Lower bounds to the Weizsacker correction

Gadre, Shridhar R. ; Pathak, Rajeev K. (1982) Lower bounds to the Weizsacker correction Physical Review A, 25 (2). pp. 668-670. ISSN 1050-2947

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Official URL: http://pra.aps.org/abstract/PRA/v25/i2/p668_1

Related URL: http://dx.doi.org/10.1103/PhysRevA.25.668


Two rigorous lower bounds to T2, the Weizsacker correction, have been derived: T2≥(π4/322/3/24)×(∫3(r)dr)1/3=T2B1[ρ] and T2>(1/72)r-2=T2B2[ρ]. The first bound is universal, while the second holds only for spherically symmetric bound systems. Numerical comparisons employing the Hartree-Fock atomic densities reveal that the bounds are not very tight; however, the ratios T2/T2B1 and T2/T2B2, though decreasing slowly with increasing Z, remain fairly constant for Z=2 through 24. The implications of these bounds in the variational context are discussed.

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