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_{ud}^{2}+ V_{us}^{2}+ V_{ub}^{2} = 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.
Table
1. List of envisaged candidates for precision mass measurements at TITAN. The
# indicates, that the mass is derived from extrapolations of systematic trends.
The expected yield and year is given, together with the production target and
ion-source (LIS=Laser Ion Source).
Isotope |
Half-live |
Present
δm |
Expected
yield (year) |
Production |
odd-Z,
T_{z}=0 b emitters, with A ł 62 |
||||
^{62}Ga |
116
ms |
28
keV |
5•10^{3
}2004 |
Zr
LIS |
^{62}Zn |
9.1
h |
10
keV |
5•10^{3
}2004 |
Zr
LIS |
^{66}As |
96
ms |
200
keV |
1•10^{4
}2003 |
Zr
ECR |
^{66}Ge |
2.3
h |
30
keV |
1•10^{4
}2004 |
Zr
Plasma |
^{70}Br |
79
ms |
360
keV |
5•10^{5
} 2004 |
Nb
Plasma |
^{70}Se |
41
min |
210
keV |
1•10^{4
}2005 |
Zr
Plasma |
^{74}Rb |
65
ms |
19
keV |
5•10^{3
}2000 |
Nb
LIS |
even-Z,
T_{z}=-1 b emitters, with 18<A<42 |
||||
^{26}Si |
2.21
s |
3
keV |
1•10^{3
}2006 |
TiC
ECR |
^{30}S |
1.18
s |
3
keV |
1•10^{3
}2006^{ } |
TiC
ECR |
^{38}Ca |
439
ms |
4
keV |
1•10^{3
}2006 |
TiC
ECR/LIS |
^{42}Ti |
200
ms |
5
keV |
1•10^{3
}2006 |
Ni
ECR |
The mass measurement of an ion confined in a Penning trap is accomplished by determining its cyclotron frequency. For a particle with mass m and charge q in a magnetic field B the cyclotron frequency is given by ω_{c}_{ }= q/m • B (or ν_{c}_{ }= q/m • B/2p ) [12]. Therefore the observation of the cyclotron frequency for a particle with charge q in a magnetic field allows one to quantify the mass m. The magnetic field B is determined with an isotope of well known mass. In an ideal case one employs ^{12}C ions or ^{12}C_{x} molecules [13], where no experimental error is present, since these atoms are used for the unit definition. The uncertainty δn of the resonance frequency n_{c }is given by the Fourier limit which is inversely proportional to the observation or interaction time T_{RF}, hence δn ≈1/T_{RF}. The deduced statistical mass uncertainty is then given by:
Where N is the number of detected ions. For
radioactive ions the factor T_{RF} is fixed essentially
by the nuclear half-life. The number of detected ions N is depending on the
production yield and the available beam time. For existing Penning traps used
for high precision experiments, the magnetic field varies between 4 – 9 Tesla.
Therefore, the only way to increase the
accuracy by a large factor at given nuclear half-life or to access much shorter-lived
isotopes at a constant accuracy aimed for is to increase the charge state q
of the ion investigated. Here, a large factor can be gained. The path to reach
high accuracy mass measurements (δm /m ≈10^{-8})
even on rather short-lived isotopes (T_{1/2} = 50 ms) is to use a Penning
trap system, in combination with a charge breeding device at an ISOL-facility.
The potential of this concept has been demonstrated by the SMILE-TRAP at
Fig 3: Comparison of the achievable mass uncertainty
for ^{74}Rb employing highly or singly charged ions. Shown are two sets
of curves, with various numbers of detected ions, as a function of excitation
time in the trap.
Figure 3 shows clearly the gain factor in precision for the case of a mass measurement for rubidium ions with mass 74, by storing highly charged ions (He-like, q=35+) as compared to operations with singly charged ions, in a magnetic field of 6 T. Displayed in the box in the graph is an excitation time corresponding to two half-lives, which is a practical assumption, given the fact, that single ions are prepared and observed in the Penning trap. With the already proven production rate of ^{74}Rb at ISAC of 14000 ions/s, an interaction time for the mass measurement of T = 100 ms, and the total efficiency of the proposed set-up including nuclear decay losses to be e= Ľ % the required beam time to reach the aimed for mass accuracy is calculated to be only a few minutes. The absolute mass uncertainty for 10 000 detected ions of ^{74}Rb ^{35+ }would in this case^{ }be δm ≈ 200 eV.