Masses, binding energies, and structure - PowerPoint Presentation

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Masses, binding energies, and structure

The same physics that leads to collectivity, lowering collective states,

also

increases the binding and affects masses

That has long been known.

What

may

be new is the magnitude of the effect on masses in models such as the IBA. On

va

voir

.

Most general IBA Hamiltonian in terms with up to four boson operators (given N)

Recall: IBA Hamiltonian

These terms

CHANGE

the numbers of s and d bosons:

MIX

basis states of the model

Crucial for structure

Crucial for masses

This lowering of the lowest state (ground state) represents extra BINDING, changing the mass.

We can calculate this with the IBA

Broad perspective on structural evolution

p-h

From Cakirli

E(5)

X(5)

1

st

order

2

nd

order

Axially symmetric

Axially asymmetric

Sph.

Def.

Sub-shell changes and binding

A~150

Crossing

Bubble

Without the

transitional nuclei

Concave and convex curves

Identifying the “

subshell “ kind of nucleon

Sub-shell changes often induce shape transitions, driven by changes in

s.p.e.’s induced largely by the monopole interaction. This can have large effects on binding as one configuration drops below another.

Valence Proton-Neutron Interaction

Development of configuration mixing, collectivity and deformation

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.

Empirical average (last) p-n interaction

Double difference of binding energies (Garrett and Zhang)

V

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

First extensive tests of specific nucleonic interactions in heavy nuclei with Density Functional

Theory.

Question: How can mass models that are accurate to only ~1

MeV

give p-n interactions accurate to 30

keV

?

Ans

: Friday.

Stoitsov

,

Cakirli

et al

Practical Structure and Binding Energy Calculations with the IBA

Dynamical symmetries

Mixing of basis states

Calculations and wave functions away from the symmetries Calculations for real nuclei

Normalizing to the level scheme data Binding energies and separation energies

dVpn

Nuclear Model Codes at Yale

Computer name: Titan

Connecting to SSH:

Quick connectHost name: titan.physics.yale.eduUser name: phy664

Port Number 22Password: nuclear_codes

cd phintm

pico filename.in (ctrl x, yes, return)

runphintm filename (w/o extension)pico

filename.out (ctrl x, return)

Caveat

Please take all specific calculations below

Cum

Grano

SalisThey were just done now, they are something new that has not really been tried, and they have not

not not

been checked. This refers especially to the way we normalize to the experimental 2+ energy. This may or may not be the correct approach. We need to think more about it.

Literature IBA calculations for

Gd

and Dy with literature parameters (kappa = 0.02)

Gd N Chi Eps

E(2)exp E(2)

IBA BE’IBA

Norm BE IBA S 2n IBA Coll

k= 0.02150 86 -1.32 1.68 638.0 1359 0.1035 2.13

0.049 152 88 -1.32 1.15

344.3 729 0.226 2.11 0.107 0.058

154 90 -1.1 0.61 123.1 151.6 0.880 1.23 0.715 0.608156 92 -0.86 0.37 89.0

80.2 1.878 0.90 2.087 1.372158 94 -0.8 0.35 79.5 74.0 2.379 0.93 2.558 0.471

160 96 -0.53 0.21 162 98 -0.3 0.02 YOU should fill in the rest of the table !!!!

Dy

86 -1.1 1.49 88 -1.09 0.92 334.6 447.7 0.399 1.34 0.298

90 -0.85 0.59 137.8 150.0 1.039 1.09 0.953 0.655 92 -0.67 0.42 98.9 92.8 1.833

0.94 1.720 0.767 94 -0.49 0.26

96 -0.31 0.1 98 -0.26 0.03

IBA (collective part) S

2n

’s for Gd (normalized)



V

pn (Z,N) values in the IBA



Vpn

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

2n(Z,N) - S2n(Z-2,N) ]

Example: Vpn

(Z,N) for 158 Dy =

Vpn

(66,92) = ¼ [ S

2n(66,92) - S2n(64,92) ] = 0.25 [ 0.767 - 1.372 ]

= -0.151 MeV

Same rough range as the data (~0.260 MeV). Is this good or bad? I have no idea. Need to look at trends. Also I did this 10 minutes ago and it could easily be wrong. Think of this as an example of what can be done, not that it has been done right. I will double check.