X-ray emission associated with radiative recombination for ${\mathrm{Pb}}^{82+}$ ions at threshold energies

For decelerated bare lead ions at a low beam energy of 10 MeV/u, the x-ray emission associated with radiative recombination (RR) at threshold energies has been studied at the electron cooler of CRYRING@ESR at GSI, Darmstadt. In our experiment, we observed the full x-ray emission pattern by utilizing dedicated x-ray detection chambers installed at $0^{\circ }$ and ${180}^{\circ }$ observation geometry. Most remarkably, no line distortion effects due to delayed emission are present in the well-defined x-ray spectra, spanning a wide range of x-ray energies (from about 5 to 100 keV), which enables us to identify fine-structure resolved Lyman, Balmer, and Paschen x-ray lines along with the RR transitions into the $K, L$, and $M$ shells of the ions. For comparison with theory, an elaborate theoretical model is established taking into account the initial population distribution via RR for all atomic levels up to Rydberg states with principal quantum number $n=165$ in combination with time-dependent feeding transitions. Within the statistical accuracy, the experimental data are in very good agreement with the results of rigorous relativistic predictions. Most notably, this comparison sheds light on the contribution of prompt and delayed x-ray emission (up to 70 ns) to the observed x-ray spectra, originating in particular from yrast transitions into inner shells.

Figure 1

Experimental setup at the electron cooler of the CRYRING@ESR storage ring. The x-ray emission from the electron-ion beam interaction region is viewed at $0^{\circ }$ and ${180}^{\circ }$ by Ge(i) detectors. X rays are measured in coincidence with down-charged ${\mathrm{Pb}}^{81+}$ projectiles detected by the particle counter installed behind the electron cooler. A length scale and a timescale, valid for a beam velocity of $\beta \approx 0.146$ (10 MeV/u), are shown at the bottom. Note that the time of flight of the ions passing the cooler section is close to 30 ns, whereas the time of flight of ions from the entrance of the cooler section up to the end of the straight section amounts to 70 ns.

Figure 2

X-ray spectra measured at observation angles of ${180}^{\circ }$ (left) and $0^{\circ }$ (right) by the two Ge(i) detectors in coincidence with 10 MeV/u ${\mathrm{Pb}}^{81+}$ projectiles detected after the electron cooler of the CRYRING@ESR storage ring. X-ray energies are given in the laboratory frame.

Figure 3

Two-dimensional presentation of the coincidence time $\mathrm{\Delta }t$ versus the x-ray emission observed a $0^{\circ }$ (laboratory frame). The coincidence time refers to the time difference between photon (start) and particle (stop) detections (relative timescale). $\mathrm{\Delta }{t}_1\approx 30$ ns refers to the cooler section; $\mathrm{\Delta }{t}_2\approx 40$ ns refers to the region outside the electron cooler.

Figure 4

State-selective rate coefficients ${\alpha }_{nl}$ calculated for RR into bare lead ions for the flattened electron velocity distribution with $k{T}_{\perp }=2.59$ meV and $k{T}_{\parallel }=51.8\mu \mathrm{eV}$ at the CRYRING@ESR electron cooler. A relativistic description of the RR process for inner shells up to $n=10$ is considered here, whereas for higher shells the nonrelativistic dipole approximation is applied.

Figure 5

Differential cross sections per vacancy calculated within the framework of the rigorous relativistic theory applied for RR of free electrons with bare lead ions at a relative electron-ion energy of 2.59 meV. (a) For the $K$ shell and (b) for the various levels of the $L$ shell (solid line: $2p_{3/2}$; dash-dotted line: $2p_{1/2}$; dashed line: $2s_{1/2}$).

Figure 6

The Lyman series and the $K$-RR measured at $0^{\circ }$ (top) and ${180}^{\circ }$ (bottom) relative to the ion-beam axis (thin gray lines). The thick red lines display results of the simulation (for details see the text). The intensity of the $K$-RR line is used for normalization. In the level diagram all possible transition types between the states with $n=1,2$ in H-like lead are shown.

Figure 7

X-ray spectra associated with prompt $L$-RR and $M$-RR radiation together with characteristic Balmer and Paschen transitions measured by two Ge(i) detectors placed at $0^{\circ }$ (top) and ${180}^{\circ }$ (bottom) with respect to the ion-beam axis (thin gray lines). The thick blue lines give the results of the cascade simulation. Two intense Balmer transitions are Balmer-${\alpha }_1, 3(j=5/2)\to 2(j=3/2)$, and Balmer-${\alpha }_2, 3(j=3/2)\to 2(j=1/2)$. In the level diagram the Balmer transitions relevant for our measurement are shown.

Figure 8

Cascade calculations of the characteristic line intensities as a function of the flight time of the charge-exchanged ${\mathrm{Pb}}^{81+}$ ions at 10 MeV/u at the electron cooler of the CRYRING@ESR storage ring. All line intensities are normalized to the $K$-RR population [gray solid (upper) line: Ly-${\alpha }_1/K$-RR; gray dash-dotted line: Ly-${\alpha }_2/K$-RR; blue solid (lower) line: Balmer-${\alpha }_1/K$-RR; blue dashed line: Balmer-${\alpha }_2/K$-RR; red dotted line: Paschen-$\alpha /K$-RR]. Calculations are performed for recombination into excited projectile states up to $n=165$.

Figure 9

Experimental results in comparison with the time-dependent theoretical model (gray columns) for characteristic line intensities normalized to that of the $K$-RR population. White columns with horizontal stripes show experimental data at $0^{\circ }$; white columns with vertical stripes show experimental data at ${180}^{\circ }$.