Structures of Exotic 131,133Sn Isotopes for r-process nucleosynthesis

Shisheng Zhang1,2 (张时声 )

1. School of Physics and Nuclear Energy Engineering,

Beihang University, Beijing 100191, China

2. Institute of Theoretical Physics,

Chinese Academy of Sciences, Beijing 100190, China

29th, June 2012

KITPC Joint Workshop on Nuclear Physics, Beijing, China

11th June – 30th June, 2012

Outline

Background and Motivation nuclear structure nuclear astrophysics

Goals Theoretical Methods Results and discussions Summary and outlook

Background : nuclear structure

Theoretical understanding?

Not yet!

Experiments: Four strong single

particle bound levels with striking similarity

level spacings strengths recently measured

in 131Sn and 133Sn

K. L. Jones et al., Nature, 465, 454 (2010).

R. L. Kozub et al.,

(submitted to PRL 2012).

Background : nuclear astrophysics

bound levels

resonant levels (above neutron

capture thresholds)

neutron capture (NC) cross section

synthesis of heavy elements in the r-

process in supernovae

NC reaction rate

R. Surman, J. Beun, G. C. McLaughlin and W. R. Hix, PRC 79, 045809 (2009).

??

Significantly impact !

Global impact of 130Sn(n,g) on r-process abundances

OUR GOAL!

3 contributions to neutron capture cross section

Background : nuclear astrophysics

S(n)

DirectCapture

Resonant Capture

H FAveraging over many closely-spaced levels • strong dependence on level density model• For Fermi gas model, when is HF applicable?

• Levels above S(n) are unknown• contribution to stotal unknown

• Strong bound single particle levels below S(n) contribute• ratios to sRC and sHF are unknown

HFRCDCtotal

g.s.

Ex

Outline

Background and Motivation nuclear structure nuclear astrophysics

Goals Theoretical Methods Results and discussions Summary and outlook

Goals

Understand the structure of the bound and resonant levels in 133Sn and 131Sn from the theoretical point of view and check if similarity appears in theoretical calculations Determine if the density of unbound resonant levels is sufficiently high to enable valid statistical model calculations for NC cross section calculations on 130,132Sn

Outline

Background and Motivation nuclear structure nuclear astrophysics

Goals Theoretical Methods Results and discussions Summary and outlook

Shell model large scale shell model (LSS)

Phenomenological models Koura-Yamada's s.p. potential (KYSPP) Nilsson s.p. potential with new parameter set

Macroscopic-microscopic model finite-range droplet model (FRDM)

Microscopic mean field model HFB RMF RMF+ACCC+BCS

Theoretical Methods

NEW!

Large scale shell model (LSS)extended paring-plus-quadrupole models with

monopole corrections (EPQQM) model Pairing terms, quadrupole-quadrupole term, octupole-

octupole term, hexadecupole-hexadecupole term, monopole corrections are included in Hamiltonian.

Model space from the experimental data: upper neutron orbits 2f7/2, 3p3/2, 1h9/2, 3p1/2, 2f5/2 (without 1i13/2

since this orbit have not been seen experimentally so far ). Unfortunately, the calculations with it require prohibitively large amounts of computer memory when NUSHELLX code used.

Shell models

H. Jin, M. Hasegawa, S. Tazaki, K. Kaneko and Y. Sun, PRC 84, 044324 (2011).

Shell model large scale shell model (LSS)

Phenomenological models Koura-Yamada's s.p. potential (KYSPP) Nilsson s.p. potential with new parameter set

Macroscopic-microscopic model finite-range droplet model (FRDM)

Microscopic mean field model HFB RMF RMF+ACCC+BCS

Theoretical Methods

NEW!

Nilsson s.p. potential with

new parameter set

Phenomenological model

J. Y. Zhang, Y. Sun, M. Guidry, L. L. Riedinger and G. A. Lalazissis, Phys. Rev. C 58, R2663 (1998).

133Sn

131Sn

AZN

llslV Nttt

3/)(1

)(2

00

220

Nucleus

Methods

133Sn 131SnBound orbitals

Resonant orbitals

Bound orbitals

Resonant orbitals

RMF+ACCC+BCS (present work)

Y Y Y Y

RMF Y 1i13/2, Y above, N

Y N

LSS Y N N N

KYSPP Y N N N

Nilsson Y 1i13/2, Y above, N

N N

FRDM Y N N N

HFB Y N N N

Previous Work:

bound orbitals: RMF (NL3 eff. interaction) resonant orbitals: RMF-ACCC

pairing correlations: BCS approx.

A fully self-consistent microscopic method!

Successfully describe the properties for 120Sn, 58-98Ni, 122-138Zr, 17Ne, 26-31Ne, 131,133Sn

RMF+ACCC+BCS Method

S. S. Zhang, S. G. Zhou, J. Meng and G. C. Hillhouse, PRC 82, 2031 (2004).

S. S. Zhang, IJMPE 82, 2031 (2009).

MPLA(2004

)

IJMPE(2009)

EPJA(201

2)

Present worksubmitted to

PRC(2012)

arXiv(201

1)

1. Narrow and not narrow 2. l =0 and l >0 3. bound-type method

Outline

Background and Motivation nuclear structure nuclear astrophysics

Goals Theoretical Method Results and discussions Summary and outlook

Results

Relative E

xcitation

En

ergy [M

eV]

Similarity

132Sn(d,p) 133Sn

130Sn(d,p) 131Sn

Q-value (arb. units)

Yiel

d (a

rb. u

nits

)

2f7/2 Ð!

3p3/2 Ð!

Ð!

Ð!

3p1/2

2f5/2

Such similarity does not happen at all shell closures…

similar

similar

Such similarities are not the norm: the case for 47,49Ca (39,41Ca) across N=28 (20) shell closure display significant changes in level spacings.

Discussion I

B. A. Brown et al, PRC 58, 2099 (1998).

Levels above the neutron capture threshold are limited. At most one s. p. resonant level 1i13/2 appears in the effective energy window.

Need 5 (s wave) -10 (high l) levels per MeV We predict level spacing far too sparse for HF

model use

Discussion II

.45.024.22/,0.2,6

;10.013.02/,5.1,0

9

9

MeVEGKTl

MeVEGKTl

effeff

effeff

T. Rauscher et. al. Atom. Data. and Nucl. Data. Tab. 75, 1 (2000).

T. Rauscher et. al. Phys. Rev. C 56, 1613 (1997).

Outline

Background and Motivation nuclear structure nuclear astrophysics

Goals Theoretical Method Results and discussions Summary and outlook

Reproduce four observed strong s.p. bound levels in 131,133Sn,

and similarity of level spacing and strength with our approach.

Such similarity does not always occur across shell closures

(e.g. N = 20, 28).

Predict no single-particle levels at energies above and near

the neutron threshold S(n), and only one level up to 2.5 MeV

above the S(n)

The density of resonant levels is too low to enable statistical

models with Fermi gas level densities to calculate neutron

capture cross sections.

Summary

Our analysis suggests that alternative methods of calculating

the neutron captures on 130,132Sn must be utilized for r-

process nucleosynthesis studies.

This result also suggests the necessity for experimental

measurements of s.p. bound and resonant level structure of

heavy neutron-rich nuclei that are in and near the r-process.

Systematical study on odd-A Sn isotopes will be made in

near future.

Outlook

Collaborators

M. S. Smith, G. Arbanas and R. L. Kozub, ORNL, USA (this work)

U. Lombardo, INFN, Italy S. G. Zhou and E. G. Zhao, ITP, Beijing

Thank you！

Fermi gas model

4/54/1

]2exp[

12)(

Ua

aUEx

totF

Total Fermi gas state density :

: the level density parameter

: spacing of the proton (neutron) s.p. states near Fermi energy.

the energy shift : is an empirical parameter equal to pairing energy; : excitation energy

)(6

2

gga a

)( gg

xEU xE

Shell model large scale shell model (LSS)

Phenomenological models Koura-Yamada's s.p. potential (KYSPP) Nilsson s.p. potential with new parameter set

Macroscopic-microscopic model finite-range droplet model (FRDM)

Microscopic mean field model HFB RMF RMF+ACCC+BCS

Methods

NEW!

Large scale shell model (LSS) realistic effective interactions :

derived from charge-dependent (CD) Bonn NN potential Model space from the experimental data :

2f7/2, 3p3/2, 1h9/2, 3p1/2, 2f5/2 and 1i13/2 (included but not confirmed from experimentally; can be estimated to be 2.6940.2 MeV; above the 132Sn + n threshold 2.45(5) MeV )

134-142Sn (even and odd Sn isotopes)

Shell models IM. P.

Kartamyshev, T. Engeland, M. Hjorth-Jensen and E. Osnes, Phys. Rev. C 76, 024313 (2007).

EXP.

EXP.

EXP.

Shell model large scale shell model (LSS)

Phenomenological models Koura-Yamada's s.p. potential (KYSPP) Nilsson s.p. potential with new parameter set

Macroscopic-microscopic model finite-range droplet model (FRDM)

Microscopic mean field model HFB RMF RMF+ACCC+BCS

Methods

NEW!

Koura-Yamada's s.p. potential (KYSPP)Central component is an extension of the

Woods-Saxon potential

Phenomenological approaches

H. Koura, M. Yamada, NPA 671, 96 (2000).

S. Chiba, H. Koura etc. PRC 77, 015809 (2008).

×

√

Shell model large scale shell model (LSS)

Phenomenological model Koura-Yamada's s.p. potential (KYSPP) Nilsson s.p. potential with new parameter set

Macroscopic-microscopic model finite-range droplet model (FRDM)

Microscopic mean field model HFB RMF RMF+ACCC+BCS

Methods

NEW!

finite-range droplet model (FRDM) with a folded-Yukawa s.p. potential Lipkin-Nogami paring

Macroscopic-microscopic

T. Rauscher, etc. PRC 57, 2031 (1998).

NLSH

×

√

Shell model large scale shell model (LSS)

Phenomenological model Koura-Yamada's s.p. potential (KYSPP) Nilsson s.p. potential with new parameter set

Macroscopic-microscopic model finite-range droplet model (FRDM)

Microscopic mean field model HFB RMF RMF+ACCC+BCS

Methods

NEW!

Skyrme-HFB

RMF model

Microscopic mean field model

T. Rauscher, etc. PRC 57, 2031 (1998).

NLSH

×

√