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## Symposium on Astro -Particle and Nuclear Physics

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**Symposium on Astro-Particle and Nuclear Physics**In Honour of 70th Birthday of Prof. Q.N. Usmani 9/13/2014 1**Energies of multi-strange α-cluster hypernuclei using**variational Monte Carlo Method MOHAMMAD SHOEB Department of Physics, Aligarh Muslim University, Aligarh-202 002, India 9/13/2014 4**Outline**• Introduction • 2. Hamiltonian in α-cluster model • 3. Potential models • 4.Variational wavefunctions • 5. Results and discussion • 6. Summary 9/13/2014 5**1. Introduction:**Aim of nuclear physics Complete knowledge of the interaction among octet of baryons in aunified way 9/13/2014 6**Motivation of studying Strange and multi-strange**hypernuclei • to extract interaction between hyperon-N • and hyperon-hyperon • Existence of hypernuclei • represent a new state of matter • may exhibit new symmetries, selection rules, etc.**Presence of hyperon(s) may modify the properties of the core**• moment inertia of deformed nucleus • rotational and vibrational states structure of nucleus • Hypernucleus provides us a opportunity to investigate properties of hyperon(s) in nuclear medium • Hyperon(s) inside nuclei may be used as probe to study the nuclear structure**It is believed that hyperons matter forming the inner core**of neutron stars would have significant effect on their properties. Schaffner-Bielich [NP 804(2008)309 and ref. their in ] has discussed that hypernuclear potential depths, two-body hyperon- nucleon and hyperon three-body forces as well as hyperon-hyperon interaction would 9/13/2014 9**have a impact on the maximum mass, mass-radius relation, and**cooling properties of neutron stars. Therefore, determination of hyperon- nucleon and hyperon-hyperon interaction becomes very important for investigating the properties of neutron stars.**Hypernuclear physics is likely to play key role**in the study: • Properties of neutron stars • Equation state of nuclear matter Figure in the next slide shows interdisciplinary nature of hypernuclei linking particle, nuclear, many-body, astrophysics etc. [ref. Erni et al arXiv: hep-ex/0903.3905]**Segr table**9/13/2014 13**Extension of the nuclear chart in a new dimension,**strangeness S**-Hypernuclear events**, ( ground and excited states), or (Hida event ) and**Hypernuclear experiments planned or operative at various**(nine) laboratories all over the World**Experimental facilities for hypernuclear physics program**List of a few leading laboratories where Hypernuclear physics program to produce and identify hypernuclei with strangeness S= -1 to -3 is being pursued • TJNAF(Thomas Jefferson National Accelerator Facility) at Newport news in USA Electro-production • FINUDA(FIsica NUclearea DA NE): A special accelerator, DA NE (Double Annular ring For Nice Experiment), designed at INFN (Instituto Nazionale di Fisica Nucleare)**Head on collision**510 MeV 510 MeV Copious production decays (M=1020MeV, 20 s) A beam of of extremely high intensity and precise low energy is expected to insert “strangeness” inside nucleus to produce hypernuclei. 9/13/2014 18**J-PARC(Japan Proton Accelerator Research Complex) at**KEK: Already a rich data related to both the spectroscopy and decay of hypernuclei at KEK have been measured. Program for production and unambiguous identification of • hypernuclei and excited states using reaction ( ) • Excited states of double-Λ hypernuclei 9/13/2014 19**ANDA ( ANnihilation at DArmstadt ): A**beam hits primary target to produce ; Stopping and absorption of in the secondary target produce hypernucei. Program to produce S= -3, -hypernuclei 9/13/2014 20**Schematic picture describing production of double Λ**hypernuclei at PANDA In primary target In secondary target, e.g. Li, Be, B,**Multi-strange hypernuclei**Schaffner et al [Ann. Phys.(NY)235(1994) 35 ] observed that a would become particle stable against the strong decay if a sufficient number of bound ’s Pauli blocked this decay mode. Thus is the lightest system suggested to study. At present production of multi-strange hypernuclei seems to be impossible. 9/13/2014 22**However, it will interesting to theoretically**study the stability of multi-strange systems. Such a study is likely to have implication on future experimental efforts in producing, identifying and measuring the properties of multi-strange hypernuclei. Therefore, we have included in our study multi-strange hypernuclei apart from strange ones.**2. Hamiltonian in α-cluster model**Hypernuclei studied in the α-cluster model using VMC s-shell: p-shell: Systems within rectangular boxes are the ones whose stability predictions are to be made. 9/13/2014 24**Hamiltonian for the five-body system in**Ξααmodel with αtreated as rigid: α 4 Ξ 3 5 Λ 2 α Λ 1**…..(1)**K. E. operator , potential energy for the phenomenological the particlepair dispersive three-body potential with Yukawa form factors. 9/13/2014 26**Hamiltonian for**in ΛΛααα model ….(2) α Λ 3 1 phenomenological repulsive Λ α 4 three-bodypotential with α 2 Gaussian form factors 5 9/13/2014 27**3. Potential Models**3.1 Two-body potentials Three-range Gaussian BB(=ΛΛ, Ξ) potentials in spin state (=s,t) ….(3) (7.26 MeV) 9/13/2014 28**Potentials**For = 9/13/2014 29**Potentials**9/13/2014 30**…(4)**(4) 9/13/2014 31**potentials for**l th partial waves that fit scattering phase shifts. potential of Chien and Brown has been used for only as the energy is not very sensitive to the choice of the potential. Ali-Bodmer potentials 9/13/2014 32**Two-range Gaussian potentials**• Isle fits of and its weak decay modes • MSA is obtained from Brueckner-Hartee-Fock Theory and slightly modified to fit • of • [Euro. Phys. J.16(2003)21] 9/13/2014 33**…..(5)**9/13/2014 34**WS24 with = 24.0, as suggested by Dover and Gal**[Ann.Phys. 146 (1983 )309],has been obtained from a analysis of old and ambiguous data (4) . In the previous slide its graph is shown by black color line. energy = -2.09 MeV for WS24 and Isle potential = -0.06 MeV for WS14 9/13/2014 35**3.2 Phenomenological Three-body potential among**and clusters Microscopic calculations of Bodmer and Usmani for shows that contribution of dispersive three-body NN force for the triad where one nucleon from each is participating 9/13/2014 36**is quite significant, neglecting it among cluster**overbinds and . In cluster model calculation we [Pramana68 (2007)943] have proposed to simulate phenomenologically the dispersive energy in the triad through a simple form (6) 9/13/2014 37**4.Variational wavefunctions**Construction of good trial wavefunction • Physics necessary to describe the ground and excited state • Reasonably efficient to compute Wavefunctions are product of two-body correlation functions and the appropriate spin functions 4.1 Wavefunctions (i)and model g.s. , degenerate doubletand , . Replacing by gives w.f. for . 9/13/2014 39**(ii) and :**model g.s. , excited state , (iii)and : model g.s. , degenerate doublet , 9/13/2014 40**Replacing by gives w.f. of .**(iv) Wavefunctions for , and (a) wavefunction for in model: = 9/13/2014 41**(b) Wavefunction for : suppress a and a**indices in the wavefunction of in (a) above (c) Wavefunction for : suppress a index in the wavefunction of in (a) above (d) Similarly wavefunction for can be obtained. 9/13/2014 42**4.2 Calculation of correlation function**A procedure developed by Urbana group. Solution of the following Schroedinger type equation etc. pair . Potential between particles . 9/13/2014 43**9/13/2014**44**9/13/2014**45**5.Procedure for energy calculation**( 8 ) For local operator H the energy can be written in a form suitable for Monte Carlo calculation. Defining local energy 9/13/2014 46**and a multivariate probability distribution**( 9) The variational energy is written as (10 ) 9/13/2014 47**9/13/2014**49**The energy is evaluated using**(i)model of :and (ii)model of : and (iii) model of : and • model of : and Similarly for other hypernuclei 9/13/2014 50