arvid, of economics and foreign policy.
Both watched the rise of Third Reich with growing horror, and soon began converting their circles of academics, artists, and expats into a hive of opposition doing what they could to aid the many classes of excommunicate humans Berlin was busily proscribing. As the Nazi enterprise intensified, that opposition demanded ever more dangerous — more treasonable — extremities.
Good friends with American diplomats, the Harnacks for a time used Arvid's placement in the Reich economic ministry to pass information to the United States. In 1940, they made contact with Soviet intelligence and from that time until the Gestapo snatched them in September 1942 the so-called** Red Orchestra sent furtive coded radio transmissions to Moscow reporting war preparations, economic data, and whatever else their circle could lay hands on among their various posts.
We have treated the fate of the Red Orchestra elsewhere in these pages; Mildred Harnack did not go to the meathook-nooses with her husband Arvid and others on December 22 because she was sentenced initially only to a term of years. These judgments came down at just the same time as the USSR was drowning the Wehrmacht in blood at Stalingrad, so there might have been a bit of personal pique when the Fuhrer personally quashed Mildred's lenient sentence and demanded a, ah, reconsideration.
"And I have loved Germany so much," she murmured as she was thrown under the fallbeil.
There's a Mildred-Harnack-Schule in Berlin (also a Mildred-Harnack-Straße); her birthday, September 16, is observed every year in Wisconsin schools — although Mildred's red associations meant that widespread recognition in her native country had to await the end of the Cold War.
Trailer for a Wisconsin Public Television documentary that can be viewed in full here.
* Then known as the Milwaukee State Normal School.
** Though this is the name history remembers them by, Red Orchestra (Rote Kapelle) was conferred by the German intelligence working to stop them. Confusingly, the name was applied to multiple different, and unrelated, spy networks.
1938: Herman Hurmevaara, Finnish Social Democrat - 2020
1919: Heinrich Bosse - 2019
1917: The only triple hanging in Montana - 2018
1906: Robert E. Newcomb and John Mueller - 2017
1894: Joe Dick, "allowed to go anywhere he desired" - 2015
1318: Dukes Erik and Valdemar Magnusson - 2014
1943: Toralf Berg, Norwegian resistance member - 2013
1912: Thomas Jennings, fingerprinted - 2012
1939: The only triple execution in Manitoba - 2011
1535: Etienne de la Forge, John Calvin's friend - 2010
1495: William Stanley, Lord Chamberlain - 2009
1973: Francisco Caamaño, the Dominican Republic's would-be Fidel - 2008
1942: Eleven members of the Red Orchestra
1941: Maurice Bavaud, who couldn't get a shot off
1943: Red Orchestra members, in the Nazi Paradise
1945: Carl Goerdeler, as penance for the German people
1943: Willi Graf, anti-Nazi medic
1942: Helmuth Huebener, Mormon anti-Nazi
1944: Max Sievers, freethinker
Entry Filed under: 20th Century,Beheaded,Capital Punishment,Death Penalty,Espionage,Execution,Germany,Guillotine,History,Intellectuals,Spies,Treason,USA,Wartime Executions,Wisconsin
Tags: 1940s, 1942, academia, anti-fascists, arvid harnack, february 16, immigrants, mildred harnack, Plotzensee Prison, red orchestra, world war ii
3 thoughts on "1943: Mildred Fish-Harnack, an American in the German Resistance"
Suzy Que says:
Unfortunately, fighting one evil with another one. Russia far surpassed the number of innocent people killed by the regime than did the NAZIs.
Sadly, this kind of story tends to gloss over the horrors of Soviet Russia.
Indeed, Suzy. Because the left dominates academia, we know far too little about Communist atrocities. While I commend anyone who fought against the National Socialists, one wonders what Soviet policies Harnack would have supported if she had lived.
Jim Starrett says:
i am always saddened and shocked when I am introduced to the individuals who especially in the early days of the Third Reich went up against Hitler. In the late 1960's I started my own research committed to the study of this horrific period. My art during the period starting in the late 1970's and up until the present focused on this period. I have not been able to sell my art except in one or two instances. That was never my goal, but I have shown my work in some very reputable galleries and museums. I just retired after 43 years of teaching art and design. I am 79.


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Transistor est un jeu vidéo de type action-RPG de science-fiction développé par Supergiant Games. Le jeu est sorti le  pour Windows et la PlayStation 4. C'est le premier titre du studio depuis la sortie de Bastion.

Synopsis
Red, une célèbre chanteuse dans la cité de Cloudbank, est attaquée par la Camerata. La Camerata est une organisation qui, avec une force robotique appelée le Process, essaye de fonder une ville idéale.
Red ayant perdu sa voix, elle s'empare d'une lame plongée dans le corps de l'inconnu, qui paraît être très proche de Red, et décide de se venger de la Camerata. Il s'avère que le Transistor (qui vient du Transistor) parle avec la voix du jeune homme tué. La lame va donc être le narrateur durant toute l'histoire. Le but de Red va être de découvrir le but de la Camerata et d'arrêter le Process, qui commence à détruire la ville et ses habitants.

Histoire

Le jeu commence avec le personnage de Red, agenouillée près du corps de l'Inconnu qui a été tué par le Transistor. Red est une chanteuse et l'attaque qui a tué le jeune homme lui a aussi volé sa voix. La conscience de l'homme ainsi que la voix de Red résident maintenant dans le Transistor. Ainsi la voix de l'homme va guider le joueur à travers la ville de Cloudbank, dans ses différents districts. Le joueur va se trouver confronté à une entité robotique intelligente appelée Process.

En étant dans le district de Goldwalk, Red découvre que le Process est contrôlé par la Camerata, un groupe de personnes haut placées. Ce sont elles qui ont essayé de tuer Red. Au fur et à mesure de l'aventure, Red découvre des citoyens ayant été tués et presque transformés par le Process, et absorbe leur conscience dans le Transistor. Retournant sur la scène où Red avait chanté la veille, elle rencontre Sybil Reisz, une membre de la Camerata qui fut amie de Red avant son assassinat. Red affronte donc Sybil qui a été « Processisée » et absorbe sa conscience dans le Transistor. Red l'utilise pour localiser le leader de la Camerata et l'un des administrateurs de Cloudbank, Grant Kendrell.

Musique
La bande-son de Transistor a été composée par Darren Korb, qui est également le compositeur de Bastion, le précédent jeu du studio Supergiant Games, avec la participation à la voix par Ashley Barrett sur les titre The Spine, In Circles, We All Become, Signals et Paper Boats.

Développement

Accueil

Transistor reçoit un accueil favorable de la presse vidéoludique. Il reçoit une note moyenne de 83 % sur Metacritic pour les versions PC et PS4 lors de leur sortie le  et de 93% sur la sortie du  sur iOS.

Notes et références

Liens externes

Action-RPG
Jeu vidéo sorti en 2014
Jeu vidéo développé aux États-Unis
Jeu vidéo indépendant
Jeu vidéo cyberpunk
Jeu Windows
Jeu Mac
Jeu Linux
Jeu PlayStation 4
Jeu iOS
Jeu vidéo avec une musique composée par Darren Korb

redpajama_set_name: RedPajamaWikipedia


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The Council on Foundations defines a family foundation as one whose funds are derived from members of a single family, though this is not a legal term and has no precise definition. The Council on Foundations suggests that family foundations have at least one family member serving as an officer or board member of the foundation and, as the donor, that individual (or a relative) must play a significant role in governing and/or managing the foundation. Most family foundations are run by family members who serve as trustees or directors on a voluntary basis. In many cases, second- and third-generation descendants of the original donors manage the foundation.
Family foundations make up over half of all private (family, corporate, independent, and operating) foundations, or 40,456 out of approximately 73,764 foundations (Foundation Center, 2011). Family foundations make up approximately one-third of the Council's membership.
Family foundations range in asset size from a few hundred thousand dollars to more than $1 billion. The holdings of family foundations total approximately $294 billion, or about 44 percent of all foundation holdings of $662 billion. Despite this, three out of five family foundations hold assets of less than $1 million. Family foundations gave away approximately $21.3 billion in grants in 2011 (The Foundation Center, 2011).
Below is everything on our site for family foundations. You can use the filtering options on the right to narrow these results.
Sample Policy on Records Retention and Destruction
Sample formal policy on records retention and destruction for board approval.
This sample document is being provided for informational purposes and is not to be shared without the permission of the Council on Foundations. Use of the sample document does not create an attorney-client relationship, and the information provided is not a substitute for expert legal, tax or other professional advice tailored to your specific circumstances. The information may not be relied upon for the purposes of avoiding any penalties that may be imposed under the Internal Revenue Code.
Sample Due Diligence Policy for Grantmaking
Sample internal policies and proceedures for grantmaking due diligence.
This sample document is being provided for informational and is not to be shared without the permission of the Council on Foundations. Use of the sample document does not create an attorney-client relationship, and the information provided is not a substitute for expert legal, tax or other professional advice tailored to your specific circumstances. The information may not be relied upon for the purposes of avoiding any penalties that may be imposed under the Internal Revenue Code.
Sample Nondiscrimination Policy
Sample nondiscrimination policy for hiring, internal promotions, training, opportunities for advancement, and terminations.
Sample Bylaws & Articles of Incorporation
These sample bylaws and articles of incorporation are not a model to copy; rather they are provided purely to illustrate what such a document might look like. Each state will have its own form or particular requirements to follow, which may differ from state to state.
For other examples and for an in-depth legal view of foundation formation, please see Creating a Charitable Foundation: Formation and Considerations.
Sample Whistleblower Policy
Editable whistleblower policies that establish procedures to prevent or detect and correct improper activities, encourage each Foundation director, officer, employee and volunteer to report what he or she in good faith believes to be a material violation of law, ensure the receipt, documentation, retention of records, and resolution of reports received, and protect reporting individuals from retaliatory action.
CDFI Fund Map of All Census Tracts Eligible for Designation as a Qualified Opportunity Zone
The CDFI Fund has identified over 41,000 population census tracts that are eligible for designation as a QOZ, including (1) 31,680 population census tracts that are Low-Income Communities (LICs) eligible for designation as QOZs; and (2) 9,453 non-LIC population census tracts that are eligible for designation if a particular LIC contiguous to the non-LIC tract is designated as a QOZ. Contiguous Tracts must be at or below 125% of the area median income.
US Impact Investing Alliance Resources on Opportunity Zones
Now that Opportunity Zones have been designated, individual and corporate investors are then given the opportunity to defer capital gains taxes when they reinvest the earnings in these communities. Additional incentives accrue over five, seven and ten years if the investment is maintained – thereby promoting the kind of patient capital that distressed communities so often lack. Get more of the resources you need to learn about Opportunity Zones from the US Impact Investing Alliance.
Mission Investors Exchange Opportunity Zones Resources
The OZ program is intended to spur long-term investments in low-income census tracts in the U.S. The new law allows investors to place unrealized capital gains (a profit from an investment that hasn't yet been sold) into authorized O Funds that invest capital into OZs. The greatest benefits would go to investors who invest for 10 or more years. Learn more from the Mission Investors Exchange about the benefits, risks, and potential of opportunity zones.
LOCUS National Opportunity Zones Ranking Report
With the creation of the federal Opportunity Zones incentive program, trillions of dollars in new private investment will flow into pre-designated low-income communities around the country. But will this investment benefit the people living in these communities now, or will they be displaced as new interest and development brings increased property values and rents? And what kind of development will result —unsustainable, car-dependent sprawl (the dominant growth paradigm in the United States today) or walkable, mixed-use communities with a variety of housing options for everyone?
Department of the Treasury Opportunity Zones Resources
Treasury and IRS have issued an initial set of proposed regulations and guidance on how the Qualified Opportunity Zone tax benefits under IRC 1400Z-2 (including the certification of Qualified Opportunity Funds and eligible investments in Qualified Opportunity Zones) will be administered.
The Long Haul: Lessons From Charitable Responses to Previous Disasters
Advice from the Field: Responding to Mass Casualty Events
Basic Tips for Disaster Giving
Disaster Relief: A Practical Guide for Foundations and Corporations
We Were There: The Role of Philanthropy in National Disasters


Alongside the Butterworth exhibition at the International Anthony Burgess Foundation in August–September of this year, The Exhibition Centre for the Use and Abuse of Books presented an evening of talks accompanying Gareth Jackson's Lord Horror — The Dark and Silver Age, an experimental film based on the Lord Horror oeuvre. This included presentations from broadcaster and art critic Bob Dickinson, art historian and journalist Michael Paraskos, and academic Jonathan Barlow, discussing Lord Horror and the culture surrounding Savoy.
To concide with this, The Exhibition Centre for the Use and Abuse of Books also commissioned a series of short films from seven artists and artist collectives who were asked to respond to the pre-Savoy small-press magazine, Corridor, published in the 1970s. Clara Casian's Burroughsian film short, A Savoyard's First Brush with Censorship, which uses Corridor #2 as its jumping-off point, is a film that looks at the context behind censorship in 1970 Manchester through personal stories, records and archive footage. Casian is currently working on a feature-length expansion for wider release.
The Butterworth exhibition was the culmination of an eventful two years for Savoy. Rising academic interest in the company started with the long-awaited publication of our graphic series Reverbstorm in book form in January 2013, and continued in November 2013 with publication of David Brittain's Eduardo Paolozzi at New Worlds, a study of the artist's connections with the British wing of the so-called New Wave of science fiction in the late 60s and early 70s. Both books featured strongly in the The Science Fiction 'New Wave' At Fifty conference at the University of East Anglia in May of this year.
The Butterworth exhibition will next be seen at Kent State University, Ohio, from January to May 2015.
On their recent tour of the UK, The Magic Band—John "Drumbo" French, Denny "Feelers Reebo" Walley, Mark "Rockette Morton" Boston, Eric Klerks and Andy Niven—played Band on the Wall, Manchester, with Savoyards in attendance. Under the redoubtable French a spellbinding show took place which can be viewed in full and in high-definition here. The best band in the world playing the best music in the world, courtesy of Captain Beefheart RIP.
Since Roger Eagle was mentioned here recently it's worth noting that a radio show of rare reggae and dub tracks from Roger's own collection can now be heard at Mixcloud. Roger was a regular contributor to Steve Barker's On The Wire show on BBC Radio Lancashire, one of the longest-running music shows in the UK, and the show is part of a growing On The Wire archive.
In our obituary notice for the great Roger Eagle (see news for July 2012) we mentioned a rare photo of the man with the equally great Captain Beefheart, taken (at a guess) during one of the Magic Band's excursions into the north of England. The temporary inaccessibility of the photo had caused it to assume fabled status in the Savoy office but here it is at last. Not the best quality since it's been photocopied a couple of times but you're unlikely to see this anywhere else. Had it turned up sooner it would have gone into a recent Savoy pot-pourri. It missed its chance in print so now it's a web exclusive.
Colin Wilson, who died on the 5th December last year, was definitely "something to be".
Wilson's inspirational debut, The Outsider, described in its 1978 edition as "the classic study of alienation, creativity and the mind of modern man", has been in print since its first publication in 1956, and will continue to be reprinted for decades to come. Savoy was privileged to publish a new edition of his uncompromising crime novel, The Killer, with a fresh introduction and additional material; the Savoy edition of David Lindsay's A Voyage to Arcturus featured Wilson's Lindsay essay, 'The Haunted Man', and a new afterword, while another essay, 'The Truth About Wilson' (about wartime comics hero Wilson the Wonder Athlete), appeared in Sieg Heil Iconographers. Wilson provided a splendid review of Robert Meadley's A Tea Dance at Savoy for Headpress magazine, and his philosophy of optimism, honed on the battlefront of a lifelong fight against pessimistic world-views, is crystalised in Colin Wilson: Philosopher of Optimism by Brad Spurgeon, published by a Savoy offshoot.
We regarded Colin Wilson as a brother-in-arms. His sensibilities were always in accord with ours. His unambiguous opinion of A Voyage to Arcturus was brave, bold and definitive: "One of the greatest books of the century. The most extraordinary feat of imagination in English fiction."
After the UK press underwent one of its periodic put-downs of Wilson, Robert Meadley wrote a book-length riposte to his detractors, The Odyssey of a Dogged Optimist, which is available on this site as a free download. The philosophy and fiction of Colin Wilson will continue to be relevant and necessary when the likes of Adam Mars-Jones, Lynn Barber, Humphrey Carpenter and the wretched Clive James are vanishing into a deserved oblivion.
Savoy regard Wilson as a significant writer and autodidact, among the very best of a generation of British literary mavericks that would include JG Ballard, Michael Moorcock, Alan Moore, Derek Raymond, Iain Sinclair and Alan Garner; a company of ferociously talented iconoclasts and anti-establishment figures. Wilson always walked his own path undeterred by the carping of the literary establishment; his thinking broke with hidebound tradition, setting him alongside the outsiders in fiction, philosophy and criminality whose example he spent his life exploring. His favourite hero from the Wizard comic, Wilson the Wonder, is a fitting analogue for one of the 20th century's greatest thinkers: always ahead of his detractors, and clearing obstacles at a single bound.
Presenting Savoy's long-overdue tribute to the most important magazine of the 1960s. Forget Oz magazine and International Times, New Worlds was a pinnacle of the 1960s' counterculture, standing in the same relation to underground publishing as The Beatles did to pop music. Without the example of New Worlds there would never have been a Savoy Books.
From 1964 to 1971, under the far-sighted editorship of Michael Moorcock, New Worlds grew from a small science-fiction monthly to what JG Ballard later called 'one of the most exciting magazines of any kind in this country'. Its writers discarded speculations about future technology and life on other planets, turning their attention to the increasingly technologised media landscape of the 20th century.
In Eduardo Paolozzi at New Worlds: Science Fiction and Art in the Sixties, David Brittain examines the magazine during its prime period, throwing light on the interactions of the art of the time with what Judith Merril and Harlan Ellison called 'the new wave of science fiction'. The work of artist Eduardo Paolozzi was showcased in the magazine along with that of Pop Art colleague Richard Hamilton. Paolozzi's close association with New Worlds was acknowledged via a masthead credit as 'Aeronautics Adviser'.
Brittain's book places Paolozzi's 'science fiction' art of the late '60s in the context of the new SF, and offers fresh insights into the way images and a fragmentary, collaged approach to writing informed the controversial prose of Ballard, Moorcock, Brian Aldiss, Norman Spinrad, M John Harrison and others.
The book contains rare and unseen images from the archives of New Worlds and the Eduardo Paolozzi Foundation, including excerpts from what is thought to be an unpublished science-fiction novel by the artist. There are also new interviews about the magazine and its times with editor Moorcock, art editor Christopher Finch, designer Charles Platt, contributor Michael Butterworth, and critic John Clute.
With an introduction by Rick Poynor, and endpaper illustrations by Pamela Zoline. Design by John Coulthart.
Eduardo Paolozzi at New Worlds is available from Savoy, Amazon and specialist art outlets.
The new hand-grenade of a book from David Britton!
Letting his romancer's torch shine on Holocaustic goings-on in modern-day Manchester, the Mac Daddy Horror sashays forth as a giant glass rapscallion, puffing out his killing philosophy. In their customary role as the Devil's idle hands, Meng and Ecker spread a freaky-deaky comedic 'Umgawa!!!' over Porchfield Gardens.
The Razor Kings' Magic Garden unveils its bounteous nourishing beauty to refugees turned blue from Planet Auschwitz. Oooh'weee. All things are well—not.
Invictus Horror is a one-hundred-and-thirty-page hardback copiously illustrated in black-and-white and colour by Kris Guidio bowing-in at the top of his game.
Available from Savoy or from all good bookshops and Amazon.


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EAPC Home / News / New EAPCers / Welcome Scott Wullschleger
Welcome Scott Wullschleger
Melanie Schmidt, Marketing Assistant
We are pleased to welcome Scott Wullschleger, AIA, as the newest Architect/Project Manager in our St. Paul office.
Scott graduated from North Dakota State University in 2012 with his Master of Architecture degree then began his architectural career at a firm in Mankato, MN where his project work included healthcare, multi-family residential, banks, and retail.
In 2016, Scott went to work as an Architectural Designer at Nor-Son in Wayzata, MN designing high-end single-family homes. Over a five year period, Scott was employed with another firm in Hopkins where his project work included restaurants, clinics, offices, and industrial buildings. Most recently, Scott worked at HDR in Minneapolis where he managed several healthcare projects including a recent 16,000 SF behavioral health unit.
At EAPC, Scott will utilize his extensive experience within our healthcare sector, focusing on clinics, hospitals, and behavioral health. "Scott is not only a significant addition to the St. Paul office but will be an asset to EAPC across the region. He is a real team player and his leadership and communication skills have been demonstrated routinely as he has led the design and production of multiple healthcare projects," said Jim Anderson, St. Paul Office Manager.
Growing up in Mankato, Scott took interest in travel, particularly family trips to Disney where he was inspired by the diverse architecture. "Although Walt Disney World tends to be viewed as inauthentic in our industry, it was my introduction to how design can shape experience. As I grew older, I found an appreciation for the urban planning aspect and the connectivity through mass transit and extensive walking paths. It also provided me glimpses of other destinations I would go on to explore," said Scott.
When not designing, Scott and his wife Laura enjoy time with their two girls, Odella (3 years) and Jolie (6 mos). They love to travel when they can and plan on some trips back to Disney with the girls.
Welcome to EAPC, Scott!
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