Multiphonon approach to the nuclear excited states

1. Multiphonon approach to the nuclear excited states Petr Veselý Erlangen, Germany 7th February 2007

2. Plan of the Seminar • The model of independent particles • The nuclear excitations – single phonon approaches • The nuclear excitations – multiphonon approach • Problems and challenges of the multiphonon model • Outlook

3. The model of independent particles

4. The model of independent particles • The HF ground state gives good results for the mean values of any single-particle operators (e.g. all densities or currents, quadrupole moment operators). • The HF wave equation is not good description of the real nuclear ground state. • The HF wave function does not respect some of the basic symmetries of nuclear Hamiltonian – e.g. the translational or rotational symmetry

5. The excited states ? – The single phonon approaches Approximation – we suppose the nuclear excited states are general combinations of the 1particle-1hole excitations… TDA – the phonons respect the boson commutation rels. (vibrational quanta) TDA does not correlate the ground state RPA – “generalization” of TDA bosons, correlation of the ground state and restauration of broken symmetries. But we pay for it! – The quasiboson approximation

6. The excited states ? – Multiphonon approach Is it possible to describe nuclear excitations generally – without restriction to only 1p-1h excitations and employing approximations such like quasiboson?

7. The excited states ? – Multiphonon approach

8. Problems and challenges of Multiphonon model • Redundancy of basis in particle-hole formalism – Choleski method • Problem of the c.m. motion separation – dynamic separation of collective and internal degrees of freedom by method of F. Palumbo (Nucl. Phys. 99, 100 (1967)) • efficiency of the calculation – reasonable cut of phonon basis (is not possible in the particle-hole formalism)?

9. Outlook • Include the quasiparticle formalism – important for non-spherical nuclei • Conection with selfconsistent methods – mean field and interaction generated selfconsistently • Possible application for wider range of nuclei (especially heavy nuclei) – “reasonable” cut of phonon basis Anyway it is useful to know also about some other fields in nuclear physics. There is no universal model to describe such difficult thing like nucleus in all aspects. We should play (sometimes) also with other “nuclear people” – shell model, few-body physics…

10. Some spectra