Probing monopole double giant resonances by dilepton (E0) emission

Giant resonances provide an invaluable tool to analyze excitations embedded in the continuum part of nuclear spectra. The study of double phonon excitations at high energies has recently been the subject of considerable interest, both theoretically and experimentally. The double dipole giant resonance (GDR2) was observed in 208 Pb by measuring in coincidence the two γ rays that ensue from the decay of the GDR2 to the GDR and from this to the ground state. Even the deexcitation of the double monopole giant resonance through E0 dilepton emission was recently experimentally explored. This intense experimental activity was well matched by theoretical analysis of the origin and mechanisms of decay of double giant resonances. In this paper we will present a formalism to study 2p plus 2p2h excitations within the shell model (TDA approximation) by using the multistep shell model method (MSM) and including the continuum by means of the Berggren representation. As a representation to span the shell model space we choose a set of single-particle states which satisfy outgoing boundary conditions corresponding to a Woods-Saxon potential. This set includes bound states and the so-called Gamow resonances. A complete set in the Berggren representation should also include scattering states. Since wide states can be considered as part of the proper continuum we included in the basis only bound states and resonances no wider than 200 keV. Already this represents a drastic truncation of the basis because most high lying states are wide. The study of correlated states that result as the coupling of collective excitations can be studied conveniently within the MSM. In this method one solves the shell model problem in several consecutive steps. In each step one describes a given system in terms of quantities related to the systems evaluated in the previous steps. The resulting violations of the Pauli principle as well as the over counting of independent shell-model states are corrected by using the overlap matrix among basis states. In our case we have to evaluate the particle-particle (pp), i. e. |α2> = P+(α2)| 0>, hole-hole (hh), i. e. |α-2> = P(α-2)| 0>, and particle-hole (ph), i. e. |α0> = Q+(α0)| 0> excitations. We use a separable residual interaction. With this interaction we calculated the TDA ph states in 208 Pb, the pp states in 210 Pb and 210 Po and the hh states in 206 Pb and 206 Hg. We found a reasonable agreement between our calculation and the available experimental data. To analyze the effect of 2p2h excitations on the width of the GMR we evaluated the strength function S(E), which is essentially the imaginary part of the response function. We have also calculated the partial decay widths Γn,ch of the resonances. We have found that that coupling contributes significantly to the width of the giant resonances as well as to the corresponding particle decay. However, we have found that double giant resonances are not mixed with other degrees of freedom and, as a result, their widths is about √ 2 times the width of the corresponding giant resonance. We have studied the decay pattern of the double giant resonance excitations and found that in 208 Pb the double monopole giant resonance is likely to be detected by measuring dilepton (e+,e-) emission. (authors)