Anticrossing spectrometry with synchrotron light

The anticrossing structure of the $1s7l$ manifold of the helium atom in combined dc electric and magnetic fields is studied using a broadband photoexcitation with synchrotron light. The anticrossing signal is provided by the yield of atoms in the metastable $1s2s$ states to which the $1s7l$ states cascade. The mapping resolution depends solely on the homogeneity of the two fields in the target region, which is formed by the intersection of the synchrotron beam and the helium atom beam. The measured positions, as well as anticrossing intensities and widths, measured in the region of 1–1.5 kV/cm and 0–10 mT are in excellent agreement with the results of our extended theoretical simulations based on highly accurate zero-field wave functions. By centering the photoexcitation window to 65.110 and 65.130 eV, the same technique is applied to look for the anticrossings in the vicinity of the $7^{+}{}^1{P}_1^o–7d{}^3{D}_1^o$ and $7d{}^1{P}_1^o–8^{-}{}^1{P}_1^o$ pairs of doubly excited states, respectively.

Figure 1

Schematic of the experimental setup with the light beam and the supersonic atomic beam intersecting in the center of electric-field plates and magnetic-field coils.

Figure 2

Emission cascades in the He atom started by broadband photoexcitation of (a) the $n=7$ SES manifold and (b) the $7^{+}{}^1{P}_1$ and $7d{}^3{D}_1$ DESs below the $N=2$ ionization threshold.

Figure 3

Multiplet coupling due to $V_{\mathrm{so}}$ (SO), dc electric-field (F), and magnetic-field (B) interaction.

Figure 4

Energy levels $E_1$ and $E_2$ [Eq. (7)] and the first $[d{E}_1/d\delta F$ and $d{E}_2/d\delta F$, Eq. (10)] and second $[d{E}_1^2/d\delta F^2$, Eq. (13)] derivatives in a.u. depending on the electric-field detuning $\delta F$. Also presented is the field dependence of weights of asymptotic states $[w_{{\eta }_1}$ and $w_{{\eta }_2}$, Eq. (11)] and of their product $w_{{\eta }_1}{w}_{{\eta }_2}$ [Eq. (12)] in the vicinity of the anticrossing for $E_a+E_b=0$ a.u., $\gamma =0.7$ a.u., and $v=0.8$ a.u.

Figure 5

Measured (black dots) MY dependence on the dc electric field $F$ for different values of the magnetic field $B$. For a clear comparison the calculated probabilities $P_{\mathrm{MY}}$ to populate metastable states [pink (gray) curves] are offset by 0.002 for each 0.25-mT increase of $B$. Measured MY trends are denoted by the coil current and have an offset according to the magnetic-field calibration.

Figure 6

(a) Energy levels of the $n=7$ manifold as a function of $F$ at $B=0$ showing also the parent multiplet type. (b) Scaled level gradients uncover positions of anticrossings. Experimental data are shown by black circles and three Lorentzians fitted to the calculated trend by solid lines. The one-step decay contribution is given by the dotted line. (c) The $F$ dependence of ${}^1\mathrm{P}$ and ${}^3\mathrm{P}$ weights for the 26 photoexcited levels with $M=0$. Bold lines denote weights for levels that form crossings with the largest observed TMY signal.

Figure 7

(a) Gradients of energy levels in the $n=7$ manifold at $B=8.5$ mT (black curves). Measured MYs are shown by black points and calculated MYs by the red (gray) curve. The distribution of coupling strengths $\left|v\right|$ sticks to zero. (b) The ${}^{1}P(M=0)$ multiplet weight (red curves) and the sum of ${}^3{L}_J$ multiplet weights (black curves) and their product $w_{1P1}^i{w}_{3LJ}^i$ (blue curves) for each level in the manifold. The sum of products for all levels is denoted by the thick blue line.

Figure 8

Effective branching ratios ${\nu }_s$ and ${\nu }_t$ for the production of SMY and TMY, respectively, for a broadband photoexcitation of the $n=7$ manifold of states when (a) $B=0$ and (b) $B=8.5$ mT. Arrows beside the graphs indicate the vertical scale to be used.

Figure 9

(a) The MY dependence on photon energy for $F=0$ in the region of the $n=7$ DES for two different beamline slit settings [$30\mu \text{m}$ and $100\mu \text{m}$ (solid line), $30\mu \text{m}$ and $200\mu \text{m}$ (dashed line)]. Bars denote calculated energy positions [10] and the expected MY from DESs [24]. Also shown is the measured MY and modeled $P_{\mathrm{MY}}$ trends as a function of $F$ when the $n=7$ SES manifold is populated by radiative decay of photoexcited $7^{+}{}^1{P}_1$ and $7d{}^3{D}_1$ DESs for (b) $B=0$ and (c) $B=7$ mT. The $M$-specific $P_{\mathrm{MY}}$ curves are offset for 0.35.