unveiling nuclear structure with spectroscopic methods beihang university, beijing, sep. 18, 2014
TRANSCRIPT
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Unveiling nuclear structure with spectroscopic methods
Beihang University, Beijing, Sep. 18, 2014
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Atomic spectroscopy (Hydrogen spectrum)
Infrared/Raman spectroscopy of molecules (Vibration-Rotation Spectrum of HCl)
Spectroscopy provides a unique way to explore micro. world
Bohr model
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What do we study in nuclear physics?
Jochen Erler et al., Nature 486, 509 (2012)
Excitations (angular momentum, Temperature, …)
Ground state
neutron
proton
• Exciting the atomic nuclei and then observing the gamma-raye.g. Coulomb excitation, inelastic scattering, etc.• Producing nucleus at excited states and then observing the gamma-raye.g. Fusion/fragmentation, etc
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Physics of low-spin states
http://www.nndc.bnl.gov/chart
Connection between low-lying states and underlying shell-structure
Magic numbers: 8, 20, 28, 50, 82, 126
Closed-shell Open-shell
Excitation energy of the first 2+ state
keV 3.89E+4 1.16E+3 2.74E+4 8.22E+2 1.93E+4 5.78E+2 1.35E+4 4.07E+2 9.57E+3 2.87E+2 6.74E+3 2.02E+2 4.74E+3 1.42E+2 3.34E+3 1.00E+2 2.35E+3 7.05E+1 1.65E+3 4.97E+1 1.16E+3 3.50E+1
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Magic number and nuclear shell structure
Where are the magic numbers from?
Large separation energy
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Magic number and nuclear shell structure
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Magic number and nuclear shell structure
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.
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.
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Magic number and nuclear shell structure
leading to the
K. L. Jones et al., Nature 465, 454 (2010)
(d,p) reaction
s.p. energy structure can be probed with (d,p) reaction.
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Excitation of nuclei with magic number
Lowest excitation
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Excitation of nuclei with magic number
leading to the
E2
E2
0+
2+ (6.917 MeV)
E2
High excitation energy
16O
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Excitation of nuclei with magic number
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
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.
E2
16O from NNDC
Many non-collective excitations
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Deformation and Nilsson diagram
Ring & Schuck (1980)
β
Nilsson model: deformed HO+LS+L^2
Deformed the shell structure
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Deformation and Nilsson diagram Nilsson diagram
Jahn-Teller effect: geometrical distortion (deformation) that removes degeneracy can lower the energy of system.
shell structure is changed by deformation.
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Q. S. Zhang, Z. M. Niu, Z. P. Li, JMY, J. Meng, Frontiers of Physics (2014)
Deformation and nuclear shapes Systematic calculation of nuclear ground state with CDFT
PC-PK1
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Shape transition and coexistence
http://www.nndc.bnl.gov/chart
Excitation energy of the first 2+ state
N=60
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Rotation of quadrupole deformed nucleiNuclear quadrupole deformed shapes:
prolate
oblate
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Quadrupole vibration of atomic nuclei
Imposed by invariance of exchange two phonons
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Quadrupole vibration of atomic nuclei
114Cd
Strong anharmonic effect
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The rotation-vibration model
(1952)5DCH
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Evolution of nuclear shape and spectrum
W. Greiner & J. Maruhn (1995)
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Evolution of nuclear shape
From NNDC
A microscopic theory to describe the shape evolution and change in low-energy nuclear structure with respect to nucleon number.
3.88 2.47 3.74 2.33 3.60 2.18 3.46 2.04 3.32 1.90 3.18 1.76 3.03 1.62 2.89 1.48 2.75 1.34 2.61 1.19 2.47 1.05
unknown
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5
Construct 5-dimensional Hamiltonian(vib + rot)
E(Jπ), BE2 …
Cal. Exp.
3D covariant Density Functional
ph + pp
Coll. Potential
Moments of inertia
Mass parameters
Diagonalize:Nuclear spectroscopy
Niksic, Li, Vretenar, Prochniak, Meng & Ring, PRC79, 034303 (09)Libert, Girod & Delaroche, PRC60, 054301 (99)
Prochniak & Rohozinski, JPG36, 123101 (09)
Courtesy of Z.P. Li
5DCH based on EDF calculation
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Spectrum
Characteristic features:
Sharp increase of R42=E(41)/E(21) and B(E2; 21→01) in the yrast band
X(5)
Courtesy of Z.P. Li
Shape transition in atomic nuclei/5DCH
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Microscopic description of nuclear collective excitations
• 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.
Projections and GCM on top of CDFT:
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.
Variation of energy with respect to the weight function f(q) leads to the Hill-Wheeler-Griffin (HWG) integral equation:
Definition of kernels:q‘
rotation & vibration/shape mixing
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Q. S. Zhang, Z. M. Niu, Z. P. Li, JMY, J. Meng, Frontiers of Physics (2014)
cranking approximation
Validity of cranking approximation
Significant improv. on BE: 2.6 -> 1.3 MeV
575 e-e nuclei
unbound
Corrected by the DCE
Rotational energy
Not good if deformation collapse
Correlation energy beyond MF approximationN. Chamel et al., NPA 812, 72 (2008)
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SLy4(TopGOA): M. Bender, G. F. Bertsch, and P.-H. Heenen, PRC73, 034322 (2006).
SLy4
Correlation energy beyond MF approximation
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Symmetry conservation and configuration mixing effect on nuclear density profile
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bubble
best candidate
Reduced s. o. splitting of (2p3/2; 2p1/2)
true bubble
Semi-bubble
G. Burgunder (2011)
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JMY, S. Baroni, M. Bender, P.-H. Heenen, PRC 86, 014310 (2012)
GCM+1DAMP+PNP (HFB-SLy4): bubble structure is quenched by configuration mixing effect.
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M. Grasso et al., PRC79, 034318 (2009)
SLy4 (HF)
JMY et al., PRC86, 014310 (2012)JMY et al., PLB 723, 459 (2013)
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 34Si are quenched by
dynamical correlations.
The charge density in
36S has been reproduced
excellently by the MR-
CDFT calculation with PC-
PK1 force.
2s1/2 orbitalunoccupied
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Deformation has significant influence on the central depletion.
The 34Si has the largest central depletion in Si isotopes.
Central depletion factor:g.s. wave function:
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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)
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Benchmark for Bohr Hamiltonian in five dimensions
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Triaxiality in nuclear low-lying states
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Existence of shape isomer state (E0)E. Bouchez et al., PRL 90, 082502 (2003)
Evidence of the oblate deformed g.s. (Coulex)
Lifetime measurements of 2+ and 4+ states (RDM)
prolate shape?
H. Iwasaki et al., PRL 112, 142502 (2014)
Evidence for rapid oblate-prolate shape transition
Large collectivity of 4+ statesuggests a prolate character of the excited states.
=Different model calc.
A. Gade et al., PRL 95, 022502 (2005)
prolate
oblate
Shape transition in a single-nucleus
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Direct measurement on the shape of 2+ state
GOSIA
GCM+PN1DAMP (axi.)
Preliminary results
Reorientation effect
Nara Singh et al., in preparation (2014)
5DC
H
???
In collaboration with experimental group
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Nara Singh et al., in preparation (2014)
Preliminary results
GOSIA
5DCH (Triaxial)
5DC
H
Reorientation effect
Direct measurement on the shape of 2+ state
???
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Nara Singh et al., in preparation (2014)
Preliminary results
GOSIA
5DCH (Triaxial)
5DC
H
Reorientation effect
Direct measurement on the shape of 2+ state
???
Sato & Hinohara, (NPA2011)
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Nara Singh et al., in preparation (2014)
Preliminary results
GOSIA
5DC
H
Reorientation effect
Direct measurement on the shape of 2+ state
???
♦
T. Rodriguez, private communication (2014)
GCM+PN3DAMP
1336
1613 2909
M22=0.87 ebM02=0.82 eb
GCM (D1S)
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Nara Singh et al., in preparation (2014)
Preliminary results
GOSIA
5DC
H
Reorientation effect
Direct measurement on the shape of 2+ state
???
♦GCM (D1S)GCM+PN3DAMP (PC-PK1)
♦GCM (PCPK1)
M22=0.14 ebM02=0.77 eb
Preliminary results
Preliminary results
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Hypernucleusin 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
O. Hashimoto and H. Tamura, PPNP 57, 564 (2006) The facilities built at J-PARC enable the study of hypernuclear γ-ray spectroscopy.
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Description of hypernuclear low-lying states based on EDF
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Low-energy excitation spectra
β = 1.2
Application to 9ΛBe
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Low-energy excitation spectra
[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.
8Be analog band
genuinely hypernuclear
9Be analog band
Application to 9ΛBe
[ ]Ic l
Cluster model
Motoba, et al.
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Low-energy excitation spectra
[1] T. Motoba, H. Bandō, and K. Ikeda, Prog. Theor. Phys.70, 189 (1983).
92.8(s1/2 0⊗ +)+..
91.9(s1/2 2⊗ +)+..
51.6(p1/2 0⊗ +)+44.5(p3/2 2⊗ +)+…
52.4(p3/2 0⊗ +)+22.0(p3/2 2⊗ +) +21.7(p1/2 2⊗ +)+…
cI
s
l
j
cI I j
(lj ⊗Ic)
cI
s
l
L
I L s
Application to 9ΛBe
( )sc LI l
Motoba, et al.
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Low-energy excitation spectra
Application to 9ΛBe
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Jie Meng (PKU)
Zhongming Niu (Anhui U.)
Peter Ring (TUM&PKU) Dario Vretenar (Zagreb U.)
Kouichi Hagino (Tohoku U.)Hua Mei (Tohoku U. & SWU)T. Motoba (Osaka Electro-Communications U.)
Michael Bender (U. Bordeaux)Paul-Henri Heenen (ULB)Simone Baroni (ULB)
Acknowledge to all collaborators evolved in this talk
Zhipan Li, Xian-ye Wu, Qian-shun Zhang (SWU)
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Physics of high-spin states
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In case of 9Be (a + a + n)
n n
AllowedForbidden by Pauli principle
1
2j l s sm m m m
For p state, l = 1, ml = 0, ±1ml = 0 Parallel to axialml = ±1 Perpendicular to axial
1s1/2
1p3/2
1p1/2
1/2[110]
3/2[101]
1/2[101]
8
zNn Asymptotic quantum numbers: Projection of the single-particle angular momentum, j, onto the symmetry axis (mj);:N The principal quantum number of the major shell;:zn 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);