"Seniority-Zero" Excited States of the Pairing Hamiltonian

The seniority-zero excited-state spectrum of the Hamiltonian $H=\Sigma \stackrel{}{k>\mathrm{}0\mathrm{}}{\epsilon }_k({a_k}^{†}{a}_k+{a_{-k}}^{†}{a}_{-k})-G \Sigma \stackrel{}{k,l>\mathrm{}0\mathrm{}}{a_k}^{†}{a_{-k}}^{†}{a}_{-l}{a}_l$ is studied in detail. Approximate excited-state wave functions of the form ${\psi }^{\lambda }=\Sigma \stackrel{}{\alpha }F(\lambda ,\alpha )\Sigma \stackrel{}{i}D(\alpha ,i){a_i}^{†}{a_{-i}}^{†}\Sigma \stackrel{}{j>i}D(\alpha ,j){a_j}^{†}{a_{-j}}^{†}\cdots |0\mathrm{}〉$ are developed. These solutions are compared with exact solutions of a small system and the agreement is quite good. A somewhat larger system is studied in order to see how the excited-state spectrum changes as the number of separable functions is increased. The method is applied to heavy nuclei and is in good agreement with observed $0^{+}$ excited states for nuclei having 144 to 150 neutrons. A theoretical $0^{+}$ spectrum is displayed for each even neutron system from 144 to 152 neutrons.