Laser-microwave double and triple resonance experiments were performed on c
louds of Ba+ ions confined in a Penning ion trap to induce and detect elect
ronic and nuclear spin flip transitions. Collisions with buffer gas molecul
es in the trap was used to reduce the lifetime of a long lived metastable s
tate of the ions, in which population trapping might occur, and to cool the
ions to the ambient temperature. Loss of ions from the trap by collisions
were prevented by coupling the magnetron and reduced cyclotron motions by a
n additional r.f. field at the sum frequency of the two motions. Electronic
Zeeman transitions in Ba-138(+) and Ba-135(+) were observed at a full widt
h of about 3 kHz at a transition frequency of 80 GHz. The uncertainty of th
e line center was 3 x 10(-9). From the magnetic field calibration by the cy
clotron resonance of electrons stored in the same trap the g(J)-factor for
both isotopes could be determined to 2 x 10(-8). From radiofrequency induce
d Delta m(I) = 1 transitions of Ba-135(+) the nuclear g-factor could be det
ermined 5 x 10(-6) Both measurements improve earlier results by about one o
rder of magnitude.