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Register a new userIsospin Properties of ($K^-$, $N$) Reactions for the Formation of Deeply-bound Antikaonic Nuclei
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The formation of deeply-bound antikaonic $K^-/bar{K}^0$ nuclear states by nuclear ($K^-$, $N$) reactions is investigated theoretically within a distorted-wave impulse approximation (DWIA), considering the isospin properties of the Fermi-averaged $K^-+ N to N + bar{K}$ elementary amplitudes. We calculate the formation cross sections of the deeply-bound $bar{K}$ states by the ($K^-$, $N$) reactions on the nuclear targets, $^{12}$C and $^{28}$Si, at incident $K^-$ lab momentum $p_{K^-}$ = 1.0 GeV/c and $theta_{rm lab} = 0^{circ}$, introducing a complex effective nucleon number $N_{rm eff}$ for unstable bound states in the DWIA. The results show that the deeply-bound $bar{K}$ states can be populated dominantly by the ($K^-$, $n$) reaction via the total isoscalar $Delta T=0$ transition owing to the isospin nature of the $K^-+ N to N + bar{K}$ amplitudes, and that the cross sections described by ${rm Re}N_{rm eff}$ and ${rm Arg}N_{rm eff}$ enable to deduce the structure of the $bar{K}$ nuclear states; the calculated inclusive nucleon spectra for a deep $bar{K}$-nucleus potential do not show distinct peak structure in the bound region. The few-body $bar{K}otimes [NN]$ and $bar{K}otimes [NNN]$ states formed in ($K^-$, $N$) reactions on $s$-shell nuclear targets, $^3$He, $^3$H and $^4$He, are also discussed.
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The formation of a deeply-bound $K^-pp$ state by the $^3$He(in-flight $K^-$,$n$) reaction is investigated theoretically in the distorted-wave impulse approximation using the Greens function method. The expected inclusive and semi-exclusive spectra at $p_{K^-}$ = 1.0 GeV/c and $theta_n = 0^{circ}$ are calculated for the forthcoming J-PARC E15 experiment. We employ optical potentials between the $K^-$ and ``$pp$ core-nucleus, and demonstrate systematically the dependence of the spectral shape on $V_0$ and $W_0$, which are the real and imaginary parts of the strength for the optical potential, respectively. The necessary condition to observe a distinct peak of the $K^-pp$ bound state with $I=1/2$, $J^pi=0^-$ in the spectrum turns out to be that the value of $V_0$ is deeper than $sim-100$ MeV and $W_0$ shallower than $sim-100$ MeV, of which the strength parameters come up to recent theoretical predictions.
We review recent claims of the existence of deeply bound kaonic states in nuclei. Also we study in details the (K-,p) reaction on C12 with 1 GeV/c momentum kaon beam, based on which a deep kaon nucleus optical potential was claimed in [1]. In our Monte Carlo simulation of this reaction we include not only the quasi-elastic K- p scattering, as in [1], but also K- absorption by one and two nucleons followed by the decay of the hyperon in pi N, which can also produce strength in the region of interest. The final state interactions in terms of multiple scattering of the K-, p and all other primary particles on their way out of the nucleus is also considered. We will show that all these additional mechanisms allow us to explain the observed spectrum with a standard shallow kaon nucleus optical potential obtained in chiral models. [1] T. Kishimoto et al., Prog. Theor. Phys. 118, 181 (2007).
The formation of a deeply-bound $K^- pp$ state with $I=1/2$, $J^pi=0^-$ by the $^3$He(in-flight $K^-$, $n$) reaction is theoretically investigated in a distorted-wave impulse approximation using the Greens function method. The expected inclusive and semi-exclusive spectra at $p_{K^-} = 1.0$ GeV/c and $theta_{rm lab} = 0^{circ}$ are calculated for the forthcoming J-PARC E15 experiment. We demonstrate these spectra with several types of phenomenological $K^-$-``$pp$ optical potentials $U^{rm opt}(E)$ which have an energy-dependent imaginary part multiplied by a phase space suppression factor, fitting to recent theoretical predictions or experimental candidates of the $K^-pp$ bound state. The results show that a cusp-like peak at the $pi Sigma N$ threshold is an unique signal for the $K^-pp$ bound state in the spectrum including the [$K^-pp$] $to$ $Y + N$ decay process from the two-nucleon $K^-$ absorption, as well as a distinct peak of the $K^-pp$ bound state. The shape of the spectrum is explained by a trajectory of a moving pole of the $K^-pp$ bound state in the complex energy plane. The importance of the spectrum with [$K^-pp$] $to$ $Y + N$ from the two-nucleon $K^-$ absorption is emphasized in order to extract clear evidence of the $K^-pp$ bound state.
The isospin breaking effects due to the Coulomb interaction in weakly-bound nuclei are studied using the Gamow Shell Model, a complex-energy configuration interaction approach which simultaneously takes into account many-body correlations between valence nucleons and continuum effects. We investigate the near-threshold behavior of one-nucleon spectroscopic factors and the structure of wave functions along an isomultiplet. Illustrative calculations are carried out for the T=1 isobaric triplet. By using a shell-model Hamiltonian consisting of an isoscalar nuclear interaction and the Coulomb term, we demonstrate that for weakly bound or unbound systems the structure of isobaric analog states varies within the isotriplet and impacts the energy dependence of spectroscopic factors. We discuss the partial dynamical isospin symmetry present in isospin-stretched systems, in spite of the Coulomb interaction that gives rise to large mirror symmetry breaking effects.
Recently, we have applied for the first time the angular momentum and isospin projected nuclear density functional theory to calculate the isospin-symmetry breaking (ISB) corrections to the superallowed beta-decay. With the calculated set of the ISB corrections we found |V_{ud}|=0.97447(23) for the leading element of the Cabibbo-Kobayashi-Maskawa matrix. This is in nice agreement with both the recent result of Towner and Hardy [Phys. Rev. {bf C77}, 025501 (2008)] and the central value deduced from the neutron decay. In this work we extend our calculations of the ISB corrections covering all superallowed transitions A,I^pi=0^+,T=1,T_z rightarrow A,I^pi=0^+,T=1,T_z+1 with T_z =-1,0 and A ranging from 10 to 74.
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