Large-scale multiconfigurational Dirac-Fock calculations of the hyperfine-structure constants and determination of the nuclear quadrupole moment of <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow></mrow><mrow><mn>49</mn></mrow></msup></mrow><mi mathvariant="normal">Ti</mi></math></span>

Jacek Bieroń; Charlotte Froese Fischer; Ian P. Grant

doi:10.1103/PhysRevA.59.4295

Large-scale multiconfigurational Dirac-Fock calculations of the hyperfine-structure constants and determination of the nuclear quadrupole moment of $^{49} Ti$

Jacek Bieroń, Charlotte Froese Fischer, and Ian P. Grant

Phys. Rev. A 59, 4295 – Published 1 June 1999

Abstract

The multiconfiguration Dirac-Fock (MCDF) model is employed to compute the hyperfine interaction constants of the ${3 d}^{2} 4 s^{2} D_{3 / 2},$ ${3 d}^{2} 4 s^{2} D_{5 / 2},$ ${3 d}^{3}^{2} G_{7 / 2},$ ${3 d}^{3}^{2} G_{9 / 2},$ and ${3 d}^{3}^{2} P_{3 / 2}$ levels of titanium ion. The wave function expansions are obtained with the active space expansion method, where configuration state functions of a specific parity and J value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the expectation values to be achieved. The calculated electric quadrupole hyperfine constants are used to evaluate the nuclear electric quadrupole moment of isotope 49 of titanium, for which the value $Q = 0.247 (11) b$ is found.