We consider the multidimensional Newton-Einstein equation in static electromagnetic field $$\eqalign{ \dot p = F(x,\dot x), F(x,\dot x)=-\nabla V(x)+{ 1\over c}B(x)\dot x,\cr p={ \dot x \over \sqrt{ 1-{ |\dot x|^2 \over c^2}}}, \dot p={ dp\over dt}, \dot x={ dx\over dt}, x\in C^1(\R,\R^d),}\eqno{ (*)}$$ where $V \in C^2(\R^d,\R),$ $B(x)$ is the $d\times d$ real antisymmetric matrix with elements $B\_{ i,k}(x)={ \pa\over \pa x\_i}\A\_k(x)-{ \pa\over \pa x\_k}\A\_i(x)$, and $|\pa^j\_x\A\_i(x)|+|\pa^j\_x V(x)| \le \beta\_{ |j|}(1+|x|)^{ -(\alpha+|j|)}$ for $x\in \R^d,$ $|j| \le 2,$ $i=1..d$ and some $\alpha > 1$. We give estimates and asymptotics for scattering solutions and scattering data for the equation $(*)$ for the case of small angle scattering. We show that at high energies the velocity valued component of the scattering operator uniquely determines the X-ray transforms $P\nabla V$ and $PB\_{ i,k}$ for $i,k=1..d,$ $i\neq k.$ Applying results on inversion of the X-ray transform $P$ we obtain that for $d\ge 2$ the velocity valued component of the scattering operator at high energies uniquely determines $(V,B)$. In addition we show that our high energy asymptotics found for the configuration valued component of the scattering operator doesn't determine uniquely $V$ when $d\ge 2$ and $B$ when $d=2$ but that it uniquely determines $B$ when $d\ge 3.$
Categories: math-ph math.MP