Rimantas LAZAUSKAS, 07/07/2009 Elastic p- 3 H scattering below the n- 3 He threshold

Rimantas LAZAUSKAS, 07/07/2009 Why 4N scattering? Few-nucleon systems: Few-nucleon systems: present the most natural testground for the inter-nucleon interaction models Present interaction models (>70 years of research): o Phenomenological (INOY,ISUJ,..) o Meson exchange theory (Nijm, AV18, CD-Bonn,…) o Chiral perturbation theory (Idaho, Epelbaum,…) 2N is made to work with perfect fits (  2 /data~1.) and several parameters 3N problems begin, requires one more fit to fix energies (3N-Force), no effective remedies for some scattering observables Beyond 3N: the most accessible testground A=3-12 bound states, but not easy to find uncorelated observables

Rimantas LAZAUSKAS, 07/07/2009 Why 4N scattering? Ab-initio calculations very limited beyond A=4 system: first very promising calculations exist using GFMC (K. Nollett et al.), NCSM (S. Quaglioni on friday) and RGM (previous talk) require benchmarking. A=4 scattering below break-up threshold became accessible and well established using ab-initio methods: FY, AGS (A. Deltuva et al.), HH (M. Viviani et al.) as well as RGM (H.M. Hofmann et al.) Very rich dynamics of 4N

Rimantas LAZAUSKAS, 07/07/2009 Why 4N scattering? Basis is infinite Solution is searched by decomposing FY components in the partial wave basis Radial parts of the amplitudes are developed in the spline basis, converting differential equations into linear algebra problem. Extensions are made to incorporate 3NF and Coulomb interaction Faddeev-Yakubovski (FY) equations in configuration space Convergence Reality is finite. Convergence xx yy zz

Rimantas LAZAUSKAS, 07/07/ He continuum No Coulomb Becomes a bound state!!! 0-0- B=] [ MeV

Rimantas LAZAUSKAS, 07/07/2009 p- 3 H scattering/convergence INOY potential j max =max(j x,j y,j z ) jxjx jxjx jyjy jyjy jzjz lzlz 0.76 MeV n+ 3 He p+ 3 H 0+0+

Rimantas LAZAUSKAS, 07/07/2009 p- 3 H scattering lengths 0.76 MeV n+ 3 He p+ 3 H 0+0+

Rimantas LAZAUSKAS, 07/07/2009 p- 3 H scattering below n- 3 He threshold Exp: Balashko et al., Sov. Phys. JETP 9 (1959) 137; Jarmie et al., Phys. Rev 130 (1963)1987; Ennis et al., Phys. Rev. 95 (1954) 772  c.m. =120°

Rimantas LAZAUSKAS, 07/07/2009 p- 3 H scattering below n- 3 He threshold Exp: Balashko et al., Sov. Phys. JETP 9 (1959) 137; Jarmie et al., Phys. Rev 130 (1963)1987; Ennis et al., Phys. Rev. 95 (1954) 772  c.m. =120°

Rimantas LAZAUSKAS, 07/07/2009 p- 3 H scattering below n- 3 He threshold E p =300 keV E p =900 keV Exp: Y. G. Balashko et al., Journ. Izv. Rossiiskoi Akademii Nauk, Ser. Fiz. 28 (1964) 1124; Proc. Nuclear Physics Congress, Paris (1964) 255

Rimantas LAZAUSKAS, 07/07/2009 Conclusion Accurate theoretical calculations for 4N scattering are now available Continuum of 4 He turns to be a rich laboratory to test NN & NNN interactions: revealing some discrepencies already for 0 + state More experiments in 4N sector and in particular for low energies will be very appreciated Acknowledgements: The numerical calculations have beenperformed at IDRIS (CNRS, France). We thank the staff members of the IDRIScomputer center for their constant help.