Proton-neutron interactions

The key to structural evolution

6+ 690

4+ 330

0+ 0

2+ 100

J E (keV)

?Without

rotor

paradigm

Paradigm

Benchmark

700

333

100

0

Rotor J(J + 1)

Amplifies structural

differences

Centrifugal stretching

Deviations

Identify additional

degrees of freedom

Detour before starting

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

Sn – Magic: no valence p-n interactions

Both valence protons and

neutrons

Two effects

Configuration mixing, collectivity

Changes in single particle energies and shell structure

Microscopic mechanism of first order phase transition (Federman-Pittel, Heyde)

Monopole shift of proton s.p.e. as function of neutron number

Gap obliteration

2-space 1-space

(N ~ 90 )

Can we see this experimentally?

A simple signature of phase transitions

MEDIATED

by sub-shell changes

Bubbles and Crossing patterns

Seeing structural evolution Different perspectives can yield different insights

Onset of deformation Onset of deformation as a phase transition

mediated by a change in shell structure

Mid-sh.

magic

“Crossing” and “Bubble” plots as indicators of phase transitional regions mediated by sub-shell changes

A~100

52 54 56 58 60 62 64 66

1,6

1,8

2,0

2,2

2,4

2,6

2,8

3,0

3,2

Z=36 Z=38 Z=40 Z=42 Z=44 Z=46

R4/

2

Neutron Number

36 38 40 42 44 46

1,6

1,8

2,0

2,2

2,4

2,6

2,8

3,0

3,2

N=52 N=54 N=56 N=58 N=60 N=62 N=64 N=66

R4/

2

Proton Number

B(E2; 2+ 0+ )

Sudden changes in R4/2

signify changes in structure, usually from spherical to deformed

structure

Onset of deformation

Sph.

Def.

Observable

Nucleon number, Z or N

R4/2

E2

1/E2

Often, esp. in exotic nuclei, R4/2 is not available. A easier-to-obtain observable, E(21

+), in the form of 1/ E(21

+), can substitute equally well

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

Total mass/binding energy: Sum of all interactions

Mass differences: Separation energies shell structure, phase transitions

Double differences of masses: Interaction filters

Masses:

Macro

Micro

Masses and Nucleonic Interactions

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

Measurements of p-n Interaction Strengths

Vpn

Average p-n interaction between last protons and last neutrons

Double Difference of Binding Energies

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

Vpn (Z,N)  = 

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

p n p n p n p n

Int. of last two n with Z protons, N-2 neutrons and with each other

Int. of last two n with Z-2 protons, N-2 neutrons and with each other

Empirical average interaction of last two neutrons with last two protons

-- -

-

Valence p-n interaction: Can we measure it?

Orbit dependence of p-n interactions

82

50 82

126

High j, low n

Low j, high n

82

50 82

126

Z 82 , N < 126

11

3

Z > 82 , N > 126

3

Z > 82 , N < 126

2

2

Behavior of p-n interactions

208Hg

In terms of proton and neutron orbit filling, p-n interaction

p-n interaction is short range similar orbits give largest p-n interaction

HIGH j, LOW n

LOW j, HIGH n

50

82

82

126

Largest p-n interactions if proton and neutron shells are filling similar orbits

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

Empirical p-n interaction strengths indeed strongest along diagonal.

82

50 82

126

High j, low n

Low j, high n

Neidherr et al, preliminary

BEWARE OF FALSE BEWARE OF FALSE CORRELATIONS!CORRELATIONS!

BEWARE OF FALSE BEWARE OF FALSE CORRELATIONS!CORRELATIONS!

W. Nazarewicz, M. Stoitsov, W. Satula

Microscopic Density Functional Calculations with Skyrme forces and

different treatments of pairing

Realistic Calculations

Density Functional Theory

Would you like to see it again? OK.

My understanding of DFT:

So, I hope all this is clear.

Anyway, Nazarewicz, Stoitsov and Satula calculated masses for over 1000 nuclei across the nuclear chart with several interactions, and, from these masses, computed the p-n interactions using the same double difference expression. Lots of results. A few examples:

http://workshop.turkfizikdernegi.org

Principal Collaborators

• Burcu Cakirli (Istanbul) dVpn, Bubbles, Masses

• Klaus Blaum (MPI – Heidelberg) Masses

• Magda Kowalska (CERN – ISOLDE) Masses

• And the GSI Schottky and CERN-ISOLDE mass groups for their measurements of Hg, Rn and Xe masses

Backups