Pre-asymptotic behavior of single-particle overlap integrals of non-Borromean two-neutron halos

N. K. Timofeyuk, L. D. Blokhintsev, J. A. Tostevin
2003 Physical Review C  
For non-Borromean two-neutron halo nuclei, modifications to the behavior of single-particle overlap integrals will arise due to the correlations of the two interacting nucleons in the halo. An additional contribution to the overlap integral can be obtained using the Feynman diagram approach. This additional term is modeled using a simple local potential model. We show that these modifications may play a role in detailed interpretations of experimental results from single-nucleon knockout,
more » ... er, and other reactions that probe the single-nucleon overlap functions. It is well known that when a neutron or proton is added to a stable nucleus, the separation energy of this last nucleon does not decrease monotonically. The one-nucleon separation energy S A (1N) from a nucleus of mass A depends on that of the previous nucleon, S AϪ1 (1N). If S A (1N) ϽS AϪ1 (1N) then, in general, the pairing interaction between nucleons will act to increase S Aϩ1 (1N). Thus, a characteristic staggering behavior is predicted theoretically and observed experimentally in the systematics of the S(1N). Near the limits of nuclear stability one finds a class of nuclei for which the one-and two-nucleon separation energies S A (1N) and S A (2N) are very similar, and where both are significantly smaller than those for stable nuclei. Several examples of such nuclei are shown in Table I . These weakly bound systems, with S A (2N)ϷS A (1N), and for which the A-, (A Ϫ1)-, and (AϪ2)-body nuclei are all particle stable, are referred to in this paper as non-Borromean two-neutron ͑or proton͒ halo nuclei. Over the last decade it has been established that nuclei close to the edge of stability display shell melting and intruder states phenomena ͓1͔. Nuclear breakup, knockout, and transfer reactions have recently been proposed ͓2͔ and used ͓3,4͔ to study experimentally the strengths of the intruder states on several non-Borromean two-neutron halo systems. The theoretical interpretation of the experimental data from these reactions relies on nuclear structure and reaction theories in which the single-particle state information enters through the one-nucleon overlap integrals. An important feature of these direct reaction mechanisms is that their amplitudes are primarily sensitive to the behavior of the onenucleon overlaps at and beyond the nuclear surface. Asymptotically, these single-particle overlaps decrease exponentially with a decay constant determined by the S A (1N). Most theoretical analyses of experimental data assume that these overlaps can be calculated using simple two-body potential models. These suggest that for radii outside of the range of the binding interaction, which for very weakly bound systems give the main contribution to the reaction, the asymptotic behavior for these overlaps is already achieved. In this paper, we discuss the possibility that for non-Borromean two-nucleon halo nuclei this assumed asymptotic behavior of the one-nucleon overlaps may be reached only at much larger distances than for ordinary nuclei. The resulting changes in the overlap functions in the nuclear surface and beyond may therefore affect analyses and the interpretation of experimental results. The physics behind this nonstandard behavior of the onenucleon overlaps is the correlations of the two nucleons of the halo outside of the nuclear core. As we attempt to remove a single nucleon to large distances r, beyond the range of its interactions with all the other nucleons, the remaining A Ϫ1 nucleons will rearrange as if the removed nucleon was absent. In the non-Borromean two-nucleon cases of interest here, however, this AϪ1 configuration is a one-nucleon halo nucleus with a separation energy S AϪ1 (1N) considerably smaller than that of the first removed nucleon. So, for a range of r beyond the nuclear core the separated nucleon will continue to overlap and interact with the halo nucleon of the (AϪ1)-body subsystem. Thus, although far from the center of mass of the (AϪ1)-body residual nucleus, the removed nucleon will be affected by these correlations of the two halo nucleons. This will lead to surface and preasymptotic deviations from the overlap functions calculated using potential models, out to large distances. These deviations may also be different for different orbital angular momenta ᐉ of the last nucleon, and so may affect the interpretation of experiments which aim to probe the occupancies of normal and intruder single-particle states. The one-nucleon overlap integral I(r) is defined as the overlap between the ͑translationally invariant͒ many-body wave functions ⌿ A and ⌿ AϪ1 of the nuclei, with masses A and AϪ1, and the spin-isospin wave function N of the removed nucleon, where r is the vector separation between the centers of mass of the (AϪ1)-body residue and the removed nucleon. Below, we consider only the ᐉϭ0 case and assume that the removed nucleon is a neutron. The best way to establish the asymptotic behavior of I(r) is to consider its Fourier transform I(q). The latter has a pole at imaginary momentum qϭi, where ϵ A (1N) RAPID COMMUNICATIONS PHYSICAL REVIEW C 68, 021601͑R͒ ͑2003͒
doi:10.1103/physrevc.68.021601 fatcat:ug5dfjc7aveuhdqp4yft4cs7j4