High Accuracy Mass Measurements for Fundamental Symmetry Studies

The binding energy of the atomic nucleus is certainly one of the most fundamental properties of such many body systems. Accurate mass measurements serve as a testing ground for nuclear models and stimulate their further improvement, and are required for weak interaction studies in nuclear β-decay. Accurate mass measurements of high precision (δm /m < 10^-8) on very short-lived isotopes (T_1/2 ≈ 50 ms) are needed to experimentally test the theoretical corrections, which are employed to determine V_ud, the dominant matrix element of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. The CKM matrix should be unitary, based on fundamental concepts, however, the present experimental results lead to V_ud²+ V_us²+ V_ub² = 0.9740 ± 0.0014, [7] which points to a 2.2 sigma deviation from the expected value. High accuracy mass measurements would help to test the applied theoretical corrections for the determination of V_ud, and may ultimately help determine, if the deviation from unitarity is due to the reached precision or a nature-made effect. Should the effect be intrinsic to nature, this would strongly imply ‘physics beyond the Standard Model’.

Fig 2: Calculated contribution of theoretical corrections d_C to the ft value. The data of the nine well known superallowed b emitters are connected, where the others, not connected points are the new proposed b emitters, where complete experimental data sets not yet exist.

The experimental data needed are the ft values for superallowed b transitions. These allow one to determine G_v, the vector coupling constant, which then can be used to determine the V_ud matrix element for the up-down quark mixing. G_v can basically be obtained from the experimental ft values and employing the well-known relationship which is true for 0+ ® 0+  b transitions.  f is the statistical rate function, t is the partial half-life for the transition. FT is defined as the corrected ft value, were isospin symmetry breaking correction d_C and the transition-dependent part of radiative correction d_R are applied. D^V_R  is the radiative correction part that is independent of the transition, and K is a constant. In order to be able to determine the source of the deviation from unitary, one needs to exclude the possibility of erroneous theoretical corrections. To test this, the experimental precision has to be better than the theoretical corrections applied [8]. For the partial half-live, the experimental achievements have been demonstrated on this level of precision [9] and are even further developed [10].

The experimental requirements for the statistical rate function f can be determined in the following way: fµ Q⁵, and δf/f µ 5•δQ/Q, where Q is defined as the total available energy for the nuclear decay, hence the mass difference between the mother and daughter nucleus, minus the electron rest mass. In order to test the theoretical corrections on the necessary level needed, is δf/f < 0.1% that means δQ/Q < 0.02%, or in absolute values, to give an example for the case of ⁷⁴Rb, where Q = 10.4 MeV, δQ < 2 keV, corresponding to a mass uncertainty for mother and daughter nucleus of δm /m < 2•10^-8. The case of ⁷⁴Rb would clearly be the first mass measurement for TITAN, since the other needed properties of this nucleus were already determined at ISAC. Other candidates for TITAN measurements are listed in table 1, together with predicted ISAC yields. In the first series of these measurements one would focus on the new list of odd-Z, T_z=0  b emitters, with A ³ 62. The motivation for precision measurements in these nuclei comes from the fact that the calculated values [11] of the corrections are larger than those for the nine well know transitions nuclei.

If the experimental precision can be reached this would clearly be a valuable test of the accuracy of the theoretical corrections, specifically of the d_C part. The second series of measurements would focus on the enhancement in precision in the already fairly well known masses of the nuclei with even-Z, T_z=-1 b emitters, with 18 <A <42. The corrections in this series of transitions are smaller than for the heavier ones, but still larger than for the nine well known candidates. By reaching the better experimental precision, the results from these measurements will help understand the underlying concepts of the corrections.