Effective widths and integrated cross sections for two-photon transitions in 178 Hf

The possibility to produce an increase of the activity of an isomeric sample by irradiating the sample with a laser pulse and the X-ray pumping of nuclear transitions have been discussed some time ago. We have studied recently the rates for two-photon transitions from isomeric states to given final states, induced by an incident flux of photons having a continuous energy distribution. In this work we have calculated integrated cross sections for two-photon processes in 178 Hf. The calculations are based on tabulated nuclear data. We have assumed that the nucleus is initially in a state |i> of energy Ei and spin Ji, which in general is different from the isomeric state. By absorbing an incident photon of energy Eni, the nucleus makes a transition to a higher intermediate state |n> of energy En, spin Jn and half-life tn. The state |n> then decays into a lower state |l> of energy El and spin Jl by the emission of a gamma-ray photon having the energy Enl or by internal conversion. In some cases the state |l> may be situated above the initial state |i>, and in these cases the transition |n>→|l> is followed by further gamma-ray transitions to lower states. We have analyzed two-photon transitions in 178 Hf for which there is an intermediate state |n> of known energy En, spin Jn and half-life tn, for which the intermediate state is connected by a known gamma-ray transition to the initial state |i> and to a lower state |l>, and for which the relative intensities Rni, Rnl, Rnl' of the transitions to lower states are known. The cross sections are summed over all lower states |l> which are possible for a given pair of initial and intermediate states |i>, |n>. The effective widths Γefftot and the integrated cross sections σinttot are given. The largest integrated cross section found among the listed 24 two-photon processes in 178 Hf has the value 1.65 x 10-26 cm2 keV. However, all the two-photon processes having a relatively large value of the integrated cross section, have as components transitions between regular, low-J levels of 178 Hf. If the initial state is the isomeric state at Ei = 2446 keV, the nuclear parameters required for the calculation of the two-photon integrated cross section are known at present only for the intermediate state at En = 2573 keV, then the integrated cross section of this two-photon process has the value 2.09 x 10-35 cm2 keV. (authors)