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Diffusion of muonic hydrogen in hydrogen gas and the measurement of the 1$s$ hyperfine splitting of muonic hydrogen
by J. Nuber, A. Adamczak, M. Abdou Ahmed, L. Affolter, F. D. Amaro, P. Amaro, P. Carvalho, Y. -H. Chang, T. -L. Chen, W. -L. Chen, L. M. P. Fernandes, M. Ferro, D. Goeldi, T. Graf, M. Guerra, T. W. Hänsch, C. A. O. Henriques, M. Hildebrandt, P. Indelicato, O. Kara, K. Kirch, A. Knecht, F. Kottmann, Y. -W. Liu, J. Machado, M. Marszalek, R. D. P. Mano, C. M. B. Monteiro, F. Nez, A. Ouf, N. Paul, R. Pohl, E. Rapisarda, J. M. F. dos Santos, J. P. Santos, P. A. O. C. Silva, L. Sinkunaite, J. -T. Shy, K. Schuhmann, S. Rajamohanan, A. Soter, L. Sustelo, D. Taqqu, L. -B. Wang, F. Wauters, P. Yzombard, M. Zeyen, J. Zhang, A. Antognini
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Submission summary
| Authors (as registered SciPost users): | Pedro Amaro · Thomas Graf · Mauro Guerra · Jonas Nuber |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2211.08297v2 (pdf) |
| Date submitted: | 2022-12-31 10:36 |
| Submitted by: | Nuber, Jonas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Experimental, Computational |
Abstract
The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy. In the proposed experiment, the $\mu$p atom is excited by a laser pulse from the singlet to the triplet hyperfine sub-levels, and is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after this cycle modifies the $\mu$p atom diffusion in the hydrogen gas and the arrival time of the $\mu$p atoms at the target walls. This laser-induced modification of the arrival times is used to expose the atomic transition. In this paper we present the simulation of the $\mu$p diffusion in the H$_2$ gas which is at the core of the experimental scheme. These simulations have been implemented with the Geant4 framework by introducing various low-energy processes including the motion of the H$_2$ molecules, i.e. the effects related with the hydrogen target temperature. The simulations have been used to optimize the hydrogen target parameters (pressure, temperatures and thickness) and to estimate signal and background rates. These rates allow to estimate the maximum time needed to find the resonance and the statistical accuracy of the spectroscopy experiment.
Current status:
Reports on this Submission
Anonymous Report 1 on 2023-4-21 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2211.08297v2, delivered 2023-04-21, doi: 10.21468/SciPost.Report.7083
Report
The authors report on the first complete simulation for the planned measurements of the muonic hydrogen ground-state hyperfine splitting (HFS) by the CREMA collaboration at PSI.
The first part rigorously describes the diffusion of muonic hydrogen atoms in hydrogen gas and their implementation in a simulation using the Geant4 framework using double-differential collision rates for the scattering between muonic hydrogen atoms and H2 molecules. They use an elegant way to convert calculated partial differential cross-sections in the center of mass to scattering rates in the laboratory reference system while including the thermal motion of the H2 molecules. Then in the second part, this simulation tool is combined with the inputs from previous separate studies on the multi-pass laser cavity and x-ray detection system and is used to optimize various experimental parameters, predict event rates versus background, and estimate the time needed to find the resonance and the achievable accuracy in the proposed HFS spectroscopy experiment. These simulations will also be helpful to define the requirements for the experiment and contribute to improving it.
The work reported here, which is understood as being part of a doctoral thesis, shows undeniable originality in the field. The manuscript is well-written, structured, and extensively referenced. Therefore I recommend the publication of this manuscript with only a few relatively minor corrections, mostly of stylistic aspects, listed below that the authors should address.
Some minor corrections:
(1) Page 4, figure 1:
In Fig. 1, the author used "Entrance counter" while in the main text "entrance detector" is employed (in five places). The same wording should be used throughout the manuscript.
(2) Page 4, figure caption 1: "X-rays" should be "x rays".
(3) Page 12, last sentence:
Add a reference to Fig. 3 at the end of the sentence (e.g., "(see Fig. 3)") to redirect the reader to that figure.
(4) Page 13, figure caption 5, middle: "incoupled" should be "in-coupled".
(5) Page 13, figure 5:
Both graphs in (b) and (c) have the same horizontal axis title "z [mm]". The graph in (c) should be along the x-axis according to the last line of the figure caption.
(6) Page 14, figure caption 6:
This figure is missing a second y-axis since both "mean free path" and "probability distribution" are shown on the same graph.
(7) Page 17, last paragraph of section 6:
Here detector-related backgrounds are mentioned, but the x-ray detection has been introduced yet, only shown in Fig. 1. It would be beneficial to the reader if a very brief description of the x-ray detection scheme could be added here, or already in section 2. This would help us understand the high detection efficiency for muonic Au events used in section 7.
(8) Page 17, equation (6) and after:
The unit used here for rates is "1/s". It is uneasy to read "0.088 1/s" or "500 1/s". Such a notation is not standard. It is recommended to:
- in equations 6, 7, and 8, use the notation "[1/s]" or "s$^{-1}$" for clarity,
- in the main text, use "500/s" or "500 s$^{-1}$" (in five places, and two in figure caption 11).
In Table 1, the notation "[1/s]" is correct.
(9) Page 20, 5 lines from the bottom: "Fig. 10 (a)" should be "Fig. 10a".
(10) Page 21, line 1: "Fig. 10 (b)" should be "Fig. 10b".
(11) References:
Update [15], [23], and [41] since already published. Add missing doi to [27].
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Author: Jonas Nuber on 2023-05-17 [id 3679]
(in reply to Report 1 on 2023-04-21)Thank you very much for your review and the proposed corrections, which helped us to improve the quality of the manuscript. We fully agree with all the proposed changes.
In the following, we address the changes made following the numbering scheme of the referee:
(1)-(5) All of these corrections were implemented as requested
(6) In fact, this plot was hard to read due to the missing second axis. As the scale of the probability distributions is not important here, we simply added an axis without tics, labeled as “Probability distribution [arbitrary scale]”. The label and axis were highlighted in gray to differentiate it from the black curve for the mean free path. Furthermore, we added little arrows to indicate which axis should be considered for which plot. The new version of the plot is attached as figure_6.pdf
(7) A brief description of the detection system was added to the text in the end of section 6.3 (last paragraph).
(8) We decided to use the notation s^{-1} in the text, equations and figure captions, while keeping the notation [1/s] in Table 1. Indeed, this improves the readability.
(9)-(11) All the changes were made accordingly
We will send the corrected version of the article to the editor-in-charge, as we reckon it should not be uploaded here according to the instructions.
Attachment:
figure_6.pdf