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Register a new userSecondary $gamma$-ray decays from the partial-wave $T$ matrix with an $R$-matrix application to ${}^{15}{rm N}(p,alpha_1gamma){}^{12}{rm C}$
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The secondary $gamma$ rays emitted following a nuclear reaction are often relatively straightforward to detect experimentally. Despite the large volume of such data, a practical formalism for describing these $gamma$ rays in terms of partial-wave $T$-matrix elements has never been given. The partial-wave formalism is applicable when $R$-matrix methods are used to describe the reaction in question. This paper supplies the needed framework, and it is demonstrated by the application to the ${}^{15}{rm N}(p,alpha_1gamma){}^{12}{rm C}$ reaction.
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The $^{15}{rm N}(p,gamma)^{16}{rm O}$ reaction provides a path from the CN cycle to the CNO bi-cycle and CNO tri-cycle. The measured astrophysical factor for this reaction is dominated by resonant capture through two strong $J^{pi}=1^{-}$ resonances at $E_{R}= 312$ and 962 keV and direct capture to the ground state. Recently, a new measurement of the astrophysical factor for the $^{15}{rm N}(p,gamma)^{16}{rm O}$ reaction has been published [P. J. LeBlanc {it et al.}, Phys. Rev. {bf C 82}, 055804 (2010)]. The analysis has been done using the $R$-matrix approach with unconstrained variation of all parameters including the asymptotic normalization coefficient (ANC). The best fit has been obtained for the square of the ANC $C^{2}= 539.2$ fm${}^{-1}$, which exceeds the previously measured value by a factor of $approx 3$. Here we present a new $R$-matrix analysis of the Notre Dame-LUNA data with the fixed within the experimental uncertainties square of the ANC $C^{2}=200.34$ fm${}^{-1}$. Rather than varying the ANC we add the contribution from a background resonance that effectively takes into account contributions from higher levels. Altogether we present 8 fits, five unconstrained and three constrained. In all the fits the ANC is fixed at the previously determined experimental value $C^{2}=200.34$ fm${}^{-1}$. For the unconstrained fit with the boundary condition $B_{c}=S_{c}(E_{2})$, where $E_{2}$ is the energy of the second level, we get $S(0)=39.0 pm 1.1 $ keVb and normalized ${tilde chi}^{2}=1.84$, i.e. the result which is similar to [P. J. LeBlanc {it et al.}, Phys. Rev. {bf C 82}, 055804 (2010)]. From all our fits we get the range $33.1 leq S(0) leq 40.1$ keVb which overlaps with the result of [P. J. LeBlanc {it et al.}, Phys. Rev. {bf C 82}, 055804 (2010)]. We address also physical interpretation of the fitting parameters.
We review some aspects of R-matrix theory and its application to the semi-empirical analysis of nuclear reactions. Important applications for nuclear astrophysics and recent results for the ${}^{12}{rm C}(alpha,gamma){}^{16}{rm O}$ reaction are emphasized.
We investigate structure of $^{13}_Lambda{rm C}$ and discuss the difference and similarity between the structures of $^{12}{rm C}$ and $^{13}_Lambda{rm C}$ by answering the questions if the linear-chain and gaslike cluster states, which are proposed to appear in $^{12}{rm C}$, survives, or new structure states appear or not. We introduce a microscopic cluster model called, Hyper-Tohsaki-Horiuchi-Schuck-Ropke (H-THSR) wave function, which is an extended version of the THSR wave function so as to describe $Lambda$ hypernuclei. We obtained two bound states and two resonance (quasi-bound) states for $J^pi=0^+$ in $^{13}_Lambda{rm C}$, corresponding to the four $0^+$ states in $^{12}{rm C}$. However, the inversion of level ordering between the spectra of $^{12}{rm C}$ and $^{13}_Lambda{rm C}$, i.e. that the $0_3^+$ and $0_4^+$ states in $^{13}_Lambda{rm C}$ correspond to the $0_4^+$ and $0_3^+$ states in $^{12}{rm C}$, respectively, is shown to occur. The additional $Lambda$ particle reduces sizes of the $0_2^+$ and $0_3^+$ states in $^{13}_Lambda{rm C}$ very much, but the shrinkage of the $0_4^+$ state is only a half of the other states. In conclusion, the Hoyle state becomes quite a compact object with ${^{9}_Lambda{rm Be}}+alpha$ configuration in $^{13}_Lambda{rm C}$ and is no more gaslike state composed of the $3alpha$ clusters. Instead, the $0_4^+$ state in $^{13}_Lambda{rm C}$, coming from the $^{12}{rm C}(0_3^+)$ state, appears as a gaslike state composed of $alpha+alpha+^{5}_Lambda{rm He}$ configuration, i.e. the Hoyle analog state. A linear-chain state in a $Lambda$ hypernucleus is for the first time predicted to exist as the $0_3^+$ state in $^{13}_Lambda{rm C}$ with more shrunk arrangement of the $3alpha$ clusters along $z$-axis than the $3alpha$ linear-chain configuration realized in the $^{12}{rm C}(0_4^+)$ state.
We used a high-resolution magnetic spectrograph to study neutron pair-correlated $0^+$ states in $^{136}$Ba, produced via the $^{138}{rm Ba}(p,t)$ reaction. In conjunction with state-of-the-art shell model calculations, these data benchmark part of the dominant Gamow-Teller component of the nuclear matrix element (NME) for $^{136}$Xe neutrinoless double beta ($0 ubetabeta$) decay. We demonstrate for the first time an evaluation of part of a $0 ubetabeta$ decay NME by use of an experimental observable, presenting a new avenue of approach for more accurate calculations of $0 ubetabeta$ decay matrix elements.
R-matrix theory was originally developed to describe nuclear reactions. The framework was further extended to describe {beta} decay to unbound states. However, at the time writing, no clear description of {gamma} decays to unbound states exist. Such a description will be presented in this note.
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