# What can be learn from binding energy differences

- Slides: 17

What can be learn from binding energy differences ? The example of d Vpn M. Bender (CENBG, Bordeaux), P-H Heenen (ULB, Brussels) 01/02/2011 ISOLDE

Synopsis Our tool: the beyond mean-field method d Vpn , definition and hopes: p-n interaction? Analysis of d Vpn in simple models Can our BMF model reproduce data? (yes) Analysis of d Vpn within our model Conclusions: d Vpn is not an indicator of p-n interactions. • Be careful when interpreting beautiful in theory terms • • • 01/02/2011 ISOLDE

The beyond mean-field method: 3 steps correlations • Set of mean-field wave functions depending on axial q generated by HFB with a Skyrme EDF deformation • Symmetry restoration N, Z, J: rotation • new wave functions generated by mixing of projected meanfield | J 0 q> vibration f. J, k (q) determined by minimizing the energy with the same interaction used to generate the mean-field

Systematic calculation of nuclei with even N and Z Bender, Bertsch, Heenen, Phys. Rev. C 73 (2006) 034322 Include correlations due to deformation symmetry restoration configuration mixing correlations in BE evaluated by comparison with spherical HFB (similar global study also by Stoistov et al, PRL 98 (2007) 132502, limited to deformation Collectivity-induced quenching of signatures for shell closures M. Bender, G. F. Bertsch, and P. -H. Heenen Phys. Rev. C 78, 054312 (2008))

d. Vpn: empirical p-n interaction? d. Vpn = ¼ [(B(N, Z)-B(N, Z-2))-(B(Z-2, N)-B(Z-2, N-2))] = ¼ [S 2 n (N, Z) - S 2 n (N, Z-2) ] = ¼ [S 2 p (N, Z) - S 2 p (N-2, Z) ] Interpreted as a signature of the proton-neutron interaction of the last 2 protons with the last two neutrons (PRC 80 2009 044323)

A proton – neutron interaction? • 01/02/2011 ISOLDE

These conditions are unrealistic • ? ? ? 01/02/2011 ISOLDE

Three calculations: 1. spherical mean-field (close to a liquid drop) 2. deformed mean-field 3. beyond mean-field

LD spherical deformed beyond experiment 01/02/2011 ISOLDE

deformation energy deformation +beyond mf E contribution of deformation and beyond mf 01/02/2011 ISOLDE

Collaboration meeting 20 -21 January Bordeaux-Brussels-GANIL-Lyon-Saclay the anonymous physicists 01/02/2011 ISOLDE