X-ray Spectroscopy of Muonic Atoms Isolated in Vacuum with Transition Edge Sensors
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X‑ray Spectroscopy of Muonic Atoms Isolated in Vacuum with Transition Edge Sensors S. Okada1,14 · T. Azuma1 · D. A. Bennett2 · P. Caradonna3 · W. B. Doriese2 · M. S. Durkin2 · J. W. Fowler2 · J. D. Gard2 · T. Hashimoto4 · R. Hayakawa5 · G. C. Hilton2 · Y. Ichinohe6 · P. Indelicato7 · T. Isobe8 · S. Kanda8 · M. Katsuragawa3 · N. Kawamura9 · Y. Kino10 · Y. Miyake9 · K. M. Morgan2 · K. Ninomiya11 · H. Noda12 · G. C. O’Neil2 · T. Okumura1 · C. D. Reintsema2 · D. R. Schmidt2 · K. Shimomura9 · P. Strasser9 · D. S. Swetz2 · T. Takahashi3 · S. Takeda3 · S. Takeshita9 · H. Tatsuno5 · Y. Ueno1 · J. N. Ullom2 · S. Watanabe13 · S. Yamada5 Received: 20 August 2019 / Accepted: 15 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract High-resolution X-ray spectroscopy of the highly charged muonic atoms/ions isolated in vacuum is an ideal probe to explore quantum electrodynamics under extremely strong electric fields, which is one of the major topic in fundamental atomic physics. A feasibility test measurement with a low-density neon gas target was performed by observing X-rays emitted by muonic neon via the 5 → 4 transition, ∼ 6.3 keV, using a multi-pixel array of superconducting transition-edge-sensor (TES) microcalorimeters at the J-PARC muon facility. We successfully demonstrated the feasibility of muonic atom X-ray spectroscopy with a gas target at a pressure as low as 0.1 atom using TES array under an intense pulsed muon beam. Keywords Transition-edge sensor · TES · X-ray spectroscopy · Muonic atom · QED
1 Introduction Negatively charged muon can be bound by the Coulomb field of an atomic nucleus. This system, so-called muonic atom, is essentially a hydrogen-like atom. The muon is about 200 times more massive than the electron. The Bohr radius is therefore 200 times smaller, and thus the internal electric field strength is to be 40,000 times higher than that of normal atoms. The electric field is proportional to the cube of the atomic number Z, as shown in Fig. 1. A heavier muonic atom has therefore an extremely * S. Okada [email protected] Extended author information available on the last page of the article
13
Vol.:(0123456789)
Journal of Low Temperature Physics N Ne
1023
Ar
Kr
Xe
Pb
U
Muonic ions
1022
n=1 for muonic ions
21
n=2
20
n=3 n=4
1019
....
Internal electric field of muonic atom [V/m]
10 10
Schwinger-criticalfield strength : 1.32 x 1018 [V/m]
1018 1017 (Normal hydrogenlike ions, n=1)
1016 1015 1014 1013 1012 0
10
20
30
40
50
60
70
80
90
Atomic unit of electric field : 5.14 x 1011 [V/m]
Atomic number Z Fig. 1 Internal electric field strength of muonic atom for each principal quantum numbers from n = 1 to 14, and of normal hydrogenlike atom for n = 1 , as a function of atomic number Z, calculated only with Coulomb interaction
strong electric field even larger than the Schwinger-critical-field strength [1–4], 1.32 ×1018 [V/m], where the electric field becomes nonlinear in quantum electrodynamics (QED). Vacuum polarization is the dominant QED
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