What do (ordinary) nuclei look like? Charge densities of magic - PowerPoint PPT Presentation

Overview Basics Highlights Outlook CI QMC CC React SM NM DFT Atoms What do (ordinary) nuclei look like? Charge densities of magic nuclei (mostly) shown Proton density has to be “unfolded” from ρ charge ( r ) , which comes from elastic electron scattering Roughly constant interior density with R ≈ ( 1 . 1–1 . 2 fm ) · A 1 / 3 Roughly constant surface thickness = ⇒ Like a liquid drop! Dick Furnstahl New methods

Overview Basics Highlights Outlook CI QMC CC React SM NM DFT Atoms What do (ordinary) nuclei look like? Charge densities of magic nuclei (mostly) shown Proton density has to be “unfolded” from ρ charge ( r ) , which comes from elastic electron scattering Roughly constant interior density with R ≈ ( 1 . 1–1 . 2 fm ) · A 1 / 3 Roughly constant surface thickness = ⇒ Like a liquid drop! Dick Furnstahl New methods

Overview Basics Highlights Outlook CI QMC CC React SM NM DFT Atoms Semi-empirical mass formula ( A = N + Z ) Z 2 ( N − Z ) 2 E B ( N , Z ) = a v A − a s A 2 / 3 − a C A 1 / 3 − a sym + ∆ A Many predictions! Rough numbers: a v ≈ 16 MeV, a s ≈ 18 MeV, a C ≈ 0 . 7 MeV, a sym ≈ 28 MeV √ Pairing ∆ ≈ ± 12 / A MeV (even-even/odd-odd) or 0 [or 43 / A 3 / 4 MeV or . . . ] Surface symmetry energy: a surf sym ( N − Z ) 2 / A 4 / 3 Much more sophisticated mass formulas include shell effects, etc. Dick Furnstahl New methods

Overview Basics Highlights Outlook CI QMC CC React SM NM DFT Atoms Semi-empirical mass formula per nucleon Z 2 ( N − Z ) 2 E B ( N , Z ) = a v − a s A − 1 / 3 − a C A 4 / 3 − a sym A 2 A Divide terms by A = N + Z Rough numbers: a v ≈ 16 MeV, a s ≈ 18 MeV, a C ≈ 0 . 7 MeV, a sym ≈ 28 MeV Surface symmetry energy: a surf sym ( N − Z ) 2 / A 7 / 3 Now take A → ∞ with Coulomb → 0 and fixed N / A , Z / A Surface terms negligible Dick Furnstahl New methods

Overview Basics Highlights Outlook CI QMC CC React SM NM DFT Atoms Nuclear and neutron matter energy vs. density [Akmal et al. calculations shown] Uniform with Coulomb turned off 40 APR Density n (or often ρ ) NRAPR RAPR Fermi momentum n = ( ν / 6 π 2 ) k 3 F 20 E/A (MeV) Neutron matter ( Z = 0) has Neutron matter positive pressure Symmetric nuclear matter 0 ( N = Z = A / 2) saturates Nuclear matter Empirical saturation at about E / A ≈ − 16 MeV and -20 0 0.05 0.1 0.15 0.2 0.25 n ≈ 0 . 17 ± 0 . 03 fm − 3 -3 n (fm ) Dick Furnstahl New methods