We propose a new method for treating both nuclear and Coulomb breakup processes with high accuracy and computational speed. The scattering amplitude of breakup reaction is decomposed into the lower and higher partial-wave parts. The former is calculated with the continuum-discretized coupled-channels method (CDCC) and the latter with a new version of CDCC in which the trajectory of projectile is assumed to be a straight line. Validity of this hybrid calculation is tested for $^{58}\mathrm{Ni}(^{8}\mathrm{B},^{7}\mathrm{Be}+p)^{58}\mathrm{Ni}$ at $240\phantom{\rule{0.3em}{0ex}}\text{MeV}$. The hybrid calculation is opening the door to the systematic analysis of $^{8}\mathrm{B}$ dissociation measured at RIKEN, MSU, and GSI, to determine the astrophysical factor ${S}_{17}(0)$ accurately.
Energy levels of the double-\ensuremath{\Lambda} hypernuclei ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{7}\mathrm{He},$ ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{7}\mathrm{Li},$ ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{8}\mathrm{Li},$ ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{9}\mathrm{Li},$ ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{9}\mathrm{Be},$ and ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{10}\mathrm{Be}$ are predicted on the basis of an $\ensuremath{\alpha}+x+\ensuremath{\Lambda}+\ensuremath{\Lambda}$ four-body model, where ${x=n,p,d,t,}^{3}\mathrm{He},$ and $\ensuremath{\alpha},$ respectively. Interactions between the constituent particles are determined so as to reproduce reasonably the observed low-energy properties of the $\ensuremath{\alpha}+x$ nuclei ${(}^{5}\mathrm{He},{}^{5}\mathrm{Li},{}^{6}\mathrm{Li},{}^{7}\mathrm{Li},{}^{7}\mathrm{Be},{}^{8}\mathrm{Be})$ and the existing data for \ensuremath{\Lambda}-binding energies of the $x+\ensuremath{\Lambda}$ and $\ensuremath{\alpha}+x+\ensuremath{\Lambda}$ systems ${(}_{\ensuremath{\Lambda}}^{3}\mathrm{H},{}_{\ensuremath{\Lambda}}^{4}\mathrm{H},{}_{\ensuremath{\Lambda}}^{5}\mathrm{He},{}_{\ensuremath{\Lambda}}^{6}\mathrm{He},{}_{\ensuremath{\Lambda}}^{6}\mathrm{Li},{}_{\ensuremath{\Lambda}}^{7}\mathrm{Li},{}_{\ensuremath{\Lambda}}^{8}\mathrm{Li},{}_{\ensuremath{\Lambda}}^{8}\mathrm{Be},{}_{\ensuremath{\Lambda}}^{9}\mathrm{Be}).$ An effective \ensuremath{\Lambda}\ensuremath{\Lambda} interaction is constructed so as to reproduce, within the \ensuremath{\alpha}+\ensuremath{\Lambda}+\ensuremath{\Lambda} model, the ${B}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}$ of ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{6}\mathrm{He},$ which was extracted from the emulsion experiment, the NAGARA event. With no adjustable parameters for the $\ensuremath{\alpha}+x+\ensuremath{\Lambda}+\ensuremath{\Lambda}$ system, ${B}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}$ of ground and bound excited states of the double-\ensuremath{\Lambda} hypernuclei with $A=7--10$ are calculated within the Gaussian-basis coupled-rearrangement-channel method. The Demachi-Yanagi event, identified recently as ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{10}\mathrm{Be},$ is interpreted as an observation of its ${2}^{+}$ excited state on the basis of the present calculation. Structural changes in the $\ensuremath{\alpha}+x$ core nuclei, due to the interaction of the \ensuremath{\Lambda} particles, are found to be substantial, and these play an important role in estimating the \ensuremath{\Lambda}\ensuremath{\Lambda} bond energies of those hypernuclei.
We propose a fully quantum-mechanical method of treating four-body nuclear breakup processes in scattering of a projectile consisting of three constituents, by extending the continuum-discretized coupled-channels method. The three-body continuum states of the projectile are discretized by diagonalizing the internal Hamiltonian of the projectile with the Gaussian basis functions. For $^6$He+$^{12}$C scattering at 18 and 229.8 MeV, the validity of the method is tested by convergence of the elastic and breakup cross sections with respect to increasing the number of the basis functions. Effects of the four-body breakup and the Borromean structure of $^6$He on the elastic and total reaction cross sections are discussed.
Muon catalyzed fusion ($\ensuremath{\mu}\mathrm{CF}$) has recently regained considerable research interest owing to several new developments and applications. In this regard, we have performed a comprehensive study of the most important fusion reaction, namely, ${(dt\ensuremath{\mu})}_{J=v=0}\ensuremath{\rightarrow}\ensuremath{\alpha}+n+\ensuremath{\mu}+17.6\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ or ${(\ensuremath{\alpha}\ensuremath{\mu})}_{nl}+n+17.6\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$. The coupled-channel Schr\"odinger equation for the reaction is thus solved, satisfying the boundary condition for the muonic molecule ${(dt\ensuremath{\mu})}_{J=v=0}$ as the initial state and the outgoing wave in the $\ensuremath{\alpha}n\ensuremath{\mu}$ channel. We employ the $dt\ensuremath{\mu}$- and $\ensuremath{\alpha}n\ensuremath{\mu}$-channel coupled three-body model. All the nuclear interactions, the $d\text{\ensuremath{-}}t$ and $\ensuremath{\alpha}\text{\ensuremath{-}}n$ potentials, and the $dt\text{\ensuremath{-}}\ensuremath{\alpha}n$ channel-coupling nonlocal tensor potential are chosen to reproduce the observed low-energy ($1--300$ keV) astrophysical $S$ factor of the reaction $d+t\ensuremath{\rightarrow}\ensuremath{\alpha}+n+17.6\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, as well as the total cross section of the $\ensuremath{\alpha}+n$ reaction at the corresponding energies. The resultant $dt\ensuremath{\mu}$ fusion rate is $1.15\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Substituting the obtained total wave function into the $T$ matrix based on the Lippmann-Schwinger equation, we have calculated absolute values of the fusion rates ${\ensuremath{\lambda}}_{\mathrm{f}}^{\mathrm{bound}}$ and ${\ensuremath{\lambda}}_{\mathrm{f}}^{\mathrm{cont}.}$ going to the bound and continuum states of the outgoing $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\mu}$ pair, respectively. We then derived the initial $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\mu}$ sticking probability ${\ensuremath{\omega}}_{S}^{0}={\ensuremath{\lambda}}_{\mathrm{f}}^{\mathrm{bound}}/({\ensuremath{\lambda}}_{\mathrm{f}}^{\mathrm{bound}}+{\ensuremath{\lambda}}_{\mathrm{f}}^{\mathrm{cont}.})=0.857%$, which is $\ensuremath{\approx}7%$ smaller than the literature values $(\ensuremath{\approx}0.91%--0.93%)$ and can explain the recent observations (2001) at high D-T densities. We have much improved the sticking-probability calculation by employing the $D$-wave $\ensuremath{\alpha}\text{\ensuremath{-}}n$ outgoing channel with the nonlocal tensor-force $dt\text{\ensuremath{-}}\ensuremath{\alpha}n$ coupling and by deriving ${\ensuremath{\omega}}_{S}^{0}$ based on the absolute values of the ${\ensuremath{\lambda}}_{\mathrm{f}}^{\mathrm{bound}}$ and ${\ensuremath{\lambda}}_{\mathrm{f}}^{\mathrm{cont}.}$. We also calculate the absolute values for the momentum and energy spectra of the muon emitted during the fusion process. The most important result is that the peak energy is 1.1 keV although the mean energy is 9.5 keV owing to the long higher-energy tail. This is an essential result for the ongoing experimental project to realize the generation of an ultraslow negative muon beam by utilizing the $\ensuremath{\mu}\mathrm{CF}$ for various applications, e.g., a scanning negative muon microscope and an injection source for the muon collider.
Formalism of coupled-channels variational method is sketched and then applied to the analysis of 16O(d, d)16O, 16O(d, p)17O(1s, 3.27 MeV) and 17O(1s)(p, p)17O(1s) reactions at 11 ∼60 MeV. It is found that the effect of coupling of the proton channel is significant at 11 MeV, but decreases rapidly as energy increases, and may be neglected at ≳ 40 MeV. The effect of the coupling of deuteron breakup channels tends to decrease as energy increases, but more slowly than the proton channel coupling. It is still non-negligible at 60 MeV.
