A Monte Carlo approach to the study of medium-light hypernuclei properties Diego Lonardoni University of Trento - Physics Department INFN - Gruppo Collegato di Trento December 16, 2011
Outline 1. The method DMC DMC for nuclei: AFDMC 2. Hypernuclei hyperon-nucleon interaction AFDMC for hypernuclei 3. Preliminary results 4. Conclusions and perspectives
Diffusion Monte Carlo DMC = projection method = it (R, )=H (R, ) (R, )=e (H E 0) (R, 0) = c n e (E n n=0 E 0 ) n (R) (R, 0) = n=0 c n n (R) lim (R, )=c 0 0 (R)
Diffusion Monte Carlo (R, + d )= R ( + d ) = R e (H E 0)d R G(R,R,d ) R ( ) dr walkers kinetic term potential term d d d
Nucleon-nucleon interaction 2 body 3 body
Nucleon-nucleon interaction 2 body n V ij = v p (r)o p ij p=1 O p=1,8 ij = {1, i j,s ij, L ij S ij } {1, i j } O p=9,14 ij = L 2 ij,l 2 ij ( i j), (L ij S ij ) 2 {1, i j } O p=15,18 ij = T ij, ( i j) T ij,s ij T ij, z i + z j 3 body V ijk = C SW 2 O 2,SW ijk + C PW 2 O 2,P W ijk + C R 3 O 3, ijk R + C R O R ijk
Auxiliary Field Diffusion Monte Carlo Problem: P e 1 2 d O2 = A i c i i Z!(A A! Z)! 4A components Idea: Hubbard-Stratonovich transformation e 1 2 d O2 = 1 2 dx e x2 2 + d xo MC calculation auxiliary field
Auxiliary Field Diffusion Monte Carlo AV6: O p=1,6 ij = {1, i j,s ij } {1, i j } V SD +V SI V SD = 1 2 + 1 2 + 1 2 A n=1 3A n=1 3A n=1 3 =1 ( ) n O n ( )2 ( ) n O n ( )2 3 =1 ( ) n O n ( )2 A ( ) i,j : A A A ( ) i,j A ( ) i,j : 3A 3A : 3A 3A good for Hubbard-Stratonovich 15A auxiliary fields rotation of spin-isospin states
Hypernuclei = u + d + s single hypernucleus double hypernucleus
Hypernuclei STAR @ RHIC - HI collider - anti -hypernuclei - exotica? PANDA @ FAIR - anti-proton beam - double -hypernuclei - -ray spectroscopy SPHERE @ JINR - heavy ion beams - single -hypernuclei - weak decay JLAB - electron-production - single -hypernuclei - -wavefunction BNL - heavy ions beams - anti-hypernuclei - single -hypernuclei - double -hypernuclei KAOS @ MAMI C - electron-production - single -hypernuclei - -wavefunction FINUDA @ DAFNE - e + e collider - stopped-k reaction - single -hypernuclei - -ray spectroscopy ALICE @ LHC - URHIC collider - anti -hypernuclei - exotica? HypHI @ GSI - heavy ion beams - single -hypernuclei at extreme isospins - magnetic moments KEK J-PARC - intense K beams - single and double -hypernuclei - -ray spectroscopy for single 2000 2010 2020 KEK BNL FINUDA JLAB SPHERE KAOS STAR HypHI PANDA ALICE J-PARC
Hypernuclei H. Ðapo, B.-J. Schaefer, and J. Wambach. Appearance of hyperons in neutron stars. Phys. Rev. C, 81(3):035803, Mar 2010
Hypernuclei H. Ðapo, B.-J. Schaefer, and J. Wambach. Appearance of hyperons in neutron stars. Phys. Rev. C, 81(3):035803, Mar 2010
Hyperon-nucleon interaction [1] 2 body 3 body
Hyperon-nucleon interaction [1] 2 body V i (r) =v 0 (r)+v 0 (r)"(p x 1) + 1 4 v T 2 (m r) i v 0 (r) =v c (r) v 2 (r) v c (r) =W c 1+e r r a 1 HS ok! v 2 (r) = vt 2 (m r) only 2-body 3 body HS ok! operators V ij = C SW 2 O 2,SW ij + C PW 2 O 2,P W ij + C D O D ij
The idea nucleus hypernucleus nuc = Det N J NN hyp = Det N J NN Det J N propagator via HS 15A +3A A auxiliary fields B = nuc H N nuc nuc nuc hyp H N + H hyp hyp hyp Hyp: nuclear effects cancel information about the hyperon-nucleon interaction
The idea: behind the scene Starting point: robust method for nuclei + good wave function different AFDMC approaches different single particle orbitals work in progress present and future collaborations
The idea: behind the scene 4 He binding energy -31.6-31.7-31.8-31.9 V4 potential Code PsiT-weight Code PsiT-weight Code Elocal-weight Skyrme.orb HF-B1.orb HF-B1.orb -32.0 Code PsiT-weight HF-V4p.orb -32.1 energy [MeV] -32.2-32.3-32.4-32.5-32.6-32.7-32.8-32.9 GFMC Phys.Rev.Lett.89182501-1:4(2002) -33.0 0e+00 1e-05 2e-05 3e-05 4e-05 5e-05 6e-05 7e-05 8e-05 9e-05 1e-04 d [1/MeV]
The idea: behind the scene 4 He binding energy -18.0-19.0-20.0 energy [MeV] -21.0-22.0-23.0-24.0-25.0-26.0-27.0-28.0 V6 potential GFMC Phys.Rev.Lett.89182501-1:4(2002) Code PsiT-weight Code Elocal-weight Code Elocal-weight Code Elocal-weight HF-B1.orb HF-B1.orb Skyrme.orb HF-V6p.orb -29.0-30.0-31.0-32.0-33.0-34.0 0e+00 1e-05 2e-05 3e-05 4e-05 5e-05 6e-05 7e-05 8e-05 9e-05 1e-04 d! [1/MeV]
Hypernuclei preliminary results 7.00 5 He -separation energy 6.50 6.00 5.50 energy [MeV] 5.00 4.50 4.00 3.50 3.00 exp [2] 3 body NN V4 +V N HF-B1.orb V6 +V N HF-B1.orb V4 +V N +V NN HF-B1.orb V6 +V N +V NN HF-B1.orb 2.50 2.00 1.50 1.00 [2] Journal of Physics G: Nuclear and Particle Physics, 32(3):363-373, 2006 0.50 0e+00 1e-05 2e-05 3e-05 4e-05 5e-05 6e-05 7e-05 8e-05 9e-05 1e-04 d [1/MeV]
Hypernuclei preliminary results 0.10 5 He density 0.09 0.08 N-density V4 +V N HF-B1.orb -density V4 +V N HF-B1.orb 0.07 density [1/fm 3 ] 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 r [fm]
Hypernuclei preliminary results 0.10 5 He density 0.09 0.08 N-density V4 +V N +V NN HF-B1.orb -density V4 +V N +V NN HF-B1.orb 0.07 density [1/fm 3 ] 0.06 0.05 0.04 3 body NN 0.03 0.02 0.01 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 r [fm]
Hypernuclei preliminary results 0.10 5 He density 0.09 0.08 N-density V6 +V N HF-B1.orb -density V6 +V N HF-B1.orb 0.07 density [1/fm 3 ] 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 r [fm]
Hypernuclei preliminary results 0.10 5 He density 0.09 0.08 N-density V6 +V N +V NN HF-B1.orb -density V6 +V N +V NN HF-B1.orb 0.07 density [1/fm 3 ] 0.06 0.05 0.04 3 body NN 0.03 0.02 Hyp: ok! 0.01 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 r [fm]
Conclusions and perspectives AFDMC algorithm can be easily extended to the study of hypernuclear systems study of heavier -hypernuclei: 7 He, 17 O development of an accurate hyperon-nucleon potential study of -hypernuclei: 6 He development of an accurate hyperon-hyperon potential
Conclusions and perspectives deeper investigation in the AFDMC algorithm To do (high priority) better trial wave function single particle orbitals correlation functions
Thank you [1] Hypernuclear potentials: A. A. Usmani, Steven C. Pieper, and Q. N. Usmani. Variational calculations of the separation energy of the hypernucleus. Phys. Rev. C, 51(5):2347 2355, May 1995. 17 O A. A. Usmani and S. Murtaza. Variational Monte Carlo calculations of 5 He hypernucleus. Phys. Rev. C, 68(2):024001, Aug 2003. A. A. Usmani. 5 N space exchange correlation effects in the He hypernucleus. Phys. Rev. C, 73(1):011302, Jan 2006.