Single Particle & Collective Properties (Contributors: Angela Bonaccorso, Roy Lemmon, Valerie Lapoux, Yorick Blumenfeld.)

Abstract  
         A key experimental study within the programme will be to explore how the spectroscopic factors and occupancy of the 3s_1/2 proton orbital changes in the heavy neutron-rich Pb isotopes. The absolute occupancy of the 3s_1/2 proton orbital of ^208Pb was measured to be only 70-80% relative to the IPSM. How does this occupancy change as neutrons are added to ^208Pb ? One-proton removal reactions and (d,^3He) transfer reactions using beams of neutron-rich Pb isotopes from EURISOL will allow this important effect to be measured.
Keywords 
Shell model, single particle  degrees of freedom, spectroscopic factors, isospin.

Physics case
Isospin Dependence of Correlations

Despite the enormous success of the independent particle shell model (IPSM) in explaining many nuclear static and dynamic properties at low excitation energies, the concept of independent particle motion is only an approximation and effects will exist beyond the mean field level. This is a consequence of the structure of the underlying nucleon-nucleon (N-N) interaction. Nucleons interact via the strong force, described by Quantum Chromodynamics. While it is not yet possible to derive a realistic NN interaction starting from QCD in this non-perturbative regime, the interaction is reasonably well known empirically. Fits to N-N scattering data reveal a complicated character to the interaction, with a strongly repulsive central interaction at small internucleon distances, strong tensor components at medium distances and long-range components. These features lead to properties of nuclear wave functions that are beyond what is describable in terms of an independent particle model. For example, the long-range component of the nucleon-nucleon force gives rise to correlations that usually make it necessary to explicitly take into account the mixing of many valence configurations. The inclusion of these residual interactions in the shell model (SM) allows a much more detailed understanding of nuclear structure to be reached and this model has been verified many times. The short-range and tensor parts of the N-N interaction also have a very important, not to say dominating, influence without which not even nuclear binding can be explained. The consequences of these short-range correlations are that the momentum distributions of nucleons acquire a tail extending to very high momenta k, and at the same time, part of the strength, located in independent particle descriptions at low excitation energy E, is moved to very high excitation energies. Most experimental investigations are confined to rather low momenta and energies, i.e. to the region where the strength is dominated by the independent particle properties. In this region, the consequences of short-range correlations are indicated primarily by a depopulation of states in comparison to the predictions of independent particle models. According to several calculations for infinite matter and finite nuclei using different realistic N-N potentials, a depopulation of the order of 15 to 20% is expected.

Observable
Momentum distribution of the projectile like fragment. Gamma-rays in coincidence for nucleon removal. Simultaneous detection of target recoils, projectile like fragments and gamma rays for transfer.

Proposed experiment

(i)	One nucleon transfer reactions such as (p,d) or (d,^3He) in inverse kinematics with incident exotic beam energies of 5 – 30 MeV/nucleon. Arrays that allow the simultaneous detection of target recoils, projectile like fragments and gamma rays with high efficiency and resolution will be necessary. Ideally,  Beam intensities greater than 10^4 pps will be necessary.

(ii)  One-nucleon removal reactions with incident exotic beam energies of 50 – 200 MeV/nucleon. The momentum distribution of the projectile like fragment should be measured in a high resolution magnetic spectrometer. The excited states of the core can be tagged using gamma rays measured in a high efficiency, high resolution, gamma-ray array.  Beam intensities as low as 1 pps can be utilised.

Requirements:
Beam properties
Beam intensities greater than 10^4 pps will be necessary. Beam energies of 5 – 30 MeV/nucleon
for transfer and 50 – 200 MeV/nucleon for nucleon removal.

Detection
Detection of target recoils, projectile like fragments and gamma rays with high efficiency and resolution will be necessary. Polarised targets of H and D should be developed as then unambiguous measurements of the j-values of the orbitals can be made. Magnetic spectrometer.
High efficiency, high resolution, gamma-ray array. The gamma ray array will need to have a granularity and/or position resolution capable of compensating for the Doppler shifts of the gamma-rays emitted from the high energy projectile like fragment.

Theoretical support
Improved theoretical descriptions of the reaction mechanisms will need to be developed The absolute spectroscopic factors would be expected to reflect the isospin dependence of the occupancies as described above. However, to obtain the absolute occupancies from the measurements of the spectroscopic factors, an approach such as the CERES sum rule, applicable for proton occupancies, will need to be applied. This sum rule requires measurements of charge density differences obtained by elastic electron scattering to be available. Such measurements will be made by the ELISE eA collider, under construction at the new FAIR facility at GSI.