Isotope shifts of double-excitation resonances in helium

Isotopic effects on double-excitation resonances in ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ were observed in photoionization spectra using synchrotron radiation with high monochromator resolution. In ${}^3\mathrm{He}$, the resonances were found to be shifted to lower energies with respect to ${}^4\mathrm{He}$ by $\Delta E=3.06\pm 0.07\text{meV}$, in good agreement with theoretical expectations based on normal and specific mass shifts. From the experimental data, the resonance parameters $E_r$, $\Gamma$, and $q$ of the resonances $2,-1_3,$ $2,1_4,$ and $2,0_7$ were analyzed in detail using a double-convolution fit procedure that considers the different Doppler broadenings of the states in ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$. In this way, the resolution function of the monochromator could be derived, which can be accounted for in a quantitative way on the basis of the properties of undulator radiation and the optical design of the monochromator.

Figure 1

Photoionization spectra of the resonances $2,-1_n$ (with $n=3$ to 6), $2,1_n$ (with $n=4$ to 7), and $2,0_7$ in ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$, respectively, measured on a ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ gas mixture. The resonance positions are marked for ${}^4\mathrm{He}$ (${}^3\mathrm{He}$) by solid (dash-dotted) vertical bars.

Figure 2

Photoionization spectra of a ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ gas mixture recorded in the regions of (a) the $2,-1_3$ and $2,1_4$ resonances; and (b) the $2,0_7$ resonance of doubly excited helium. The solid lines through the data points represent the fit results obtained with a monochromator function consisting of a Gaussian plus a Lorentzian (for details, see text). The solid (dash-dotted) subspectra represent the resonances of ${}^4\mathrm{He}$ (${}^3\mathrm{He}$). Simulations of a resonance with $q=3$, and with $\Gamma =1$ and $100\mu \text{eV}$, respectively, are plotted in the inset of (a) using a Gaussian resolution function with a width of $1\text{meV}$.

Figure 3

Derived resolution function $f(E^{\ast },{\Omega }_M)$ of the PGM monochromator, $E^{\ast }=E^{\prime }-E^{″}$ is the energy with respect to the monochromator energy $E^{\prime }$, $\mathrm{G}+\mathrm{G}$ represents one monochromator-resolution model given by the sum of two Gaussians, while $G+L$ stands for the other model given by the sum of a Gaussian and a Lorentzian function. The dash-dotted curve represents the results of ray-tracing simulations (see text).

Figure 4

Monochromatic intensity distribution on focusing mirror $M_3$ for the two undulator settings, with $K=2.19$ and 2.18, respectively.

Figure 5

Schematics of beamlime $\mathrm{U}125∕1\text{−}\text{PGM}$ at BESSY II. Two plane gratings G with 300 and $1200\text{lines}∕\text{mm}$ can be selected. $M_1$: toroidal mirror with tangential radius $R=658760\text{mm}$ and sagittal radius $\rho =1772\text{mm}$, $M_2$ plane mirror, $M_3$: cylindrical mirror with $\rho =1040\text{mm}$, $M_4$: spherical mirror with $R=46200\text{mm}$, $M_5$: cylindrical mirror with $\rho =101\text{mm}.$