* MASATOSHI KAJITA*, Nat. Ins. Info. Comm. Tech., Koganei, Tokyo 184-8795, Japan; MINORI ABE, Dep. of Chemistry, Tokyo Metro. Univ., Hachioji, Tokyo 192-0397, Japan.

Small number of molecular ions in a linear trap can be sympathetically cooled with atomic ions and form a string crystal at the position, where the electric field is zero. Molecular ions in a strinc crystal are advantageous to measure the transition frequencies without Stark shift induced by the trap electric field, but it is required to localize small number of molecular ions in a single quantum state. ^{40}CaH^{+} molecular ion is advantageous to solve this problem, because (1) molecular ion with rotational constant of 141 GHz is localized in the vibrational-rotational ground state when the surrounding temperature is lower than 10 K, and (2) there is no hyperfine splitting in the J=0 state.

In this presentation, we porpose to measure the ^{40}CaH^{+} X^{1}
\left( v,N,F,M\right) =\left( 0,0,1/2,\pm1/2\right)
\left( v_{u},0,1/2,\pm1/2\right) \left( v_{u}=1,2,3,,,\right) transition with the uncertainty lower than 10^{-16}. With these transitions, Zeeman shift is less than 10^{-16}/G (given by the slight dependence of schielding effect by electron cloud on the vibrational state) and electric quadrupole shift is zero because of F=1/2.

The J=0
0 transition is one-photon forbidden, and it can be observed also by Raman transition using two lasers. Stark shift induced by Raman lasers actually dominates the measurement uncertainty. When v=0
1 transition is observed using Raman lasers in the 6000-15000 /cm, Stark shift with saturation power is of the order of 1.5×10^{-14} and it is higher for overtone transitions. With the following Raman laser frequencies, total Stark shift induced by two Raman lasers is zero.

v=0 1 24527 /cm and 23079 /cm v=0 2 24600 /cm and 21745 /cm

v=0 3 26237 /cm and 22017 /cm v=0 4 25354 /cm and 19814 /cm

The ^{40}CaH^{+} X^{1}
\left( v,N,F,M\right) =\left( 0,0,1/2,\pm1/2\right)
\left( v_{u},0,1/2,\pm1/2\right) \left( v_{u}=1,2,3,,,\right) transition can be measured with the uncertainty lower than 10^{-16}, and it is useful to test the variation in the proton-to-electron mass ratio.