INPC Tokyo June 4 8 2007 Exotic Nuclei

INPC Tokyo June 4 -8, 2007 Exotic Nuclei and Yukawa’s Forces Takaharu Otsuka University of Tokyo / RIKEN / MSU T. Suzuki Nihon U. R. Fujimoto Hitachi Ltd. H. Grawe GSI Y. Akaishi KEK P. Ring TUM D. Abe T. Matsuo M. Honma Y. Utsuno G. Lalazissis Many experimentalists Tokyo Hitachi Ltd. U. Aizu JAEA Thessaloniki

Outline 1. Introduction - Past and present issues 2. Shell structure and magic numbers of exotic nuclei 3. Deformation driven by tensor force 4. Relevant topics (neutrino, Lattice QCD, Superheavy) 5. Summary

Studies on exotic nuclei in 1990’s Left-lower part of the Nuclear Chart proton halo Stability line and drip lines Proton number are not so far from each other Physics of loosely bound neutrons, e. g. , halo while other issues like 32 Mg neutron halo 11 Li リチウム１１ Neutron number neutron skin A nuclei (mass number) stable exotic -- with halo

Neutron halo Strong tunneling of loosely bound excess neutrons About same radius 11 Li 208 Pb Breakup of 11 Li Nakamura et al. , Phys. Rev. Lett. 96, 252502 (2006) F 7 -1 Nakamura

Proton number In the 21 st century, a wide frontier emerges between the stability and drip lines. Stability line Drip line What happens here ? 1990’s neutron halo etc. 中性子数 Neutron number （同位元素の種類） A nuclei (mass number) stable exotic Riken’s work

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

The Key : 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 effective central forces in NN interaction (as represented by s meson, etc. ) nuclear binding This talk : First-order tensor-force effect (at medium and long ranges) One pion exchange Tensor force

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

N=16 gap : Ozawa, et al. , PRL 84 (2000) 5493; Brown, Rev. Mex. Fis. 39 21 (1983) d 3/2 d 5/2 Tensor force only exchange term Example : Dripline of F isotopes is 6 units away from O isotopes Sakurai et al. , PLB 448 (1999) 180, …

Nuclei or regions to be discussed Island of Inversion 51 Sb 36 Kr Neutrino reaction 42 Si Superheavy 50 Sn R process 78 Ni Chart provided by Sakurai

2. Shell structure and magic numbers of exotic nuclei

51 Sb case Opposite monopole effect from tensor force with neutrons in h 11/2. 1 h 11/2 protons 1 g 7/2 protons Z=51 isotopes h 11/2 g 7/2 No mean field theory, (Skyrme, Gogny, RMF) explained this before. Tensor by p+ r meson exchange + common effect (Woods-Saxon) 1 h 11/2 neutrons Exp. data from J. P. Schiffer et al. , Phys. Rev. Lett. 92, 162501 (2004)

Hartree-Fock calculation including tensor force Single-particle energies of exotic Ni isotopes w/o tensor with tensor Gogny-type (finite-range) + Tensor Force N=28 Gap Z=28 Gap neutron g 9/2 TO, Matsuo, Abe, Phys. Rev. Lett. 97, 162501 (2006)

Contributions of Kinetic+Central, 2 -body LS, and Tensor components to the change of f 7/2 – f 5/2 gap in going from N=40 to N=50 (g 9/2 occupancy) Kin+Cent and LS : almost the same among three calculations Tensor : largest effect TO, Matsuo, Abe, Phys. Rev. Lett. 97, 162501 (2006)

Hartree-Fock-Bogoliubov calculation including tensor force Poster by Abe QW-048 D 1 S Two neutron separation energy Sn no tensor GT 3 tensor Kr EXP ng 7/2 nh 11/2 Heavy Sn and Kr are more bound

6 4 2 g 2 7 6 5 4 3 2 1 f 7/2 -f 5/2 p d 5/2 -d 3/2 p 3/2 -p 1/2 p 1 g 1 h f 7/2 -f 5/2 a a 16 O 40 C 48 C i r n b 56 N 90 Z 132 S 208 P a a 16 O 40 C 48 C Crucial for i r n b 56 N 90 Z 132 S 208 P 42 Si mentioned later M. Zalewski, W. Satuła, J. Dobaczewski, (preliminary) 1 i An example by Dobaczewski et al. d 5/2 -d 3/2 Zero-range version of tensor force p 3/2 -p 1/2 (Skyrme 1956, Stancu et al. 1977) Sk. P original Sk. P T Tensor + SO*0. 8 Spin-orbit splittings [Me. V] Sk. P 1 g 1 h n 8 Skyrme + Tensor’Sk. P : TManynrecent works

October, 2006 April, 2007 F 10 -2 Dec. 22, 2006

Relativistic Mean Field Exchange terms Proton 1 h 11/2 – 1 g 7/2 gap Relativistic Hartree-Fock Lalazissis et al. NL 3 is used Full tensor Half tensor No tensor Long et al. , Toki et al. , …

3. Deformation driven by Tensor-force

Recent finding about the shell-model interaction Effective shell-model interaction (refined empirically) = central part + tensor p + r meson exchange ~ (for medium- and long-range parts) + … This feature is true also in G-matrix A new shell-model interaction has been constructed for the sd + pf shells.

Chiral Perturbation of QCD Short range central forces have complicated origins and should be adjusted. S. Weinberg, PLB 251, 288 (1990) Tensor force is explicit

Tensor force can drive nuclei to (or from) deformation f 7/2 d 3/2 Si isotopes Exp. neutron s 1/2 d 5/2 proton Strong oblate full Deformation ? Potential Energy Surface 42 14 Si 28 Tensor force removed from cross-shell interaction Z=28 gap is reduced also by tensor force

Debate over 42 Si Nature 435 (2005), MSU 44 S -> 42 Si cross section small deformed PRL accepted (2007), GANIL 42 Si oblate 44 S prolate Cauier et al. Shell Model, Werner et al. Skyrme model, Lalazissis et al. RMF, Peru et al. Gogny model, Rodriguez-Guzman et al. Gogny model

Modification to the Island of Inversion Terry et al, PLB 640 (2006) 86 Low-lying 3/2 - level (0. 765 Me. V) in 27 Ne N=20 gap smaller N=20 gap changes ~6 Me. V ~3 Me. V O Ne Mg Ca Expansion of the territory Neyens et al. Mg Tripathi et al. Na Dombradi et al. Ne

3. Intriguing relevant topics

Relevance to Weak Processes Neutrino reaction cross section is enlarged by using interaction containing full tensor force Over Woosley Over PSDMK 2 Presented by Suzuki H 4 -2 Temperaturte of supernovae explosion

Tensor effective forces are close to bare ones. accepted by PRL sstt central force calculated by a Lattice QCD calculation Presented by Ishii D 1 -4 Calculations for tensor and 3 -body forces will be great

Modification of superheavy magic gap by tensor force Occupations of 1 k 17/2 and 2 h 11/2 reduces Z=114 gap to a half value Energy (Me. V) 3 p 1/2 3 p 3/2 1 k 17/2 2 f 5/2 2 h 11/2 Z=114 2 f 7/2 1 i 13/2 N=184 1 h 9/2 Proton single-particle energies by Woods-Saxon potential (A=300) Neutron Story similar to Z=64 subshell closure

Summary There are typically 20~100 isotopes between the stability and drip lines. They may give us a rich field of “harvest” from the NN interaction. By changing N (Z) so much, unknown or unrecognized aspects of the NN interaction may emerge. This was the motivation of the project of the tensor force. The outcome so far are …

Summary - 2 - Shell evolution due to tensor force - is a robust mechanism -- also for many classical cases -- - occurs from p-shell to superheavies developments in pf shell ex. N=34 new magic ANL, MSU, GANIL, REX-ISOLDE - affects deformation (ex. Doubly-magic 42 Si strongly oblate) - Free tensor force (like p+r) many-body structure more input from Ch. P. , eff. field th. , lattice QCD - Other cases … Weak processes, astrophysical implications, …. 11 Li and tensor force Myo F 3 -3

Thanks to Yukawa, mesons create variety and richness of exotic nuclei.