International Workshop XLV on
Gross Properties of Nuclei and Nuclear Excitations
Neutron star mergers: From gravitational waves to nucleosynthesis
Hirschegg, Austria
January 18 (15-21), 2017

Quantum Self-Organizationand its implication in nucleosynthesis

Takaharu Otsuka

University of Tokyo / MSU / KU Leuven

Yusuke Tsunoda (CNS, Tokyo), Tomoaki Togashi (CNS, Tokyo)
Noritaka Shimuzu (CNS, Tokyo) , Tositaka Kajino (NAO)
Supported by MEXT and JICFuS as a priority issue (Elucidation of the fundamental laws
and evolution of the universe) to be tackled by using Post ‘K’ Computer

Outline•

Nuclear shapes and quantum phase transition•

Phase Transition in Zr isotopes and Quantum Self-organization•

Implications to nucleosynthesis•

Summary and Perspectives

Schematic picture of shape evolution (sphere to ellipsoid & vice versa)

excitation energy- gradual changes throughout the nuclear chart –seniority

Distance from the nearest closed shell in N or Z
From “Nuclear Structure from a Simple Perspective”, R.F. Casten (2001)

2+ and 4+ level properties of Sm isotopes
Ex (2+) :excitation energy of first 2+ state

R 4/2 = Ex (4+) / Ex(2+)

1800

Ratio

1600

Energy (MeV)

rotational (deformed)

3.5

1400
1200

32.5
21000

vibrational (spherical)

800

1.5

600

shape transition(Δ N = 8)

1400
0.5

200080

82

84

86

8890

92

Neutron number, N

94

96

080

82

84

86

88

90

92

Neutron number, N

Can this be a kind of Phase Transition ?

9496

itIntu,…
ivelyThis effect becomes larger as the nucleus
moves away from the closed shell.

quadrupole force
deformation =resistance power
resistance power ß for instance, pairing force
Assumed to be a constant, for a moment.
We come back to this point later !
The quadrupole force is a part of nuclear forces.
Its effect is expressed, for example, in Casten’s Np Nn model, as< quadrupole force > = α N p N n
α : parameterN p : number of valence protons
N n : number of valence neutrons5Outline•

Nuclear shapes and quantum phase transition•

Phase Transition in Zr isotopes and Quantum Self-organization•

Implications to nucleosynthesis•

Summary and Perspectives

Can the shape transition be a “Phase Transition” ?
Phase Transition :A macroscopic system can change qualitatively from a stable state (e.g. ice for H2O)
to another stable state (e.g., water for H2O) as a function of a certain parameter(e.g., temperature).
The phase transition implies this kind of phenomena of macroscopic systems
consisting of almost infinite number of molecules,
where thermodynamics can be applied.

Quantum Phase Transition (QPT)
The concept of the phase transition cannot be applied to microscopic systems
as it is. In the QPT, the ground state of a quantum (microscopic) system
undergoes abrupt and qualitative change (of order parameter)
as a (control) parameter changes.

The shape transition occurs rather gradually.
The usual shape transition may not fulfill the condition being abrupt.
Where can we see it ?
If it occurs in atomic nuclei, what is the underlying mechanism ?

possible scenario
parameter = N(almost) no mixing
completely different shapes
Note that sizable mixing occurs usually in finite quantum systems.
The definition of Quantum Phase Transition :an abrupt change in the ground state of a many-body system
by varying a physical parameter at zero temperature. (cf., Wikipedia)

Numerical part of the present work :Monte Carlo Shell Model calculation-Effective interaction:
JUN45 + snbg3 + VMU
known effective interactions+ minor fit for a part of
T=1 TBME’s
Nucleons are excited fully
within this model space(no truncation)

We performed Monte Carlo Shell
Model (MCSM) calculaNons, where
the largest case corresponds to thediagonalizaNon of 3.7 x 10 23
dimension matrix.

VMU
1d3/2
0g7/2
2S1/2
1d5/2
0g9/2
1p1/2
1p3/2
0f5/2

snbg3

1d3/2
0g7/2
2S1/2
1d5/2
0g9/2

JUN45proton

2p3/2
1f7/20h11/2

neutron
56Ni

Togashi, Tsunoda, TO et al. PRL117, 172502 (2016)

2+1 systematics

abrupt change
Quantum Phase Transition

10

FRDM: S. Moeller et al. At. Data Nucl. Data Tables 59, 185 (1995).
IBM: M. Boyukata et al. J. Phys. G 37, 105102 (2010).
HFB: R. Rodriuez-Guzman et al. Phys. Lett. B 691, 202 (2010).

11

Crossing without mixing
Quantum Phase Transition(1st order)

50

abrupt change

60

N70

MCSM wave funcNon on PotenNal Energy Surface (T-plot)
eigenstate

Slater determinant
intrinsic deformation• PES is calculated
amplitude
projection on Jπ
by CHF0+1 state of 68Ni
• LocaNon of circle :quadrupole
deformaNon of
unprojected MCSM
oblatebasis vectors• Area of circle :overlap probability
between eachprojected basis andspherical
eigen wave funcNon

triaxial

prolate

100ZrQuantum Phase
Transition(1st order)
due to crossing
without mixing

98Zr

14

Underlying mechanism :Type II shell evolution

f5/2
p3/2

g9/2

g9/2

p3/2.1/2, f5/2

proton
sph.

g7/2
h11/2
d3/2
d5/2

neutrondef.

Neutron effective single-particleenergies are self-reorganized by
nuclear forces (tensor and central)and certain configurations, so as toreduce resistance power against
deformation.
- a case of type II shell evolution -A clean example of tensor-force driven shell evolution
g9/2

k2
k1

thProton f5/2 - p3/2 inversion in Cu due toneutronkoccupancyof g9/2
1

k2

Flanagan et al., PRL 103,142501 (2009) ISOLDE exp.

Flanagan et al., PRL 103, 142501 (2009)

Franchoo et al., PRC 64, 054308 (2001)“level scheme … newly established for 71,73Cu”“… unexpected and sharp lowering of the πf5/2 orbital”“… ascribed to the monopole term of the residual int. ..”more neutrons in g9/2
TO, Suzuki, et al. PRL 104, 012501 (2010)

Shell Evolution - from Type I to Type II Type I Shell Evolution : different isotopes: particles

Type II Shell Evolution : within the same nucleus: particles: holes

TO and Tsunoda, J. Phys. G: Nucl. Part. Phys. 43 (2016) 024009

Underlying mechanism :Type II shell evolution

f5/2
p3/2

g9/2

g9/2

p3/2.1/2, f5/2

proton
sph.

g7/2
h11/2
d3/2d5/2

neutrondef.

Neutron effective single-particle
energies are self-reorganized by
nuclear forces (tensor and central)and certain configurations, so as toreduce resistance power against
deformation.
- a case of type II shell evolution -quadrupole force
deformation =resistance power
resistance power ß pairing force
single-particle energies
Atomic nuclei can “organize” their single-particle energies
by taking particular configurations of protons and neutrons
optimized for each eigenstate, thanks to orbit-dependences ofmonopole components of nuclear forces (e.g., tensor force).
Quantum Self Organization
Type I and II shell evolutions are simpler examples
19

Next page : spherical single-particle energies are often treated being constantWoods-Saxon potential
Parameters are constant within a given nucleus

Nilsson model Hamiltonian

quadrupole deformed field“Nuclear structure II” by Bohr and Mottelson

spherical field
constant within a region
Spin-orbit force
A= 68 1.28
A=100 1.12
A=186 0.91

Intuitively speaking,quadrupole force
deformation =resistance power
resistance power ß pairing force
single-particle energies
Analogy to electric current,

voltagecurrent =resistance21Outline•

Nuclear shapes and quantum phase transition•

Phase Transition in Zr isotopes and Quantum Self-organization•Implications to nucleosynthesis•

Summary and Perspectives

What is the possible implications to nucleosynthesis ?
A preliminary conceptual scheme.
99Nb

100Nb

ββ

Beta decays can be delayed
due to differencesin shapes and configurations(incl., unoccupied g7/2).
Beta decays become faster for
deformed states with N larger.
(n, γ) reactions may proceed,
while the captured neutron
may stay in higher orbits forsome time. ->(γ, n) ?

captured neutron(n, γ)
neutron threshold(n, γ)

slow γ decay
98Zr

2s99Zr7s

100Zr

Underlying mechanism :Type II shell evolution

f5/2
p3/2

g9/2

g9/2

p3/2.1/2, f5/2

proton
sph.

h11/2
d3/2
d5/2

neutrondef.

beta decay to g9/2

31 s

g7/2

Neutron effective single-particle
energies are self-reorganized by
nuclear forces (tensor and central)and certain configurations, so as toreduce resistance power against
deformation.
- a case of type II shell evolution -phase transition effect ?

stability oflight Zr ?

Summary and Perspectives• The atomic nuclei are not like a simple rigid vase containing almost
free nucleons.
• Nuclear forces are rich enough to change single-particle energies foreach eigenstate. Type I and II shell evolutions are simple cases.
à shape coexistence, quantum phase transition in shapes, super def,octupole excitations, fission, etc.
• More generally, single particle energies can be self-organized,
because of (i) two quantum liquids (protons and neutrons),(ii) two major force components :e.g., quadrupole interaction : to drive deformationmonopole interaction : to control resistance• Nucleosynthesis can be affected around the phase transition
example : certain shift of abundance to higher A ?
(n, γ) populates higher levels but not lowest states,
beta decay from higher levels, more delay in beta decay, …