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A. T. GOBLE actual roots agreement amplitude factors angular momentum Ca5c chosen closed shells complex spectra computed correct phase correspondence principle coupling coefficients d°p configur determined diagonal electrostatic interaction electrostatic parameters experimental values extra-configurational Four Vector Problem group theory Houston hyperfine structure indicated intermediate coupling intervals isoelectronic j-j coupling j-j system jj values jj wave functions Kronig magnetic interaction magnetic terms matrix elements matrix multiplication Method 1 Method Method 2 J=4 multiplet notation Obi Calc observed intensities observed values overall triplet width percent perpendicular perturbation theory phase factors Phys Platinum-Like Spectra plotted in units precession pure jj levels quantum mechanics Russell Russell-Saunders coupling Russell-Saunders system Saunders second order perturbation secular equations selection rules set of calculations Shortley relations single electron Slater problem system of representation thallium Theoret ical Method theoretical values tion Tl IV values are given vector algebra Vleck wave equation