Unravel the mystery of the size of hydrogen atoms and protons!
The hydrogen atom is of great importance in quantum physics and metrology. The ionization energy of hydrogen is the minimum energy required to strike out the only electron in a hydrogen atom, and its magnitude is related to Rydberg's constant (Rydberg's constant). The two-body properties of protons and electrons can be accurately calculated according to first principles. Precise measurements of the frequency of hydrogen atomic transitions can be used to verify the validity of theories of atomic structure (i.e., relativistic quantum mechanics and quantum electrodynamics) and to determine physical constants such as the Rydberg constant R∞ and the proton charge radius rp. The values of R∞ and rp are mainly defined by the transition frequencies from the 1S and 2S levels to the nS, P, and D levels with principal quantum numbers up to 12. However, in 2010, the researchers found that the measured value of rp in the 2S–2P interval in μ hydrogen was 7σ lower than the previously determined standard value (CODATA 2010). This discovery became the origin of the "proton size mystery". Although in the CODATA 2018 adjustments, R∞ and rp were revised based on the evaluation of multiple outcomes in H and μH, there are still some biases and inconsistencies. SO FAR, ALL HIGH-PRECISION MEASUREMENTS OF TRANSITION PHENOMENA HAVE INVOLVED LONG-LIFE 1S AND/OR 2S ENERGY LEVELS. The energies of these two proton penetrating states are sensitive to rp, which leads to a correlation between R∞ and rp and becomes central to the mystery of proton size. One possible way to solve this puzzle is to measure the transitions of the Rydberg states of the higher-order energy levels involving the non-penetration of protons and determine the R∞ because these transitions are also long-lived but not sensitive to rp. Optical transitions involving higher-order energy levels are affected by their sensitivity to stray fields and have not been considered so far.
Recently, Simon Scheidegger and Frédéric Merkt of the Swiss Federal Institute of Technology in Zurich controlled the hydrogen atom through an electric field to excite the electrons in the hydrogen to their highly excited energy levels, improving the stability of the electrons, and accurately measuring the energy absorbed by the electrons when they transition from a low energy level to a high excited energy level, resulting in a highly accurate estimate of Rydberg's constant. This method can be used to determine the Rydberg constant far away from the proton and avoid the uncertainty caused by the proton size. The work reports a precise measurement of the Rydberg constant of a hydrogen atom with a principal quantum number n between 20 and 30. The work was published in the latest issue of Physical Review Letters in a paper titled "Precision-Spectroscopic Determination of the Binding Energy of a Two-Body Quantum System: The Hydrogen Atom and the Proton-Size Puzzle". Nature.
The experimental setup is shown in Figure 1. Experimental measurements were made at a repetition rate of 25 Hz, and the pulsed double-swept supersonic beam of hydrogen atoms was generated by a cryogenic pulse valve equipped with a dielectric barrier discharge. Its transverse velocity distribution (vx, vy) corresponds to a temperature of 40 μK, and the average beam velocity can be adjusted from 1000 ms-1 to 1700 ms-1 by varying the valve temperature between 40 K and 160 K. In the magnetically shielded photoexcitation region, the Rydberg state of hydrogen is obtained by a two-step process. First, the ultrafinely resolved 2S–1S two-photon transition is amplified and excited by the 243 nm output pulse of a titanium-sapphire ring laser continuously operating at 729 nm. Then, after a distance of 4 cm, the long-lived 2S atoms are excited into a Rydberg-Stark state by a tunable single-mode (bandwidth≤1 kHz), linearly polarized UV laser (λ=368 nm) in a homogeneous electric field of deliberately applied intensity F, at which the ions generated during the 2S–1S excitation are repelled by the applied electric field. The ultraviolet laser propagates in a near-orthogonal configuration with respect to the ultrasonic beam, with an adjustable misalignment angle δα (lower right corner of Figure 1). Ultraviolet lasers are introduced into a vacuum chamber via optical fibers. The divergent beam leaving the fiber is collimated with an aberration compensation group of four lenses.
Figure 1. Schematic diagram of the experimental setup, the vacuum chamber includes the ultrasonic beam source and the photoexcitation area (left) and the main components of the laser system (right).
Experimental results
With beam velocities between 1000 and 1700 ms-1, δα between 0.1 and 0.06°, and electric field intensities F between 0.4 and 1.6 Vcm-1, the authors recorded 525 transition spectra from 2S(0;1) to Stark states (n=20 and 24). Figure 2 shows the spectrum of the transitions (black dots) and the calculated spectra after fitting. The experimental results show that the Stark displacement is small and insensitive to the exact value of R∞.
Figure 2. Spectra of the transition from the 2S(1) state of H to the Stark state (black dots) and the spectra calculated with the linear parameters obtained from the weighted least squares fitting (blue lines).
In Figure 3, the authors compare the R∞ values (horizontal blue lines) obtained in this work with those determined by the millimeter wave spectra of the previously reported transition between the n=27-30 circular Rydberg states, the cR ∞ values proposed in the 2010 Fundamental Constant Revision Standard, and the cR ∞ values obtained in the latest CODATA evaluation, which include Lamb shift measurements in μ meson hydrogen. The previously reported cR ∞ values are compatible with both CODATA values, and the results given in this work are 1.3σ lower than the CODATA 2018 value and 4.5σ lower than the CODATA 2010 value. Combining the measurements from this work with the rp values in the references gives a cR ∞ value of 3 289 841 960 214 (22) kHz (blue dot in Figure 3).
Previous studies have suggested that the 2S–2P3/2 transition in μ hydrogen is almost only sensitive to proton rms charge radius rp and not to R∞, whereas the measurements in this paper are almost exclusively sensitive to R∞ and not to rp when combined with the measurements in the references. Therefore, these two assays are independent of the correlation between R∞ and rp, which influence most of the determination of the amount of process based on hydrogen atomic transitions, which influence R∞ and rp. The significance of these results is that they are obtained from the spectrum of hydrogen atoms, and the rp values obtained in μ hydrogen experiments are indirectly confirmed by the R∞ values. Therefore, the differences in Figure 3 cannot be attributed to differences beyond the Standard Model in the laws of physics that govern the properties of hydrogen and μ hydrogen. The authors suggest that the (R∞;rp) values given by the orange dots in Figure 3 can be taken a step further and more precise results can be obtained by combining the measurements of the 2S–1S transition in the hydrogen atom and the Lamb shift in the μ hydrogen.
Figure 3. Scatterplot of the value of the transition frequency (R∞, rp) in a hydrogen atom.
brief summary
This work controls the hydrogen atom by an electric field, excites the electrons in the hydrogen to its highly excited energy level, improves the stability of the electrons, and accurately measures the energy absorbed by the electrons when they transition from a low energy level to a high excited energy level, resulting in a highly accurate estimate of the Rydberg constant. This method can be used to determine the Rydberg constant far away from the proton and avoid the uncertainty caused by the proton size. The work reports a precise measurement of the Rydberg constant of a hydrogen atom with a principal quantum number n between 20 and 30.
Source: Frontiers of Polymer Science