Recent results of laser spectroscopy experiments of pionic helium atoms at PSI

We would like to thank the referees for giving us such useful comments. This is our resubmission.

1. "The highest published precision for pi4He is DE =+- 2 eV [37], i.e. one should change … to about 10-4 -> … up to 2 x 10-5."

As 2 eV/10 keV = 2x10^-4 and not 2x10^-5, we modified it to read 2x10^-4.

2. "There is another pi4He X-ray experiment from the 80ies: S.Baird et al., Nucl.Phys.A 392 (1983) 297."

The reference was added.

3. "The level of precision achievable by the QED calculations (<= 10-8) – without the uncertainty stemming from the pion mass - should be stated."

This is included in the last paragraph of the text.

4. "The original sentence line 51 sounds somehow disconnected to the intended meaning?"

We modified it to read, "A two-body...."

5. "To help the reader, one should point out that the assumption for the fraction 2.3% is based on the (rather precise) experimental result ((2.30 +- 0.07)%) of [33]"

The 2.3% value is somewhat arbitrary in the sense that it depends on where one cuts on the time spectrum to define the long-lived fraction and the distribution of the pions that come to rest in the experimental target. Since our experimental setup and beam momenta are very different from those of Ref. [33], the 2.3% value is taken to be an approximation.

6. "Fig 26.2 caption lines 4/5, line 79/80 is an almost one-to-one repetition (all information needed twice?)"

The information was removed.

7. "The efficiency value (<10%) is confusing in connection to En >=25 MeV. Better to write <=10%."

The efficiency is smaller than 10%. A more precise upper limit cannot be reliably estimated based on the known efficiencies of these detectors from the literature.

8."Though it summarizes presumably a big technical effort, the details lines 96-101 may be too specific in the context of this article. Perhaps one should consider to omit them."

The technical efforts described here corresponds to the work of PSI staff members and so out of respect to PSI we would like to highlight them.

9. "Start new paragraph with line 135. It would be instructive to give the theoretical frequency also for this transition."

We added the wavelength to the sentence.

10. "Fig. 26.4(e): Caption - the meaning of the red arrow (theoretical value) should be stated explicitly e.g. by a cross reference at line 177."

We added the sentence, "The red arrow indicates the position of the spin-averaged transition frequency obtained by a three-body QED calculation"

11. "The very interesting perspectives following from this success - the very last part - the physics and technical challenges in order to exploit this discovery deserve to my opinion an extra subchapter 26.4 (entitled OUTLOOK or PERSPECTIVES etc.)."
"Secondly, the search for narrow transitions (line 187: narrower by a factor of at least 10-3 -> 10+3) together with a statement on the laser band width to achieve a good determination of the experimental frequency should give the reader a feeling of the technical expertise.
"

This proceedings paper is intended to summarize past work. Future possibilities and an estimation of the achievable precision would need a more through treatment which is not within the scope of the present paper. We added the sentence, "Laser spectroscopic techniques that are commensurate with a higher level of precision are available. "