Unveiling nuclear structure with spectroscopic methods

Beihang University, Beijing, Sep. 18, 2014

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

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

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

Magic number and nuclear shell structure

Where are the magic numbers from?

Large separation energy

Magic number and nuclear shell structure

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.

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.

Excitation of nuclei with magic number

Lowest excitation

Excitation of nuclei with magic number

leading to the

E2

E2

0+

2+ (6.917 MeV)

E2

High excitation energy

16O

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

Deformation and Nilsson diagram

Ring & Schuck (1980)

β

Nilsson model: deformed HO+LS+L^2

Deformed the shell structure

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.

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

Shape transition and coexistence

http://www.nndc.bnl.gov/chart

Excitation energy of the first 2+ state

N=60

Rotation of quadrupole deformed nucleiNuclear quadrupole deformed shapes:

prolate

oblate

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

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

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

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

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

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)

SLy4(TopGOA): M. Bender, G. F. Bertsch, and P.-H. Heenen, PRC73, 034322 (2006).

SLy4

Correlation energy beyond MF approximation

Symmetry conservation and configuration mixing effect on nuclear density profile

bubble

best candidate

Reduced s. o. splitting of (2p3/2; 2p1/2)

true bubble

Semi-bubble

G. Burgunder (2011)

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.

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

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:

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

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

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

Nara Singh et al., in preparation (2014)

Preliminary results

GOSIA

5DCH (Triaxial)

5DC

H

Reorientation effect

Direct measurement on the shape of 2+ state

???

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)

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)

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

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.

Description of hypernuclear low-lying states based on EDF

Low-energy excitation spectra

β = 1.2

Application to 9ΛBe

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.

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.

Low-energy excitation spectra

Application to 9ΛBe

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)

Physics of high-spin states

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);