document: the @xmath0 ncsm / rgm was presented in @xcite as a promising technique that is able to treat both structure and reactions in light nuclear systems . 
   this approach combines a microscopic cluster technique with the use of realistic interactions and a consistent @xmath0 description of the nucleon clusters . 
   the method has been introduced in detail for two - body cluster bases and has been shown to work efficiently in different systems @xcite . 
   however , there are many interesting systems that have a three - body cluster structure and therefore can not be successfully studied with a two - body cluster approach . 
   the extension of the ncsm / rgm approach to properly describe three - body cluster states is essential for the study of nuclear systems that present such configuration . 
   this type of systems appear , @xmath3 , in structure problems of two - nucleon halo nuclei such as @xmath1he and @xmath4li , resonant systems like @xmath5h or transfer reactions with three fragments in their final states like @xmath6h(@xmath6h,2n)@xmath2he or @xmath6he(@xmath6he,2p)@xmath2he . 
   recently , we introduced three - body cluster configurations into the method and presented the first results for the @xmath1he ground state @xcite . here 
   we present these results as well as first results for the continuum states of @xmath1he within a @xmath2he+n+n basis . 
   the extension of the ncsm / rgm approach to properly describe three - cluster configurations requires to expand the many - body wave function over a basis @xmath7 of three - body cluster channel states built from the ncsm wave function of each of the three clusters ,    @xmath8    @xmath9^{(j^{\pi}t ) }            \times \frac{\delta(x-\eta_{a_2-a_3})}{x\eta_{a_2-a_3 } } \frac{\delta(y-\eta_{a - a_{23}})}{y\eta_{a - a_{23}}}\ , ,          \label{eq:3bchannel }     \end{aligned}\ ] ]    where @xmath10 is the relative vector proportional to the displacement between the center of mass ( c.m . ) of the first cluster and that of the residual two fragments , and @xmath11 is the relative coordinate proportional to the distance between the centers of mass of cluster 2 and 3 . in eq . 
   ( [ eq1 ] ) , @xmath12 are the relative motion wave functions and represent the unknowns of the problem and @xmath13 is the intercluster antisymmetrizer . 
   projecting the microscopic @xmath14-body schrdinger equation onto the basis states @xmath15 , the many - body problem can be mapped onto the system of coupled - channel integral - differential equations @xmath16 
   g_{\nu}^{j^\pi t}(x , y ) = 0,\label{eq:3beq1 } \end{aligned}\ ] ] where @xmath17 is the total energy of the system in the c.m .  frame and @xmath18 
   are integration kernels given respectively by the hamiltonian and overlap ( or norm ) matrix elements over the antisymmetrized basis states . 
   finally , @xmath19 is the intrinsic @xmath14-body hamiltonian .    in order to solve the schrdinger equations ( [ eq:3beq1 ] ) we orthogonalize them and transform to the hyperspherical harmonics ( hh ) basis to obtain a set of non - local integral - differential equations in the hyper - radial coordinate 
   ,    @xmath20    which is finally solved using the microscopic r - matrix method on a lagrange mesh . 
   the details of the procedure can be found in @xcite .    at present 
   , we have completed the development of the formalism for the treatment of three - cluster systems formed by two separate nucleons in relative motion with respect to a nucleus of mass number a@xmath21 . 
   it is well known that @xmath1he is the lightest borromean nucleus  @xcite , formed by an @xmath2he core and two halo neutrons . 
   it is , therefore , an ideal first candidate to be studied within this approach . in the present calculations , 
   we describe the @xmath2he core only by its g.s . 
   wave function , ignoring its excited states . 
   this is the only limitation in the model space used . 
   we used similarity - renormalization - group ( srg ) @xcite evolved potentials obtained from the chiral n@xmath6lo nn interaction @xcite with @xmath22 = 1.5 @xmath23 . 
   the set of equations ( [ rgmrho ] ) are solved for different channels using both bound and continuum asymptotic conditions . 
   we find only one bound state , which appears in the @xmath24 channel and corresponds to the @xmath1he ground state . 
   [ [ ground - state ] ] ground state + + + + + + + + + + + +    [ tab : a ]    lccc approach & & e@xmath25(@xmath2he ) & e@xmath25(@xmath1he ) + ncsm / rgm & ( @xmath26=12 ) & @xmath27 mev & @xmath28 mev + ncsm & ( @xmath26=12 ) & @xmath29 mev & @xmath30 mev + ncsm & ( extrapolated ) & @xmath31 mev & @xmath32 mev +    the results for the g.s . 
   energy of @xmath1he within a @xmath2he(g.s.)+n+n cluster basis and @xmath26 = 12 , @xmath33 = 14 mev harmonic oscillator model space are compared to ncsm calculations in table [ tab : a ] . at @xmath34 12 
   the binding energy calculations are close to convergence in both ncsm / rgm and ncsm approaches . 
   the observed difference of approximately 1 mev is due to the excitations of the @xmath2he core , included only in the ncsm at present . 
   therefore , it gives a measure of the polarization effects of the core . 
   the inclusion of the excitations of the core will be achieved in a future work through the use of the no - core shell model with continuum approach ( ncsmc ) @xcite , which couples the present three - cluster wave functions with ncsm eigenstates of the six - body system . 
   contrary to the ncsm , in the ncsm / rgm the @xmath2he(g.s.)+n+n wave functions present the appropriate asymptotic behavior . 
   the main components of the radial part of the @xmath1he g.s . 
   wave function @xmath35 can be seen in fig . 
   ( [ fig:1 ] ) for different sizes of the model space demostrating large extension of the system . in the left part of the figure , 
   the probability distribution of the main component of the wave function is shown , featuring two characteristic peaks which correspond to the di - neutron and cigar configurations . 
   a thorough study of the converge of the results with respect to different parameters of the calculation was presented in @xcite , showing good convergence and stability . 
   he+@xmath36+@xmath36 relative motion wave function for the @xmath37 ground state , @xmath38 and @xmath39 are the distances between the two neutrons and between the @xmath40 particle and center of mass of the two neutrons , respectively . in the right , the three main components of the radial part of the @xmath1he g.s . 
   wave functions @xmath35 for @xmath26=6,8,10 , and 12 . , title="fig:",height=226 ] he+@xmath36+@xmath36 relative motion wave function for the @xmath37 ground state , @xmath38 and @xmath39 are the distances between the two neutrons and between the @xmath40 particle and center of mass of the two neutrons , respectively . in the right , the three main components of the radial part of the @xmath1he g.s .  wave functions @xmath35 for @xmath26=6,8,10 , and 12 . , 
   title="fig:",height=207 ]    [ [ continuum - states ] ] continuum states + + + + + + + + + + + + + + + +    the use of three - cluster dynamics is essential for describing @xmath1he states in the continuum . 
   therefore , this formalism is ideal for such study . using continuum asymptotic conditions 
   , we solved the set of equations ( [ rgmrho ] ) in order to obtain the low - energy phase shifts for the @xmath41 and @xmath42 channels in the continuum . in our preliminary results , 
   we obtain the experimentally well - known @xmath43 resonance as well as a second low - lying @xmath44 resonance recently measured at ganil @xcite . 
   a resonance is also found in the @xmath45 channel while no low - lying resonances are present in the @xmath46 or @xmath47 channels . in fig . 
   [ fig:2 ] some of the preliminary phase shifts for different channels are shown . 
   results for bigger model spaces and a study of their stability respect to the parameters in the formalism are presently being calculated and will be presented elsewhere . 
   he for different @xmath48 channels.,height=226 ] 
   in this work , we present an extension of the ncsm / rgm which includes three - body dynamics in the formalism . this new feature permits us to study a new range of systems that present three - body configurations . in particular , we presented results for both bound and continuum states of @xmath1he studied within a basis of @xmath2he+n+n . 
   the obtained wave functions feature an appropriate asymptotic behavior , contrary to bound - state @xmath0 methods such as the ncsm . 
   computing support for this work came from the llnl institutional computing grand challenge program and from an incite award on the titan supercomputer of the oak ridge leadership computing facility ( olcf ) at ornl . prepared in part by llnl under contract 
   de - ac52 - 07na27344 . 
   support from the u.s . 
   doe / sc / np ( work proposal no . 
   scw1158 ) and nserc grant no . 401945 - 2011 is acknowledged . 
   triumf receives funding via a contribution through the canadian national research council . 
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summary: we introduce an extension of the @xmath0 no - core shell model / resonating group method ( ncsm / rgm ) in order to describe three - body cluster states . 
   we present results for the @xmath1he ground state within a @xmath2he+n+n cluster basis as well as first results for the phase shifts of different channels of the @xmath2he+n+n system which provide information about low - lying resonances of this nucleus . 
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