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Paper text:
in quantum mechanics the decay of two fragments is well determined by energy and momentum conservation laws .
but the decay of three particles is a much more complicated issue .
the energies of the decaying fragments are not fixed .
the energy distribution of the three - body final state after the decay is an observable , and can be used to understand the structure of the initial state and the decay mechanism itself . on the other hand ,
the intermediate path connecting the initial and final states is not an observable .
the only way to extract information about the decay mechanism is to try to understand the measurable final state by means of theoretical models .
the decay is usually interpreted as either sequential via an intermediate configuration or direct to the continuum .
the interpretations are often used to derive reaction rates for the inverse process in astrophysical environments .
it is therefore important to have a reliable interpretation of the data .
we have focused our attention on three - body decaying nuclei involved in stellar nucleosynthesis reactions , @xmath0c , @xmath1be and @xmath2be .
for all three there are experimental data available that help us to test the validity of our theoretical model .
the three - body decaying nuclei are described as three - body systems within the complex - scaled hyperspherical adiabatic expansion method @xcite . according to this method ,
the angular part of the hamiltonian is first solved keeping fixed the value of the hyperradius @xmath3 .
its eigenvalues serve as effective potentials while the eigenfunctions , @xmath4 are used as a basis to expand the total wave - function @xmath5 the @xmath3-dependent expansion coefficients , @xmath6 , are the hyperradial wave functions obtained from the coupled set of hyperradial equations .    @xmath0c is described as three @xmath7-particles , @xmath1be as two @xmath7-particles and one neutron , and @xmath2be as one @xmath7-particle and two protons .
our hamiltonian contains short - range and coulomb potential ( between charged particles ) .
we have considered @xmath8 potential from @xcite , @xmath7-nucleon from @xcite and nucleon - nucleon from @xcite .
these potentials have been built in order to reproduce the two - body scattering data .
on top of these interactions we include a structureless three - body potential of the form @xmath9 , fitted to reproduce the resonance energies .
this potential is included because at short distances the structure of these nuclei is not necessarily of three - body character .
the complex scaling method helps us to treat the resonances as if they were bound states .
the many - body initial state resonance evolves into three clusters at large distances .
the total angular momentum and parity @xmath10 is conserved in the process .
this symmetry imposes constraints on the resulting momentum distributions .
the energy distribution is the probability for finding a given particle at a given energy .
it can be measured experimentally and is the only information that allows us to study the decay path , that can be either sequential or direct or a mixture .
the information about the energy distributions of the fragments after the decay is contained in the large - distance part of the wave - function , which must be accurately computed .
the single particle probability distributions are obtained after monte carlo integration of the absolute square of the large - distance wave - function .
within this theoretical framework we have extensively studied the decay of the low - lying @xmath0c resonances @xcite .
our results have been compared to recent experimental data @xcite with a high level of agreement . moreover ,
our suggestion to change the previously assigned spin and parity of the 13.35  mev state @xcite from @xmath11 to @xmath12 has been supported by the experimental community @xcite .
we have studied the five lowest resonances of @xmath1be @xcite and compared them to the experimental data from @xcite .
[ fig9 ] shows the angular distributions of these resonances , _
i.e. _ the probability for finding one of the decaying particles in a certain direction with respect to the direction formed by the other two . in all the cases
we have removed the sequential decay via @xmath13be(@xmath14 ) .
this kind of plot contains information about the angular momentum of the first particle relative to the centre - of - mass of the other two .
we observe that the angular distribution patterns are different for different @xmath10 states .
these features are clearly distinguishable , demonstrating that these observables can be used to determine the large - distance structure of these resonances .
the initial state can still be determined only through the theoretical information about the dynamical evolution of the resonances .
the @xmath2be is an unbound nucleus which has only two low - lying resonances , @xmath14 and @xmath15 .
its decay has been recently measured @xcite and compared to theoretical predictions given by our formalism .
we have not found any signatures of sequential decay of these resonances via intermediate two - body states .
we show in fig .
[ fig6 ] the angular distributions for the two resonances of @xmath2be .
the upper panels can be compared directly to the experimental data from @xcite .
they show that the @xmath7-particle prefers to come out perpendicular to the direction formed by the two protons .
we have applied a general method to compute the momentum distributions of three - body decaying light - nuclei resonances .
we have conjectured that the energy distributions of the decay fragments are insensitive to the initial many - body structure .
the energy distributions are then determined by the energy and three - body resonance structure as obtained in a three - body cluster model .
these momentum distributions are determined by the coordinate space wave - functions at large distances , which much be computed with a high accuracy .
the method has been applied previously to the study of the decay of @xmath0c resonances with great success . in this contribution
we have shown the angular distribution of the low - lying @xmath1be and @xmath2be resonances decaying into @xmath16 and @xmath17 respectively .
our distributions are open to experimental tests .    this work has been partly supported by funds provided by micinn ( spain ) under the contracts fis2008 - 01301 and fpa2010 - 17142 and the spanish consolider - ingenio programme cpan ( programme
csd2007 - 00042 ) .
we have studied the three - particle decay of @xmath0c , @xmath1be and @xmath2be resonances . 
 these nuclei have been described as three - body systems by means of the complex scaled hyperspherical adiabatic expansion method . 
 the short - distance part of the wave - function is responsible for the energies whereas the information related to the observable decay properties is contained at large distances , which must be computed accurately . as an illustration 
 we show the results for the angular distribution of @xmath1be and @xmath2be resonances .