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Corresponding author.

Deceased.

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The adapted DIRAC experiment at the CERN PS accelerator observed for the first time long-lived hydrogenlike

The DIRAC collaboration aims to check low-energy QCD predictions using double-exotic

The decay probability of short-lived

After investigation of

These large atom decay lengths in the laboratory (lab) system open a possibility to measure the energy splitting between

In this Letter, the DIRAC collaboration presents the first lifetime measurement of long-lived

To investigate long-lived

Method to investigate long-lived

Top view of the DIRAC setup: 1—target station with insertion, showing the Be target, magnetic field, and Pt breakup foil; 2—first shielding; 3—microdrift chambers (MDC); 4—scintillating fiber detector (SFD); 5—ionization hodoscope (IH); 6—second shielding; 7—vacuum tube; 8—spectrometer magnet; 9—vacuum chamber; 10—drift chambers (DC); 11—vertical hodoscope (VH); 12—horizontal hodoscope (HH); 13—aerogel Cherenkov; 14—heavy gas Cherenkov; 15—nitrogen Cherenkov; 16—preshower (PSh); 17—muon detector. (The plotted symmetric and asymmetric events are a

The DIRAC setup

The events are reconstructed by means of the DIRAC

Coulomb

The cross section of

In complete analogy, the production of

The relative yield between atoms and Coulomb pairs

The short-lived

The populations of all atomic states with quantum numbers

Population of long-lived states: In this Letter, the transport equations are solved numerically for all states with principal quantum numbers

Figure

Populations

Figure

Summed populations

The following numerical values are calculated: the sum of the long-lived state population at the Be exit is 6.04% for

As mentioned above, the cut of the infinite set of transport equations at

An additional correction to this value may arise from the accuracy of atom-atom cross sections. In the case of the Be target, an estimation shows that the summed population of long-lived states for

Decay in gap and breakup in Pt for long-lived atoms: In the 96 mm gap between the Be target and the Pt foil, the populations of the atomic states alter depending on their lifetime

Table

Summed (over

Finally, the expected total probability

The analysis of

Events with transverse

Table

Number

Atomic pairs from the

In the two-dimensional (

The

An additional one-dimensional

In summary, the analysis of the two-dimensional (

This result agrees within errors with

A long-lived atom lifetime is evaluated by means of two analyses. In the first simplified analysis, all long-lived atoms are considered as objects, which have one common lifetime, the average momentum

In the second more sophisticated analysis, the populations of the pionium states are described in terms of transport equations for the whole path from the production point in the Be target to the exit of the Pt foil. For the gap between Be and Pt, radiation transition rates and annihilation of short-lived states are included in the transport equations. The variation of the different

The solid line curve in Fig.

Probability

Accounting for the additional calculation errors, discussed in the “Population of long-lived states” subsection, leads to a wider error band for

The magnetic field between the Be target and the Pt foil transforms into an electric field in the atom c.m. system. This field mixes the wave functions of long-lived

The evaluated lifetime

We are grateful to O. V. Teryaev for the useful discussions; A. Vorozhtsov, D. Tommasini, and their colleagues from TE-MSC/CERN for the Sm-Co magnet design and construction; R. Steerenberg and the CERN-PS crew for the delivery of a high quality proton beam and the permanent effort to improve the beam characteristics. The project DIRAC has been supported by CERN, the JINR administration, the Ministry of Education and Youth of the Czech Republic by Project No. LG130131, the Istituto Nazionale di Fisica Nucleare and the University of Messina (Italy), the Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science, the Ministry of Research and Innovation (Romania), the Ministry of Education and Science of the Russian Federation and Russian Foundation for Basic Research, the Dirección Xeral de Investigación, Desenvolvemento e Innovación, Xunta de Galicia (Spain), and the Swiss National Science Foundation.