Neutrino Spin. Helicity and Polarization
Introduction to Neutrino Physics
Goldhaber — Sunyar — Grodzins
In 1958 Maurice Goldhaber, Andrew Sunyar and Lee Grodzins proposed measuring the neutrino helicity through a sequence of two quantum transitions.
Maurice Goldhaber
Andrew Sunyar
Lee Grodzins
The idea: to make the nucleus and the photon “remember” in turn the projection of the neutrino spin.
Why the nucleus has time to emit
At \(T=300\ \mathrm K\) the mean thermal energy of the nucleus and the directed recoil energy after electron capture are
\[ \langle K\rangle_{\rm th}=\frac32k_BT\simeq0.039\ \mathrm{eV}, \qquad E_R\simeq3.2\ \mathrm{eV} \simeq80\langle K\rangle_{\rm th}. \]
The nucleus \(B^*\) moves through the crystal. Collisions with lattice atoms change its momentum and may reorient its spin. What matters for the experiment is which happens first:
\[ \tau_\gamma \quad\text{or}\quad \tau_{\rm slow}. \]
\(\tau_\gamma\) is the photon emission time, \(\tau_{\rm slow}\) is the time for losing the initial direction. Complete thermalization is not required.
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\(E_R\gg\langle K\rangle_{\rm th}\): the nucleus will inevitably be slowed down. Will \(B^*\) manage to emit a photon sooner?
Estimate of the time for appreciable slowing down
After electron capture, the kinematics gives \(v_{B^*}\simeq2.0\times10^3\ \mathrm{m/s}\). For the estimate we assume that the direction of the momentum changes appreciably after a path of the order of one interatomic spacing: \(\ell_{\rm slow}\sim0.3\text{—}0.4\ \mathrm{nm}\).
\[ \tau_{\rm slow} \sim\frac{\ell_{\rm slow}}{v_{B^*}} \sim\frac{0.3\text{—}0.4\ \mathrm{nm}} {2.0\times10^3\ \mathrm{m/s}} \simeq0.15\text{—}0.20\ \mathrm{ps}. \]
This is an order-of-magnitude estimate: one interatomic spacing is taken as the path of appreciable loss of direction, with no microscopic model of the slowing down.
Decay of the excited level
For the level \({}^{152}\mathrm{Sm}^{*}\)
\[ \tau_\gamma=(3\pm1)\times10^{-14}\ \mathrm{s} \simeq0.03\ \mathrm{ps}. \]
This is roughly seven times shorter than the time for appreciable slowing down: \(\tau_{\rm slow}/\tau_\gamma\sim7\).
For exponential decay, the probability of emitting a photon before appreciable slowing down is
\[ P_{\rm emit} =1-\exp\!\left(-\frac{\tau_{\rm slow}}{\tau_\gamma}\right) \simeq1-e^{-7}\simeq0.999. \]
Almost all excited nuclei emit a photon before appreciable loss of the direction of the recoil. The resonance preserves information about the kinematics of electron capture.
The experiment uses a chain of two transitions:
\[ {}^{152m}\mathrm{Eu}(0^-)+e^- \longrightarrow {}^{152}\mathrm{Sm}^{*}(1^-)+\nu_e, \]
\[ {}^{152}\mathrm{Sm}^{*}(1^-) \longrightarrow {}^{152}\mathrm{Sm}(0^+)+\gamma. \]
The first transition creates a moving excited nucleus with spin \(1\) and fixes the direction of the recoil. The second transition occurs within \(\tau_\gamma\simeq0.03\ \mathrm{ps}\): the photon carries away the spin label, and its Doppler shift still depends on the direction of motion of the nucleus.
The short lifetime of the level turns the spectroscopic resonance into a kinematic direction filter.
\({}^{152m}\mathrm{Eu}\) — electron-capture source
\[ \Longrightarrow \]
\({}^{152}\mathrm{Sm}\) — resonant absorber
For resonant absorption the same transition in \({}^{152}\mathrm{Sm}\) is used: the source produces photons, and the samarium at rest serves as a narrow energy filter.
The neutrino turned out to be left-handed
Goldhaber, Grodzins, and Sunyar obtained
\[ \boxed{h(\nu_e)=-1\pm0.3}. \]
The sign unambiguously indicated: electron neutrinos are produced left-handed.
The result agrees with the maximal parity violation in the weak interaction.
