arXiv subjects
Publications and source records attributed to B. F. Gibson.
The structure of the three-body $nnΛ$ system, which has been observed recently by the HypHI collaboration, is investigated taking $ΛN-ΣN$ coupling explicitly into account. The $YN$ and $NN$ interactions employed in this work reproduce the binding energies of $^3_Λ$H, $^4_Λ$H and $^4_Λ$He. We do not find any $^3_Λn$ bound state, which contradicts the interpretation of the data reported by the HypHI collaboration.
An OBE potential model for the ^{1}S_0 S = -2 interaction is analyzed with emphasis on the role of coupling between the Lambda Lambda, N Xi, and Sigma Sigma channels. Singlet scalar exchange, an approximation to two-pion exchange, is significant in all channels; surprisingly, the one-pion exchange component is almost negligible. The size of the channel coupling as a function of the overall strength of the OBE model potential is examined. Implications of the analysis for the binding energy of ^{6}_{Lambda Lambda}He are considered; the new experimental datum may suggest a consistency between the extracted Lambda Lambda matrix element and the relation implied by SU(3) among OBE baryon-baryon interactions. \\
The proton-proton parity-violating longitudinal asymmetry is calculated in the lab-energy range 0--350 MeV, using a number of different, latest-generation strong-interaction potentials--Argonne V18, Bonn-2000, and Nijmegen-I--in combination with a weak-interaction potential consisting of rho- and omega-meson exchanges--the model known as DDH. The complete scattering problem in the presence of parity-conserving, including Coulomb, and parity-violating potentials is solved in both configuration- and momentum-space. The predicted parity-violating asymmetries are found to be only weakly dependent upon the input strong-interaction potential adopted in the calculation. Values for the rho- and omega-meson weak coupling constants $h^{pp}_ρ$ and $h^{pp}_ω$ are determined by reproducing the measured asymmetries at 13.6 MeV, 45 MeV, and 221 MeV.
Radiative capture of the K-minus by the deuteron as a reaction for measurement of the Lambda-neutron scattering lengths. The use of spin information to separate the singlet and triplet scattering lengths is treated.
We calculate the contributions of a particular set of charge asymmetric $ΛN$ interactions to the difference of the separation energies of $^4_Λ$He and $^4_Λ$H. We use perturbation theory with four-body variational Monte Carlo wave functions calculated from a Hamiltonian with two- and three-hadron forces. We compare with the data and with an earlier calculation made by one of us which employed a two-body wave function of the $Λ$-nucleus type.
The reaction $Ξ^-d\to nΛΛ$ is studied within the framework of the Faddeev equations as a possible tool to gain insight into the final state $Λ$--$Λ$ interaction. The neutron differential energy spectrum gives a final state interaction that is sensitive to both the $Λ$--$Λ$ amplitude at threshold, and the coupling between the $Λ$--$Λ$ and $Ξ$--$N$ channels. The latter is a result of interference between two mechanisms for the production of the final state, which suggests that this reaction could give a measure of flavor SU(3) violation in the two-baryon system.
We re-examine the puzzling $π^+$ emission from the weak decay of $^4_Λ$He and propose an explanation in terms of a three-body decay of the virtual $Σ^+$. Such a resolution of the $π^+$ decay puzzle is consistent with the calculated $Σ^+$ probability in light $Λ$ hypernuclei as well as the experimentally observed $π^+$ energy spectrum and $s$--wave angular distribution.
The Nijmegen OBE potential D is SU(3) rotated to model the strangeness -2 sector of the baryon-baryon force. Soft core repulsion is introduced to regularize the singular nature of the OBE functions. The strength of the $^1$S$_0$ $t=0$ interaction is adjusted to model three scenarios: (1) a bound state, (2) a narrow virtual, or antibound, state, and (3) an unbound state in which the force is weakly attractive. Using a separable approximation to these potentials, the binding energy of $^{6}_{ΛΛ}$He is calculated in an $ΛΛα$ model. The resultant binding energies suggest that the strength of the $^1$S$_0$ $t=0$ $ΛΛ$ and the $nn$ interactions should be similar, if the coupling between the $ΛΛ$ and $ΞN$ channels is taken into consideration.
The $ΛΛ$ interaction resulting from the SU(3) rotation of the S-wave component of the Nijmegen OBE potential $D$ is used to calculate the binding energy of $^{ 6}_{ΛΛ}$He as a $ΛΛα$ three-body system, and the neutron differential energy spectrum for the reaction $Ξ^- + d \to n + Λ+ Λ$.
The importance of n-p radiative capture, utilizing polarized cold neutrons, as a means of measuring the weak pion coupling constant is reviewed. Parity conserving processes of the form k_gamma*[s_n,k_n] can contribute to the s_n*k_gamma photon asymmetry in any such experiment, if the apparatus is not perfectly symmetric. For an incident laboratory neutron energy of 0.003 eV a value of A^{PC}_{gamma}=0.67*10^{-8} is obtained for two different potential models (Argonne AV14 and Nijmegen Reid93). Serving as an extreme test case, the Reid soft core potential yields 0.61*10^{-8}, close to the result of the contemporary forces. Implications for extracting the weak pion coupling constant and for monitoring the beam polarization are discussed.
The criteria suggested by Welsh and Fearing (nucl-th/9606040) to judge the validity of certain soft-photon amplitudes are examined. We comment on aspects of their analysis which lead to incorrect conclusions about published amplitudes and point out important criteria which were omitted from their analysis.
A relativistic and manifestly gauge-invariant soft-photon amplitude, which is consistent with the soft-photon theorem and satisfies the Pauli Principle, is derived for the proton-proton bremsstrahlung process. This soft-photon amplitude is the first two-u-two-t special amplitude to satisfy all theoretical constraints. The conventional Low amplitude can be obtained as a special case. It is demonstrated that previously proposed amplitudes for this process, both the (u,t) and (s,t) classes, violate the Pauli principle at some level. The origin of the Pauli principle violation is shown to come from two sources: (i) For the (s,t) class, the two-s-two-t amplitude transforms into the two-s-two-u amplitude under the interchange of two initial-state (or final-state) protons. (ii) For the (u,t) class, the use of an internal emission amplitude determined from the gauge-invariance constraint alone, without imposition of the Pauli principle, causes a problem. The resulting internal emission amplitude can depend upon an electromagnetic factor which is not invariant under the interchange of the two protons.
The $ΛN - ΣN$ coupling in $Λ$--hypernuclei and $ΛΛ- ΞN$ coupling in $ΛΛ$--hypernuclei produce novel physics not observed in the conventional, nonstrange sector. Effects of $Λ\leftrightarrow Σ$ conversion in $^3_Λ$H are reviewed. The role of $ΛN - ΣN$ coupling suppression in the $A=4,5$ $Λ$--hypernuclei due to Pauli blocking is highlighted, and the implications for the structure of $^{10}_{\;\, Λ}$B are explored. Suppression of $ΛΛ- ΞN$ conversion in $^{\;\;\, 6}_{ΛΛ}$He is hypothesized as the reason that the $< V_{ΛΛ} >$ matrix element is small. Measurement of $^{\;\;\, 4}_{ΛΛ}$H is proposed to investigate the full $ΛΛ- ΞN$ interaction. The implication for $ΛΛ$ analog states is discussed.
We report 3H binding energy calculations using inversion potentials generated from phase shifts corresponding to contemporary nucleon-nucleon potentials as well as modern phase shift analyses. We place limits upon local potential triton binding energy calculations due to the underlying uncertainties in their fit to the nucleon-nucleon phase shifts: 7.7 +/- 0.2 MeV. We explore the role of the nonlocality of momentum dependent potentials in the triton binding energy. In particular, we find the additional binding energy in the case of the Bonn-B potential is due to a long range nonlocality, which may correspond to a three-nucleon force when the Hamiltonian is restricted to local interactions.
Motivated by the $Σ$-hypernuclear states reported in ($K^-,π^{\pm}$) experiments, we have explored the possibility that there exists a particle-stable $Σ^- nn$ bound state. For the Jülich à hyperon-nucleon, realistic-force model, our calculations yield little reason to expect a positive-parity bound state in either the $J = \frac{1}{2}$ or the $J = \frac{3}{2}$ channels.
A novel soft-photon amplitude is proposed to replace the conventional Low soft-photon amplitude for nucleon-nucleon bremsstrahlung. Its derivation is guided by the standard meson-exchange model of the nucleon-nucleon interaction. This new amplitude provides a superior description of $ppγ$ data. The predictions of this new amplitude are in close agreement with potential-model calculations, which implies that, contrary to conclusions drawn by others, off-shell effects are essentially insignificant below pion-production threshold.
A modified Low procedure for constructing soft-photon amplitudes has been used to derive two general soft-photon amplitudes, a two-s-two-t special amplitude $M^{TsTts}_μ$ and a two-u-two-t special amplitude $M^{TuTts}_μ$, where s, t and u are the Mandelstam variables. $M^{TsTts}_μ$ depends only on the elastic T-matrix evaluated at four sets of (s,t) fixed by the requirement that the amplitude be free of derivatives ($\partial$T/$\partial$s and /or $\partial$T/$\partial t$). Likewise $M^{TuTts}_μ$ depends only on the elastic T-matrix evaluated at four sets of (u,t). In deriving these amplitudes, we impose the condition that $M^{TsTts}_μ$ and $M^{TuTts}_μ$ reduce to $\bar{M}^{TsTts}_μ$ and $\bar{M}^{TuTts}_μ$, respectively, their tree level approximations. The amplitude $\bar{M}^{TsTts}_μ$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle s-channel exchange diagrams, while the amplitude $\bar{M}^{TuTts} _μ$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle u-channel exchange diagrams. The precise expressions for $\bar{M}^{TsTts}_μ$ and $\bar{M}^{TuTts}_μ$ are determined by using the radiation decomposition identities of Brodsky and Brown. We point out that it is theoretically impossible to describe all bremsstrahlung processes by using only a single class of soft-photon amplitudes. At least two different classes are required: the amplitudes which depend on s and t or the amplitudes which depend on u and t. When resonance effects are important, the amplitude $M^{TsTts}_μ$, not $M^{Low(st)}_μ$, should be used. For processes with strong u-channel exchange effects, the amplitude $M^{TuTts}_μ$ should be the first choice.
Using separable $NN$ and $ΛN$-$ΣN$ potentials in the Faddeev equations, we have demonstrated that the predicted enhancement in the $Λd$ cross section near the $Σd$ threshold is associated with resonance poles in the scattering amplitude. The positions of these poles, on the second Riemann sheet of the complex energy plane, are determined by examining the eigenvalues of the kernel of the Faddeev equations. This suggests that for a certain class of $ΛN$-$ΣN$ potentials we can form a $Σ$-hypertriton with a width of about 8 MeV.