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
×
√