Nuclear recoil spectroscopy of levitated particles

We propose a method for the detection and characterization of nuclear decay processes. Specifically, we describe how nuclear decay recoil can be observed within small particles levitated in an optical trap with high positional resolution. Precise measurements of the magnitude of each recoil as well as their rate of occurrence can provide accurate information about the isotopic composition of a radioactive sample. We expect that this technique for nuclear material characterization will be especially useful in the area of nuclear forensic analysis.

Figure 1

(a) Schematic diagram of $\alpha \mathrm{decay}$ in a free solid particle: the solid particle containing the daughter atom (not pictured) recoils in the opposite direction to that of the alpha particle. (b) Schematic diagram of $\beta \mathrm{decay}$ in a free solid particle: a neutrino ($\nu$) and a beta particle initiate recoil of the solid particle. (c) Simplified model of the recoil of the solid particle in an optical trap approximated as a 1D harmonic oscillator.

Figure 2

(a) Recoil rate as a function of particle diameter for ${}^{241}\mathrm{Pu}, {}^{239}\mathrm{Pu}$, and ${}^{235}\mathrm{U}$ particles in oxide form ($\mathrm{PuO}{}_2$ and $\mathrm{UO}{}_2$). (b) Particle displacement due to nuclear recoil as a function of particle diameter in a 1-kHz optical trap. The $\beta \mathrm{recoil}$ is calculated under the assumption of a zero neutrino momentum and mean $\beta \mathrm{energy}$.

Figure 3

Performance of a 9-kHz optical trap: (a) The displacement due to $\alpha \mathrm{decay}$ in a ${}^{239}\mathrm{Pu}$ sample is compared to the thermal noise at ambient conditions. (b) The displacement due to $\alpha \mathrm{decay}$ in a ${}^{239}\mathrm{Pu}$ sample is compared to the amplitude of the c.m. motion of a particle cooled to 1.5 mK, and also compared to the motion of a particle cooled to the $T_{\text{SQL}}$ of 0.42 $\mu \mathrm{K}$, rescaled from $T_{\text{SQL}}\sim 5.6\mu \mathrm{K}$ for a 120 kHz trap, as reported in [4, 23].

Figure 4

SNR for $\alpha -\mathrm{recoil}$ spectroscopy in a 9-kHz optical trap for a ${}^{239}\mathrm{PuO}_2$ sample at different temperatures: $T_{\text{c.m.}}=1.5\mathrm{mK}, T_{\text{noise}}=0.1\mathrm{mK}$ (as demonstrated in [3]), and $T_{\text{SQL}}=0.42\mu \mathrm{K}$.

Figure 5

$\alpha -\mathrm{recoil}$ spectroscopy in a 9-kHz optical trap for a ${}^{209}\mathrm{Po}$ sample containing 9% ${}^{208}\mathrm{Po}$ and 1% ${}^{210}\mathrm{Po}$: (a) $d=70\mathrm{nm}$ and (b) $d=140\mathrm{nm}$. The insets demonstrate the resolved (a) and unresolved (b) nuclear energy structure of ${}^{209}\mathrm{Po}$ decay: $\alpha -\mathrm{particle}$ kinetic energies of $\sim 4883$ and $\sim 4885\mathrm{keV}$ are related to the ${}^{205}\mathrm{Pb}$ daughter being in the excited and ground states, respectively. The upper horizontal axes relate the displacement of the solid particles to the kinetic energy of the emitted nuclear particles.

Figure 6

$\alpha -\mathrm{recoil}$ spectroscopy in a 0.9-kHz optical trap for an 80% ${}^{239}\mathrm{Pu}$/20% ${}^{240}\mathrm{Pu}$ particle ($d=300\mathrm{nm}$) at $T_{\text{SQL}}=42\mathrm{nK}$ with and without $\gamma -\mathrm{recoil}$ broadening. Inset demonstrates that the SNR for detecting $\alpha \mathrm{recoil}$ ($E_{\alpha }=5105.5\mathrm{keV}$) in small particles is dominated by the associated $\gamma \mathrm{decay}$ ($E_{\gamma }=51.7\mathrm{keV}$).

Figure 7

(a) $\alpha -\mathrm{recoil}$ spectrum for a recently purified ${}^{241}\mathrm{Pu}$ sample containing 1% ${}^{241}\mathrm{Am}$ for various particle diameters. (b) $\alpha -$ and $\beta -\mathrm{recoil}$ spectrum for an aged ${}^{241}\mathrm{Pu}$ sample containing 4.5% ${}^{241}\mathrm{Pu}$ and 86% ${}^{241}\mathrm{Am}$ for $d=0.2\mu \mathrm{m}$. The beta part of the spectrum is plotted in the approximations of massless neutrino and no distortion by the Coulomb potential.