The unitary pole approximation for the binding energy of 4He

Two-particle resonance poles and the energy spectra of three- and four-particle systems

“…Before the resonance pole moves to "critical positions" near the real k-axis the decrease in E ~ and E ~ observed in Table 1 can be directly correlated to changes in the two-particle bound state wave function at short range. In this respect our present results are consistent with our previous observations [10,11]. Movement of the resonance poles towards the real kaxis is associated with a breakdown of the bound state pole dominance of the three-particle amplitudes, and a ground state collapse of the many (three and more)-particle ground state for separable interactions of rank-one.…”

“…As long as these poles are far enough from the real k-axis the three-particle ground state energy is largely determined by the position and residues of the twoparticle bound (antibound) state pole. This observation also applies to the four-particle system, but to a somewhat lesser extent [11], and is the content of the bound state pole dominance assumption. Before the resonance pole moves to "critical positions" near the real k-axis the decrease in E ~ and E ~ observed in Table 1 can be directly correlated to changes in the two-particle bound state wave function at short range.…”

“…This is not unexpected in view of the higher density of the four-particle system in its ground state. Details of the solution of the four-particle equations are given elsewhere [10,11]. In Table 1 are listed the bound state energies for the four-particle system from near the (3 + 1) threshold to indefinitely large values when the two-particle resonance is close enough to the real axis.…”

The charge form factor of the model triton for two-particle interactions with continuum bound states

“…The Two-particle Interactions and Their Threeparticle Binding Energies It was shown by Sofianos et al (1) that for a series of separable interactions of rank one Al...A,, hereafter relabelled A,' ... A,', that a collapse occurs for the three-and four-particle binding energies E, and E,, if there is a resonance pole in the Fredholm determinant ~' ( k ) sufficiently close to the real kaxis, even if k moves to very (unrealistically) high values. Arguments were given why this should always be the case for separable potentials of rank one.…”

“…For this purpose we have calculated the charge form factors of most of the two-particle interactions which were employed by Sofianos et al (1) and Pantis et al (2,3) and give the results in this article. In Sect.…”