Interference effects in the intensity of (blue) and (red) branches between a pure Hund’s case (b) lower state, , and an upper state that is mixed in this basis. Plotted is the transition intensity (scaled to 1) as a function of the mixing coefficient, . In (a) the transition is into the states , from a lower state, . The plot for the case of the upper state is a mirror image of the plot in (a) with the axis as the axis of reflection. Plot (a) is a square of the sum of and contribution plotted in (b) for both (blue) and (red) transitions. Distortion of the pattern in (a) by -mixing is shown in (c). Here both states involved in the transition are -mixed in addition to being -mixed, the lower state is and the upper state is , with and . Both (a) and (b) plots were produced using Eq. (5) from Ref. 3, but with a correction that in that equation should appear with the exponent instead of . It was assumed that , , and in the plot. The intensities are scaled in the same manner as in (a). Since there are no states in the CaF Rydberg supercomplex, there are no interferences in the branches excited from a intermediate state.
Transition dipole moments for which of the Rydberg electron changes by , in a.u. Part (a) gives the variation in the ⟨, , ⟩ transition dipole moment with , calculated using hydrogenic wavefunctions (for integer values of ). (b) displays the dependence of the intracomplex (same-) transition dipole moments on the quantum defect, , for the ⟨, , ⟩ transition moment, where varies between and 1. Nonhydrogenic dipole moments were evaluated using the method described in Ref. 38.
Calculated or experimentally observed (where available) energies of all of the core-nonpenetrating states that belong to the cluster in . Most of the states are located near the center of the cluster, especially at higher values of and . Outliers are found among lower-, lower- states for which the evolution toward Hund’s case (d) is not complete, or where core-penetration effects are non-negligible.
Stark effect in the energy region around the integer value of , experimentally observed in double resonance spectra from the intermediate state, in the polarization arrangement. A weak electric field causes the Stark manifolds associated with different values of to appear, but as the field increases, these manifolds overlap and, owing to Stark interactions among them, are expected to merge when the field increases sufficiently. The electric field in V/cm is given on the right hand side of the plot. The values of the dominant zero-field bright features are marked on the plot.
Interaction among , , and 13.19 states. The labels at high correspond to the assignments in Ref. 6. Marker sizes approximately represent the experimentally observed intensities of the spectral features. The interactions among these three states become apparent only for rotational levels, and could remain unnoticed if the lowest- rotational assignments are not available.
Calculated (upper traces) and experimentally observed (lower traces) Stark effect in the double resonance spectra of the Rydberg states of CaF in the vicinity of . Spectra are accessed through the level of the intermediate state (accessed through an pump transition from the ground state) in the polarization arrangement. The electric fields are (a) , (b) , (c) , and (d) . For the discussion of occasional disagreements between the observed and calculated transition intensities see Sec. V B.
Stacked double resonance spectra at (a) and (b) , recorded from , 1, 2, and 3 (bottom to top), in the polarization arrangement. Electric-field-induced mixing (, , , ) results in intensity borrowing and the appearance of new features in the spectrum. Transitions that terminate in different values of are color-coded according to the value of , with the corresponding values of given in the same color on the plot.
Double resonance spectrum of CaF at in the vicinity of , recorded from in RHCP-RHCP-vertical (red) and RHCP-LHCP-vertical (blue) arrangements. The arrow identifies the region in the spectrum where the -mixing within a particular cluster due to the external electric field is incomplete, but polarization dependence associated with a -type transition into the bright state is still preserved.
Double resonance spectrum of CaF at in the vicinity of , recorded from in (red) and (blue) arrangements. The arrow identifies a feature that exhibits a distinct -like polarization dependence at , even though the surrounding features have lost the polarization dependence characteristic of a each value due to -mixing induced by the field. This polarization behavior, different from other features in the cluster at the same electric field amplitude, is explained by an accidental degeneracy between two states that have different values of .
Selection rules for interactions discussed in the text. Matrix elements for these types of interactions are nonzero when the conditions from the table are satisfied.
Best fit values for the mixing coefficients of rotationless , , , , and states. The basis state was not included in the fit, as it was not located near an integer value of . Its -decomposition corresponds to that of Ref. 5. Nonunity in the sum of squared mixing coefficients is due to the loss of basis state character due to coupling with higher- states.
Assignments of lowest-, low- [denotes , where is the projection of on the ion-core rotational axis], -states .
Assignments of lowest-, low-, -states .
Assignments of lowest-, low-, -states .
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