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Register a new userP-wave Lambda N - Sigma N coupling and the spin-orbit splitting of 9 Lambda Be
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Authors
Y. Fujiwara Kyoto
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We reexamine the spin-orbit splitting of 9 Lambda Be excited states in terms of the SU_6 quark-model baryon-baryon interaction. The previous folding procedure to generate the Lambda alpha spin-orbit potential from the quark-model Lambda N LS interaction kernel predicted three to five times larger values for Delta E_{ell s}=E_x(3/2^+)-E_x(5/2^+) in the model FSS and fss2. This time, we calculate Lambda alpha LS Born kernel, starting from the LS components of the nuclear-matter G-matrix for the Lambda hyperon. This framework makes it possible to take full account of an important P-wave Lambda N - Sigma N coupling through the antisymmetric LS^{(-)} force involved in the Fermi-Breit interaction. We find that the experimental value, Delta E^{exp}_{ell s}=43 pm 5 keV, is reproduced by the quark-model G-matrix LS interaction with a Fermi-momentum around k_F=1.0 fm^{-1}, when the model FSS is used in the energy-independent renormalized RGM formalism.
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The previous Faddeev calculation of the two-alpha plus Lambda system for 9 Lambda Be is extended to incorporate the spin-orbit components of the SU_6 quark-model baryon-baryon interactions. We employ the Born kernel of the quark-model Lambda N LS interaction, and generate the spin-orbit component of the Lambda alpha potential by the alpha-cluster folding. The Faddeev calculation in the jj-coupling scheme implies that the direct use of the quark-model Born kernel for the Lambda N LS component is not good enough to reproduce the small experimental value Delta E^exp_{ls}=43 +- 5 keV for the 5/2^+ - 3/2^+ splitting. This procedure predicts three to five times larger values in the model FSS and fss2. The spin-orbit contribution from the effective meson-exchange potentials in fss2 is argued to be unfavorable to the small ls splitting, through the analysis of the Scheerbaum factors for the single-particle spin-orbit potentials calculated in the G-matrix formalism.
The $Lambda p$ interaction close to the $Sigma N$ threshold is considered. Specifically, the pronounced structure seen in production reactions like $K^-d to pi^- Lambda p$ and $ppto K^+ Lambda p$ around the $Sigma N$ threshold is analyzed. Modern interaction models of the coupled $Lambda N - Sigma N$ systems generate such a structure either due to the presence of a (deuteron-like) unstable bound state or of an inelastic virtual state. % A determination of the position of the prominent peak as observed in various experiments for the two aforementioned reactions leads to values that agree quite well with each other. Furthermore, the deduced mean value of $2128.7pm 0.3$ MeV for the peak position coincides practically with the threshold energy of the $Sigma^+ n$ channel. This supports the interpretation of the structure as a genuine cusp, signaling an inelastic virtual state in the $^3S_1-^3D_1$ partial wave of the $Sigma N$ isospin 1/2 channel. % There is also evidence for a second peak (or shoulder) in the data sets considered which appears at roughly 10-15 MeV above the $Sigma N$ threshold. However, its concrete position varies significantly from data set to data set and, thus, a theoretical interpretation is difficult.
The complexity of threshold phenomena is exemplified on a prominent and long-known case - the structure in the $Lambda p$ cross section (invariant mass spectrum) at the opening of the $Sigma N$ channel. The mass splitting between the $Sigma$ baryons together with the angular momentum coupling in the $^3S_1$-$^3D_1$ partial wave imply that, in principle, up to six channels are involved. Utilizing hyperon-nucleon potentials that provide an excellent description of the available low-energy $Lambda p$ and $Sigma N$ scattering data, the shape of the resulting $Lambda p$ cross section is discussed and the poles near the $Sigma N$ threshold are determined. Evidence for a strangeness $S=-1$ dibaryon is provided, in the form of a deuteron-like (unstable) $Sigma N$ bound state. Predictions for level shifts and widths of $Sigma^-p$ atomic states are given.
We study the central part of Lambda N and Lambda Lambda potential by considering the correlated and uncorrelated two-meson exchange besides the omega exchange contribution. The correlated two-meson is evaluated in a chiral unitary approach. We find that a short range repulsion is generated by the correlated two-meson potential which also produces an attraction in the intermediate distance region. The uncorrelated two-meson exchange produces a sizeable attraction in all cases which is counterbalanced by omega exchange contribution.
We investigate properties of bound and resonance states in the $_{Lambda}^{9}$Be nucleus. To reveal the nature of these states, we use a three-cluster $2alpha+Lambda$ microscopic model. The model incorporates Gaussian and oscillator basis functions and reduces a three-cluster Schr{o}dinger equation to a two-body like many-channel problem with the two-cluster subsystems ($_{Lambda}^{5}$He and $^8$Be) being in a bound or a pseudo-bound state. Influence of the cluster polarization on the energy and widths of resonance states in $_{Lambda}^{9}$Be and on elastic and inelastic $_{Lambda}^{5}$He+$alpha$ scattering is analyzed.
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