Goldhaber experiment

The Goldhaber experiment , named after Maurice Goldhaber , is a quantum physics experiment that was first carried out in 1957 at the Brookhaven National Laboratory . It was used for the first time to determine the helicity of the neutrino after the parity violation of the weak interaction had been discovered a year earlier .

background

In the experiment, a ¹⁵²Eu core is used in an isomeric (metastable) state that decays upon K capture . A neutrino is emitted:

{\ displaystyle {} ^ {\ text {152m}} {\ text {Eu}} + {\ text {e}} ^ {-} \ rightarrow {} ^ {\ text {152}} {\ text {Sm} } ^ {*} + \ nu _ {e} +950 \, {\ text {keV}}}

The daughter nucleus ¹⁵²Sm is in an excited state after the decay , which is indicated by the star. The excitation energy is released a short time later through gamma emission:

{\ displaystyle {} ^ {\ text {152}} {\ text {Sm}} ^ {*} \ rightarrow {} ^ {\ text {152}} {\ text {Sm}} + \ gamma +961 \, {\ text {keV}}}

The de-excitation energy is distributed here, however, to the recoil of the Sm core and the gamma quantum.

The electron capture and the subsequent de-excitation meet a number of requirements, without which the experiment would not be possible in this form:

Spin sequence 0 ^- → 1 ^- → 0 ⁺
Almost the same decay energies for both transitions (deviation approx. 1%)
Very short lifetime of the ¹⁵² Sm ^* (τ = 3 × 10 ⁻¹⁴ s)

When planning the experiment, Goldhaber was initially not sure whether there was even an isotope that met these requirements.

Determination of the direction of flight of the neutrino

Schematic structure of the Goldhaber experiment.

The graphic on the right shows the setup of the experiment. The detection of the gamma quanta from the Sm decay is based on the resonant scattering of the gamma quanta on an Sm ₂ O ₃ target, which is attached in a ring around the detector. The lead shield prevents decay photons from the ¹⁵² Eu source from reaching the detector directly. The resonant scattering takes place via nuclear magnetic resonance absorption of the photon by an Sm nucleus and subsequent spontaneous emission:

{\ displaystyle \ gamma + {} ^ {\ text {152}} {\ text {Sm}} \ rightarrow {} ^ {\ text {152}} {\ text {Sm}} ^ {*} \ rightarrow {} ^ {\ text {152}} {\ text {Sm}} + \ gamma}

A resonant absorption at the samarium would normally not be possible, since the photon emitted by the ¹⁵² Sm ^* after the decay of the ¹⁵² Eu in the source does not have the entire energy of 961 keV due to the core recoil: the recoil energy is about 3.2 eV, while the natural line width is only about 10 ⁻² eV. Accordingly, no absorption can take place, since the energy of the photon is significantly smaller than the required excitation energy.

However, in this case the ¹⁵² Sm ^* atom is not at rest, but moves shortly before because of the emission of the neutrino. Due to the very short service life, there is no relaxation here due to interactions with the lattice of the surrounding solid. Since the energy of the emitted neutrino corresponds approximately to the energy of the gamma transition, the two energies should compensate each other by Doppler shift of the wavelength, provided that the gamma quantum and the neutrino were emitted in opposite directions (as shown in the figure). With an emission opposite by 180 °, the deviation of the energy of the gamma quantum from the resonance energy is only about 10 ⁻⁴ eV, which is significantly smaller than the natural line width of 10 ⁻² eV. This “trick” makes resonant absorption possible; but only if the neutrino was emitted upwards - otherwise the energy difference is too great and the gamma quanta do not reach the detector. In this way one receives information about the emission direction of the neutrino.

Determination of the neutrino helicity

The neutrino helicity can be derived from the consideration of the spin structure of the decay. Of course, the conservation of the angular momentum must be taken into account. In the following simple arrows indicate the momentum of the particles and double arrows indicate the spin, whereby a short double arrow stands for spin ½.

The decay of the ^152m Eu, the output core in 0 is ^- state. Since the transition is a pure Gamow-Teller decay , the daughter kernel has the state 1 ^- . The angular momentum of the initial state is ½, because the nucleus has a spin of 0 and the K-shell electron has the orbital angular momentum l = 0, but spin ½. Since the neutrino carries a spin ½, the spin of the daughter nucleus must be opposite to that of the neutrino. The following two decays can thus take place:

{\ displaystyle {\ begin {array} {ccccccccccc} \ Leftarrow && \ Rightarrow && \ Leftarrow \ Leftarrow && \ Rightarrow && \ Leftarrow && \ Rightarrow \ Rightarrow \\ {} ^ {152} {\ text {Eu}} & \ longrightarrow & \ nu _ {e} & + & {} ^ {152} {\ text {Sm}} ^ {*} & \ quad {\ text {or}} \ quad & {} ^ {152} {\ text {Eu}} & \ longrightarrow & \ nu _ {e} & + & {} ^ {152} {\ text {Sm}} ^ {*} \\ && \ longleftarrow && \ longrightarrow &&&& \ longleftarrow && \ longrightarrow \\ \ end {array}}}

It follows from this that the neutrino in the laboratory system has the same helicity as the ¹⁵² Sm ^* daughter core: in the first case −1, in the second +1.

In the subsequent gamma emission, the photon has the quantum numbers 1 ^- . The ¹⁵² Sm nucleus is a gg nucleus (samarium: Z = 62, N = 90) and therefore in the state 0 ⁺ . In the case of an emission below 180 ° with respect to the direction of emission of the neutrino, the following applies:

{\ displaystyle {\ begin {array} {ccccccccccc} \ Leftarrow \ Leftarrow &&&& \ Leftarrow \ Leftarrow && \ Rightarrow \ Rightarrow &&&& \ Rightarrow \ Rightarrow \\ {} ^ {152} {\ text {Sm}} ^ {*} & \ longrightarrow & {} ^ {152} {\ text {Sm}} & + & \ gamma & \ quad {\ text {or}} \ quad & {} ^ {152} {\ text {Sm}} ^ { *} & \ longrightarrow & {} ^ {152} {\ text {Sm}} & + & \ gamma \\\ longrightarrow &&&& \ longrightarrow && \ longrightarrow &&&& \ longrightarrow \\\ end {array}}}

In the case of resonant scattering, the helicity of the photon corresponds to that of the ¹⁵² Sm ^* nucleus, and thus that of the neutrino:

{\ displaystyle {\ mathcal {H}} (\ gamma) = {\ mathcal {H}} (\ nu)}

The helicity of the photon can now be determined by the fact that the cross-section for Compton scattering depends strongly on the polarization of the scattering material. This is implemented in the experiment in such a way that a magnetized iron block is placed between the source and the absorber (see graphic). As a result, about 7–8% of the electrons in iron are polarized. A photon scattered in the iron loses part of its energy so that resonance absorption can no longer take place. If there should be a preferred helicity of the photons and thus of the neutrinos, the counting rates would have to differ with opposite polarizations of the iron because of the different degrees of scattering. (Here it should be noted again that only neutrinos emitted upwards lead to a detection of the photons in the detector!)

In fact, the count rate comparison yields a neutrino helicity of

{\ displaystyle {\ mathcal {H}} (\ nu _ {e}) = - 1 {,} 0 \ pm 0 {,} 3}

.

consequence

The experiment has shown that neutrinos are only left-handed in nature , while antineutrinos are right-handed. It is thus an impressive confirmation of the VA theory which predicts the parity violation of the weak interaction .

Individual evidence

^ Maurice Goldhaber, Lee Grodzins and Andrew W. Sunyar : Helicity of Neutrinos . In: Physical Review . 109, No. 3, 1958, pp. 1015-1017. doi : 10.1103 / PhysRev.109.1015 .

literature

Bogdan Povh , Klaus Rith, Christoph Scholz and Frank Zetsche: Particles and Cores . 6th edition, Springer, 2004, ISBN 3-540-21065-2
Walter Greiner , Berndt Müller : Calibration theory of the weak interaction . 2nd edition, Harri Deutsch, 1995, p. 19 f, ISBN 3-8171-1427-3

[Goldhaber1958-1] Maurice Goldhaber, Lee Grodzins and Andrew W. Sunyar : Helicity of Neutrinos . In: Physical Review . 109, No. 3, 1958, pp. 1015-1017. doi : 10.1103 / PhysRev.109.1015 .