#### Abstract

The seniority-zero excited-state spectrum of the Hamiltonian $H=\Sigma \stackrel{}{k>\mathrm{}0\mathrm{}}{\epsilon}_{k}({{a}_{k}}^{\u2020}{a}_{k}+{{a}_{-k}}^{\u2020}{a}_{-k})-G\Sigma \stackrel{}{k,l\mathrm{}0\mathrm{}}{{a}_{k}}^{\u2020}{{a}_{-k}}^{\u2020}{a}_{-l}{a}_{l}$ is studied in detail. Approximate excited-state wave functions of the form ${\psi}^{\lambda}=\Sigma \stackrel{}{\alpha}F(\lambda ,\alpha )\Sigma \stackrel{}{i}D(\alpha ,i){{a}_{i}}^{\u2020}{{a}_{-i}}^{\u2020}\Sigma \stackrel{}{j>i}D(\alpha ,j){{a}_{j}}^{\u2020}{{a}_{-j}}^{\u2020}\cdots |0\mathrm{}\u3009$ 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.

DOI: http://dx.doi.org/10.1103/PhysRev.138.B326

- Received 10 November 1964
- Published in the issue dated April 1965

© 1965 The American Physical Society