Structure of exotic nuclei

Structure of exotic nuclei Takaharu OtsukaUniversity of Tokyo / RIKEN / MSU A presentation supported by the JSPS Core-to-Core Program　“International Research Network for Exotic Femto Systems (EFES)” 7th CNS-EFES summer school Wako, Japan August 26 – September 1, 2008 Day 2

Outline Section 1: Basics of shell model Section 2: Construction of effective interaction and an example in the pf shell Section 3: Does the gap change ? - N=20 problem - Section 4: Force behind Section 5: Is two-body force enough ? Section 6: More perspectives on exotic nuclei

Day-1 lecture : Introduction to the shell model What is the shell model ? Why can it be useful ? How can we make it run ? Basis of shell model and magic numbers density saturation + short-range interaction + spin-orbit splitting  Mayer-Jensen’s magic number  Valence space (model space) For shell model calculations, we need also TBME (Two-Body Matrix Element) and SPE (Single Particle Energy)

An example from pf shell (f7/2, f5/2, p3/2, p1/2) Phenomenological Microscopic G-matrix + polarization correction + empirical refinement • Start from a realistic microscopic interaction M. Hjorth-Jensen, et al., Phys. Repts. 261 (1995) 125 • Bonn-C potential • 3rd order Q-box + folded diagram • 195 two-body matrix elements (TBME) and 4 single-particle energies (SPE) are calculated  Not completely good（theory imperfect) • Vary 70 Linear Combinations of 195 TBME and 4 SPE • Fit to699 experimental energy data of 87 nuclei GXPF1 interaction M. Honma et al., PRC65 (2002) 061301(R)

G-matrix vs. GXPF1 two-body matrix element output <ab;JT | V | cd ; JT > 7= f7/2, 3= p3/2, 5= f5/2, 1= p1/2 • T=0 … attractive • T=1 … repulsive • Relatively large modifications in • V(abab ; J0) with large J • V(aabb ; J1) pairing input

Systematics of 2+1 • Shell gap • N=28 • N=32 for Ca, Ti, Cr • N=34 for Ca ?? • Deviations in Ex • Cr at N≧36 • Fe at N≧38 • Deviations in B(E2) • Ca, Ti for N≦26 • Cr for N≦24 • 40Ca core excitations • Zn, Ge • g9/2 is needed

GXPF1 vs. experiment th. exp. th. exp. 57Ni 56Ni

56Ni (Z=N=28) has been considered to be a doubly magic nucleus where proton and neutron f7/2 are fully occupied. Probability of closed-shell in the ground state doubly magic 　　⇒　Measure of breaking of this conventional idea Ni neutron Ni proton 48Cr total

States of different nature can be reproduced within a single framework 54Fe yrast states • 0p-2h configuration • 0+, 2+, 4+, 6+ …p(f7/2)-2 • more than 40% prob. • 1p-3h … 1st gap • One-proton excitation • 3+, 5+ • 7+～11+ • 2p-4h … 2nd gap • Two-protons excitation • 12+～ p-h : excitation from f7/2

58Ni yrast states • 2p-0h configuration • 0+, 2+…n(p3/2)2 • 1+, 3+, 4+…n(p3/2)1(f5/2)1 • more than 40% prob. • 3p-1h … 1st gap • One-proton excitation • 5+～8+ • 4p-2h … 2nd gap • One-proton & • one-neutron excitation • 10+～12+ p-h : excitation from f7/2

N=32, 34 magic numbers ? Issues to be clarified by the next generation RIB machines

Effective single particle energy • Monopole part of the NN interaction • Angular averaged interaction Isotropic component is extracted froma general interaction. In the shell model, single-particle properties are considered by the following quantities …….

Effective single-particle energy (ESPE) ESPE is changed by Nvm Monopole interaction, vm N particles ESPE : Total effect on single-particle energies due to interaction with other valence nucleons

Effective single-particle energies Z=22 Z=20 Z=24 f5/2 n-n p-n new magic numbers ? 34 32 p1/2 p3/2 Lowering of f5/2 from Ca to Cr - weakening of N=34 - Why ? Rising of f5/2 from 48Ca to 54Ca - emerging of N=34 -

Exotic Ca Isotopes : N = 32 and 34 magic numbers ? 51Ca 53Ca 52Ca 54Ca 2+ 2+ ? exp. levels :Perrot et al. Phys. Rev. C (2006), and earlier papers

Exotic Ti Isotopes 53Ti 54Ti 2+ 56Ti 55Ti 2+

ESPE (Effectice Single- Particle Energy) of neutrons in pf shell G f 5/2 GXPF1 f 5/2 Why is neutron f 5/2 lowered by filling protons intof 7/2 Ca Ni

Changing magic numbers ? We shall come back to this problem after learning under-lying mechanism.

nuclei (mass number) stable exotic -- with halo A Proton number  Neutron number  Studies on exotic nuclei in the 80~90’s Left-lower part of the NuclearChart Stability line and drip lines are not so far from each other  Physics of loosely bound neutrons, e.g., halo while other issues like 32Mg proton halo neutron halo リチウム１１ 11Li neutron skin

About same radius 11Li 208Pb Strong tunneling of loosely bound excess neutrons Neutron halo Nakamura’s lecture

In the 21st century, a wide frontier emerges between the stability and drip lines. Stability line Drip line nuclei (mass number) stable exotic Riken’s work A Neutron number  Proton number  中性子数　（同位元素の種類） huge area

Also in the 1980’s, 32Mg low-lying 2+

Basic picture was deformed 2p2h state energy intruder ground state stable exotic pf shell gap ~ constant N=20 sd shell Island of Inversion 9 nuclei: Ne, Na, Mg with N=20-22 Phys. Rev. C 41, 1147 (1990), Warburton, Becker andBrown

One of the major issues over the millennium was to determine the territory of the Island of Inversion • Are there clear boundaries in all directions ? • Is the Island really like the square ? Which type of boundaries ? Shallow (diffuse & extended) Straight lines Steep (sharp)

Small gap vs. Normal gap v ~ < f(Qp Qn) > dv=large For larger gap, fmust be larger  sharp boundary v=0 normal For smaller gap, f is smaller  diffuse boundary Max pn force intruder N semi-magic open-shell dv=smaller The difference dv is modest as compared to “semi-magic”. Inversion occurs for semi-magic nuclei most easily

Na isotopes : What happens in lighter ones with N < 20 Original Island of Inversion

Electro-magnetic moments and wave functions of Na isotopes Q ― normal dominant : N=16, 17― strongly mixed : N=18― intruder dominant : N=19, 20Onset of intruder dominance before arriving at N=20 m Monte Carlo Shell Model calculation with full configuration mixing : Phys. Rev. C 70, 044307 (2004), Utsuno et al. Config. Exp.: Keim et al. Euro. Phys. J. A 8, 31 (2001)

N=17 N=16 N=18 N=19 Level scheme of Na isotopesby SDPF-M interaction compared to experiment

Major references on MCSM calculations for N~20 nuclei "Varying shell gap and deformation in N~20 unstable nuclei studied by the Monte Carlo shell model", Yutaka Utsuno, Takaharu Otsuka, Takahiro Mizusaki and Michio Honma, Phys. Rev. C60, 054315-1 - 054315-8 (1999) “Onset of intruder ground state in exotic Na isotopes and evolution of the N=20 shell gap”, Y. Utsuno, T. Otsuka, T. Glasmacher, T. Mizusaki and M. Honma, Phys. Rev. C70, (2004), 044307. Many experimental papers include MCSM results.

WBB (1990) SDPF-M (1999) ~5MeV ~2MeV Ne O Mg Ca Monte Carlo Shell Model (MCSM) results have been obtained by the SDPF-M interaction for the full-sd + f7/2 + p3/2 space. Effective N=20 gap between sd and pf shells Expansion of the territory Neyens et al. 2005Mg Tripathi et al. 2005Na Dombradi et al. 2006Ne Terryet al.2007Ne

Phys. Rev. Lett. 94, 022501 (2005), G. Neyens, et al. Strasbourg unmixed Tokyo MCSM USD (only sd shell) 2.5 MeV 0.5 MeV 31Mg19

New picture Conventional picture deformed 2p2h state deformed 2p2h state spherical normal state energy energy ? intruder ground state intruder ground state stable stable exotic exotic pf shell pf shell gap ~ constant gap changing N=20 N=20 sd shell sd shell

Effective N=20 gap between sd and pf shells Island of Inversion Expansion of the territory constant gap SDPF-M (1999) ? ~6MeV ~2MeV Ne O Mg Ca ? Shallow (diffuse & extended) Straight lines Steep (sharp) Island of Inversion is like a paradise

Why ?

From undergraduate nuclear physics, density saturation + short-range NN interaction + spin-orbit splitting Mayer-Jensen’s magic number with rather constant gaps (except for gradual A dependence) Robust mechanism - no way out -

Key to understand it : Tensor Force One pion exchange ~ Tensor force

Key to understand it : Tensor Force p meson : primary source r meson (~ p+p) : minor (~1/4) cancellation Ref:Osterfeld, Rev. Mod. Phys. 64, 491 (92) p, r Multiple pion exchanges  strong effectivecentral forces in NN interaction (as represented bysmeson, etc.)  nuclear binding This talk : First-order tensor-force effect (at medium and long ranges) One pion exchange  Tensor force

V ~ Y2,0~ 1 – 3 cos2q q=p/2 q=0 repulsion attraction How does the tensor force work ? Spin of each nucleon is parallel, because the total spin must be S=1 The potential has the following dependence on the angle qwith respect to the total spin S. q S relative coordinate

Deuteron : ground state J = 1 Total spin S=1 Relative motion : S wave (L=0) + D wave (L=2) proton Tensor force does mix neutron The tensor force is crucial to bind the deuteron. Without tensor force, deuteron is unbound. No S wave to S wave coupling by tensor force because of Y2 spherical harmonics

Effective single particle energy • Monopole part of the NN interaction • Angular averaged interaction Isotropic component is extracted froma general interaction. In the shell model, single-particle properties are considered by the following quantities …….

Intuitive picture of monopole effect of tensor force wave function of relative motion spin of nucleon large relative momentum small relative momentum repulsive attractive j> = l + ½, j< = l – ½ TO et al., Phys. Rev. Lett. 95, 232502 (2005)

Monopole Interaction of the Tensor Force j< neutron j> j’< proton j’> Identity for tensor monopole interaction ( j’j>) ( j’j<) (2j> +1) vm,T+ (2j<+1)vm,T= 0 vm,T: monopole strength for isospin T T. Otsuka et al., Phys. Rev. Lett. 95, 232502 (2005)

Major features spin-orbitsplitting varied Opposite signs T=0 : T=1 = 3 : 1 (same sign) Only exchange terms (generally for spin-spin forces) neutron, j’< proton, j> tensor proton, j> neutron, j’<

Tensor Monopole Interaction : total effects vanished for spin-saturated case j< neutron no change j> j’< proton j’> Same Identity with different interpretation ( j’j>) ( j’j<) (2j> +1) vm,T+ (2j<+1)vm,T= 0 vm,T: monopole strength for isospin T

j< neutron Tensor Monopole Interaction vanished for s orbit j> s1/2 proton For s orbit, j> and j< are the same : ( j’j>) ( j’j<) (2j> +1) vm,T+ (2j<+1)vm,T= 0 vm,T: monopole strength for isospin T

Monopole Interaction of the tensor force is considered to see the connection between the tensor force and the shell structure

tensor no s-wave to s-wave coupling differences in short distance : irrelevant Tensor potential

Proton effective single-particle levels (relative to d3/2) Tensor monopole f7/2 d3/2 d5/2 neutron proton p + rmeson tensor exp. Cottle and Kemper, Phys. Rev. C58, 3761 (98) neutrons in f7/2

Structure of exotic nuclei