Renormalization group analysis of nuclear current operators

A Wilsonian renormalization group (WRG) equation for nuclear current operators in two-nucleon systems is derived. Nuclear current operators relevant to low-energy Gamow-Teller transitions are analyzed using the WRG equation. We employ the axial two-body current operators from phenomenological models and heavy-baryon chiral perturbation theory, which are quite different from one another in describing small scale physics. After reducing the model space of the operators using the WRG equation, we find that there still remains a significant model dependence at \Lambda = 200 MeV, where \Lambda is the sharp cutoff specifying the size of the model space. A model independent effective current operator is found at a rather small cutoff value, \Lambda = 70 MeV. By simulating the effective current operator at \Lambda=70 MeV, we obtain a current operator based on a pionless theory, thereby arguing an equivalence relation between nuclear current operators of phenomenological models and those of effective field theories.Comment: 26 pages, 11 figure

Radiative decay of the sub-threshold 11−1_1^- and 21+2_1^+ states of 16^{16}O in cluster effective field theory

Radiative decay of the sub-threshold $1_1^-$ and $2_1^+$ states of $^{16}$O is studied in cluster effective field theory. The wave function normalization factors for initial and final states of the radiative decay amplitudes are deduced by using the phase shift data of elastic $\alpha$-$^{12}$C scattering for $l=0,1,2$, which are related to the asymptotic normalization coefficients of $0_1^+$, $1_1^-$, $2_1^+$ states of $^{16}$O for the two-body $\alpha$-$^{12}$C channel; then only one unfixed parameter remains in each of the radiative decay amplitudes. We fit the parameters to the experimental radiative decay rates and apply the fitted parameters to the study of radiative $\alpha$ capture on $^{12}$C, $^{12}$C($\alpha$,$\gamma$)$^{16}$O. The order of magnitude of astrophysical $S$ factors of $E1$ and $E2$ transitions of $^{12}$C($\alpha$,$\gamma$)$^{16}$O is reproduced compared to the experimental data, and we discuss an improvement in the calculation of $S$ factors of $^{12}$C($\alpha$,$\gamma$)$^{16}$O.Comment: 22 pages, 6 figure