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International Workshop on Polarized Sources and Targets (PST)

Measurement of the occupation number of metastable atoms in the hyperfine-substate β$_3$ in an atomic hydrogen beam

Moritz Westphal, R. Engels, Nicolas Faatz, Chrysovalantis S. Kannis, Berthold Klimczok, Aditya Mandiwal, Maike Maubach, Helmut Soltner

Published Mar 14, 2023• 0 citations
Publisher

Abstract

After its discovery in 1947 by Willis Eugene Lamb and Robert C. Retherford the Lamb shift was used to create Lamb shift polarimeter to separate the $2S_{1/2}$ $\alpha_{1}$ and $\alpha_{2}$ hyperfine substates of hydrogen as well as the $\alpha_{3}$ substate of deuterium. But for a new project at the Technical University of Munich, investigation of the bound-beta decay of a neutron into a hydrogen atom and a neutrino, a Lamb shift polarimeter is needed that is also capable of separating the $\beta_{3}$ substate of hydrogen. Unfortunately, our first attempt to use a Sona transition unit to exchange the occupation numbers between $\alpha_{1}$ and $\beta_{3}$ failed, because of the unexpected complexity of the transitions in this unit [1]. The second idea of using a new kind of spinfilter which uses two radio frequencies to separate all four hyperfine substates of hydrogen also failed. Our third attempt is now to build a transition unit that can induce magnetic dipole transitions between $\alpha_{2}$ and $\beta_{3}$ as well as between $\alpha_{2}$ and $\beta_{4}$ ($\pi$ transitions, i.e. an exchange of the occupation numbers of these states). This is a similar transition to what is used in atomic beam sources, in this case not for ground state atoms but for metastable atoms, which requires a much lower radio frequency. Another difference of this new idea is the smaller interaction time of the atoms with the photons inside the transition unit due to their much higher velocity of roughly $2\cdot10^5$ m/s compared to velocities of about $10^3$ m/s in an atomic beam source.

DOI
10.22323/1.433.0007

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Measurement of the occupation number of metastable atoms in the hyperfine-substate β3_33​ in an atomic hydrogen beam
After its discovery in 1947 by Willis Eugene Lamb and Robert C. Retherford the Lamb shift was used to create Lamb shift polarimeter to separate the 2S1/22S_{1/2}2S1/2​ α1\alpha_{1}α1​ and α2\alpha_{2}α2​ hyperfine substates of hydrogen as well as the α3\alpha_{3}α3​ substate of deuterium. But for a new project at the Technical University of Munich, investigation of the bound-beta decay of a neutron into a hydrogen atom and a neutrino, a Lamb shift polarimeter is needed that is also capable of separating the β3\beta_{3}β3​ substate of hydrogen. Unfortunately, our first attempt to use a Sona transition unit to exchange the occupation numbers between α1\alpha_{1}α1​ and β3\beta_{3}β3​ failed, because of the unexpected complexity of the transitions in this unit [1]. The second idea of using a new kind of spinfilter which uses two radio frequencies to separate all four hyperfine substates of hydrogen also failed. Our third attempt is now to build a transition unit that can induce magnetic dipole transitions between α2\alpha_{2}α2​ and β3\beta_{3}β3​ as well as between α2\alpha_{2}α2​ and β4\beta_{4}β4​ (π\piπ transitions, i.e. an exchange of the occupation numbers of these states). This is a similar transition to what is used in atomic beam sources, in this case not for ground state atoms but for metastable atoms, which requires a much lower radio frequency. Another difference of this new idea is the smaller interaction time of the atoms with the photons inside the transition unit due to their much higher velocity of roughly 2⋅1052\cdot10^52⋅105 m/s compared to velocities of about 10310^3103 m/s in an atomic beam source.
Since the early days of quantum mechanics, hydrogen, as the simplest of all atoms, has been studied or used to investigate new physics. In the past this knowledge has been applied to develop a polarimeter where the initial nuclear polarization of a proton beam could be determined. The key component of this Lamb-shift polarimeter is the so called spin filter, which is able to separate one of four metastable hydrogen hyperfine states by quenching the remaining three hyperfine states to the ground state. Unfortunately, the conventional spin filter is only able to filter two out of the four hyperfine states individually. Therefore, this work provides the necessary theory as well as experimental conditions to build a new generation of spin filter which permits the separation and transmission of any metastable hydrogen hyperfine state as well as for its isotopes in a corresponding beam. This knowledge is applicable for other experiments in different fields of research, e.g. the bound beta decay, axion research or parity violation experiments.
Design of a Lamb-Shift Polarimeter for 3^33He Ions and Atoms
In high energy physics experiments 3^33He2+^{2+}2+ nucleons are suitable to test the internal structure of neutrons, which makes them the perfect substitute. Moreover, it is one of the atomic species for which high polarization values are achievable through the use of optical pumping methods. Therefore, nuclear polarized sources for 3^33He2+^{2+}2+ ions are currently under development. Consequently, detector systems validating their nuclear polarization value need to be established. Such a detector system, based on the Lamb-shift polarimeter, is introduced in this work. Its advantage is that it can operate at low energies in the range of 10 to 100 keV, which makes pre-acceleration unnecessary. In addition, a fast evaluation of the nuclear polarization within seconds leads to shorter disruptions for beam times. Another option of this Lamb-shift polarimeter might be that it can serve as a valuable tool for further investigation of the bound tritium decay into 3^33He atoms, similar to the hydrogen spin filter for the bound beta decay of the free neutron.
Since the early days of quantum mechanics hydrogen, as the simplest of all atoms, has been studied or used to investigate new physics. In parallel, this knowledge leads to different applications, e.g. a spin filter to separate metastable hydrogen atoms in single hyperfine substates with electron spin m_s=1/2. Subsequently, this work provides the necessary theory as well as experimental conditions to build a new generation of spin filter which permits the separation of all four individual metastable hydrogen hyperfine states as well as for its isotopes in a corresponding beam.
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasidegenerate 2P1/22{P}_{1/2}2P1/2​ levels that are removed from the 2S2S2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift, and the hyperfine effects. The van der Waals shift becomes commensurate with the $2S\ensuremath{-}2{P}_{3/2}$ fine-structure splitting only for close approach (R<100a0R<100{a}_{0}R<100a0​, where a0{a}_{0}a0​ is the Bohr radius) and one may thus restrict the discussion to the levels with n=2n=2n=2 and J=1/2J=1/2J=1/2 to a good approximation. Because each SSS or PPP state splits into an F=1F=1F=1 triplet and an F=0F=0F=0 hyperfine singlet (eight states for each atom), the Hamiltonian matrix a priori is of dimension 64. A careful analysis of the symmetries of the the problem allows one to reduce the dimensionality of the most involved irreducible submatrix to 12. We determine the Hamiltonian matrices and the leading-order van der Waals shifts for states that are degenerate under the action of the unperturbed Hamiltonian (Lamb shift plus hyperfine structure). The leading first- and second-order van der Waals shifts lead to interaction energies proportional to 1/R31/{R}^{3}1/R3 and 1/R61/{R}^{6}1/R6 and are evaluated within the hyperfine manifolds. When both atoms are metastable 2S2S2S states, we find an interaction energy of order ${E}_{h}\ensuremath{\chi}{({a}_{0}/R)}^{6}$, where Eh{E}_{h}Eh​ and L\mathcal{L}L are the Hartree and Lamb shift energies, respectively, and $\ensuremath{\chi}={E}_{h}/\mathcal{L}\ensuremath{\approx}6.22\ifmmode\times\else\texttimes\fi{}{10}^{6}$ is their ratio.
Polarized atomic beam sources have been in operation for many years to produce either nuclear polarized atomic hydrogen or deuterium beams. In recent experiments, such a source was used to polarize both isotopes independently at the same time. By recombination of the atoms, hydrogen-deuterium molecules with all possible nuclear spin combinations can be created. Those spin isomers are useful for further applications, like precision spectroscopy, as polarized targets for laser-particle acceleration, polarized fuel for fusion reactors, or as an option for future measurements of electric dipole moments.
We have observed the crossing of the atomic hydrogen levels ${\ensuremath{\beta}}_{B}(2{S}_{\frac{1}{2}}, {m}_{J}=\ensuremath{-}\frac{1}{2}, {m}_{I}=\ensuremath{-}\frac{1}{2})$ and ${e}_{B}(2{P}_{\frac{1}{2}}, {m}_{J}=+\frac{1}{2}, {m}_{I}=\ensuremath{-}\frac{1}{2})$ near 605 G. A new atomic-beam method is used. H atoms are excited to the metastable 2S2S2S state by electron bombardment. The $2S({m}_{J}=\ensuremath{-}\frac{1}{2})$ state is quenched in the bombardment region. The 2S(mJ=+12)2S({m}_{J}=+\frac{1}{2})2S(mJ​=+21​) beam passes through a zero-field region where 13\frac{1}{3}31​ of it is converted to the single hyperfine level ${\ensuremath{\beta}}_{B}$. The ${\ensuremath{\beta}}_{B}$ atoms enter a uniform magnetic field parallel to the beam. With no externally applied electric field, 92% of them reach the detector. When we apply an electrostatic field of about 0.7 V/cm perpendicular to the beam, the ${\ensuremath{\beta}}_{B}$ atoms are strongly quenched near the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing point. Observed quenching agrees with the Bethe-Lamb theory of the 2S2S2S lifetime in external fields. We measure magnetic field by the nuclear magnetic resonance frequency of protons in water. Natural asymmetry and minor experimental corrections reduce the observed center of the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ quenching resonance by 1 part in 104{10}^{4}104. The corrected ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing occurs at 2577.57\ifmmode\pm\else\textpm\fi{}0.25 kc/sec, proton nmr in water. From this, we calculate the Lamb shift S\mathcal{S}S in H, n=2n=2n=2. With a diamagnetic shielding correction, and the accurately known 2S2S2S hyperfine interval, we get $\mathcal{S}=1058.07\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec. This disagrees with $\mathcal{S}=1057.77\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec from the Lamb experiments.