text:
\section{Introduction} The Standard Model of elementary particles naturally incorporates the sources for $CP$ (charge and parity) violation represented by the Cabibbo–Kobayashi–Maskawa (CKM) matrix \cite{C,KM} and the QCD vacuum angle\ \cite{Peccei1977,Weinberg1978,Wilczek1978} (see also Refs.\ \cite{yamanaka2017,chupp2019} and further references therein). While the elements of the CKM matrix are measured to a high accuracy, the exact value of the QCD vacuum angle $\bar{\theta}$ is not known. In recent years, the precision in modern atomic and molecular EDM experiments has been improved to such a level that constraints on $\bar{\theta}$ and other $CP$-violating parameters imposed by these experiments are approaching or even exceeding those of particle physics\ \cite{Griffith2009,Baker2006,Hudson2011,Baron2014,Parker2015,Pendlebury2015,Graner2016}. For example, experiments with diamagnetic atoms and molecules targeting the nuclear Schiff moments have placed significant bounds on the nucleon EDMs
\cite{Harrison1969,Hinds1980,Wilkening1984,Schropp1987,Cho1991,Vold1984,Chupp1994,Stoner1996,Bear1998,
Rosenberry2001,romalis2001,Griffith2009,Graner2016,Parker2015,Bishof2016} whereas those using paramagnetic polar molecules \cite{Hudson2011,Loh2013,PbO2013,HfF2017,BaF2018,ACMEII} give rise to the most stringent constraints on the electron EDM.

In paramagnetic atoms, an atomic EDM may be induced by the following contact $CP$-odd semileptonic operators
\begin{equation}\label{contact-interaction}
{\cal L} = \frac{G_F}{\sqrt2}  C_{SP}^p\, \bar e i \gamma_5 e\,
\bar p p
+ \frac{G_F}{\sqrt2} C_{SP}^n\, \bar e i \gamma_5 e\,
\bar n n \,,
\end{equation}
where $G_F$ is the Fermi coupling constant, $e$, $p$ and $n$ are respectively the electron, proton and neutron fields; $C_{SP}^p$ and $C_{SP}^n$ are the electron couplings to the proton and neutrons, respectively. The subscript $SP$ denotes the nucleon-scalar and electron pseudoscalar two-fermion bilinears.

In polarised polar molecules, the interaction\ \eqref{contact-interaction} induces shifts of energy levels. The measurement of these shifts places constraints on the value of $C_{SP}\equiv C_{SP}^p Z/A + C_{SP}^n N/A$, where $A$ and $Z$ are the nuclear mass and charge numbers, and $N=A-Z$ is the number of neutrons. The most stringent constraint on $C_{SP}$ is placed by the ACME collaboration\ \cite{ACMEII}, which used the molecule $^{232}{\rm ThO}$, (90\% C.L.)
\begin{equation}
    \left|C_{SP}\right|_{\rm Th}
< 7.3 \times 10^{-10}\,.
\label{Csp-constr}
\end{equation}

The coupling constant $C_{SP}$ receives contributions from various sources, which include interactions with the nucleon EDM $d_{p,n}$. The parameters $d_{p,n}$ may, in turn, be expressed in terms of more fundamental ones, namely, the $CP$-odd $\pi$-meson-nucleon coupling constants $\bar g^{(0,1)}_{\pi NN}$, the quark chromo-EDMs $\tilde{d}_{d,u}$ and the QCD vacuum angle $\bar{\theta}$. Our aim is to determine the leading dependence of $C_{SP}$ on the parameters $d_{p,n}$, $\bar g^{(0,1)}_{\pi NN}$, $\tilde{d}_{d,u}$ and $\bar{\theta}$ for ${}^{232}$Th and several other atoms of experimental interest, including Ba, Yb, Hf, Pb and Ra. Note that $CP$-violating effects rapidly increase with nuclear charge (see next sections). Therefore, in molecules the effects come from the heaviest nucleus.

In a recent paper \cite{FPRS}, the contributions to $C_{SP}$ from the two-photon and $\pi,\eta$-meson exchanges between electrons and nucleons were calculated. These contributions led to a limit on the QCD vacuum angle $|\bar{\theta}|\lesssim 3\times 10^{-8}$. In this paper, we take into account additional contributions to  $C_{SP}$ which are comparable or even bigger than those calculated in Ref.~\cite{FPRS}, namely, contribution of nucleon transitions in discrete spectrum (which are enhanced by small energy denominators in perturbation theory). We take into account the effect of the  Coulomb interaction in intermediate electron states. In heavy atoms like thorium with $Z=90$, the parameter $Z \alpha \sim 1$ and the Coulomb interaction is important.

As we will demonstrate further, the addition of the new contributions allows us to significantly improve the limits on the QCD vacuum angle and other $CP$-violating hadronic parameters. We stress that these results play important role in the search of axion-like dark matter \cite{Roussy2020} which manifests itself as  oscillating $\bar\theta$-term (see, e.g., Ref.\ \cite{Graham-Rajendran}).

It is important to note that, according to a theorem by Schiff \cite{Schiff}, atomic electrons completely shield the nuclear EDM. However, it can be measured through the nuclear Schiff moments and magnetic quadrupole moments \cite{Schiffmoment1,Schiffmoment2,quadrupole}, or by means of applying an oscillating electric field and observing nuclear spin rotations as argued in the Refs.~\cite{Dzuba86,Victor18,my1,my2,my3}. However, since the Schiff theorem applies only to a system which interacts electrically, the interaction of the atomic electrons with the magnetic dipole moment of the nucleus allows for a non-zero atomic EDM induced by a nuclear EDM \cite{Schiff}. This paper is devoted to the study of the mechanism for the production of the atomic EDM from the combined electric and magnetic interactions between the atomic electrons and the nucleus.

In Ref.~\cite{Ginges}, it was argued that for atoms with vanishing nuclear spins there are no non-vanishing contributions to the atomic EDM from $CP$-violating nuclear scalar polarizability. However, the analysis of Ref.\ \cite{Ginges} did not take into account specific near-nucleus electronic contributions which cannot be reduced to the $CP$-violating nuclear scalar polarizability and are significantly enhanced by relativistic effects in heavy atoms. Indeed, since the electronic $s$ and $p$ Dirac wave functions for a point-like nucleus are singular at the origin, the electronic matrix elements between these states are formally divergent and thus make significant contributions to the induced atomic EDM. In this paper, we will systematically analyze the contributions to the atomic EDM from such matrix elements in atoms with vanishing nuclear spins and compare them with those arising from the contact electron-nucleon interaction \eqref{contact-interaction}. This will allow us to obtain the leading-order dependence $C_{SP}=C_{SP}(d_{p,n},\bar g^{(0,1)}_{\pi NN},\tilde{d}_{d,u},\bar{\theta})$ for several atoms of experimental interest and deduce improved limits on the $CP$-violating hadronic parameters.

The rest of the paper is organized as follows. In Sect.~\ref{Atomic EDM due to contact electron-nucleon interaction}, we present an estimate for the atomic EDM arising from the contact electron-nucleon interaction. Section \ref{Contribution to the atomic EDM from nucleon permanent EDMs} is devoted to the computation of the atomic EDM induced by nucleon permanent EDMs. In Sect.~\ref{Constraints}, we compare the contributions to the atomic EDM from the contact electron-nucleon interaction and the nucleon permanent EDMs and find relations between the constant $C_{SP}$ and $CP$-violating hadronic parameters. In Sect.~\ref{Conclusion} we give a summary of our results and provide some comments on assumptions and precision. Technical details of calculations of electronic and nuclear matrix elements are collected in appendices.

Throughout this paper we use natural units with $c=\hbar=1$.

\section{Atomic EDM due to contact electron-nucleon interaction}
\label{Atomic EDM due to contact electron-nucleon interaction}
In an atom, the $CP$-odd interaction\ \eqref{contact-interaction} between a valence electron and the nucleus is described by the Hamiltonian \cite{NewBounds1985}
\begin{equation}
H_{\rm cont}=\frac{iG_F}{\sqrt{2}}AC_{SP}\gamma_0\gamma_5 \rho({\bf R})\,,
\label{Hcont}
\end{equation}
where $\gamma_0=\left( \begin{smallmatrix}
\mathbbm{1}_{2\times2} & 0 \\ 0 & -\mathbbm{1}_{2\times2}
\end{smallmatrix}\right)$
and $\gamma_5=
\left( \begin{smallmatrix}
0& -\mathbbm{1}_{2\times2}  \\  -\mathbbm{1}_{2\times2} &0
\end{smallmatrix}\right)$ are the Dirac matrices, $\bf R$ is the position vector of the electron and $\rho({\bf R})$ is the normalized nuclear charge density. In the leading approximation, $\rho({\bf R})$ is constant inside the nucleus of radius $R_0$ and vanishes outside, $\rho({\bf R})=3\theta(R_0-R)/(4\pi R_0^3)$, where $\theta(x)$ is the Heaviside step function.

Matrix elements of the operator (\ref{Hcont}) receive non-vanishing contributions only from small distances, where the nuclear density $\rho({\bf R})$ is different from zero. In heavy nuclei, the $s_{1/2}$ and $p_{1/2}$ electron wave functions have large relativistic enhancement inside the nucleus, as compared with other wave functions corresponding to higher angular momenta $l$ which are negligible at the nucleus ($\propto R^l$) \cite{NewBounds1985}. As a result, the atomic EDM receives dominant contributions from the matrix element of the operator \eqref{Hcont} with the $s_{1/2}$ and $p_{1/2}$ states,
\begin{equation}
\label{de_contact}
{\bf d}\approx 2\frac{\bra{s_{1/2}}e{\bf R}\ket{p_{1/2}}\bra{p_{1/2}}H_{\rm cont}\ket{s_{1/2}}}{E_{p_{1/2}}-E_{s_{1/2}}}\,,
\end{equation}
where $E_{{s}_{1/2}}$ and $E_{{p}_{1/2}}$ are the energies of the $s_{1/2}$ and $p_{1/2}$ states, respectively, and $-e$ is the electron charge.

Here, we will estimate the matrix element $\bra{p_{1/2}}H_{\rm cont}\ket{s_{1/2}}$ for heavy atoms. In subsequent sections, this matrix element will be compared with those of $CP$-odd operators originating from nucleon EDMs.

For an atom with a point-like nucleus, the $s_{1/2}$ and $p_{1/2}$ valence electron wave functions have simple analytic expressions, see Eqs.\ \eqref{Bessel}. For an extended nucleus model with constant charge density, it is sufficient to consider a simple continuation of the wave functions \eqref{Bessel} to the region inside the nucleus as
\begin{subequations}\label{psi-ass}
\begin{eqnarray}
\ket{s_{1/2}} &= &c_{s_{1/2}} \frac{ R_0^{\gamma-1}}{\Gamma(2\gamma+1)} \left(\frac{2Z}{a_B}\right)^{\gamma}\left(
\begin{array}{c}
-(\gamma+1) \Omega^{-1}_{\mu } \\
\frac{iZ\alpha R}{R_0}\Omega^1_{\mu}
\end{array}
\right)\,,\\
\ket{p_{1/2}} &= & c_{p_{1/2}}\frac{ R_0^{\gamma-1}}{\Gamma(2\gamma+1)} \left(\frac{2Z}{a_B}\right)^{\gamma} \left(
\begin{array}{c}
\frac{(1-\gamma)R}{R_0} \Omega^1_{\mu } \\
iZ\alpha \Omega^{-1}_{\mu}
\end{array}
\right)\,,
\end{eqnarray}
\end{subequations}
where $\Omega^{\kappa }_{\mu}$ is the spherical spinor, $a_B$ is the Bohr radius, $\gamma=\sqrt{1-Z^2\alpha^2}$ is the relativistic factor and $\alpha\approx1/137$ is the fine structure constant. The values of the normalization constants $c_{s_{1/2}}$, $c_{p_{1/2}}$ are not specified here, as our final results will be independent from these constants.

With the wave functions \eqref{psi-ass}, the matrix element of the operator \eqref{Hcont} reads
\begin{equation}
\bra{p_{1/2}}H_{\rm cont}\ket{s_{1/2}} = -c_{s_{1/2}}c_{p_{1/2}}\frac{G_F C_{SP}}{10\sqrt2\pi}\frac{1+4\gamma}{\Gamma(2\gamma+1)^2}\frac{AZ\alpha}{R_0^2}
\left(\frac{2ZR_0}{a_B}\right)^{2\gamma}.
\label{matrix-contact}
\end{equation}
For heavy nuclei, this matrix element is significantly enhanced due to the factor $AZ^{2\gamma+1}$.
Since we will compare Eq.\ \eqref{matrix-contact} with the contribution from nucleon EDMs, which is not enhanced that strongly, it appears that for the ratio of the effects (which is the contribution from nucleon EDMs to the effective constant $C_{SP}$) lighter nuclei may have bigger $C_{SP}$ than heavy ones.

\section{Contribution to the atomic EDM from nucleon permanent EDMs}\label{Contribution to the atomic EDM from nucleon permanent EDMs}

In this section, we calculate the contribution to the atomic EDM originating from permanent nucleon EDMs. Since electric interactions alone cannot give rise to atomic EDMs due to the Schiff theorem \cite{Schiff}, such a contribution can only arise when both the electric and magnetic electron-nucleon interactions are taken into account. We start with the review of the effective Hamiltonian of this interaction and in subsequent subsections calculate the nuclear and electronic matrix elements of this Hamiltonian.

\subsection{Effective Hamiltonian for the \texorpdfstring{$CP$}{}-odd electron-nucleon interaction}
Let ${\bf d}_i = d_i \boldsymbol{\sigma}_i$ and $\boldsymbol{\mu}_i=\mu_0 (g_i^l {\bf l}_i + g_i^s {\bf s}_i)$ be the operators of electric and magnetic dipole moments of the $i$-th nucleon in the nucleus. Here $d_i = d_{p,n}$ are the proton and neutron permanent EDMs, $\mu_0$ is the nuclear magneton, $g_{i}^l=g_{p,n}^l$ and $g_{i}^s=g_{p,n}^s$ are the orbital and spin $g$-factors of the nucleons. The operators ${\bf d}_i$ and $\boldsymbol{\mu}_i$ couple with the electric and magnetic fields of the valence electron, yielding the interaction Hamiltonian\footnote{In general, in addition to the nucleon EDMs, there are other $CP$-violating operators at hadronic level including three-pion and four-nucleon couplings. In Ref.~\cite{Bsaisou}, contributions to the nuclear EDM due to these operators were found for some light nuclei. In this paper, we focus only on the contributions to the atomic EDM due to the nucleon permanent EDMs.}
\begin{subequations}\label{mix_H}
\begin{align}
H&=-\sum_{i=1}^A\left(H^d_i+H^\mu_i\right)\,,\label{HInt}\\
H^d_i&=\frac{e\,{\bf d}_i\cdot\left({\bf R}-{\bf r}_{i}\right)}{\left|{\bf R}-{\bf r}_{i}\right|^3}\,,\label{HE}\\
H^\mu_i&=\frac{e\,\boldsymbol{\mu}_i\cdot\left[\left({\bf R}-{\bf r}_{i}\right)\times\boldsymbol{\alpha}\right]}{\left|{\bf R}-{\bf r}_{i}\right|^3}\,,
\label{HB}
\end{align}
\end{subequations}
where ${\bf r}_{i}$ are the position vectors of the nucleons and $\boldsymbol{\alpha}=
\left(\begin{smallmatrix}
0 & \boldsymbol{\sigma} \\ \boldsymbol{\sigma} & 0
\end{smallmatrix}\right)$ are Dirac matrices acting on electron wave functions.

The unperturbed atomic states will be denoted by $|mm'\rangle= |m\rangle|m'\rangle$, where $|m\rangle$ and $|m'\rangle$ are electronic and nuclear states, respectively.\footnote{In what follows, the nuclear quantum number will be distinguished from the electronic ones with the apostrophe.} The first-order contributions to the atomic EDM due to the interaction Hamiltonian\ \eqref{mix_H} vanish for spinless nuclei which we consider in this paper, $\langle 0' | {\bf s}|0'\rangle=0$. The leading non-vanishing contributions to the atomic EDM arise in the second order of the perturbation theory (see Ref.\ \cite{Ginges} for further details),
\begin{equation}
{\bf d}= -2\sum_{m,n,n'}\frac{\bra{0}e\mathbf{R}\ket{m}\bra{0'm}H\ket{nn'}\bra{n'n}H\ket{00'}}{\left(E_{m}-E_{0}\right)\left[\Delta E_{n}+{\rm sgn}(E_n)\Delta E_{n'}\right]}\,,\label{datom}
\end{equation}
where the sum is taken over the excited states with $m\ne 0$ and $nn'\ne 00'$. Here, $E_n$ and $E_{n'}$ are energies of electronic and nuclear excitations, respectively, whereas $\Delta E_{n}\equiv E_{n}-E_{0}$ and $\Delta E_{n'}\equiv E_{n'}-E_{0'}$. Note that the sum over the intermediate electronic states $\ket{n}$ includes both positive and negative energy levels which are inherent in Dirac's theory. The negative energy states contribute to Eq.~(\ref{datom}) with opposite sign of $\Delta E_{n'}$ because they may be interpreted as blocking contributions for the electrons from the Dirac sea which cannot be excited to the occupied electron orbitals.  Therefore, contribution of the transitions from the Dirac sea must be subtracted. (See also Refs.~\cite{Plunien91,Pachucki93,Plunien95} for analogous account of the negative energy states within the problem of atomic energy shift due to nuclear polarizability.)

As is argued in Sect.~\ref{Atomic EDM due to contact electron-nucleon interaction}, the atomic EDM \eqref{datom} receives leading contributions from the matrix elements with $\ket{0}=\ket{s_{1/2}}$ and $\ket{m}=\ket{p_{1/2}}$. As a result, Eq.\ \eqref{datom} may be cast in the form  \eqref{de_contact}, with the contact interaction operator $H_{\rm cont}$ replaced with an effective interaction Hamiltonian $H_{\rm eff}$ defined by
\begin{equation}\label{EffectiveMatrixElement}
H_{\rm eff}\equiv -\sum_{nn'\ne 00'}\frac{\ket{m}\bra{0'm}H\ket{nn'}\bra{n'n}H\ket{00'}\bra{0}}{\Delta E_{n}+{\rm sgn}(E_n)\Delta E_{n'}}\,.
\end{equation}
Substituting the operators \eqref{mix_H} into Eq.~\eqref{EffectiveMatrixElement}
and keeping only linear in ${\bf d}_i$ terms we find
\begin{equation}\label{Scalar contribution}
\bra{p_{1/2}}H_{\rm eff}\ket{s_{1/2}}=-\sum_{n' \ne 0'}\sum_{i,j=1}^A\mathcal{M}^{n'}_{ij}\,,
\end{equation}
where $\mathcal{M}^{n'}_{ij}$ is
\begin{equation}\label{ME}
\begin{aligned}
\mathcal{M}^{n'}_{ij}
&=\sum_{n}\frac{\bra{p_{1/2}0'}H^\mu_i\ket{n'n}\bra{nn'}H^d_j\ket{0's_{1/2}}}{\Delta E_{n}+{\rm sgn}(E_n)\Delta E_{n'}}+(s_{1/2}\leftrightarrow p_{1/2})\,.\\
\end{aligned}
\end{equation}
In subsequent subsections, we will compute the nuclear and electronic matrix elements in this expression and present the results for the matrix element (\ref{Scalar contribution}).

\subsection{Integration over radial nuclear coordinates}\label{IIIB}
The form of the nuclear matrix elements $\bra{0'}H^\mu_i\ket{n'}$ and $\bra{0'}H^d_i\ket{n'}$ depends on the specific nuclear model. To compute these matrix elements we consider an approximation in which the nuclear wave functions are given by
\begin{equation}\label{NucWave}
\ket{n'}=\prod_{i=1}^A R_{n'}(r_i)\Theta_{n'}(\hat{\bf r}_i)\,,
\end{equation}
where $\hat{\bf r}_i={\bf r}_i/r_i$ is the unit vector pointing in the direction of ${\bf r}_i$ and $R_{n'}(r_i)$ is the radial wave function.

The function $\Theta_{n'}(\hat{\bf r}_i)$ in Eq.~(\ref{NucWave}) specifies the angular dependence of $\ket{n'}$. For a spherical nucleus, it is convenient to use the spherical basis, in which the nucleon states have definite total angular momenta $j_i^{n'}$ and total magnetic quantum numbers $\mu_i^{n'}$. In this case, one may take $\Theta_{n'}(\hat{\bf r}_i)=\Omega^{\kappa_i^{n'}}_{\mu_i^{n'}}(\hat{\bf r}_i)$ where $\Omega^{\kappa_i^{n'}}_{\mu_i^{n'}}$ is the two-component spherical spinor. On the other hand, for deformed nuclei, one usually employs the Nilsson basis \cite{Nilsson}, in which nucleon states have
orbital magnetic quantum numbers $m_i^{n'}$ and spin projections $s_i^{n'}=\pm 1/2$.

In the spin-flip matrix elements produced by the nucleon magnetic moment and EDM operators, the radial wave functions in the bra and ket states are the same and we may average over their oscillations, taking\footnote{We stress that the function
(\ref{R}) is needed only to generalize the point-like interaction operators (\ref{mix_H}) to the model with extended nucleus. Upon averaging the operators (\ref{mix_H}) over nuclear density (\ref{R}) the short-distance singularity of the electronic operators is spread and effectively regularized. Physically this means that the electron interacts with a nuclear charge distribution which has no singularity at the origin. One could model the nuclear charge distribution with the more realistic Woods-Saxon formula. However, we have checked that the use of the Woods-Saxon formula changes the electronic matrix elements by about 1\% which is not essential within this work.}
 \begin{equation}
\label{R}
    |R_{n'}(r_i)|^2 =\frac{3}{R_0^3}\theta(R_0-r_{i})\,.
\end{equation}
Using the radial function (\ref{R}), one may integrate over the radial variable $ r_i$ in the matrix elements $\bra{0'}H^\mu_i\ket{n'}$ and $\bra{0'}H^d_i\ket{n'}$, keeping only the leading dipole terms with respect to the electronic coordinate $\bf R$. For that purpose, we note that the operators (\ref{HE}) and (\ref{HB}) depend on the function
\begin{equation}\label{Nabla}
\frac{{\bf R}-{\bf r}_i}{|{\bf R}-{\bf r}_i|^3}=-\nabla_{\bf R}\frac1{|{\bf R}-{\bf r}_i|}
=-\nabla_{\bf R}\sum_{L=0}^\infty \frac{r^L_< }{ r^{L+1}_>}P_L(\cos\varphi)\,,
\end{equation}
where $r_<\equiv\min(R,r_i)$, $r_>\equiv\max(R,r_i)$ and $\varphi$ is the angle between $\bf R$ and ${\bf r}_i$. In this expansion, it is sufficient to keep only the $L=0$ term which reads $\theta(R-r_i)/R+\theta(r_i-R)/r_i$, because after applying the derivative $\nabla_{\bf R}$ it amounts to the dipole term with respect to the electronic coordinate $\bf R$. Taking into account only this term and integrating over the nuclear coordinates $r_i$, one may cast the nuclear matrix elements $\bra{0'}H^\mu_i\ket{n'}$ and $\bra{0'}H^d_i\ket{n'}$ in the form
\begin{subequations}\label{16}
\begin{eqnarray}
\bra{0'}H^\mu_i\ket{n'}&=&e\textbf{M}\cdot\bra{\Theta_{0'}}\boldsymbol{\mu}_i\ket{\Theta_{n'}}\,,\label{Fmu1}\\
\bra{0'}H^d_i\ket{n'}&=&e\textbf{D}\cdot\bra{\Theta_{0'}}{\bf d}_i\ket{\Theta_{n'}}\,,\label{Fd1}
\end{eqnarray}
\end{subequations}
where the operators $\textbf{M}$ and $\textbf{D}$ act only on electronic variables
\begin{subequations}\label{EffectiveOps}
\begin{eqnarray}
\textbf{M}&\equiv&
\left[\theta(R-R_0)\frac{1}{R^2}+\theta(R_0-R)\frac{R}{R_0^3} \right](\hat{\bf R}\times\boldsymbol{\alpha})\,,\label{Fmu2}\\
\textbf{D}&\equiv&
\left[ \theta(R-R_0)\frac{1}{R^2}+\theta(R_0-R)\frac{R}{R_0^3}\right]\hat{\bf R}\,.\label{Fd2}
\end{eqnarray}
\end{subequations}
Here $\hat{\bf R}={\bf R}/R$ is the unit vector pointing in the direction of $\bf R$.

Substituting Eqs.\ \eqref{16} into Eq.\ \eqref{ME}, one may factorize the matrix element $\mathcal{M}^{n'}_{ij}$ into nuclear and electronic parts as
\begin{subequations}
\label{3.12}
\begin{align}
\mathcal{M}^{n'}_{ij}&=c_{s_{1/2}}c_{p_{1/2}}d_i\,\Xi^{n'}_{i}M(\Delta E_{n'})\delta_{ij}\,,\label{Diagonal}\\
\Xi^{n'}_{i}&=\bra{\Theta_{0'}}\boldsymbol{\mu}_i\ket{\Theta_{n'}}\bra{\Theta_{n'}}\boldsymbol{\sigma}_i\ket{\Theta_{0'}}\,,\label{beta-n}\\
M(\Delta E_{n'})
&=\frac{\alpha}{3c_{s_{1/2}}c_{p_{1/2}}}\sum_{n}\frac{\bra{p_{1/2}}{\bf M}\ket{n}\bra{n}\textbf{D}\ket{s_{1/2}}}{\Delta E_{n}+{\rm sgn}(E_n)\Delta E_{n'}}+(s_{1/2}\leftrightarrow p_{1/2})\,,\label{EMatrix}
\end{align}
\end{subequations}
where we have separated the normalization constants $c_{s_{1/2}}$ and $c_{p_{1/2}}$ out of the electronic matrix element $M(\Delta E_{n'})$.

Equations \eqref{3.12} deserve some comments. First, we note that the matrix element \eqref{Diagonal} is represented by a diagonal matrix with respect to nucleon indices $ij$. Indeed, the two matrix elements in the right-hand side\ of Eq.~(\ref{beta-n}) should involve the same nucleon because they both have the same initial and final nuclear states $|0'\rangle$ and $|n'\rangle$. Secondly, in passing from Eqs.~(\ref{16}) to Eqs.~(\ref{3.12}), we have implemented the substitution $({\bf M}\cdot \boldsymbol{\mu})({\bf D}\cdot {\bf d}) \to \frac13 ({\bf M}\cdot {\bf D})(\boldsymbol{\mu} \cdot  {\bf d})$ which is applicable inside the matrix elements. Note that the nuclear matrix element (\ref{beta-n}) is scalar for spinless nuclei which we consider in this paper.

For each nuclear energy $\Delta E_{n'}$, the value of the function $M(\Delta E_{n'})$ in Eq.~(\ref{EMatrix}) is calculated by directly summing over the intermediate electronic states $|n\rangle$, which occupy both the discrete and continuum spectra. The contribution from the discrete spectrum appears negligible as compared with the continuum one (see Refs.~\cite{Plunien91,Plunien95} for analogous calculations). Therefore, in what follows, we will consider intermediate electronic states $|n\rangle$ from the continuum spectrum represented by Dirac-Coulomb wave functions described in Appendix \ref{AppB2}.

\subsection{Nuclear spin-flip matrix elements for spherical and deformed nuclei}\label{Nuclear spin-flip}
The nuclear matrix elements \eqref{beta-n} correspond to M1 spin-flip nuclear transitions. The computations of these matrix elements slightly differ for spherical and deformed nuclei. For the former, one uses $\Theta_{n'}(\hat{\bf r}_i)=\Omega^{\kappa_i^{n'}}_{\mu_i^{n'}}(\hat{\bf r}_i)$ and the matrix elements of the total momentum ${\bf j}_i$ vanish for fine structure doublets. As a result, substituting the operators ${\bf d}_i$ and $\boldsymbol{\mu}_i$ into Eq.~\eqref{beta-n} and using the identity ${\bf l}={\bf j}-{\bf s}$, the nuclear matrix elements may be written as $\Xi^{n'}_{i}= 2\mu_0(g^s_i - g^l_i)\left|\bra{\Theta_{n'}}{\bf s}_{i}\ket{\Theta_{0'}}\right|^2$. For deformed nuclei, the angular functions may be chosen as $\Theta_{n'}(\hat{\bf r}_i)=Y^{l_i^{n'}}_{m_i^{n'}}(\hat{\bf r})\zeta_{\pm1/2}$, where $Y^{l_i^{n'}}_{m_i^{n'}}(\hat{\bf r})$ are spherical harmonics and $\zeta_{\pm1/2}$ is a two-component unit spinor. In this case, one may verify that $\bra{\Theta_{0'}}{\bf l}_i\ket{\Theta_{n'}}\bra{\Theta_{n'}}{\bf s}_i\ket{\Theta_{0'}}=0$. Thus, for deformed nuclei, in Eq.\ \eqref{beta-n} we have $\Xi^{n'}_{i}= 2\mu_0g^s_i\left|\bra{\Theta_{n'}}{\bf s}_i\ket{\Theta_{0'}}\right|^2$. These two cases may be combined in one expression
\begin{equation}
\Xi^{n'}_{i}=2 \mu_0 \left(g_{i}^s- \epsilon g_{i}^l\right)|\bra{\Theta_{0'}}{\bf s}_i\ket{\Theta_{n'}}|^2\,,
\label{beta-n-spherical}
\end{equation}
where
\begin{equation}
    \epsilon = \left\{
    \begin{array}{ll}
        1\quad&\mbox{for spherical nuclei} \\
        0 & \mbox{for deformed nuclei.}
    \end{array}
    \right.
\end{equation}

In Eq.\ \eqref{beta-n-spherical}, the values of the $g$-factors for the proton and neutron are $g_p^l = 1$, $g_p^s = 5.586$, $g_n^l = 0$ and $g_n^s = -3.826$, respectively. The energies $\Delta E_{n'}$ and matrix elements $\bra{\Theta_{0'}}{\bf s}_i\ket{\Theta_{n'}}$ of the M1 spin-flip transitions are listed in Appendix \ref{NuclearSection} for different nuclei of interest.

\subsection{Matrix element of the effective Hamiltonian}
It is convenient to denote the energies and matrix elements for proton M1 spin-flip transitions as $\Delta E_p$ and $\bra{0'}{\bf s}\ket{n'}_p$, and for neutron transitions as $\Delta E_n$ and $\bra{0'}{\bf s}\ket{n'}_n$. Substituting the nuclear matrix elements \eqref{beta-n-spherical} into Eq.~(\ref{Diagonal}), the matrix element \eqref{Scalar contribution} may be presented in the form
\begin{equation}
    \bra{p_{1/2}} H_{\rm eff}\ket{s_{1/2}}
    =-2c_{s_{1/2}}c_{p_{1/2}}\mu_0\left[ d_p (g_p^s-\epsilon g_p^l) M_p
    + d_n (g_n^s-\epsilon g_n^l ) M_n\right]\,,
\label{matrix-d}
\end{equation}
where the quantities $M_p$ and $M_n$ are defined by
\begin{subequations}\label{MpMnDef}
\begin{eqnarray}
M_{p} &\equiv&  \sum_{\Delta E_p}|\bra{0'}{\bf s}\ket{n'}_p|^2 M(\Delta E_p)\,,\\
M_{n} &\equiv&  \sum_{\Delta E_n}|\bra{0'}{\bf s}\ket{n'}_n|^2 M(\Delta E_n)\,.
\label{Mpn}
\end{eqnarray}
\end{subequations}
Note that for deformed nuclei Eqs.~(\ref{matrix-d}) and (\ref{MpMnDef}) simplify, because in the Nilsson basis $|\bra{0'}{\bf s}\ket{n'}_{p,n}|^2=1$ and $\epsilon=0$.

The details of the numerical computations of the coefficients $M_p$ and $M_n$ are given in Appendix \ref{AppB} and the results are presented in Table~\ref{Electronic}. In particular, for $^{180}{\rm Hf}$ and $^{232}$Th they are:
\begin{equation}\label{3.16}
\begin{aligned}
 ^{180}{\rm Hf}: &\quad &     M_{p}=121a_B^{-1}\,,\qquad M_{n}=114a_B^{-1}\,,\\
 ^{232}{\rm Th}: &\quad &     M_{p}=244a_B^{-1}\,,\qquad M_{n}=385a_B^{-1}\,.
\end{aligned}
\end{equation}
Substituting these values into Eq.~(\ref{matrix-d}), we find
\begin{subequations}\label{317}
\begin{align}
\bra{p_{1/2}} H_{\rm eff}\ket{s_{1/2}}_{{}^{180}{\rm Hf}} &= -2 c_{s_{1/2}}c_{p_{1/2}}\frac{\mu_0}{a_B}
(673.7 d_p -436.2 d_n) \,,\\
\bra{p_{1/2}} H_{\rm eff}\ket{s_{1/2}}_{{}^{232}{\rm Th}} &= -2 c_{s_{1/2}}c_{p_{1/2}}\frac{\mu_0}{a_B}
(1363 d_p -1473 d_n) \,.
\end{align}
\end{subequations}

In Sect.~\ref{Constraints}, we will compare these quantities with the matrix element of the contact interaction (\ref{matrix-contact}) and will find the limits on the nucleon EDMs implied by the experimental constraints on $C_{SP}$. However, before proceeding further, let us make a few comments about the details and the accuracy of our calculation of the matrix elements \eqref{317}.

The leading contributions to the atomic EDM from nucleon EDMs arise from $s_{1/2}$ - $p_{1/2}$ electron matrix elements, because these states are significantly enhanced near the nucleus by the absence of the centrifugal barrier and relativistic effects \cite{khriplovich1991parity}. Therefore, we ignore contributions from matrix elements with higher-$l$ wave functions which are very small near the nucleus ($\propto r^l$).

We call attention to the fact that the effective electron-nucleon interactions \eqref{EffectiveOps} fall with the distance (similar to the effect of the ordinary nuclear polarizability) because they have dipole nature. These interactions give the main contributions to the matrix elements at distances from about nuclear radius to hundreds of nuclear radii. Thus, it is localised in the near-nucleus region with $R\ll a_B/Z^{1/3}$, where $a_B$ is the Bohr radius. It is important to note that in this region the inter-electron interaction and screening are negligible, and we can use approximate electron wave functions (\ref{B2}) for $s_{1/2}$ and $p_{1/2}$ bound states. The virtual excited electronic states are described by Dirac-Coulomb wave functions in the continuum spectrum (\ref{HyperGeo}) while the excited states in the discrete spectrum give negligible contributions. For those radial wave functions, which are singular at the origin for a point-like nucleus, we consider their regular polynomial continuation inside the nucleus such that at the origin they behave similarly to the solutions for the Dirac particle inside of a constantly charged ball. This approximation does not break the accuracy of our results.

The radial integrals in the electronic matrix elements are calculated numerically. To control the accuracy of numerical integration, we checked our numerical methods by calculating the energy shifts (contributions to the Lamb shifts) in heavy one-electron ions due to the nuclear polarizability. The error in this calculation does not exceed 5\% as compared with earlier calculations for Th, U, Pu, Cm and other heavy atoms \cite{Plunien91,Plunien95}. Technically, this energy shift is characterised by electronic matrix elements with electric electron-nucleon interaction while in our work we have similar matrix elements with combined electric and magnetic interaction. This comparison serves as a good check of the accuracy of our numerical methods in the electronic part of the calculations. However, the main error in Eq.~(\ref{317}) stems from the quantities $M_p$ and $M_n$ where we expect the errors of our calculations for the nuclear matrix elements and corresponding energies to be under 50\%. This estimate is based on the comparison of the reduced transition probabilities for M1 spin-flip transitions calculated within the single-particle nuclear shell model employed in our work with the results of more sophisticated nuclear calculations presented in Ref.~\cite{nuc-res} for some heavy nuclei (see comments at the end of Appendix~\ref{NuclearSection}). Thus, we conclude that the error in our calculation of the matrix elements \eqref{317} is within 50\% for all atoms. This level of accuracy is typical for most of calculations of $CP$-violating hadronic effects quoted, e.g., in Eqs.~(\ref{dp-theta}) and (\ref{gandtheta}). Further errors originating from relations between hadronic $CP$-violating parameters will be introduced into the calculation later when we derive relations between $C_{SP}$ and these parameters. Note also that constraints on hadronic $CP$-violating parameters in heavy atoms have usually logarithmic scale where the accuracy of up to a factor of two is acceptable.

\section{Constraints on \texorpdfstring{$CP$}{}-odd hadronic parameters}\label{Constraints}

In this section, we will compare the matrix element (\ref{matrix-d}) with the corresponding matrix element of the contact interaction (\ref{matrix-contact}). This will allow us to determine the dependence of the coupling constant $C_{SP}$ on the nucleon permanent EDMs $d_p$ and $d_n$. Then, employing the experimental constraint (\ref{Csp-constr}) we will determine the limits on the parameters $d_{p}$ and $d_n$ originating from the EDM experiments with paramagnetic molecules. We will also present the constraints on other hadronic parameters, which follow from the obtained ones.

\subsection{Limits on nucleon EDMs}
In Eq.~\eqref{matrix-d}, we computed the contributions to the atomic EDM \eqref{de_contact} due to the nucleon EDMs. It is natural to compare these contributions with that due to the contact interaction $H_{\rm cont}$. Equating the matrix elements of these interactions (\ref{matrix-contact}) and (\ref{matrix-d}) we find the relation between the constant $C_{SP}$ and the parameters $d_p$ and $d_n$:
\begin{equation}\label{relationspherical}
C^{(d)}_{SP}=\frac{20\sqrt2}{G_F}\frac{\Gamma(2\gamma+1)^2}{1+4\gamma}\frac{\pi\mu_0 R_0^2}{AZ\alpha}\left(\frac{a_B}{2ZR_0}\right)^{2\gamma}\left[ d_p (g^s_p-\epsilon g^l_p) M_p +d_n (g^s_n-\epsilon g^l_n) M_n \right]\,.
\end{equation}
We point out that the right-hand side of Eq.\ \eqref{relationspherical} is independent of the wave functions normalization constants $c_{s_{1/2}}$ and $c_{p_{1/2}}$.

We stress that the contribution to $C_{SP}$ \eqref{relationspherical} originates from discrete nuclear intermediate excited states while the authors of Ref.~\cite{FPRS} found analogous contributions due to virtual nuclear excitations to continuum spectrum,
\begin{equation}\label{Pospelov's contribution}
    C^{(c)}_{SP}=\frac{8\sqrt{2}m_e\alpha^2{\rm ln}(A)}{G_Fp_Fm_N}\left(\frac{Z}{A}\frac{\mu_p}{\mu_0}\frac{d_p}{e}+\frac{N}{A}\frac{\mu_n}{\mu_0}\frac{d_n}{e}\right)\,.
\end{equation}
Here $p_F\approx250$ MeV is the Fermi momentum of the nucleus, $m_N$ is the nucleon mass and $\mu_{p}$, $\mu_n$ are the nucleon magnetic moments  ($\mu_p/\mu_0=2.793$, $\mu_n/\mu_0=-1.913$). The superscripts $(d)$ and $(c)$ in Eqs.~\eqref{relationspherical} and \eqref{Pospelov's contribution} refer to the contributions of discrete and continuum intermediate nuclear states, respectively.

Combining the two contributions \eqref{relationspherical} and \eqref{Pospelov's contribution}, we find the leading-order dependence of $C_{SP}=C^{(d)}_{SP}+C^{(c)}_{SP}$ on nucleon EDMs,
\begin{equation}
C_{SP}=(\lambda_1d_p+\lambda_2d_n)\times \frac{10^{13}}{e\cdot{\rm cm}}\,,
\label{num-relation}
\end{equation}
where the numerical values of the coefficients $\lambda_1$ and $\lambda_2$ for several atoms of interest are presented in Table\ \ref{Results}.

The relation \eqref{num-relation} represents the central results of this paper.
It allows us to place limits on the nucleon EDMs. Taking into account the most recent constraints on $|C_{SP}|$ from the ${}^{180}$HfF$^+$ \cite{HfF2017} and ${}^{232}$ThO \cite{ACMEII} EDM experiments (see also Ref.~\cite{fleig2018}), we obtain the limits on $d_p$ and $d_n$. These results are collected in Table \ref{Limits} at the end of this section.

We note that since the quantities $\lambda_{1,2}$ and the corresponding limits on $d_{p,n}$ are directly linked to the effective matrix elements $M_{p,n}$, the errors in these quantities are similar to those incurred in the computation of $M_{p,n}$, i.e., around 50\%.

\subsection{Limits on \texorpdfstring{$CP$}{}-odd pion-nucleon coupling constants}

The nucleon EDM may appear due to more fundamental interactions. In this subsection, we assume that the dominant contribution to the nucleon EDM is stipulated by the $CP$-odd pion-nucleon interaction.

The $CP$-odd pion-nucleon interactions with coupling constants $\bar g^{(0)}_{\pi NN}$ and $\bar g^{(1)}_{\pi NN}$ may induce atomic EDMs through different mechanisms: (i) they contribute to the nucleon EDMs via one-loop quantum corrections \cite{POSPELOV2005} and (ii) they contribute to the effective nucleon-electron interaction through one- and two-loop contributions to the nucleon polarizability \cite{FPRS}. In this section, we revisit all these contributions and combine them with those from $d_p$ and $d_n$ found in the previous subsection. This will allow us to find the constraints on $\bar g^{(0)}_{\pi NN}$ and $\bar g^{(1)}_{\pi NN}$ originating from the EDM experiments with paramagnetic atoms and molecules.

We recall that the coupling constants $\bar g^{(0)}_{\pi NN}$ and $\bar g^{(1)}_{\pi NN}$ enter the $CP$-odd pion-nucleon interaction as follows:
\begin{equation}
    {\cal L}_{\pi NN} = \bar g_{\pi NN}^{(0)} \bar N \tau^a N \pi^a
    + \bar g_{\pi NN}^{(1)} \bar N N \pi^0 \,,
\label{L}
\end{equation}
where $N$ is the nucleon doublet, $\pi^a,\pi^0$ are the pion fields, and $\tau^a$ are isospin Pauli matrices. This interaction is responsible for the one-loop quantum correction to the nucleon EDM which were originally estimated in Ref.~\cite{CVVW1979} and revisited in subsequent papers \cite{Hockings,Ottnad,Guo},
\begin{subequations}
\label{dp-g-relation}
\begin{eqnarray}
    d_n &\approx& \frac{e g_A \bar g^{(0)}_{\pi NN}}{8\pi^2 F_\pi}
    \left( 2\ln \frac{m_p}{m_\pi} +\frac\pi2\frac{m_\pi}{m_p}-1\right)    \approx 1.1 \times 10^{-14} \bar g^{(0)}_{\pi NN} \,e\cdot{\rm cm}\,,\\
    d_p&\approx&\frac{e g_A \bar g^{(0)}_{\pi NN}}{8\pi^2 F_\pi}
    \left( 1-2\pi \frac{m_\pi}{m_p}-2 \ln\frac{m_p}{m_\pi} \right)\approx -1.3 \times 10^{-14} \bar g^{(0)}_{\pi NN} \,e\cdot{\rm cm}\,,
\end{eqnarray}
\end{subequations}
where $g_A\approx1.3$ is the axial triplet coupling constant, $F_\pi \approx 93 $ MeV is the pion decay constant, $m_\pi \approx 135 $ MeV is the pion mass and $m_p\approx m_n\approx 938$~MeV is the nucleon mass.
In Eqs.~(\ref{dp-g-relation}) we keep only the terms originating from the meson cloud and omit the (counter)terms corresponding to short-distance effects (see, e.g., \cite{Ottnad,Guo,yamanaka2017}). The latter terms depend on low-energy constants with unknown values which bring a high level of uncertainty in the relations (\ref{dp-g-relation}). An accurate study of these short-distance effects goes beyond the scope of this paper.

There are one- and two-loop quantum contributions to the nucleon polarizability $\beta_{p,n}=\beta_{p,n}^{(1)}+\beta_{p,n}^{(2)}$, which involve interaction vertices (\ref{L}) \cite{FPRS} \footnote{In Eqs.~(\ref{nucl-pol-a}) and (\ref{nucl-pol-b}), the last terms account for the contributions from $\eta$ meson exchange with the mass $m_\eta$. These mesons have $CP$-odd meson-nucleon interaction with coupling constant $\bar g_{0,\eta}\approx 5\bar g_{0,\pi}$.}:
\begin{subequations}
\label{nucl-pol}
\begin{align}
\beta^{(1)}_p &= -\frac{\alpha}{\pi F_\pi m_\pi^2}
 \left( \bar g^{(1)}_{\pi NN} + \bar g^{(0)}_{\pi NN} + \frac5{\sqrt3}\frac{m_\pi^2}{m_\eta^2} \bar g^{(0)}_{\pi NN} \right)\,,\label{nucl-pol-a}\\
\beta^{(1)}_n &= -\frac{\alpha}{\pi F_\pi m_\pi^2}
 \left( \bar g^{(1)}_{\pi NN} - \bar g^{(0)}_{\pi NN} + \frac5{\sqrt3}\frac{m_\pi^2}{m_\eta^2} \bar g^{(0)}_{\pi NN} \right)\,,\label{nucl-pol-b}\\
\beta_p^{(2)} &= - \frac{\alpha g_A \bar g^{(0)}_{\pi NN}}{4F_\pi m_n m_\pi} \frac{\mu_n}{\mu_0}\,,\\
\beta_n^{(2)} &=  \frac{\alpha g_A \bar g^{(0)}_{\pi NN}}{4F_\pi m_p m_\pi} \frac{\mu_p}{\mu_0}\,.
\end{align}
\end{subequations}
Note that these relations contain only the leading terms which preserve the isospin symmetry.
The nucleon polarizability corrections (\ref{nucl-pol}) amount to the following contributions to the effective coupling constant $C_{SP}$
\begin{equation}
\label{Cbeta}
    C_{SP}^{(\beta)} = -\frac{\sqrt2}{G_F}
    \left(
     \frac Z A \beta_p + \frac N A \beta_n
    \right) \frac{3\alpha m_e}{2\pi} \ln\frac{\Lambda}{m_e}\,,
\end{equation}
where the renormalization scale $\Lambda = m_\rho\approx 775$ MeV for one-loop corrections and $\Lambda=m_\pi\approx135$ MeV for the two-loop ones (see \cite{FPRS} for detail).

Now we substitute the relation (\ref{dp-g-relation}) into Eq.~(\ref{relationspherical}) or (\ref{num-relation}) and add also the contribution (\ref{Cbeta}). As a result, we find the leading-order relation between the constant $C_{SP}$ and $CP$-violating pion-nucleon couplings
\begin{equation}
    C_{SP}=\lambda_3\bar{g}^{(0)}_{\pi NN}+\lambda_4\bar{g}^{(1)}_{\pi NN}\,,
    \label{2}
\end{equation}
where the numerical values of the coefficients $\lambda_3$ and $\lambda_4$ are collected in Table~\ref{Results} for different atoms. The corresponding limits on these couplings originating from the experimental constraints are given in Table~\ref{Limits} below. We stress that these limits are based on the assumption that the $CP$-odd pion interaction (\ref{L}) gives dominant contribution to the atomic EDM.

Unfortunately, we cannot accurately estimate computational errors of our results for the coefficients $\lambda_3$ and $\lambda_4$ because they are based on the relations \eqref{dp-g-relation} and (\ref{nucl-pol}) with unknown errors. However, by comparing with other analogous calculations (e.g., \cite{Guo}) it is natural to expect that the errors in Eqs.~\eqref{dp-g-relation} and (\ref{nucl-pol}) may be of order $30\%-100\%$. Nevertheless, our relation \eqref{2} is still useful for comparison with other results for $CP$-violation in heavy nuclei, in particular, with the atomic EDMs produced by the nuclear Schiff moments,  which do not contain estimates of the theoretical errors in the nuclear calculations and should be understood on the logarithmic scale.

\subsection{Limits on quark chromo-EDM}

In this subsection, we consider the chromo-EDM of up and down quarks denoted by $\tilde d_u$ and $\tilde d_d$, respectively. Assuming that these quantities are the only sources of the nucleon EDM and $CP$-violating internucleon forces, the authors of Refs.~\cite{PospelovRitz99,FDK,PospelovRitz2001,POSPELOV2005,Abusaif} established the following relations:
\begin{subequations}\label{conversion}
\begin{align}
d_p       &=-(2.1\pm 1.1)e(\tilde{d}_u+0.125\tilde{d}_d)\,,\\
d_n       &=(1.1\pm 0.6) e(\tilde{d}_d+0.5\tilde{d}_u)\,,\\
g\bar{g}^{(0)}_{\pi NN}&=(0.8\pm 0.4)\times 10^{15}(\tilde{d}_u+\tilde{d}_d){\rm cm}^{-1}\,,\label{49c}\\
g\bar{g}^{(1)}_{\pi NN}&=(4.0\pm 2.0)\times 10^{15}(\tilde{d}_u-\tilde{d}_d){\rm cm}^{-1}\,.\label{49d}
\end{align}
\end{subequations}
These equations should be substituted into the sum of Eqs.~(\ref{relationspherical}) and (\ref{Cbeta}), giving the leading-order dependence of $C_{SP}$ on $\tilde d_{u}$ and $\tilde d_p$ as
\begin{equation}
    C_{SP}=(\lambda_5\tilde{d}_u+\lambda_6\tilde{d}_d)\times 10^{15}{\rm cm}^{-1}\,.\label{3}
\end{equation}
The numerical values of the coefficients $\lambda_5$ and $\lambda_6$ are given in Table~\ref{Results}. The corresponding constraints on the values of quark chromo-EDMs are presented in Table~\ref{Limits} below. These constraints are based on the assumption that the quark chromo-EDMs are the dominant sources of nucleon EDM and the $CP$-odd pion-nucleon interaction (\ref{L}).

In order to estimate the uncertainty in the coefficients $\lambda_{5,6}$ and the corresponding limits on $\tilde{d}_{u,d}$, we note that the relations \eqref{conversion} all have 50\% uncertainty (the error bars of the relations \eqref{49c} and \eqref{49d} were estimated in Ref.\ \cite{yamanaka2017}). Combining these with the 50\% error bars in $\lambda_{1,2}$ and assuming that the relations (\ref{dp-g-relation}) and \eqref{nucl-pol} each have 100\% uncertainty, we find that the values of $\lambda_{5}$ and $\tilde{d}_{u}$ are accurate up to a factor of 3 wheres the values of $\lambda_{6}$ and $\tilde{d}_{d}$ are accurate up to a factor of 2.

\subsection{Limit on QCD vacuum angle \texorpdfstring{$\bar\theta$}{}}

\begin{table}[tb]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
\multicolumn{2}{|c|}{} & $\lambda_1$ & $\lambda_2$ & $\lambda_3$ & $\lambda_4$ & $\lambda_5$ & $\lambda_6$ & $\lambda_7$ \\
 \hline
\multirow{3}{*}{\rotatebox[origin=c]{90}{Spherical}}         & ${}_{56}^{138}{\rm Ba}$ & 6.4 & -7.2 & -2.3 & 2.2 & 0.4 & -0.8 & 5.1 \\[0.25ex] \cline{2-9}
                                                             & ${}_{82}^{206}{\rm Pb}$ & 5.5 & -6.2 & -2.1 & 2.2 & 0.5 & -0.8 & 4.6 \\[0.25ex] \cline{2-9}
                                                             & ${}_{82}^{208}{\rm Pb}$ & 5.5 & -5.3 & -2.0 & 2.2 & 0.5 & -0.8 & 4.4 \\[0.25ex] \hline
\multirow{7}{*}[-2.5ex]{\rotatebox[origin=c]{90}{Deformed}}  & ${}_{70}^{172}{\rm Yb}$ & 9.4 & -8.4 & -2.8 & 2.2 & 0.4 & -0.8 & 6.0 \\[0.25ex] \cline{2-9}
                                                             & ${}_{70}^{174}{\rm Yb}$ & 9.3 & -9.7 & -3.0 & 2.2 & 0.4 & -0.8 & 6.3 \\[0.25ex] \cline{2-9}
                                                             & ${}_{70}^{176}{\rm Yb}$ & 9.2 & -8.6 & -2.8 & 2.2 & 0.4 & -0.8 & 6.1 \\[0.25ex] \cline{2-9}
                                                             & ${}_{72}^{178}{\rm Hf}$ & 12  & -8.2 & -3.1 & 2.2 & 0.3 & -0.8 & 6.5 \\[0.25ex] \cline{2-9}
                                                             & ${}_{72}^{180}{\rm Hf}$ & 12  & -9.0 & -3.2 & 2.2 & 0.3 & -0.8 & 6.7 \\[0.25ex] \cline{2-9}
                                                             & ${}_{88}^{226}{\rm Ra}$ & 5.7 & -5.7 & -2.1 & 2.2 & 0.5 & -0.8 & 4.6 \\[0.25ex] \cline{2-9}
                                                             & ${}_{90}^{232}{\rm Th}$ & 6.4 & -6.9 & -2.3 & 2.2 & 0.4 & -0.8 & 5.1 \\[0.25ex] \hline
\end{tabular}
\caption{\label{Results}
The results of numerical computations of the coefficients $\lambda_1,\ldots ,\lambda_{7}$ in Eqs.~\eqref{num-relation}, (\ref2), (\ref3) and (\ref4).}
\end{center}
\end{table}
\begin{table}[tb]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
                 			  & $^{232}{\rm ThO}$                   & $^{180}{\rm HfF}^+$ \\ \hline
$|C_{SP}|$       			  & $7.3\times 10^{-10}$\ \cite{ACMEII} & $1.8\times 10^{-8}$\ \cite{HfF2017,fleig2018} \\ \hline
$|d_p|$                       & $1.1\times 10^{-23}e\cdot{\rm cm}$  & $1.5\times 10^{-22}e\cdot{\rm cm}$ \\ \hline
$|d_n|$                       & $1.0\times 10^{-23}e\cdot{\rm cm}$  & $2.0\times 10^{-22}e\cdot{\rm cm}$ \\ \hline
$|\bar{g}^{(0)}_{\pi NN}|$    & $3.1\times 10^{-10}$                & $5.6\times 10^{-9}$                 \\ \hline
$|\bar{g}^{(1)}_{\pi NN}|$    & $3.3\times 10^{-10}$                & $8.2\times 10^{-9}$                 \\ \hline
$|\tilde{d}_d|$  			  & $9.3\times 10^{-25}{\rm cm}$        & $2.2\times 10^{-23}{\rm cm}$        \\ \hline
$|\tilde{d}_u|$  			  & $1.7\times 10^{-24}{\rm cm}$        & $5.8\times 10^{-23}{\rm cm}$        \\ \hline
$|\bar{\theta}|$ 			  & $1.4\times 10^{-8}$                 & $2.7\times 10^{-7}$                 \\ \hline
\end{tabular}
\end{center}
\caption{\label{Limits} Limits on absolute values of $CP$-violating hadronic parameters arising from the relations \eqref{num-relation}, (\ref2), (\ref3) and (\ref4) upon implementing the constraints on the constant $C_{SP}$ from the $^{180}{\rm HfF}^+$ \cite{HfF2017,fleig2018} and $^{232}{\rm ThO}$ \cite{ACMEII} experiments.}
\end{table}

The QCD vacuum angle $\bar\theta$ is the fundamental $CP$-odd parameter which can induce the nucleon (and atomic) EDM. In this subsection, we find the limit on $\bar\theta$ in the assumption that the nucleon EDM is dominated by contributions from the QCD vacuum angle.

The dependence of the nucleon EDMs on $\bar\theta$ was originally estimated in Ref.~\cite{CVVW1979} and refined in subsequent papers \cite{PospelovRitz99,deVries2015,bsaisou2015,deVries2016}:
\begin{equation}
\label{dp-theta}
d_p =(2.1\pm1.2)\times10^{-16}\bar{\theta}\, e\cdot{\rm cm}\,,\qquad
d_n =-(2.7\pm1.2)\times10^{-16}\bar{\theta}\, e\cdot{\rm cm}\,.
\end{equation}
The pion-nucleon coupling constants $\bar g^{(0)}_{\pi NN}$ and $\bar g^{(1)}_{\pi NN}$ can also be expressed via $\bar\theta$ as \cite{POSPELOV2005,deVries2015,Bsaisou2012} (see also Refs.~\cite{deVries2016,yamanaka2017} for reviews\footnote{We point out that the signs in the relations (103) and (104) between $\bar g^{(0,1)}_{\pi NN}$ and $\bar \theta$ quoted in Ref.~\cite{yamanaka2017} are inconsistent with the definition of ${\cal L}_{\pi NN}$ presented in that review.})
\begin{equation}\label{gandtheta}
\bar{g}^{(0)}_{\pi NN}=-(15.5\pm2.5)\times 10^{-3}\,\bar{\theta}\,,\qquad
\bar{g}^{(1)}_{\pi NN}=(3.4\pm2)\times 10^{-3}\,\bar{\theta}\,.
\end{equation}
Substituting these relations into the sum of Eqs.~(\ref{relationspherical}) and (\ref{Cbeta}) we represent $C_{SP}$ in terms of $\bar\theta$
\begin{equation}
    C_{SP}=\lambda_{7}\times10^{-2}\bar{\theta}\label{4}\,,
\end{equation}
where the value of the constant $\lambda_{7}$ is given in Table~\ref{Results} for different atoms. In particular, with the use of the corresponding value for $^{232}$Th, the experimental constraint on $C_{SP}$ (\ref{Csp-constr}) implies
\begin{equation}
\label{bar-theta-constr}
    |\bar\theta| < 1.4\times 10^{-8}\,.
\end{equation}
This constraint is close to the result advocated in the recent paper \cite{FPRS}.

Using the uncertainties in Eqs.~(\ref{dp-theta}) and (\ref{gandtheta}) and assuming that the relations (\ref{dp-g-relation}) and  \eqref{nucl-pol} each have 100\% uncertainty, we find that the error bars in the relation \eqref{4} and the corresponding limit \eqref{bar-theta-constr} are about $70\%$.

\section{Summary and discussion}\label{Conclusion}

In this paper, we demonstrated that the experiments measuring the electron electric dipole moment with paramagnetic atoms and molecules are also sensitive to nucleon EDMs. Dominant contributions to the atomic EDM in such atoms arise from the combined electric and magnetic electron-nucleus interaction. Taking into account nuclear structure effects, we derived the leading-order relations (\ref{num-relation}) between the electron-nucleus contact interaction constant $C_{SP}$ and nucleon permanent EDMs $d_p$ and $d_n$. As a result, the constraint (\ref{Csp-constr}) on the parameter $C_{SP}$ allows us to find limits on nucleon EDMs arising from the experiments with paramagnetic molecules:
\begin{equation}
    |d_p|<1.1\times10^{-23}e\cdot{\rm cm}\,,\qquad
    |d_n|<1.0\times10^{-23}e\cdot{\rm cm}\,.
\label{Concl-limits}
\end{equation}

It is instructive to compare these limits with the currently accepted ones. In particular, our limit on the neutron EDM obtained from the results of experiments with paramagnetic molecules is almost three order of magnitude weaker than the recent experimental measurements of EDM of neutron $|d_n|<1.8\times 10^{-26} e\cdot{\rm cm}$ \cite{EDMneutron}. However, for the proton EDM our limit (\ref{Concl-limits}) is just about 20 times weaker than the recent constraint on this parameter $|d_p|<5\times 10^{-25}e\cdot{\rm cm}$ \cite{FD2020} which was based on the measurements on EDM of $^{199}$Hg atom \cite{Graner2016}.\footnote{Note that this constraint is approximately two times weaker than that in Ref.~\cite{Sahoo} because the authors of Ref.~\cite{FD2020} revisited earlier calculations of nuclear Shiff moments.} Remarkably, the constraint (\ref{Concl-limits}) on the proton EDM is nearly 30 times more stringent than that found in recent $^{129}$Xe EDM experiments \cite{Xe1,Xe2}. This sensitivity of eEDM experiments to hadronic $CP$-violating parameters is actually very impressive. We expect that further improvement of accuracy in the experiments with paramagnetic molecules would push these limits.

The nucleon EDM may be expressed via more fundamental $CP$-violating parameters such as $CP$-odd pion-nucleon coupling constants $\bar g^{(0,1)}_{\pi NN}$, quark chromo-EDMs $\tilde d_{u,d}$ and the QCD vacuum angle $\bar\theta$. This allows us to find the leading-order dependence of the contact interaction coupling constant $C_{SP}$ on these parameters. The results are represented by Eqs.~(\ref{2}), (\ref{3}) and (\ref{4}) with coefficients $\lambda_3,\ldots, \lambda_7$ given in Table \ref{Results}. The corresponding limits arising on these parameters from the experiments \cite{HfF2017} and \cite{ACMEII} are presented in Table~\ref{Limits}. In particular, the QCD vacuum angle is limited as $|\bar\theta|<1.4\times10^{-8}$ which is approximately two orders of magnitude weaker than the currently accepted constraint from neutron and Hg atom EDM experiments $|\bar\theta|<10^{-10}$ \cite{PDG}, but is nearly three times more stringent than the corresponding bounds from $^{129}$Xe EDM experiments \cite{Xe1,Xe2}.
Note that the limits presented above do not include theoretical errors which often are unknown (see, e.g., calculation of the $^{199}$Hg nuclear Schiff moment in Ref.~\cite{Engel} where different interaction models give different sign of the result).
We provided error estimates for all obtained results where appropriate.
In particular, for the limits on the nucleon EDMs $d_{p,n}$ the errors do not exceed 50\%,
the relation for the QCD vacuum angle $\bar \theta$ has about 70\% uncertainty while the limit on the up quark chromo-EDM $\tilde d_u$ is accurate up to a factor of 3 and the limit on the down quark chromo-EDM $\tilde d_d$ is accurate up to a factor of 2.

We stress that obtained in this paper contributions to $C_{SP}$ from nucleon EDMs are independent from and additional to those found in Ref.~\cite{FPRS}, although they originate from the same combined electric and magnetic electron-nucleon interaction. Indeed, the authors of the paper \cite{FPRS} took into account virtual nuclear transitions from bound states to {\it continuum} for all nucleons in the nucleus, so it increases with the nucleon number $A$.  In our paper, in contrast, we consider virtual nuclear transitions to excited {\it bound} nuclear states for several external shell nucleons which can flip their spins. This contribution is enhanced by the small energy denominators and large matrix elements of the spin operator between the spin-orbit doublet components.  As we demonstrate in this paper, accounting these M1 nuclear spin-flip transitions approximately doubles the results presented in Ref.~\cite{FPRS}.

To conclude, we expect that the obtained in this paper results may place more stringent limits on $CP$-violating hadronic parameters once improved constraints on $C_{SP}$ are available from next generations of eEDM experiments \cite{Baron2014,ACMEII,Hudson2011,Loh1220,HfF2017,BaF2018}. Note that the sensitivity in these experiments improved by two orders of magnitude during the last decade.

\section*{Acknowledgements}
This work was supported by the Australian Research Council Grants No. DP150101405 and DP200100150 and the Gutenberg Fellowship. We thank Vladimir Dmitriev, Maxim Pospelov, Adam Ritz, Yevgeny Stadnik and Anna Viatkina for useful discussions.

redpajama_set_name: RedPajamaArXiv


BEIJING, June 12 (Reuters) - Chinese banks extended 1.15 trillion yuan ($179.58 billion) in net new yuan loans in May, below analysts' expectations.
Analysts polled by Reuters had predicted new yuan loans of 1.2 trillion yuan, up slightly from April's 1.18 trillion yuan.
Broad M2 money supply grew 8.3 percent in May from a year earlier, central bank data showed on Tuesday, missing forecasts for an expansion of 8.5 percent and compared with 8.3 percent in April.
Outstanding yuan loans grew 12.6 percent from a year earlier, slower than an expected 12.7 percent rise and compared with a rise of 12.7 percent in April.
China's banks extended a record 13.53 trillion yuan in new loans last year, up 7 percent from 2016, despite a government drive to reduce risks in the financial system from a rapid build-up in debt.
The People's Bank of China's surprising cut in reserve requirement ratios (RRR) on April 17 and fears of a trade war with the United States have fanned market expectations of looser policy to support the economy.


Today, and for the past two days, I've been featuring different musical settings of a prayer attributed to St. Patrick (387-461 A.D.), titled The Lorica (breastplate) of St. Patrick.
Today's setting is by composer John Rutter, directing the Cambridge Singers - a finer combination of conductor and chorus would be hard to find! This presentation is prayerfully gentle. The lyrics of Rutter's composition follow the video and below that you'll find a longer version of Patrick's inspirational prayer.


Meta NLP helps individuals recover forgotten inner resources of their subconscious and unconscious minds that can enhance and improve their recovery to maximize the functioning of their immune system. These protocols will help you to accomplish this by opening your inner pharmacy to receive new inner pharmacy prescriptions that contribute to improved functioning of your mind, brain and endocrine system.
I felt some interesting shifts as i listened to these audio files and found them very helpful. I just feel more resourceful, not like a victim anymore. I really CAN handle what I'm going through!


Purebred British White Cow (sold open) with unregistered but eligible JB Boulder heifer calf from 2016. 4-H show home price.
Bred to Windy Acres Excaliber for Jan 2, 2019 calf (confirmed bred by Biopryn). Calf will qualify for registration. She had her first calf at 2 years old and with BW of 92 lbs (unassisted).
Full mouth, heavy milk producer for her calves, good bone and very maternal. She has had all live, unassisted births. Mature weight of 1550 lbs.
She comes when we whistle and will allow some pets with proper motivation (mainly alfalfa).
Black 50% registered heifer. Super mellow, halter broke, current on shots. Reserve Champion Murray Grey heifer from Josphine County 2018. She is joining Two Byrds Dark Chocolate at a local ranch in Eagle Point. She will join with our JR bull, Two Byrds Frost next summer.
Black Angus x steer bred by local Murray grey breeder. We raise our steers on natural pasture grasses and alfalfa. No grain, no hormones, just all he can eat irrigated grass. If you are interested in grass fed all natural beef finished with Klamath Alfalfa, contact us in advance because we only raise finished product for people who preorder. He is currently 17 months and 1100 lbs. He is expected to finish at 21-22 months and 1320-1350 lbs (~800 hanging) based on current gain. We sell steers by hanging weight.
Sired by JB Colt 45, 2016 Res. National CH Yearling MG Bull.
We are using Excaliber to add Temar Lotus line to our pedigree stock. Pictured here at 21 months.
Purebred Murray grey steer. We raise our steers on natural pasture grasses and alfalfa. No grain, no hormones, just all he can eat irrigated grass. If you are interested in grass fed all natural beef finished with Klamath Alfalfa, contact us in advance because we only raise finished product for people who preorder. He is currently 11 months old. He is expected to finish at 22-23 months and 1000-1100 lbs (~650 hanging) We sell steers by hanging weight.
50% Murray grey steer. He is currently 7 months old. He is expected to finish at 22-24 months and 1100-1200 lbs (~700 hanging) We sell steers by hanging weight. Picture will be updated when able.
May have beef available in Spring and Fall 2019. Contact us for details.


Elucify, a member of the Y Combinator Winter 2016 class wants to solve an annoying and persistent problem for sales people — making sure they have the most recent customer contact data.
To solve this problem, the company created a plug-in for Salesforce.com CRM based on machine learning and artificial intelligence. The system connects to various public and private data sources looking for the most current contact information, according to Gerald Fong, Elucify CEO and co-founder.
Sales personnel simply click the Elucify button in the Salesforce record, and the tool updates the existing contact information and lists any new contacts found at the company. Typically it looks at information such as phone number, email address, current decision makers, updated company information — all the types of data a busy sales team needs. It usually takes just 5 or 10 seconds to update the record, according to Fong.
"The pain point we are focusing on is the pain sales teams run into every day. They spend time hunting for [good contact] data every day. Instead of spending time on the phone, they are spending a lot of time on various websites trying to verify [contact] information," Fong told TechCrunch.
In most companies this forces people to spend time manually cleaning up their contact information, but Elucify automates that process on a per record basis.
Most sales teams work with Customer Relationship Management tools like Salesforce to track this information. As such, you wouldn't think this would be a huge problem, but according to data from eConsultancy, sales and marketing pros estimate that as much as 30 percent of their contact data is bad.
The company has only been in existence for a few months, yet it went from ideation to Y Combinator in a matter of week, and it already already boasts three Beta customers.
The three company co-founders — which include Fong, Mihir Deo and Naveen Krishnamurthi — have found being part of Y Combinator has given them access to people with experience starting enterprise companies. The founders got YC president Sam Altman as their advisor and as young founders, they are finding the advice they are getting is helping them solve problems and open doors.
"We are starting an enterprise software company. Getting someone to pay you money is difficult. We are talking to people [in the Y Combinator network] about what mistakes they made and what problems we are thinking about," Fong said.
Their advisors and network contacts have already considered many of the issues they face on a daily basis and are helping them identify where to focus their energies.
As for the future, they just want to keep building on their early wins. CRM is a huge market and Salesforce has 60 percent of that market, Wong pointed out.
"Our goals to make a big dent in the [market of] people using Salesforce." If they can do that, that's a lot of potential customers. Down the road they hope to add their functionality to other CRM tools as well.


text:
JOSH GIBSON - WEEBLY
Next to Normal - A Broadway Show with Mental Health Themes
A psychiatrist with a private practice headquartered in San Francisco, California, Josh Gibson, MD, draws on over a decade of experience in evaluating and treating patients with a diverse range of mental health issues. In his leisure time, Josh Gibson, MD, enjoys fiction writing, music and the Golden State Warriors. The portrayal of psychiatry in the arts is another interest of his, including television shows, movies and theater.
Next To Normal, a contemporary musical with music by Tom Kitt and writing by Brian Yorkey, offers an emotional and compelling look at dealing with mental health issues in one's own family. The story focuses on a typical suburban family with two teenagers, a boy and a girl, and the effect of the mother's 16-year battle with bipolar disorder.
Next To Normal originally opened on March 27th, 2009, and ran through January 16th, 2011. During that time, the show earned several honors, including several Tony awards and the 2010 Pulitzer Prize for Drama. It also earned inclusion on the list of the year's 10 best shows from critics such as The New York Times, The Washington Post, and The Los Angeles Times.
Josh Gibson is a former psychiatrist who now works as an executive coach and consultant.
Advancement Of Psychiatry (GAP)
Arnold P. Gold Foundation Award
Josh Gibson
Josh Gibson MD

redpajama_set_name: RedPajamaCommonCrawl


text:
Canadian Describes Experience as Missionary in Zimbabwe
When we were preparing to go, we didn't know much about this southern African country. We only had a few weeks' notice and no time to research. The news we heard from others painted a bleak picture. We were starting to get nervous. We were pleasantly surprised to find a very different picture when we arrived.
Amanda Eve Wigglesworth | 25 January 2010
Source: Canadian Orthodox Messenger
I keep dreaming that I have spontaneously gotten on a plane (or two, or five) and flown back to Zimbabwe. Something about the place sank its teeth deep into me, drawing up memories of other places that bit into me with fervour—places that haunt my memories and tease me with the desire to return. It has been eleven years since I left my first love, Mauritius, and I have never shaken it. It is a part of who I am. On the journey home from Zimbabwe, I could tell that I had fallen in love again. The recurring dream of impulsively returning reinforces this sense that part of Africa has returned home with me, and that part of me is still in Africa. I must tell you about the times when Africa took me by the hand, when we walked side-by-side, when we met each other face to face, when we smiled at each other and embraced, and when we said goodbye.
When my husband Kevin and I originally applied to go on a short-term mission with the Orthodox Christian Mission Center (OCMC), we had applied for the team to Tanzania. By the time our application was processed, that team was full. We started preparations to go to Nigeria. One week before we were scheduled to leave, the team's visas were denied. It seemed that Zimbabwe was the next option. What did God have in store for us? Was He trying to tell us that it was not His will for us to go on a team this year? Were spiritual forces at work to prevent a team from going? As the departure date for Zimbabwe grew closer, people were asking if we were getting excited. Given the circumstances, I was waiting for the other shoe to drop. Would we be going to Zimbabwe? I wasn't sure. Thanks be to God,: our team did go to Zimbabwe and we were able to experience what God is doing there through the Orthodox Church and Metropolitan George.
When we were preparing to go, we didn't know much about this southern African country. We only had a few weeks' notice and no time to research. The news we heard from others painted a bleak picture. We were starting to get nervous. We were pleasantly surprised to find a very different picture when we arrived. Yes, the politics there are not good. Yes, HIV/AIDS is a huge problem (Zimbabwe has the 4th highest rates in the world). Yes, hunger is a problem. Yes, there are utility shortages. But, things have improved greatly in the last six months. We felt safe. People radiate with joy. Even when faced with extreme poverty, the poverty was easy to miss because the joy and excitement of the people overshadowed their lack of resources.
Over the next two weeks, we taught the people about many topics. They are hungry for instruction about the Orthodox Church and way of life. We found so much joy during the teaching times as we shared from our own knowledge and experience, and tried to answer their many questions. They also bared their souls to us by asking very personal questions before and after sessions, as well as during the gender- and age-specific sessions. I was able to relate on a deep level with one woman, Maria, as we shared our experiences of caring for a family member and being present as they left this world. This meaningful conversation helped to reinforce our shared humanity and the struggles that all human beings face.
We stayed in Harare (the capital) most of the time, but we also travelled to Bulawayo (the second largest city in Zimbabwe) and some small villages. In one of these villages, Mrehwa, we witnessed their Peanut Butter Project. We had never met them before, but each woman embraced every team member with such excitement, energy, and length that it appeared as though they were greeting long-lost relatives. They honoured us like dignitaries and happily showed off the village. We were also able to try grinding the peanuts and tasting the result. It tasted just like the organic peanut butter I buy at home! The women cooked a traditional Zimbabwean meal for us including meat (something that is always rare in villages). We blessed them with food, toys, school supplies, and candy which had been sent in crates from Greece. His Eminence also blessed them by buying their entire stock of peanut butter as well as handcrafts they had made (which he then distributed as gifts). The entire village was blessed that day, and so were we.
In the village of Hurungwe (outside of the town of Karoi), we participated in the service to consecrate the foundation of their church. Let me take you there :
Red dust kicks up from the ground, highlighting the stark beauty of beiges and browns in the fields and the leafless trees. The rains won't begin for at least another month—you can taste the dust coating your throat. A group of men are singing in jubilation and stomping the dust with vigour. They keep the beat of invisible drums with their hands and one man has shakers and a whistle.
The tiny village of Hurungwe has little to offer— tattered clothing, bare feet, and hungry bellies are in abundance— but today their spirits are full because today their bishop is visiting with a mission team from the United States and Canada. Today, the foundation stone of their new church will be placed into the foundation; it will go under the place where the altar will be built.
Emotions are high for everyone. The team members assist in the service and watch their names being lowered into the foundation as founders of this African church. As they clap and dance along to the songs of the Shona women, they know a part of them will remain in Africa forever.
In Marondera, we saw a building project for a new mission centre which will eventually have a church, a clinic, a school, an orphanage, and a home for a priest. His Eminence dreams big, and big things are happening as a result.
We were blessed to witness a Shona wedding of a young diaconal candidate. His ordination to become a deacon is scheduled for November 2009. The Metropolitan indicated that this young man will likely become a priest soon after he becomes a deacon. This is very exciting news because there are so many Orthodox people but so few priests to serve them.
Currently, there is one Greek priest (Fr George) who serves at the Greek cathedral in Harare, and two Shona priests. One of them, Fr Rafael, serves a community of approximately 300 people in Bulawayo. The people speak Ndebele there so Fr Rafael serves in English and the people sing in English, Ndebele, and Greek. The other priest, Fr Augustine, serves two Shona communities : St. Nektarios (over 800 members in a church that seats 200) and another community in Warren Park (approximately 300 people meeting in the yard of the priest's mother-in-law). Since the priest speaks the language of the people, these two churches are able to have services primarily in Shona, but they also use some English and Greek. Translation of services is on-going, and developing music in a local musical style
is yet to begin. Currently, the churches use Greek melodies as well as the Greek school of iconography.
I've mentioned the Greek people a few times. This may have surprised you. It certainly surprised us! In all of our expectations for Zimbabwe, we did not expect to encounter a little Cyprus and Greece! Many of the Greek people in Zimbabwe are third or fourth generation Zimbabweans. Many still refer to themselves as Rhodesians, since the country has only been called Zimbabwe for 29 years. It was hard to wrestle with the idea of white Africans, but I realized that they have lived there longer than my ancestors have been in North America. Saying that they cannot be African because they are white, is like saying a second or third generation Asian or African, cannot be North American simply because they are not white.
Despite their African roots, the Greek community has remained very distinct, and has maintained close ties with Greece and Cyprus. We enjoyed visiting with these people too, often for yummy Greek meals. We were able to tell them about our experiences with the black churches and how receptive the people are. They were able to tell us stories of Zimbabwe and how it has changed.
One Greek woman we encountered is St Efterpi of Harare. She reposed approximately six years ago. We heard stories of her life and of the miracles after her death. We saw her crypt and experienced the fragrance of myrrh that exudes when she is present. We were able to bring back some of the healing oil that exuded from her incorrupt body that was discovered when she was exhumed three years after her death. This was a very unexpected experience!
At the end of the day, it was hard to leave because of the relationships we had started to form. After two weeks of clinging to us like Velcro, a few small children will now be wondering, "Where did the white women go?" We connected with brothers and sisters in Christ of all colours, genders, and ages in various ways. As we shared our stories and the people shared theirs, we realized how much we have in common even when our day-to-day lives are so different. It was hard to say goodbye to our remarkable brothers and sisters in Christ after such a short time, but we know that they will be praying for us, our churches, and the next team that will come to serve them. Already, I am wondering whether I will be a part of that team. When God asks, "Who shall I send to Zimbabwe?" Will you answer, "Here I am, Lord. Send me"?
Amanda Eve Wigglesworth
<img border="0" hspace="4" align="left" src="http://pravmir.com/wp-content/uploads/pravmir-images/zimbabwe_100.jpg">When we were preparing to go, we didn't know much about this southern African country. We only had a few weeks' notice and no time to ...


You can usually leave it to celebrities to pick out the weirdest names for their kids ("Pilot Inspecktor Lee," we're looking at your parents). But in this case, it was a couple with the surname Miller in Arkansas, who chose the name "Shelby Mustang GT500" for their son, thereby setting him off on a life of petty crime and cruise-night exiting havoc.
On February 2, 2018, Arkansas State Troopers pinched a 29-year-old Mountain Home, Arkansas man for a seat belt violation, which inevitably spiraled into a night in the pokey for failing to show proof of liability insurance, and driving on a suspended license.
This may come as a complete shock to our gentler readers, but this is NOT SHELBY MUSTANG GT500's first offense.
The Smoking Gun reported that Shelby Mustang GT500 had been arrested in Iowa in 2014. That Shelby Mustang GT500 really gets around.
In the 2014 incident, the Des Moines Register reported: Miller, 26, went man0 y mano with patrons at the clearly appropriately named "Cheap Seats Sports Bar" in Des Moines. After departing the bar around 1 AM, he allegedly returned with a hatchet under his shirt. Cops arrested Shelby Mustang GT500 Miller for public intoxication, and for the hatchet under his shirt. He was received a probation violation charge.
It's unclear in The Smoking Gun's reporting if Shelby Mustang GT500 was given the middle name at birth, or whether it was tacked on later, like a set of those chrome portholes from the Pep Boys that you stick on your Nissan Altima decades after it left the showroom.


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You are here: Home1 / Abcam acquires MitoSciences in deal which enhances immunoassay portfol...
Abcam acquires MitoSciences in deal which enhances immunoassay portfolio
24 May 2011 /in Latest News /by connective
24 May 2011: Abcam is pleased to announce it has entered into an agreement to acquire MitoSciences Inc. a leading provider of cutting edge mitochondrial research tools. This represents a further step towards Abcam's mission of becoming the leading supplier of protein research and detection tools.
MitoSciences has over 200 products in the areas of metabolism and apoptosis, including antibody cocktails, sandwich ELISA kits, in-cell ELISA, flow cytometry antibodies and enzyme activity assays. The acquisition enhances Abcam's existing portfolio in these areas and complements an increasing range of non-antibody products. The MitoSciences product range will be available via Abcam's website and authorized distributors within six weeks. Products will carry the MitoSciences logo.
Jonathan Milner, Chief Executive of Abcam said:
"The combined companies will be the market leader in mitochondrial research and will extend our in-house manufacturing and product development capabilities in the exciting area of immunoassay platforms.
"We remain committed to providing customers with the highest quality products available and will continue to deliver MitoSciences' excellence in product performance and customer support.
"We are delighted to have this opportunity to extend our product offering to customers and strengthen our business in this research area. We look forward to welcoming the employees of MitoSciences into the Abcam team and aim for a smooth transition for existing customers."
About MitoSciences
MitoSciences was a privately held biotech company based in Eugene, Oregon (US). The Company produce and distribute immunoassay platforms and high performance monoclonal antibodies. It was founded in 2004 with the mission of advancing mitochondrial research and developing products that support critical research in cancer, neurodegeneration and metabolic disorders.
For further information contact:
Abcam +44 (0) 1223 696000
MitoSciences + 1 541 284 1800
/wp-content/uploads/2020/07/logo.png 0 0 connective /wp-content/uploads/2020/07/logo.png connective2011-05-24 09:00:002020-10-28 15:54:22Abcam acquires MitoSciences in deal which enhances immunoassay portfolio
Jonathan Milner wins Entrepreneur of the Year award Abcam acquires Ascent Scientific, a specialist provider of biochemicals


On Black Friday and Cyber Monday, we leaned instead towards Buy Nothing Day as a way to get through the mad consumerism of the holiday season. However, there are some relatively greener gadgets out there that, if people were going to rush out and get the latest and greatest devices, we're glad they were on the list instead of un-green options. The Kindle, it appears, topped that list. According to Amazon, the device had the best sales so far, outselling everything else on Amazon. Without revealing any actual numbers, Amazon has stated that Kindle had record sales in November.
"Kindle is a great gift for anyone who loves to read and it's flying off the shelves faster than any other product Amazon sells," said Ian Freed, Vice President, Amazon Kindle. "We're seeing lots of people buying from one to a handful of Kindles as gifts for friends or family, as well as many businesses and other organizations buying Kindles in large quantities for their employees or customers."
Compared to buying stacks of books to fulfill a reading fix, an e-reader is a more tree-friendly option. For avid readers, the energy-sipping devices can save a whole lot of paper and emissions from shipping books from publishing facility to store to home. Also, the Kindle 2 has received a firmware upgrade in the form of a better battery. The new battery has an 85% longer active battery life, giving it a week's worth of juice with the 3G turned on, versus four days with the old battery. And with the 3G turned off, that single charge lasts well past two weeks.
With the rush towards e-readers - specifically the Kindle, and the possibility of Apple's rumored Tablet - magazine publishers are taking note and making plans. From the rumor mill comes word that "a number of major magazine publishers are nearing an agreement to launch a joint venture that would be focused on digital distribution of their content, aiming to create a digital storefront similar to Apple's iTunes Store." If that's the case, it would show that even Apple is on-board with supporting reading books on electronic devices.
Most companies dealing in printed literature are already focused on transitioning their materials to a digital format that works with e-readers. The Nook is a prime example of a highly competitive device for the Kindle - though it has been delayed and won't hit store shelves until December 7th. Still, it's a popular holiday purchase as well, already sold out until the new year and only certificates for a Nook to be sent as soon as possible are available.
The popularity of the devices could lead to two ends - first, that the shift to digital reading is further solidified, and second, that there's a big new source of e-waste that'll be seen in the next couple years as people tire of their e-readers, upgrade to newer models next year and so on. Likely both will happen, making the greenest move by the retailers to be educating consumers on caring for their devices for as long as possible and instituting electronics recycling plans. Amazon has a section on its website dedicated to recycling Kindles, but Barnes & Noble so far lacks such easy access to similar information.


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Q: Openstack with neutron on two physical nodes We have two physical system(ubuntu14.04.2) having 2 physical NIC each.
Is it possible to install openstack(juno) with neutron on same ?
Official documentation says that we need 3 nodes with network node having 3 NICs
Any help would be greatly appreciated.
Thanks,
Deepak

A: You can install all of OpenStack on a single system for development and testing purposes.  Given that a single node installation is possible, it should follow that a two-node installation is also possible (and it is).
The documentation recommends three NICs because this leads to the simplest configuration.  However, you can run a network host with two NICs.  There are several different traffic types you'll be dealing with:

*

*Public web (Horizon) traffic

*Public API traffic (if you expose the APIs)

*Internal API traffic

*Tenant internal network traffic (traffic between Nova instances and the compute host)

*Tenant external network traffic (traffic between Nova instances and "the rest of the world")

*Storage (transferring Glance images, iSCSI for Cinder volumes, etc)

Being able to segment these in a meaningful fashion can lead to a more manageable and more performant environment.  With only two NICs, you are probably looking at one for "internal traffic" (interal api, storage, tenant internal networking, etc) and one for "external traffic" (dashboard, public apis, tenant external traffic).  This is certainly possible, but it means, for example, that excessive traffic from your tenants can impact access to the dashboard, and that a high volume of storage traffic can impact access to Nova instances.
If/when your environment grows beyond two nodes, you may want to investigate adding additional NICs to your configuration.

redpajama_set_name: RedPajamaStackExchange


Symptom presentation and severity may be different from child to child. It can also vary in each PANDAS/PANS exacerbation or flare, which may get worse over time. During Treatment, the child's issues may wax and wane. Below is a list of possible PANDAS/PANS symptoms a child may exhibit. Not all symptoms need to be present, and not all possibilities are listed.


This manual is an essential resource for all exercise professionals, as well as other health professionals who may counsel patients on exercise including physicians, nurses, physician's assistants, physical and occupational therapists, dieticians, and health care administrators.
New pre-exercise health screening recommendations are critical to helping more of the population begin a safe, healthy physical activity program without consulting a physician.
Significant reorganization of content will help you reach the content you need quickly.
New and expanded information on the risks of sedentary behavior, clinical exercise testing and interpretation, high intensity interval training, musculoskeletal injury risk, fitness testing protocols and norms, and an expansion of the principles of health behavior change are included.


text:
Debbie Lee Dance
Beginner Classical Ballet
Level 1&2
Pointe & Turns
Classical Ballet
Flamenco & Spanish Classico
Intensive Training Programs
Mentorship & Teaching
Youth Company
Education/School
Rates & Registration
Rates & Tuition
On-line form
info@debbieleedance.com
Debbie Lee | — | – | Carol Mendez | – | Past Instructors & Choreographers | – | –
Debbie Lee
Director / Ballet instructor / Choreographer
For over 30 plus years Ms. Lee has been immersed in the performing arts and education. She has trained, danced, coached, choreographed, directed and mentored students and dancers for classical and multi-disciplinary dance art forms for British Columbia, Ontario, Quebec, Arizona and Colorado and globally for individuals, schools and organizations since the 1970 and1980's. Ms. Lee has now resided as Founder and Artistic Director of Debbie Lee Dance Academy and Company since 2006. She received her foundation training in British Columbia under Soonee Lee, Lynnette Kelly, Lin Yee Goh, Cho Chiat Goh and Che Chun. Upon her extensive training and studies in Vaganova and French pedagogy techniques and receiving her Royal Academy of Dancing Teaching Certificate in her early 20's she continue her pursuit in dance training and professional experience for classical and contemporary dance under numerous independent professional artists across Canada and United States which has helped shape her accomplishments of today. Ms. Lee is passionate about higher dance education and mentorship. Not only has she taught for numerous schools and organization across Canada and the lower mainland of BC, she also was the Founder and Artistic Director of Richmond Hill Academy of Dance, Uxbridge Academy of Dance and DDDance Productions of Ontario, Canada. She was the school director for Telluride Dance Academy – Telluride Society of the Performing Arts (The Joffrey Ballet of Chicago, summer residency) and the Artistic Director for the Yuma Ballet Theatre Company of Arizona. Ms. Lee also had the privilege of accepting a faculty position from Jean-Philippe Malaty and Tom Mossbrucker with The School of Aspen SantaFe Ballet, the official school of Aspen Santa Fe Ballet Company, in Colorado where she spent four years as their school director. Upon retiring her position from Aspen, Colorado she continued to pursue her mentorship and coaching in countries and cities all over the globe where she has inspired students and dancers for the love of classical and contemporary arts. She has also served on The Dance Centre – The Vancouver Dance Centre Society board as one of their directors for four years. Upon her return to her hometown Vancouver in winter of 2004, Ms. Lee dedicates her tireless efforts and valuable experiences to Debbie Lee Dance Academy and Company where she shares her passion and arts education to inspire people of all ages and stages of their training. In addition to caring for the well being of each individual, she brings a unique awareness approach to the teachings of refined strong technical foundation and clean styles. She guides and illuminates each individual's natural creative gift in a progressive, focused and safe environment for dancers of today. Many students that have trained with Ms. Lee are now with National Ballet of Canada, Royal Winnipeg Ballet School, Toronto Dance Theatre, Alonzo King Lines Ballet School, San Francisco Ballet, Gothenburg Ballet, Alvin Ailey Dance School, North Carolina School of the Arts, Interlochen Arts, Boston Ballet School, Washington Ballet School, School of American Ballet Theatre, Cincinnati Ballet School, Utah Ballet, Australia Ballet School, Royal Ballet School, Aspen SantaFe Ballet Company, Bolshoi Ballet Academy, New Jersey Ballet Company just to name a few. Ms. Lee continues to travel internationally where she makes artistic appearances as a guest artist and educator across the globe and attends annually teaching seminars to bring new and progressive dance education to her teachings and Debbie Lee Dance Academy/Company's dance curriculum. Ms. Lee is devoted to her teachings with much enthusiasm and fresh energy. She is often is making guest appearances and workshops for other academies and companies.
Carol Mendez
Guest Contemporary Instructor / Choreographer
Note: All programs as of Fall 2020 with Carol Mendez is now running under the name of "AMOK".
Carol Mendes is a choreographer, dance filmmaker, and dance educator. A native of Brazil, she received her BFA in Dance and her Teaching Certificate from State University of Campinas (Brazil). She also holds a Master's of Fine Arts in Dance Performance and Choreography from New York University, Tisch School of the Arts. Her choreography has been presented at La Mama, Joe's Pub, Judson Church, Triskelion Arts, Martha Graham Studio Theater, Alvin Ailey Citigroup Theater, and at Dixon Place, among others. As a dance filmmaker, Carol has worked with the New York City Ballet Media Department as Production Assistant and Media Fellow. She co-directed and edited her own dance films screened in Brazil, Finland, US, Argentina, and France. She worked as the Production Director and Curator of WestFest Dance Festival in NYC, and she recently spent a year traveling all over the world. She was an artist in residence at Haihatus Art Center in Finland. She has also has participated in classes with Icelandic Dance Company, in Reykjavick. Carol recently received a scholarship to study the ORFF-SCHULWERK method at UNICAMP, in Brazil. She was the Production Director of the X EEMU (UNICAMP's Music Education Encounter) and her newest Dance film project "Untranslatable" has premiered at Danca em Foco back in August 2017 in Brazil. Carol just moved to Vancouver, BC a few years ago and she's looking forward to sharing her passion for dance, art, and culture in our city.
Past Instructors & Choreographers
Kee-Juan Han
Chelsea Mayoh
Suzanne Oulette
Kathryn Crawford
Meredith Kalaman
Joshua Beamish
Erica Trivett
Simone Orlando
Edmond Kilpatrick
Kostya Keshyshev
Eric Burrough
"A dance teacher not only imparts physical knowledge but also formative values. Debbie Lee has the utmost dedication to the dance – not just the skill but the art form. I am so happy my daughter is able to participate. It was evident to me her passion and commitment elicited her students' personal best."
– Dawn Lamping
Progressive Programs in:
Pointe & Demi-pointe
Professional to Recreational Divisions
Mentorship & Teacher Training Programs


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Rock Hill Fire Department: St. Patrick's Parade, 61 Glen Wild Road, Rock Hill, 2 p.m. March 14. Rockhillfiredept.com.
Summitville Fire Company 1: St. Patrick's Day Dinner, 3978 Route 209, Summitville, 4-6:30 p.m. March 14. Snow date March 15. $15; senior citizens, $13; children age 5 and under admitted for free. Take out containers available. All proceeds benefit the Summitville Fire Company 1. 888-2007.
Hudson Valley Restaurant Week, March 16-29. Restaurants will be offering three course, prix-fixe lunches at $22.95 and dinners at $32.95. See the full list of restaurants at valleytable.com/hvrw. Reservations are highly recommended at all restaurants.
Washingtonville High School: Empty Bowls Dinner And Fundraiser, 54 West Main St., Washingtonville, 5:30-7:30 p.m. March 20. Hosted by W.H.S. National Art Honor Society. Guests share a meal in the bowl of their choice. Proceeds benefit the Food Bank of the Hudson Valley and the Country Kids Food Pantry in Washingtonville. Handmade bowls and mugs range from $5-$20. Disposable bowls are $5. Snow date March 27. emptybowlswhs@gmail.com.
Washington's Headquarters State Historic Site: Women's History Month - The General's Lady, Newburgh. 2 p.m. March 22. Inspired by Martha Washington, this event pays tribute to both the impact of noteworthy historical women, and to contemporary women making a difference in the field of history and preservation in the Hudson Valley. Natalie Karl, an adjunct at SUNY New Paltz, will be the guest speaker. Topic is "Victoria Woodhull and Belva Lockwood – First Women to Run for the Presidency." Also celebrated on this day is the 2020 Martha Washington Woman of History Award recognizing a woman's outstanding contribution to Hudson Valley history. This year's recipient is Kinderhook Municipal Historian and Preservationist, Ruth Piwonka, who has been an independent curator and researcher of Dutch heritage and Hudson Valley material culture for more than 50 years. Free. 562-1195.
Anthony's Pier 9: Hospice of Orange and Sullivan Spring Gala Fundraiser, 2975 Route 9W, New Windsor, 6-11 p.m. March 21. Proceeds benefit Hospice's Home Care Program and the Kaplan Family Hospice Residence. For sponsorship opportunities, 50/50 raffle tickets, guest registration or any additional information. Tickets, $250; Table of 10, $2,250. 561-6143, ext. 366.
St. Andrew The Apostle Ukrainian Catholic Church: Ukrainian Pysanky Easter Egg Workshop, 141 Sarah Wells Trail, Campbell Hall, 12:30-3:30 p.m. March 22. $20. All necessary tools and materials provided. Registration required. 496-8753. rcholewka@gmail.com.
Washingtonville High School: Washingtonville Scholarship 5K Run, 54 West Main St., Washingtonville, 10 a.m. March 28. Community members of all ages are invited to participate. 255-1400.
Bosbobel: Demonstration of The Magic Lantern, 1601 Route 9D, Garrison, March 29. Children's show, at noon. Second show called the "Grandfather of Cinema", an illustrated history of the magic lantern at 3 p.m. As early as the 17th century, the magic lantern was used to project hand-painted slides in glowing color. Both presentations feature filmmaker, author, and arcane media specialist Joel Schlemowitz. Boscobel members, $18; $9 for children ages 5-18. Nonmembers, $22; $13 for children. The Magic Lantern is not recommended for children under the age of 5. Please pick up tickets in Boscobel's Visitor Center. Seating is limited. Advanced reservations are recommended. 265-3638. boscobel.org.