The use of scattering length of particle-target interaction due to real- valued potential to study the bound states of the particle-target system is well known in nuclear and atomic physics. In view of the current interest in using eta-nucleus scattering length to infer the existence of eta-mesic nucleus, we derive general analytic expressions that relate the binding energy and half-width of an unstable bound state to the complex-valued scattering length due to the same particle-target interaction.
The possibility of etamesic nuclei remains an open problem in nuclear physics until now. Various calculations give contradictory predictions even for the lightest real nucleus $^3$He. In this paper we present the connection of the binding energy and width to the complex scattering length for heavier nuclei than this in the hope that, with knowledge of the final state interaction this could be useful in searches of possible bound states.
We demonstrate that the binding energies and widths of eta-mesic nuclei depend strongly on subthreshold eta-N interaction. This strong dependence is made evident from comparing three different eta-nucleus optical potentials: (1) a microscopic optical potential taking into account the full effects of off-shell eta-nucleon interactions; (2) a factorization approximation to the microscopic optical potential where a downward energy shift parameter is introduced to approximate the subthreshold eta-nucleon interaction; and (3) an optical potential using on-shell eta-nucleon scattering length as the …
The nd doublet and quartet scattering lengths have been calculated based on the modern NN and 3N interactions. We also studied the effect of the electromagnetic interactions in the form introduced in AV18. Switching them off for the various nuclear force models leads to shifts of up to +0.04 fm for doublet scattering length, which is significant for present day standards. The electromagnetic effects have also a noticeable effect on quartet scattering length, which otherwise is extremely stable under the exchange of the nuclear forces. For the current nuclear force models there is a strong scat…
We investigate the relation between the η^3He binding energy and width and the (complex) η^3He scattering length. Following our systematic analysis of the eta 3He scattering length we set limits on the η^3He binding. If bound states exist the binding energy (width) should not exceed 5 MeV (10 MeV). In addition, we comment on a recently claimed observation of an η-mesic ^3He quasi-bound state by the TAPS collaboration based on ηphotoproduction data. Although our limits are in reasonable agreement with the values reported by this collaboration, our analysis of these data does not lead to a solid…
We compute a model-independent correlation between the difference of neutron-neutron and proton-proton scattering lengths |a(nn)-a^C(pp)| and the splitting in binding energies between Helium-3 and tritium nuclei. We use the effective field theory without explicit pions to show that this correlation relies only on the existence of large scattering lengths in the NN system. Our leading-order calculation, taken together with experimental values for binding energies and a^C(pp), yields a(nn)=-22.9 \pm 4.1 fm.
We discuss the possibility of producing a new kind of nuclear system by putting a few antibaryons inside ordinary nuclei. The structure of such systems is calculated within the relativistic mean--field model assuming that the nucleon and antinucleon potentials are related by the G-parity transformation. The presence of antinucleons leads to decreasing vector potential and increasing scalar potential for the nucleons. As a result, a strongly bound system of high density is formed. Due to the significant reduction of the available phase space the annihilation probability might be strongly suppre…
As an application of the new realistic three-dimensional (3D) formalism reported recently for three-nucleon (3N) bound states, an attempt is made to study the effect of three-nucleon forces (3NFs) in triton binding energy in a non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral equations with the inclusion of 3NFs, which are formulated as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in operator forms which can be incorporated in our 3D formalism. …
We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S…
We calculate the doublet and quartet neutron-deuteron scattering lengths using a nonlocal nucleon-nucleon interaction fully derived from quark-quark interactions. We use as input the $NN$ $^1S_0$ and $^3S_1$-${}^3 D_1$ partial waves. Our result for the quartet scattering length agrees well with the experimental value while the result for the doublet scattering length does not. However, if we take the result for the doublet scattering length together with the one for the triton binding energy they agree well with the so-called Phillips line.
The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. The three-nucleon system shows a discrete scale invariance that can be observed by correlations of the triton binding energy with other observables as the doublet nucleon-deuteron scattering length or the alpha-particle binding energy. The low-energy dynamics o…
We consider the non-relativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to 4He atoms and calculate the binding energ…
The spectral flow of three-body (trimer) states consisting of two heavy (impurity) particles sitting in a condensate of light bosons is considered. Assuming that the condensate is weakly interaction and that an impurity and a boson have a zero-range two-body interaction, we use the Born-Oppenheimer approximation to determine the effective three-body potential. We solve the resulting Schrödinger equation numerically and determine the trimer binding energies as a function of the coherence length of the light bosonic condensate particles. The binding energy is found to be suppressed by the presen…
We investigate the sensitivity of the three-nucleon system to changes in the neutron-neutron scattering length to next-to-leading order in the pionless effective field theory, focusing on the the triton-3He binding energy difference and neutron-deuteron elastic scattering. Due to the appearance of an electromagnetic three-body counterterm at this order, the triton-3He binding energy difference remains consistent with the experimental value even for large positive neutron-neutron scattering lengths while the elastic neutron-deuteron scattering phase shifts are insensitive. We conclude that a bo…
We consider the non-relativistic four-body system with large scattering length and short-range interactions within an effective theory with contact interactions only. We compute the binding energies of the 4He tetramer and of alpha-particle. The well-known linear correlation between the three-body binding energies and the four-body binding energies of these physical systems can be understood as a consequence of the absence of a four-body force at leading order.
The composite nature of a shallow bound state is studied by using the weak-binding relation, which connects the compositeness of the bound state with observables. We first show that the previous weak-binding relation cannot be applied to the system with a large effective range. To overcome this difficulty, we introduce the finite-range correction by redefining the typical length scale in the weak-binding relation. A method to estimate the uncertainty of the compositeness is proposed. It is numerically demonstrated that the range correction enlarges the applicable region of the weak-binding rel…
The ^3He^4He_2 three-atomic system is studied on the basis of a hard-core version of the Faddeev differential equations. The binding energy of the ^3He^4He_2 trimer, scattering phase shifts, and the scattering length of a ^3He atom off a ^4He dimer are calculated using the LM2M2 and TTY He-He interatomic potentials.
The connection of the binding energy and width of possible bound eta-mesic states is given to the complex scattering length for s-states in the hope that, with knowledge of the final state interaction this could be useful in searches of these states. In spite of the strong direct potential dependence of both observables this connection is seen to be very model independent even for various nuclei once the influence of also the effective range is considered. The importance of this term is pointed also for data analyses. Although the nucleus considered here is 12C, extension to other nuclei is im…
In this work we investigate small clusters of bosons using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ particles interacting through a soft inter-particle potential. In order to make contact with a real system, we use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with one of the most widely used $^4$He-$^4$He interactions, the LM2M2 potential. The intensity of the potential is varied in order to explore the clusters' spectra in different regions with large positive and large neg…
Background: Phase-equivalent transformations (PETs) are well-known in quantum scattering and inverse scattering theory. PETs do not affect scattering phase shifts and bound state energies of two-body system but are conventionally supposed to modify two-body bound state observables such as the rms radius and electromagnetic moments. Purpose: In order to preserve all bound state observables, we propose a new particular case of PETs, a deuteron-equivalent transformation (DET-PET), which leaves unchanged not only scattering phase shifts and bound state (deuteron) binding energy but also the bound …
$ηNNN$ and $ηNNNN$ bound states are explored in stochastic variational method (SVM) calculations within a pionless effective field theory (EFT) approach at leading order. The theoretical input consists of regulated $NN$ and $NNN$ contact terms, and a regulated energy dependent $ηN$ contact term derived from coupled-channel models of the $N^{\ast}(1535)$ nucleon resonance plus a regulated $ηNN$ contact term. A self consistency procedure is applied to deal with the energy dependence of the $ηN$ subthreshold input, resulting in a weak dependence of the calculated $η$-nuclear binding energies on t…
The np pair in the spin-singlet state is treated as a Cooper np-pair within the extension of the Nambu-Jona-Lasinio model of light nuclei, describing the deuteron as a Cooper np-pair in the spin-triplet state. For the Cooper np-pair in the spin-singlet state we compute the binding energy and express the S-wave scattering length of np scattering in the spin-singlet state in terms of the binding energy. The theoretical value of the S-wave scattering length of np scattering agrees well with the experimental data.
