Populations and lifetimes in the $v=n-\ell -1=2$ and 3 metastable cascades of $\overline{p}{\mathrm{He}}^{+}$ measured by pulsed and continuous antiproton beams

The time evolution of the state populations in the $v\equiv n-\ell -1=2$ and 3 metastable cascades of antiprotonic helium (${\overline{p}}^4{\mathrm{He}}^{+}$) atoms were studied using laser spectroscopy. The antiprotonic states $(n,\ell )=(39,35)$, (40,36), and (41,37) in the $v=3$ cascade were estimated to initially contain, respectively, $(0.28\pm 0.04)\%$, $(0.06\pm 0.02)\%$, and $(0.02\pm 0.01)\%$ of the antiprotons stopped in the helium target, while the corresponding values for states $(37,34)$, $(38,35)$, and $(39,36)$ in the $v=2$ cascade were $(0.21\pm 0.04)\%$, $(0.49\pm 0.07)\%$, and $(0.19\pm 0.07)\%$. The shortening of the state lifetimes due to collisions between $\overline{p}{\mathrm{He}}^{+}$ and helium atoms was studied. As the atomic density of the target was increased from $\rho =2\times {10}^{20}$ to $2\times {10}^{21}{\mathrm{cm}}^{-3}$, the lifetime of state $(37,34)$ decreased by an order of magnitude, whereas the higher states $(38,35)$ and $(39,35)$ were relatively unaffected. Between densities $\rho =6\times {10}^{20}$ and $2\times {10}^{22}{\mathrm{cm}}^{-3}$, a short-lived component with a time constant $\tau \sim 0.2\mu \mathrm{s}$ appeared at early times in the delayed annihilation time spectrum of $\overline{p}{\mathrm{He}}^{+}$, while the total fraction of long-lived antiprotons decreased from 3.0 to $2.5\%$. These effects were caused by the lifetime-shortening of specific $\overline{p}{\mathrm{He}}^{+}$ states such as $(37,34)$.

Figure 1

Portion of the level structure of ${\overline{p}}^4{\mathrm{He}}^{+}$, with observed transition wavelengths shown in nanometers. The solid lines indicate radiation-dominated metastable states, the wavy lines Auger-dominated short-lived states. The theoretical values for Auger [22, 33] and radiative transition [32] rates from some states $(n,\ell )$ are shown. The broken lines indicate $\overline{p}{\mathrm{He}}^{2+}$ ionic states formed after Auger emission, the curved arrows indicate Auger transitions with minimum $\mid \Delta \ell \mid$. On the left-hand scale the theoretical absolute energy of each state is plotted relative to the three-body breakup threshold.

Figure 2

Delayed annihilation time spectrum measured using a pulsed antiproton beam, with the resonance transition $(n,\ell )=(39,35)\to (38,34)$ at wavelength $\lambda =597.3\mathrm{nm}$ induced at $t=1.6\mu \mathrm{s}$ (a). The hatched area represents the estimated contribution of ${\pi }^{+}\to {\mu }^{+}\to e^{+}$ decay. The background-free spectrum was measured using a continuous antiproton beam at the same target conditions, the spike was induced at the same timing (b).

Figure 3

Schematic layout of the experiments using pulsed (top) and continuous (bottom) antiproton beams.

Figure 4

Estimated ratios of antiprotons stopping in the volume of the helium target irradiated by the laser beam, as a function of polyimide degrader thickness (a),(b). A two-dimensional projection of the target chamber, showing the spatial distribution of the stopped antiprotons at two target densities, and the degrader thicknesses indicated by the arrows (c),(d).

Figure 5

The simulated range curve of annihilation events along the longitudinal direction of the antiproton beam. Some $3\%$ of the antiprotons annihilate in nuclear reactions in-flight, the contribution of which is shown by the hatched area. The unshaded area represents antiprotons that form atoms.

Figure 6

Delayed annihilation time spectra, measured at a target pressure $P=0.5\mathrm{bar}$ and temperature $T=6.4\mathrm{K}$ (a), $P=2.7\mathrm{bar}$ and $T=5.8\mathrm{K}$ (b), and a superfluid target at $T=1.8\mathrm{K}$ (c).

Figure 7

The fractions of antiprotons surviving more than $20\mathrm{ns}$ (a), $1\mu \mathrm{s}$ (b), and $5\mu \mathrm{s}$ (c) at various densities of the helium target.

Figure 8

Typical temporal profile of the laser pulse with an energy density $\Theta =1\mathrm{mJ}∕{\mathrm{cm}}^2$ (a). Experimental (solid line) and theoretical (dotted line) profiles of the $597.3\text{−}\mathrm{nm}$ resonance spike (b). The simulated population evolution of the resonance parent state $(n,\ell )=(39,35)$ during the laser pulse (solid line), and the measured depopulation efficiency (closed circle) (c).

Figure 9

Experimental (closed circles) and theoretical (solid line) depletion efficiencies of the laser pulse tuned to the transition $(39,35)\to (38,34)$ at wavelength $\lambda =597.3\mathrm{nm}$ at various energy densities of the laser.

Figure 10

Delayed annihilation time spectra measured using the pulsed antiproton beam, the resonance transition $(n,\ell )=(39,35)\to (38,34)$ at wavelength $\lambda =597.3\mathrm{nm}$ induced at $t=0.3\mu \mathrm{s}$ (a), $2.3\mu \mathrm{s}$ (b), and $4.3\mu \mathrm{s}$ (c). The population evolution of state $(39,35)$ was measured using the pulsed (closed circles) and continuous (triangles) antiproton beams (d). All data were measured at a target pressure $P=0.5\mathrm{bar}$ and temperature $T=5.8\mathrm{K}$.

Figure 11

Delayed annihilation time spectra measured by irradiating two successive laser pulses tuned to the transition $(n,\ell )=(39,35)\to (38,34)$ at wavelength $\lambda =597.3\mathrm{nm}$, the first laser fired at $t_1=1.6\mu \mathrm{s}$, the second laser at $t_2=1.8\mu \mathrm{s}$ (a), $3.6\mu \mathrm{s}$ (b), and $5.6\mu \mathrm{s}$ (c). Time variations of the resonance intensities for cases where the first laser (closed squares) is fired at $t_1=1.6\mu \mathrm{s}$, and the second (closed circles) varied between $t_2=2.4$ and $9\mu \mathrm{s}$ (d); corresponding measurements made at a $t_1$ value of $2.6\mu \mathrm{s}$ (e), $3.6\mu \mathrm{s}$ (f), and $4.6\mu \mathrm{s}$ (g). Time variation of the resonance intensity was measured using a single laser pulse (h). Solid lines represent the best fit of a three-level cascade model.

Figure 12

The population evolution of state $(n,l)=(37,34)$ measured at five target densities, using the resonance transition $(37,34)\to (36,33)$ at wavelength $\lambda =470.7\mathrm{nm}$.

Figure 13

The delayed annihilation time spectrum measured with a single laser pulse inducing the transition $(n,l)=(37,34)\to (36,33)$ at wavelength $\lambda =470.7\mathrm{nm}$ (a). The double-resonance transition $(38,35)\to (37,34)\to (36,33)$ induced using two simultaneous laser pulses tuned to ${\lambda }_1=470.7\mathrm{nm}$ and ${\lambda }_2=529.6\mathrm{nm}$ (b). Both spectra were measured at a target pressure $P=1.3$ bar and temperature $T=5.8\mathrm{K}$. The population evolution of (38,35) (closed circles) and (37,34) (triangles) measured at four target densities (c)—(f).

Figure 14

The depletion-recovery spectrum of the transition $(n,l)=(38,35)\to (37,34)$ (a), and that of the double-resonance transition $(38,35)\to (37,34)\to (36,33)$ (b). Both spectra were measured at a target pressure $P=1.3\mathrm{bar}$ and temperature $T=5.8\mathrm{K}$. The lifetimes of (38,35) (closed circles) and (37,34) (triangles) at various densities (c).

Figure 15

The three-level cascade model. The populations in states $(n,l)=(38,35)$, (37,34) and (36,33) before laser irradiation are denoted by $P_{(38,35)}\left(t\right)$, $P_{(37,34)}\left(t\right)$, and $P_{(36,33)}\left(t\right)$; the feeding from the surrounding states by $V_{(n,l)}\left(t\right)$. The double-resonance transition induced by two simultaneous laser pulses at wavelengths ${\lambda }_1=470.7\mathrm{nm}$ and ${\lambda }_2=529.6\mathrm{nm}$ modify the state populations from $P_{(n,l)}\left(t\right)$ to $P_{(n,l)}^{\prime }\left(t\right)$.

Figure 16

Time-variation of the intensity of the resonance transition $(n,l)=(37,34)\to (36,33)$ measured using two laser pulses fired at timing $t_1$ (closed squares) and $t_2$ (closed circles) tuned to wavelength $\lambda =470.7\mathrm{nm}$. Measurements were made at three target conditions: $P=0.2\mathrm{bar}$, $T=6.4\mathrm{K}$ [(a)-(e)], $P=0.6\mathrm{bar}$, $T=6.4\mathrm{K}$ [(f)-(i)], and $P=1.0\mathrm{bar}$, $T=6.6\mathrm{K}$ [(j)-(n)]. The results of the best fit of a three-level cascade model are shown in solid lines.