We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$ H=((D-A)\cdot\boldsymbol{ \sigma})^2-V $$ with $$V=\sum_{ 1\le m\le M} \frac{ Z_m}{ |x-y_m|}$$ and a corresponding Multiparticle Quantum Hamiltonian $$ \mathsf{ H}=\sum_{ 1\le n\le N} H_{ x_n} +\sum_{ 1\le n < n'\le N}|x_n-x_{ n'}|^{ -1} $$ on the Fock space $\wedge _{ 1\le n\le N} L^2(\mathbb{ R}^3, \mathbb{ C}^2)$. Here $A$ is a self-generated magnetic fiels. Then the ground state energy is given by $$ \mathsf{ E}(A)=\inf \operatorname{ Spec}(\mathsf{ H})+\frac{ 1}{ \alpha}\int |\nabla \times A|^2\,dx $$ where the last term is the energy of magnetic field. Under assumption $\alpha Z\le \kappa^*$ (with a small constant $\kappa^*$) we study the ground State Energy $$ \mathsf{ E}^*=\inf _{ A}\mathsf{ E}(A). $$ We derive its asymptotics including Scott, and Schwinger and Dirac corrections. We also consider related topics: an excessive negative charge, ionization energy and excessive positive charge when atoms can still bind into molecules.
Categories: math-ph math.MP math.SP