Transcript slides

Correlations in Structure
among Observables
and
Enhanced Proton-Neutron Interactions
R.Burcu ÇAKIRLI
Istanbul University
International Workshop "Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects"
(SDANCA-15), 8-10 October 2015, Sofia - Bulgaria
Broad perspective on structural evolution
E(21+)
80
100
90
70
60
1600
50
40
100
3.2
90
2.8
80
850
Proton Number
Proton Number
80
R4/2
70
1.9
60
40
30
20
20
10
10
30
50
70
90
110
Neutron Number
130
150
1.4
50
30
10
2.3
10
30
50
70
90
110
130
150
Neutron Number
The remarkable regularity of these patterns is one of the beauties of nuclear
systematics and one of the challenges to nuclear theory.
Whether they persist far off stability is one of the fascinating questions
for the future
Another useful observables, charge radii, B(E2), masses (S2n)
Nuclear Radii  Mean square of charge radius  <r2>  fm2
Deformed nuclei have larger radius  sudden increase in <r2>
2
<r > [fm ]
28
2
Change in slope
Ce
Nd
Sm
Gd
Dy
Er
26
Sudden deformation
N~90
Shape transitions
24
70
76
82
88
94
Neutron Number
100
Differential observables (isotope shifts)
d<r2>N = <r2>N - <r2>(N-2) Literature  <r2> comparison with
mostly B(E2). But why not E(21+) ?
N=90, onset of deformation
Ce
Nd
Sm
Gd
Dy
Er
0.2
750
dE(21+)
2
2
d<r > (fm )
0.4
0
-750
0.0
70
76
82
88
94
Neutron Number
100
70
76
82
88
94
Neutron Number
100
d`E(21+)N = E(21+)N – E(21+)(N-2)
Brix Kopfermann plot
However, there is a better correlation
with E(21+)
Onset of deformation at N=90
Ce
Nd
Sm
Gd
Dy
Er
0.2
0.3
dE(21+)
2
2
d<r > (fm )
0.4
0.0
In both-0.3plots!!!!
Sm, Gd and Dy have a higher peak than Ce and Er
0.0
70
76
82
88
94
Neutron Number
100
70
76
82
88
94
100
Neutron Number
dE(21+)N = [ E(21+)(N-2) – E(21+)(N) ] / [ E(21+)(N-2) + E(21+)N ]
like a normalization
With R4/2
dR4/2 = R4/2 (N) – R4/2 (N-2)
1.0
Ce
Nd
Sm
Gd
Dy
Er
0.2
0.5
d R4/2
2
2
d<r > (fm )
0.4
0.0
-0.5
0.0
-1.0
70
76
82
88
94
Neutron Number
100
70
76
82
88
94
Neutron Number
100
With B(E2; 21+  01+)
dB(E2) = B(E2)(N) – B(E2)(N-2)
2
2
0.2
dB(E2)
0.4
d<r > (fm )
100
Ce
Nd
Sm
Gd
Dy
Er
0
-100
0.0
70
76
82
88
94
100
70
76
Neutron Number
Neutron Number
82
88
94
100
With S2n
dS2n = S2n(N) – S2n(N-2)
Ce
Nd
Sm
Gd
Dy
Er
0.2
0
dS2n (MeV)
2
2
d<r > (fm )
0.4
-1
-2
-3
0.0
-4
70
76
82
88
94
Neutron Number
100
70
76
82
88
94
Neutron Number
100
70
94
70
100
76
82
88
94
100
0.4
2
d<r2>
0.2
2
26
2
88
d<r > (fm )
2
<r > [fm ]
82
Ce
Nd
Sm
Gd
Dy
Er
Yb
28
<r2>
76
0.0
24
0.3
1.5
dE(21+)
E(21+)
E(21+) [MeV]
2.0
1.0
0.5
d E(21+)
0.0
-0.3
Each plot has a different trend
0.0
1.0
3.2
0.5
d R4/2
R4/2
R4/2
2.6
dR4/2
0.0
2.0
-0.5
Each plot has the same trend
1.4
-1.0
01 ) (W.u.)
100
+
100
dB(E2)
0
-100
0
Ce
Nd
Sm
Gd
Dy
Er
Yb
S2n
S2n (MeV)
20
15
0
dS2n (MeV)
B(E2:21
+
B(E2)
dB(E2)
200
-1
dS2n
-2
-3
-4
10
70
Cakirli, Casten, Blaum, PRC 82, 061306 (2010) (R)
76
82
88
94
Neutron Number
100
70
76
82
88
94
100
Other regions are similar too
Neutron Number
S2n  binding energy difference  two binding energy (masses)
dS2n  S2n diffference  4 masses
Masses reflect all interaction in the nucleus
Various combinations of masses can isolate specific interactions
Another filter with 4 masses : dVpn
For even-even nuclei
|dVpn (Z,N)| = ¼ [ {B(Z,N) - B(Z, N-2)}
-{B(Z-2, N) - B(Z-2, N-2)} ]*
Average p-n interaction between the last 2 protons and the last neutrons 
Zth and (Z-1)th protons with Nth and (N-1)th neutrons
Extract a measure of the p-n interaction strength
*J.D.Garrett and J.-Y.Zhang, Cocoyoc, 1988, Book of Abtsracts
J.-Y. Zhang, R. F. Casten, and D. S. Brenner, Phys. Lett. B 227, 1 (1989)
R.B.Cakirli, D.S.Brenner, R.F.Casten and E.A.Millman, PRL 94, 092501 (2005)
Empirical dVpn
400
Os
Pt
Pb
Po Ra
70
Th
300
Rn
Hg
U
150
dVpn (keV)
dVpn (keV)
450
16
20
12
Sm 64Gd 66Dy 68Er
62
Yb
300
24
74
W
72
Hf
200
0
dV
106 pn
can
be interpreted
116
126
136
by considering Neutron
the orbit(nl
j) occupations
Number
90
94
98
102
106
110
Neutron Number
Deformed nuclei – should be considered
in terms of Nilsson orbits K [N, nz, L]
126
82
50

High j, low n
82

* p-n interaction is short range
* Similar orbits give largest p-n interaction
-To try to understand this effect we
calculated spatial overlaps of proton
and neutron wave functions.
- Similar trend is seen in light nuclei
for N=Z but it will not be discussed
now.
Odd-Z -- middle panel -- enhanced peaks
without the muting effects of pairing
Heavy nuclei - empirical valence p-n interactions from masses
Note peaks at Nval ~ Zval
New result, not recognized
before, that shows the
effect in purer form
Locus of peaks in p-n
interactions. Relation to
onset of collectivity
D. Bonatsos, S. Karampagia, R.B.Cakirli, R.F.Casten, K.Blaum, L.Susam, Phys. Rev. C 88, 054309 (2013)
Go further with Nilsson orbits
Note: the last filled proton-neutron Nilsson orbitals for
the nuclei where dVpn is largest are usually related by
DK[DN, Dnz, DL]=0[110]
168 Er
7/2[523]
R. B. Cakirli, K. Blaum, and R. F. Casten, Phys. Rev. C 82, 061304(R) (2010)
Synchronized filling of 0[110] proton
and neutron orbit combinations and
the onset of deformation
Similarity of Nilsson patterns
as deformation changes,
and high overlaps of 0[110] orbit pairs,
leads to maximal collectivity
near the Nval ~ Zval line*
0[110]
*D. Bonatsos, S. Karampagia, Cakirli, Casten, Blaum, Amon,
Phys. Rev. C 88, 054309 (2013)
Calculate spatial overlaps
of proton and neutron wave functions.
Compare to empirical dVpn values (top panel)
Overall agreement is good
Some disagreements, esp. in upper right
But note that calculations
do not take into account -softness
Note: Large values, for example,
Z~52-64 and N ~92-108
5/2[413] with 5/2[512]
and
1/2[420] with 1/2[521]
that do not satisfy 0[110]
Measurement of masses in the future
at FAIR, FRIB, and RIKEN
Bonatsos, Karampagia, Cakirli, Casten, Blaum, Amon, PRC 88, 054309 (2013)
Conclusions

The study is useful for future measurements : <r2>, spectroscopic observables,
masses and future theoretical approaches

Striking correlations of observables representing single particle motion, nuclear
radii and collective observables -- to our knowledge, not recognized heretofore

The separation energy is a good filter for studying structure using masses. Another
filter, dVpn , gives insight into average p-n interactions

Enhanced valence p-n interactions are closely correlated with the development of
collectivity, shape changes, and the emergence of deformation in nuclei.

Proton-neutron Nilsson orbits for largest p-n interactions satisfy 0[110]. Spatial
overlaps confirm large interactions for such cases and agree reasonably well with
dVpn

Highly interacting 0[110] pairs fill almost synchronously in heavy nuclei even as
the deformation increases: saturation in R4/2, emergence of deformation.

Extensive, realistic, Density Functional Theory calculations work nicely in
predicting p-n interaction strengths (in many mass regions)
Collaborators
R.F. Casten
D. Bonatsos
K. Blaum
L. Amon
Thanks for your attention !
Typical nuclear structure observables for even-even nuclei such as the first excited
2$^+$ state energy, and the ratio between the 4$^+$ and 2$^+$ states (R$_{4/2}$),
give us the information about the evolution of structure. In one part of this talk,
such observables and their differentials, including spectroscopic data and masses
and correlations among them will be discussed. In addition, since the separation
energy is a good filter for structure using masses, another filter, $\deltaV_{pn}$,
for heavy nuclei will also be presented and discussed in terms of spatial-spin orbit
overlaps between proton and neutron wave functions. We will discuss that protonneutron pairs of orbitals that fill almost synchronously in deformed medium mass and
heavy nuclei, satisfy 0[110] differences in Nilsson quantum numbers and correlate with
changing collectivity.
These data and results will be discussed in terms of the growth of collectivity
in nuclei as a function of the numbers of valence nucleons.
d<r2>
d E(21+)
dR4/2
dB(E2)
dS2n
Empirical valence p-n interactions from masses, dVpn
For even-even nuclei
|dVpn (Z,N)| = ¼ [ {B(Z,N) - B(Z, N-2)}
-{B(Z-2, N) - B(Z-2, N-2)}]*
*J.D.Garrett and J.-Y.Zhang, Cocoyoc, 1988, Book of Abtsracts, J.-Y. Zhang, R. F. Casten, and D. S. Brenner, Phys.
Lett. B 227, 1 (1989), R.B.Cakirli, D.S.Brenner, R.F.Casten and E.A.Millman, PRL 94, 092501 (2005)
Ne
Mg
Si
S
Ar
Ca
dVpn (keV)
4000
3000
dVpn has singularities for N = Z
in light nuclei
2000
Van Isacker, Warner, Brenner
PRL 74, 4607 (1995).
1000
8 10 12 14 16 18 20 22 24 26 28
Neutron Number
B-H: Their own results show that the p-n
components in fact dominate
450
EXP
pn
dV
TH
dVpn
p-n
168Er
Def.
keV
300
150
Other
0
600
Trans.
EXP dV TH
pn
dVpn
p-n
152Nd
keV
400
200
Other
0
-200
TH
EXP dVpn
450
Sph
dVpn
p-n
208Pb
keV
300
150
Other
0
Why did we get interested in the region ( ~ 168Er ) ?
400
val
20
16
12
Sm 64Gd 66Dy 68Er
62
dVpn (keV)
70
Yb
300
Van Isacker, Warner, Brenner, PRL 74, 4607 (1995).
24
74
W
4000
Hf
3000
72
dVpn (keV)
N
dVpn has singularities for N = Z
in light nuclei
200
90
94
98
102
106
110
Neutron Number
* dVpn has peaks for Nval ~ Zval !!!!
That is, equal numbers of valence protons and
neutrons – similar to light nuclei
* And the trajectory of these maxima coincides
with the emergence of deformation (soon)
Ne
Mg
Si
S
Ar
Ca
2000
* Wigner energy, related to SU(4), spin-isospin
1000
symmetry. Physics is high overlaps of the last
proton and neutron wave functions when they
8 10
12 14 16 18 20 22 24 26 28
fill identical
orbits.
Neutron Number
* Expected to vanish in heavy nuclei due to:
Coulomb force for protons, spin-orbit force
which brings UPOs into different positions in
each shell and protons and neutrons occupying
different major shells.
dVpn (Z,N) =
-¼ [ {B(Z,N)
-
B(Z, N-2)}
p
n
-
{B(Z-2, N)
p
n
Interaction of last two n with Z protons,
N-2 neutrons and with each other
p
-
- B(Z-2, N-2)} ]
n
p
n
Interaction of last two n with Z-2 protons,
N-2 neutrons and with each other
Average p-n interaction between the last 2 protons and the last 2 neutrons
 Zth and (Z-1)th protons with Nth and (N-1)th neutrons
dV eepn (Z;N) = −1/4({BE(Z;N) −BE(Z;N − 2)}− {BE(Z − 2;N) −BE(Z − 2;N − 2)});
dV eopn (Z;N) = −1/2({BE(Z;N) −BE(Z;N − 1)}− {BE(Z − 2;N) −BE(Z − 2;N − 1)});
dV oepn (Z;N) = −1/2({BE(Z;N) −BE(Z;N − 2)}− {BE(Z − 1;N) −BE(Z − 1;N − 2)});
dV oopn (Z;N) = −1/1({BE(Z;N) −BE(Z;N − 1)}− {BE(Z − 1;N) −BE(Z − 1;N − 1)})