On the Q-value of the tritium β-decay

– We report here the atomic masses of H and He determined by using the Penning trap mass spectrometer Smiletrap. The measurements are based on cyclotron frequency determinations of H and He using H+2 ions as mass reference. The mass values for H and He are 3.016 049 278 7(25) u and 3.016 029 321 7(26) u, respectively. From these masses a new Q-value of the tritium β-decay was derived resulting in 18.589 8(12) keV, being the most accurate value at present. The Q-value of the tritium β-decay is related to the possible rest mass of the electron antineutrino. Introduction. – Q-values of nuclear decays and reactions involve masses of atoms in the initial and final states. In some cases such Q-values are related to fundamental questions in current physics requiring an extremely high mass precision. Such a case is the Q-value of the tritium β-decay. Neutrino oscillations, which recently have been observed [1–3], require the existence of rest masses for the three neutrinos but give only a lower limit of 0.05 eV to the mass of the electron antineutrino. By studying the shape of the β-spectrum of tritium in the region that refers to energy of the last 50 eV with electrostatic electron spectrometers, it has been possible to set an upper limit of the mass to about 2 eV for m(νe) [4–7]. In the planned Katrin experiment [8] it will be possible to measure a neutrino mass as low as 0.3 eV. This method of determining m(νe) could use a very accurate Q-value for calibration purpose. There are a number of Q-values available from end point determinations of the tritium β-decay. The uncertainty in the weighted average of these measurements is about 1 eV. These measurements should be checked by an independent and at least as accurate method, i.e. a Penning trap measurement. Already in 1993 a Q-value measurement using mass determinations in a Penning trap was reported [9], which was based on the mass measurement of He and H. However, 10 years later in ref. [10] we showed that the mass values of both He and He were too low by 7 nu and 14 nu, respectively (roughly a 5σ deviation in both cases). Therefore the Q-value reported in ref. [9] did not seem reliable and should thus be remeasured. (∗) E-mail: [email protected] © EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx.doi.org/10.1209/epl/i2005-10559-2 Sz. Nagy et al.: Tritium Q-value 405 Based on our measurements, a preliminary Q-value of 18.588(3) keV was reported in refs. [11, 12]. Due to the fact that the two ions used, H and He, are not q/A-doublets, these measurements resulted in a relatively large systematic uncertainty in the Q-value. In this paper, a new Q-value is reported which is derived from mass measurements involving He and H ions. Experimental procedure. – The ion production and mass measurements with Smiletrap have been described in detail in ref. [11]. Here only a short description is given, sufficient for understanding the mass measurements described in this paper. The H and He and He ions which are used here, were all produced in the electron beam ion source Crysis [13–15] at the Manne Sieghbahn Laboratory. Although Crysis was designed for the production of highly charged ions, it has now been possible to find ion source conditions such that singly charged He ions and H ions were produced from disassociated molecules (H2). Only a small amount of gas is required even for several days of ion production, an important fact when dealing with radioactive elements. For the production of He ions, high-purity (> 99.99%) helium gas was used and for He isotopically enriched (> 99%) gas. The tritium ions were produced from a commercial tritium source of about 10Ci (4ml) [16]. The tritum was delivered as H2 (> 98%) gas absorbed in a uranium bed of 1.7 g inside a tiny gas bottle. The He gas created during the transportation and storage of the bottle was removed by pumping on the bottle. After the removal of the He gas, the H2 gas is released from the uranium by heating the bottle to about 400 ◦C. A buffer volume of ∼ 5ml was filled with 0.5 atm tritium gas from which it was introduced into Crysis via a needle valve. From measurements of the buffer volume pressure it was possible to estimate that only 0.14ml of the tritium gas was used during the 4 days of the experiment. The ions are ejected from Crysis in a bunch of ∼ 10 ions with 100μs pulse length at an energy of 3.5 keV. This ion pulse is transported over a distance of about 15 meters to the Smiletrap area, using electrostatic quadrupole lenses and deflectors. After charge selection in a 90◦ magnet the ions are decelerated in an electrostatic lens system before they enter the pre-trap and are captured. The pre-trap is an open-ended cylindrical Penning trap inside a warm solenoid of 0.25T. Due to phase space properties and the fact that the ion pulse is much longer than the dimension of the pre-trap, only a small fraction of the beam is captured, typically 1000 ions. After the ions are captured the potential of the trap is lowered from 3.5 keV to 0V in about 30ms. The ions are then transported through a series of drift tubes at −1 keV to the hyperbolic precision Penning trap inside a 4.7T superconducting magnet. The ions are again decelerated before entering the precision trap. An entrance aperture with a diameter of 1mm prevents ions with too large radial energies to enter the trap. The ions are then subject to an evaporation process by changing the trap potential from 5 to 0.1V, leaving only the coldest ions in the trap. After this procedure on average 1–2 ions are left in the trap. In a Penning trap a homogeneous magnetic field confines the ions in a plane perpendicular to B, and an electric quadrupole field confines the ions axially. The mass of an ion is derived from cyclotron frequency determinations. The cyclotron frequency of an ion with mass m and charge qe moving perpendicular to a magnetic field B is given by the well-known equation, νc = qeB/(2πm). In the combined magnetic and electric field the ions move in three independent modes, each one with its own frequency: an axial motion νz, independent of the magnetic field, and two radial motions, the so-called magnetron and reduced cyclotron motions, denoted ν− and ν+, respectively. In Smiletrap these frequencies are for an ion with q/A = 1/2 about 240 kHz, 810Hz and 36MHz, respectively. It can be shown [17] that the sum of these frequencies is equal to the cyclotron frequency, νc = ν− + ν+. The cyclotron frequency is measured by the time-of-flight technique developed by Gräff et al. [18]. The segmented ring electrode of 406 EUROPHYSICS LETTERS the trap is used for an azimuthal quadrupole excitation near the true cyclotron frequency νc. After the excitation the ion is ejected from the trap and the flight time to a detector located 500mm above the trap is measured. If the ion is in resonance it gains radial energy which is converted into axial kinetic energy in the fringe field of the magnet [19]. Therefore, ions in resonance have a shorter time of flight. A frequency scan using a 1 second non-interrupted excitation time results in a resonance with a FWHM of about 1Hz. A typical time-of-flight resonance spectrum is given in fig. 1. The expected sidebands of the resonance [19] are suppressed. This is mainly due to the initial spread in the magnetron radius, since the ions are not cooled in the pre-trap, and due to an incomplete conversion from magnetron to reduced cyclotron motion during excitation. The most precise measurement of the magnetic field in the trap is done by measuring the cyclotron frequency of an ion with a sufficiently well-known mass. In this work we have used H2 ions since its mass is known to 1.4 × 10−10 [11]. The H2 ions are produced by rest gas electron-impact ionization in the pre-trap. In order to eliminate a time dependence in the magnetic field, the cyclotron frequencies of the reference ion and the ions of interest is measured alternatively in 3min. Typically, the time of flight is measured at 21 equidistant frequencies around the resonance center twice for the first ion specie, before the other ion specie is measured after which the procedure is repeated. For each ion specie this takes 1.5min and it takes only a few seconds to reprogram all settings that differ for the two ion species. The mass of the ion is determined from the cyclotron frequency ratio between the ion of interest and that of the reference ion. To deduce the mass of the neutral atom one has to correct for the mass (qion ·me) of the missing electrons and their atomic binding energies E: matom = νref νion qion qref mref + qion ·me − E. (1) The uncertainty in the electron mass is known so accurately that it contributes to an uncertainty in the mass which is much less than 1 × 10−10 [20]. For light ions such as He and