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• 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