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Tensor Optimized Few-body Model for s-shell nuclei

Tensor Optimized Few-body Model for s-shell nuclei. ２３．８．２０１１. APFB11. Kaori Horii , Hiroshi Toki (RCNP, Osaka univ.) Takayuki Myo, (Osaka Institute of Technology) Kiyomi Ikeda (RIKEN Nishina Center). Introduction.

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Tensor Optimized Few-body Model for s-shell nuclei

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  1. Tensor Optimized Few-body Model for s-shell nuclei ２３．８．２０１１ APFB11 Kaori Horii, Hiroshi Toki (RCNP, Osaka univ.) Takayuki Myo, (Osaka Institute of Technology) Kiyomi Ikeda (RIKEN Nishina Center)

  2. Introduction Realistic NN interaction ⇒ strong short range repulsion and tensor interaction ★Deuteron result with AV8’ potential ＊D-wave component is small, the probability is 5% ＊The dominant attraction of 80% is caused by the tensor interaction. ★Method for treating the strong tensor int. Tensor Optimized Shell Model (TOSM) Myo, Toki, Ikeda We expect to develop medium and heavy nuclei using realistic NN int.

  3. Motivation TOSM +UCOM (only S-wave relative motion) 4He calculation with NN int (AV8’). T.Myo et al (2009) H.Kamada et al (2001) ＊Where is the difference between TOSM and the rigorous calculation? ＊What should be done to improve the description of nuclei ? Few-body technique (relative coordinates) by introducing the spirit of TOSM approximation. 　→ Tensor Optimized Few-body Model (TOFM)

  4. Tensor Optimized Few-body Model (TOFM) TOFM (Few-body) TOSM (Shell-Model) ******* ＊D-wave state contains a single Y2 function in the relative coordinates. ( No double and triple Y2 , No Y1 functions) ＊The most essential Y2 function is in the relative coordinate x1 ＊small variational model space

  5. Tensor Optimized Few-body Model (TOFM) TOFM (Few-body) TOSM (Shell-Model) ******* ＊D-wave state contains a single Y2 function in the relative coordinates. ( No double and triple Y2 , No Y1 functions) ＊The most essential Y2 function is in the relative coordinate x1 ＊small variational model space Deuteron like state (S=1,T=0) TOFM wave function describes the deuteron like state in nuclei.

  6. Tensor Optimized Few-body Model (TOFM) Jacobi coordinate x1,x2,x3 For 4He Total J=0, S-wave(L=0,S=0), D-wave(L=2,S=2) ＊Correlated gaussian basis with the global vector Few Body System 42(2008 )33-72 Y.Suzuki, et al global vector TOFMapprox. ＊Variational calculation on the basis of the Stochastic Variational Method (SVM) Gaussian range matrix A are given as random parameters

  7. ★Numerical resultfor 3H with AV8’ potential Few Body System 42(2008 )33-72 Y.Suzuki, et al Kinetic Energy [MeV] LS Energy Central Tensor TOFM results compare almost perfectly with the rigorous few-body calculation.

  8. ★Numerical resultfor 4He with AV8’ potential (w/o Coul.) Few Body System 42(2008 )33-72 Y.Suzuki, et al Kinetic Energy [MeV] LS Energy Central Tensor The missing strength come from the kinetic and tensor matrix elements. The inclusion of double Y2 functions brings the total energy very close.

  9. ★4He~ Comparison with Tensor Optimized Shell Model (TOSM) ~ TOFM (Few-body) TOSM (Shell-Model) T. Myo et al, PTP121,No3(2009)511, ＊The energy values are better than the TOSM result. ＊The large differences come from the kinetic and tensor components. ＊TOSM calculation can be improvedby taking more suitable UCOM correlation function in the short range correlation.

  10. Correlation function with TOFM w.f. H.Kamada et al (2001) PRC64, 044001 S-wave and D-wave Correlation functions for 2H,3H, and 4He ＊The dip structure below 1 fm reflects the presence of the strong short range repulsion. ＊The magnitude of the peak reflects the size of nuclei. ＊d-wave components are found significant and similar among the three nuclei. S 4He (1.52 fm) 3H (1.78 fm) 2H (1.95 fm) D

  11. 4He (1.52 fm) 3H (1.78 fm) 2H (1.95 fm) Correlation function with TOFM w.f. H.Kamada et al (2001) PRC64, 044001 S-wave and D-wave Correlation functions for 2H,3H, and 4He we normalize the correlation functions to those of 4He. ＊The same short range behavior below 1 fm for both S and D ＊The size of nuclei determine the correlation function at large distance. ＊This is an important finding for the study of heavier nuclei. S D

  12. AV8’ (with tensor) MT-V (w/o tensor) Correlation function for S-wave To improve the TOSM (shell-model) results ⇒ the short range correlation is treated by the UCOM 　 ⇒ UCOM function form is obtained with the central MT-V[1] int. Difference of S-wave Correlation function for 4He between AV8’ and MT-V ＊The short range behavior of the correlation function depends on the properties of interaction. ＊It is interesting to modify the correlation function in the UCOM. S [1]R.A.Malfliet and j.A..Tjon, NPA127, 61(1969)

  13. Summary & Outlook ＊ We have formulated a tensor-optimized few-body model (TOFM) in the spirit of the TOSM ＊ TOFM app. has a small variational model space (single Y2 in D-wave) ＊ The good reproduction of the rigorous results indicates that nuclei like to have deuteron configuration. ＊ The short range behaviors of correlation function are very similar for the s-shell nuclei. ＊The correlation function in UCOM should be studied further in the TOSM flamework. ＊ The present study is very encouraging to extend our study for nuclei with A>5 in TOFM flamework. EX) 5He structure, 4He+n Phase Shift, 8Be(4He+4He RGM)…

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