• Shell structure: ~ 1 MeV• Quantum phase transitions: ~ 100s keV• Collective effects: ~ 100s keV• Interaction filters: ~ 10-15 keV

Binding energies, Separation energies: Collectivity, symmetries, quantum phase transitions

What is the origin of simple patterns in complex nuclei?What is the origin of simple patterns in complex nuclei?

Double differences of masses – Interaction filters: p-n interactions

What is the nature of the nuclear force that binds What is the nature of the nuclear force that binds protons and neutrons?protons and neutrons?

Macro

Micro

Mass measurements of n-rich nuclei Collective Structure and the Microscopic

Drivers of Structural Evolution

Sn

Ba

Sm Hf

Pb

5

7

9

11

13

15

17

19

21

23

25

52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124 128 132

Neutron Number

S(2

n)

MeV

Collective contributions to masses can vary significantly for small parameter changes in collective models.

Masses: complementary observable to spectroscopic data in pinning down structure.

Particularly important far off stability where data will be sparse

B.E

(M

eV)

Examples of IBA calculations of rare earth nuclei

B.E S2n(Coll.) for two calcs.

S2n(Coll.) for two calcs.

Er Gd

Valence Proton-Neutron Interaction

Development of configuration mixing, collectivity and deformation – competition

with pairing

Changes in single particle energies and magic numbers

Partial history: Goldhaber and de Shalit (1953); Talmi (1962); Federman and Pittel ( late 1970’s); Casten et al (1981); Heyde et al (1980’s); Nazarewicz, Dobacewski et al (1980’s); Otsuka et al( 2000’s) and many others.

Microscopic perspective

Measurements of p-n Interaction Strengths

Average p-n interaction between

last two protons and last two neutrons

Vpn (Z,N)  =  ¼ [ {B(Z,N) - B(Z, N-2)}  -  {B(Z-2, N) - B(Z-2, N-2)} ]

Ref: J.-y. Zhang and J. D. Garrett

Orbit dependence of p-n interactions

p-n interaction is short range similar orbits give larger p-n interactions

HIGH j, LOW n

LOW j, HIGH n

50

82

82

126

Largest p-n interactions if proton and neutron shells have filling fractional filling

Empirical p-n interaction strengths indeed strongest along diagonal.

Empirical p-n interaction strengths stronger in like regions than unlike

regions.

New Xe masses (ISOLTRAP/ ISOLDE)

Neidherr et al

Nazarewicz, Stoitsov, Satula

Though DFT gives masses only to ~ 1 MeV, the filter allows us to study

subtle, important correlation effects at the 10-30 keV level.

But quantitative microscopic calculations

needed

Two regions of parabolic

anomalies.

Two regions of octupole

correlations

Possible signature?

Backups

Sn – Magic: no valence p-n interactions

Both valence protons and

neutrons

NpNn

Scheme

Critical role of the valence p-n interaction

82

50 82

126

Z 82 , N < 126

11

Z 82 , N < 126

1 2

Z > 82 , N < 126

2

3

3

Z > 82 , N > 126

208Hg208Hg

Direct correlation of observed growth rates of collectivity with empirical p-n interaction strengths

p-n interactions and the evolution

of structure

W. Nazarewicz, M. Stoitsov, W. Satula

Microscopic Density Functional Calculations with Skyrme forces and

different treatments of pairing

Realistic Calculations