Unveiling nuclear structure with
spectroscopic methods
Beihang University, Beijing, Sep. 18, 2014
Spectroscopy provides a unique way to explore micro. world
 Atomic spectroscopy (Hydrogen spectrum)
Bohr
model
 Infrared/Raman spectroscopy of molecules
(Vibration-Rotation Spectrum of HCl)
What do we study in nuclear physics?
Excitations (angular momentum, Temperature, …)
proton
neutron
Jochen Erler et al., Nature 486, 509 (2012)
• Exciting the atomic nuclei and then observing the gamma-ray
e.g. Coulomb excitation, inelastic scattering, etc.
• Producing nucleus at excited states and then observing the gamma-ray
e.g. Fusion/fragmentation, etc
Physics of low-spin states
Connection between low-lying states and
underlying shell-structure
Magic numbers: 8, 20, 28, 50, 82, 126
Closed-shell
Open-shell
keV
3.89E+4
2.74E+4
1.93E+4
1.35E+4
9.57E+3
6.74E+3
4.74E+3
3.34E+3
2.35E+3
1.65E+3
1.16E+3
1.16E+3
8.22E+2
5.78E+2
4.07E+2
2.87E+2
2.02E+2
1.42E+2
1.00E+2
7.05E+1
4.97E+1
3.50E+1
Excitation energy of
the first 2+ state
http://www.nndc.bnl.gov/chart
Magic number and nuclear shell structure
Large separation energy
Where are the magic numbers from?
Magic number and nuclear shell structure
Magic number and nuclear shell structure
Maria Mayer in 1948 published evidence
for the particular stability for the numbers
20, 50, 82 and 126. it sparked a lot of
interest in the USA and with Haxel, Jensen
and Suess in Germany.
leading to the simultaneous publication of
the papers (1949) by Mayer and the
German group on the shell model with a
strong spin-orbit coupling.
Magic number and nuclear shell structure
s.p. energy structure
can be probed with
(d,p) reaction.
leading to the
(d,p) reaction
K. L. Jones et al., Nature 465, 454 (2010)
Excitation of nuclei with magic number
Lowest excitation
Excitation of nuclei with magic number
16O
2+ (6.917
E2
0+
leading to the
High excitation energy
E2
E2
MeV)
Excitation of nuclei with magic number
16O
Maria Mayer in 1948 published evidence
for the particular stability for the numbers
20, 50, 82 and 126. it sparked a lot of
interest in the USA and with Haxel, Jensen
and Suess in Germany.
from NNDC
leading to the simultaneous publication of
the papers by Mayer and the German
group on the shell model with a strong
spin-orbit coupling.
leading to the
E2
Many non-collective excitations
E2
Deformation and Nilsson diagram
β
Deformed the shell structure
Nilsson model: deformed HO+LS+L^2
Ring & Schuck (1980)
Deformation and Nilsson diagram
Nilsson diagram
shell structure is changed by
deformation.
Jahn-Teller effect: geometrical
distortion (deformation) that
removes degeneracy can lower
the energy of system.
Deformation and nuclear shapes
Systematic calculation of nuclear ground state with CDFT
Q. S. Zhang, Z. M. Niu, Z. P. Li, JMY, J.
Meng, Frontiers of Physics (2014)
PC-PK1
Shape transition and coexistence
Excitation energy of the first 2+ state
N=60
http://www.nndc.bnl.gov/chart
Rotation of quadrupole deformed nuclei
Nuclear quadrupole deformed shapes:
oblate
prolate
Quadrupole vibration of atomic nuclei
Imposed by invariance of exchange two phonons
Quadrupole vibration of atomic nuclei
114Cd
Strong anharmonic effect
The rotation-vibration model
(1952)
5DCH
Evolution of nuclear shape and spectrum
W. Greiner & J. Maruhn (1995)
Evolution of nuclear shape
3.88
3.74
3.60
3.46
3.32
3.18
3.03
2.89
2.75
2.61
2.47
unkno
wn
A microscopic theory to
describe the shape evolution
and change in low-energy
nuclear structure with respect
to nucleon number.
From NNDC
2.47
2.33
2.18
2.04
1.90
1.76
1.62
1.48
1.34
1.19
1.05
5DCH based on EDF calculation
Construct
Coll. Potential
Moments of inertia
Mass parameters
5-dimensional
Hamiltonian
3D covariant
Density
Functional
(vib + rot)
Diagonalize:
Nuclear spectroscopy
E(Jπ), BE2 …
Cal.
Exp.
ph + pp
Courtesy of Z.P. Li
Libert, Girod & Delaroche, PRC60, 054301 (99)
Prochniak & Rohozinski, JPG36, 123101 (09)
Niksic, Li, Vretenar, Prochniak, Meng & Ring, PRC79, 034303 (09)5
Shape transition in atomic nuclei/5DCH
 Spectrum
 Characteristic features:
X(5)
Sharp increase of
R42=E(41)/E(21)
and B(E2; 21→01)
in the yrast band
Courtesy of Z.P. Li
Microscopic description of nuclear collective excitations
Projections and GCM on top of CDFT:
rotation & vibration/shape mixing
•
•
•
•
α distinguishes the states with the same angular momentum J
|q> is a set of Slater determinants from the constrained CDFT calc.
PJ and PN are projection operators onto J and N.
K=0 if axial symm. is assumed.
Variation of energy with respect to the weight function f(q) leads to the HillWheeler-Griffin (HWG) integral equation:
q‘
Definition of kernels:
JMY, J. Meng, P. Ring, and D. Vretenar, PRC 81 (2010) 044311;
JMY, K. Hagino, Z. P. Li, J. Meng, and P. Ring, PRC 89 (2014) 054306.
Correlation energy beyond MF approximation
N. Chamel et al., NPA 812, 72 (2008)
unbound
cranking approximation
Validity of cranking approximation
575 e-e nuclei
Corrected by the DCE
Rotational energy
Significant improv. on BE: 2.6 -> 1.3 MeV
Q. S. Zhang, Z. M. Niu, Z. P. Li, JMY,
J. Meng, Frontiers of Physics (2014)
Not good if deformation collapse
Correlation energy beyond MF approximation
SLy4
SLy4(TopGOA): M. Bender, G. F. Bertsch, and P.-H. Heenen, PRC73, 034322 (2006).
Symmetry conservation and configuration mixing effect on
nuclear density profile
bubble
best candidate
Semi-bubble
true bubble
Reduced s. o.
splitting of
(2p3/2; 2p1/2)
G. Burgunder (2011)
GCM+1DAMP+PNP (HFB-SLy4):
bubble structure is quenched by
configuration mixing effect.
JMY, S. Baroni, M. Bender, P.-H. Heenen,
PRC 86, 014310 (2012)
SLy4 (HF)
2s1/2 orbital
unoccupied
The central depletion in
the proton density of
34Si
is shown in both RMF and
SHF calculations.
Both central bump in
36S
and central depletion in
M. Grasso et al., PRC79, 034318 (2009)
34Si
are quenched by
dynamical correlations.
The charge density in 36S
has been reproduced
excellently by the MRCDFT calculation with PCPK1 force.
JMY et al., PLB 723, 459 (2013)
JMY et al., PRC86, 014310 (2012)
g.s. wave function:
Central depletion factor:
Deformation has significant influence on the central depletion.
 The 34Si has the largest central depletion in Si isotopes.
Spherical state:
bubble structure in 46Ar
Dynamical deformation:
No bubble structure
Inverse of 2s1/2 and 1d3/2
around 46Ar leads to bubble
structure in spherical state.
X. Y. Wu, JMY, Z. P. Li, PRC89, 017304 (2014)
Benchmark for Bohr Hamiltonian in five dimensions
Triaxiality in nuclear low-lying states
Shape transition in a single-nucleus
 Existence of shape isomer state (E0)
E. Bouchez et al., PRL 90, 082502 (2003)
 Evidence of the oblate deformed g.s. (Coulex)
A. Gade et al., PRL 95, 022502 (2005)
prolate shape?
Different model calc.
=
prolate
oblate
 Lifetime measurements of 2+ and 4+ states (RDM)
H. Iwasaki et al., PRL 112, 142502 (2014)
Large collectivity of 4+ state
suggests a prolate character of
the excited states.
Evidence for rapid oblateprolate shape transition
 Direct measurement on the shape of 2+ state
In collaboration with experimental group
Nara Singh et al., in preparation (2014)
GOSIA
Reorientation effect
???
GCM+PN1DAMP (axi.)
 Direct measurement on the shape of 2+ state
Nara Singh et al., in preparation (2014)
GOSIA
Reorientation effect
???
5DCH (Triaxial)
 Direct measurement on the shape of 2+ state
Nara Singh et al., in preparation (2014)
GOSIA
Reorientation effect
???
5DCH (Triaxial)
Sato & Hinohara,
(NPA2011)
 Direct measurement on the shape of 2+ state
Nara Singh et al., in preparation (2014)
GOSIA
Reorientation effect
???
GCM (D1S)♦
GCM+PN3DAMP
M22=0.87 eb
M02=0.82 eb
1613
2909
1336
T. Rodriguez, private
communication (2014)
 Direct measurement on the shape of 2+ state
Nara Singh et al., in preparation (2014)
GOSIA
Reorientation effect
???
GCM (D1S)♦
GCM+PN3DAMP (PC-PK1)
♦
GCM (PCPK1)
M22=0.14 eb
M02=0.77 eb
 The facilities built at J-PARC enable the study of hypernuclear γray spectroscopy.
O. Hashimoto and H. Tamura, PPNP 57, 564 (2006)
Hypernucleus
in excited state
H. Tamura et al., Phys. Rev. Lett. 84 (2000) 5963
K. Tanida et al., Phys. Rev. Lett. 86 (2001) 1982
J. Sasao et al., Phys. Lett. B 579 (2004) 258
Description of hypernuclear low-lying states based on EDF
Application to 9ΛBe

Low-energy excitation spectra
β = 1.2
Application to 9ΛBe

Low-energy excitation spectra
Cluster model
9Be
analog
band
[ Ic  l ]
Motoba, et al.
genuinely
hypernuclear
8Be
analog
band
[1] R.H. Dalitz, A. Gal, PRL 36 (1976) 362.[2] H. Bando, et al., PTP 66 (1981) 2118.;
[3] T. Motoba, H. Bandō, and K. Ikeda, Prog. Theor. Phys.70, 189 (1983).[4]H. Bando, et al., IJMP 21 (1990) 4021.
Application to 9ΛBe

I  Ls
Low-energy excitation spectra
l
s
I  Ic  j
L
s
l
Ic
Ic
j
52.4(p3/2⊗0+)+22.0(p3/2⊗2+) +21.7(p1/2⊗2+)+…
51.6(p1/2⊗0+)+44.5(p3/2⊗2+)+…
91.9(s1/2⊗2+)+..
92.8(s1/2⊗0+)+..
( I c l ) sL
Motoba, et al.
[1] T. Motoba, H. Bandō, and K. Ikeda, Prog. Theor. Phys.70, 189 (1983).
(lj ⊗Ic)
Application to 9ΛBe

Low-energy excitation spectra
Acknowledge to all collaborators evolved in this talk
Peter Ring (TUM&PKU)
Dario Vretenar (Zagreb U.)
Jie Meng (PKU)
Zhongming Niu (Anhui U.)
Kouichi Hagino (Tohoku U.)
Hua Mei (Tohoku U. & SWU)
T. Motoba (Osaka ElectroCommunications U.)
Michael Bender (U. Bordeaux)
Paul-Henri Heenen (ULB)
Simone Baroni (ULB)
Zhipan Li, Xian-ye Wu,
Qian-shun Zhang (SWU)
Physics of high-spin states
In case of 9Be (a + a + n)
8
1p1/2
1
2
For p state, l = 1, ml = 0, ±1
ml = 0
Parallel to axial
ml = ±1
Perpendicular to axial
m j  ml  ms
1/2[101]
3/2[101]
n
ms  
n
1p3/2
1/2[110]
1s1/2
Forbidden by
Pauli principle
Allowed
Asymptotic quantum numbers   Nnz 
 :Projection of the single-particle angular momentum, j, onto the symmetry axis (mj);
N :The principal quantum number of the major shell;
nz :The number of nodes in the wave function along the z axis;
 : The projection of the orbital angular momentum l on the symmetry axis (ml);