Theoretical estimations for the astrophysical S-factor and the d(alpha,gamma)6Li reaction rates are obtained on the base of the two-body model with the alpha-d potential of a simple Gaussian form, which describes correctly the phase-shifts in the S-,
P-, and D-waves, the binding energy and the asymptotic normalization constant in the final S-state. Wave functions of the bound and continuum states are calculated by using the Numerov algorithm of a high accuracy. A good convergence of the results for the E1- and E2- components of the transition is shown when increasing the upper limit of effective integrals up to 40 fm. The obtained results for the S-factor and reaction rates in the temperature interval 10E+6 K < T < 10E+10 K are in a good agreement with the results of Ref. A.M. Mukhamedzhanov, et.al., Phys. Rev., C 83, 055805 (2011), where the authors used the known asymptotical form of wave function at low energies and a complicated potential at higher energies.
A possibility of the construction of a periodic table for the excited baryon spectrum is shown in the frame of a relativistic chiral quark model based on selection rules derived from the one-pion exchange mechanism. It is shown that all the $N^*$ and
$Delta^*$ resonances appearing in the $pi N$ scattering data and strongly coupling to the $pi N$ channel are identified with the orbital configurations $(1S_{1/2})^2(nlj)$. Baryon resonances corresponding to the orbital configuration with two valence quarks in excited states couple strongly to the $pi pi N$-channel, but not to the $pi N$ channel. At low energy scale up to 2000 MeV, the obtained numerical estimations for the SU(2) baryon states (up to and including F-wave $N^*$ and $Delta^*$ resonances) within the schematic periodic table are mostly consistent with the experimental data. It is argued that due-to the overestimation of the ground state N(939) and Roper resonance N(1440) almost by the same amount and that the Roper resonance is a radial excitation of the N(939), the lowering mechanism for the both baryon states must be the same. The same mechanism is expected in the $Delta$ sector. At higher energies, where the experimental data are poor, we can extend our model schematically and predict seven new $N^*$ and four $Delta^*$ resonances with larger spin values.
Some one-neutron halo nuclei can emit a proton in a beta decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core+neutron bound state and final core+proton scatter
ing states. The decay probability per second is evaluated for the $^{11}$Be, $^{19}$C and $^{31}$Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.
A convergence of the valence quark self-energies in the 1S, 2S, $1P_{1/2}$, $1P_{3/2}$ orbits induced by pion and gluon field configurations, is shown in the frame of a relativistic chiral quark model. It is shown that in order to reach a convergence
, one needs to include contribution of the intermediate quark and anti-quark states with the total momentum up to $j=25/2$. It is argued that a restriction to the lowest mode when estimating the self-energy is not good approximation.
Spectrum of the Pauli projector of a quantum many-body system is studied. It is proven that the kern of the complete many-body projector is identical to the kern of the sum of two-body projectors. Since the kern of the many-body Pauli projector defin
es an allowed subspace of the complete Hilbert space, it is argued that a truncation of the many-body model space following the two-body Pauli projectors is a natural way when solving the Schr{o}dinger equation for the many-body system. These relations clarify a role of the many-body Pauli forces in a multicluster system.
The lower excitation spectrum of the nucleon and $Delta$ is calculated in a relativistic chiral quark model. Corrections to the baryon mass spectrum from the second order self-energy and exchange diagrams induced by pion and gluon fields are estimate
d in the field -theoretical framework. Convergent results for the self-energy terms are obtained when including the intermediate quark and antiquark states with a total momentum up to $j=25/2$. Relativistic one-meson and color-magnetic one-gluon exchange forces are shown to generate spin 0, 1, 2, etc. operators, which couple the lower and the upper components of the two interacting valence quarks and yield reasonable matrix elements for the lower excitation spectrum of the Nucleon and Delta. The only contribution to the ground state nucleon and $Delta$ comes from the spin 1 operators, which correspond to the exchanged pion or gluon in the l=1 orbit, thus indicating, that the both pion exchange and color-magnetic gluon exchange forces can contribute to the spin of baryons. Is is shown also that the contribution of the color-electric component of the gluon fields to the baryon spectrum is enormously large (more than 500 MeV with a value $alpha_s=0.65$) and one needs to restrict to very small values of the strong coupling constant or to exclude completely the gluon-loop corrections to the baryon spectrum. With this restriction, the calculated spectrum reproduces the main properties of the data, however needs further contribution from the two-pion exchange and instanton induced exchange (for the nucleon sector) forces in consistence with the realistic NN-interaction models.
M1 transitions from the $^6$Li($0^+;T=1$) state at 3.563 MeV to the $^6$Li($1^+$) ground state and to the $alpha+d$ continuum are studied in a three-body model. The bound states are described as an $alpha+n+p$ system in hyperspherical coordinates on
a Lagrange mesh. The ground-state magnetic moment and the gamma width of the $^6$Li(0$^+$) resonance are well reproduced. The halo-like structure of the $^6$Li$(0^+)$ resonance is confirmed and is probed by the M1 transition probability to the $alpha+d$ continuum. The spectrum is sensitive to the description of the $alpha+d$ phase shifts. The corresponding gamma width is around 1.0 meV, with optimal potentials. Charge symmetry is analyzed through a comparison with the $beta$-delayed deuteron spectrum of $^6$He. In $^6$He, a nearly perfect cancellation effect between short-range and halo contributions was found. A similar analysis for the $^6$Li($0^+;T=1$) $gamma$ decay is performed; it shows that charge-symmetry breaking at large distances, due to the different binding energies and to different charges, reduces this effect. The present branching ratio $Gamma_{gamma}(0^+to alpha+d)/Gamma_{gamma}(0^+to1^+)approx 1.3times 10^{-4}$ should be observable with current experimental facilities.
