Integrodifferential equation for few- and many-body systems

Abstract

A complete derivation of a new two-variable integrodifferential equation valid for threeand many-boson systems is given here for the first time, and it is shown to be exact if all correlations higher than those of two-body type can be neglected. Its equivalence to the Faddeev equation for three bodies and its applicability to many-body systems are discussed in detail. Three-body forces are included. It is shown that the threeand four-body binding energies obtained by means of this equation are in good agreement with those obtained from the most sophisticated variational, Faddeev, and Faddeev-Yakubovsky calculations. This indicates that our new two-variable integrodifferential equation should also be useful for larger systems, in particular since unlike other methods it does not suffer from the disadvantage of rapidly increasing complexity with A. We also show that a simple adiabatic method for the solution of this equation {and hence also for the Faddeev equation) is quite sufficient, due to the closeness of the upper and lower bounds obtained in this way. Finally we apply the adiabatic method to nuclear three-body scattering and even include the effect of breakup for spin-dependent forces. It is found that asymptotic behavior is reached for a value of the hyperradius of the order of 3S fm.where

Threshold scattering of the η-meson off light nuclei

“…Therefore the use of more accurate nuclear wave functions is of utmost importance. Such realistic wave functions can be constructed, for instance, by means of the Integrodifferential Equation Approach (IDEA) [28,29], and are in progress. Table I.…”

Translationally-Invariant Coupled Cluster Theory Applied to the 4He Nucleus

“…Standard coupled cluster theory assumes for the ground-state wave function the general form (8) where each 8n corresponds to np -nh excitations with respect to some suitable model or reference state Wo. We have shown in the previous section that this ansatz will spoil the centre-of-mass factorizability property and that at least operators 81 and 82 must appear in a special combination.…”

“…For this function it is possible to write down an integro-differential equation following the CC evaluation method [26]or by means of an Euler-Lagrange variational approach, as in the case of Jastrow correlations [13], or, finally, by following a method similar to the hyperspherical harmonics method of describing nuclei [8]. Actually, if the quadratic terms were omitted from eq.…”

“…In this manner we will be able to show explicitly the way CC theory describes the nuclear wave function in coordinate space. In turn, this will permit us to connect CC theory with such other theories as the Jastrow variational theory [7] or the hyperspherical harmonics integro-differential equation method [8], which are entirely described in coordinate space.…”

“…(5) of ref. [27]). For present purposes we have decided to work in the harmonic oscillator basis, by using directly eqs.…”