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Register a new userComponents of an algebraic solution of the multichannel problem of low-energy n-${}^{12}$C scattering plus sub-threshold (${}^{13}$C) states
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The effects of components in an assumed model interaction potential, as well as of the order to which its deformation is taken, upon resonances in the low-energy cross sections and upon sub-threshold bound states of the compound nucleus (${}^{13}$C) are discussed.
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We use an underground counting lab with an extremely low background to perform an activity measurement for the $^{12}$C+$^{13}$C system with energies down to $Erm_{c.m.}$=2.323 MeV, at which the $^{12}$C($^{13}$C,$p$)$^{24}$Na cross section is found to be 0.22(7) nb. The $^{12}$C+$^{13}$C fusion cross section is derived with a statistical model calibrated using experimental data. Our new result of the $^{12}$C+$^{13}$C fusion cross section is the first decisive evidence in the carbon isotope systems which rules out the existence of the astrophysical S-factor maximum predicted by the phenomenological hindrance model, while confirming the rising trend of the S-factor towards lower energies predicted by other models, such as CC-M3Y+Rep, DC-TDHF, KNS, SPP and ESW. After normalizing the model predictions with our data, a more reliable upper limit is established for the $^{12}$C+$^{12}$C fusion cross sections at stellar energies.
The neutron yield in $^{12}$C(d,n)$^{13}$N and the proton yield in $^{12}C(d,p)^{13}$C have been measured by deuteron beam from 0.6 MeV to 3 MeV which is delivered from a 4-MeV electro static accelerator bombarding on the thick carbon target. The neutrons are detected at $0degree$, $24degree$, $48degree$ and the protons at $135degree$ in the lab frame. The ratios of the neutron yield to the proton one have been calculated and can be used as an effective probe to pin down the resonances. The resonances are found at 1.4 MeV, 1.7 MeV, 2.5 MeV in $^{12}C(d,p)^{13}$C and at 1.6 MeV, 2.7 MeV in $^{12}$C(d,n)$^{13}$N. This method provides a way to reduce the systematic uncertainty and helps to confirm more resonances in compound nuclei.
A multi-channel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. Positive (scattering) and negative (sub-threshold) solutions can be found to predict both the compound nucleus sub-threshold spectrum and all resonances due to coupled channel effects that occur on a smooth energy varying background.
The $^{12}$C(n, 2n)$^{11}$C cross section was measured from just below threshold to 26.5 MeV using the Pelletron accelerator at Ohio University. Monoenergetic neutrons, produced via the $^3$H(d,n)$^4$He reaction, were allowed to strike targets of polyethylene and graphite. Activation of both targets was measured by counting positron annihilations resulting from the $beta^+$ decay of $^{11}$C. Annihilation gamma rays were detected, both in coincidence and singly, using back-to-back NaI detectors. The incident neutron flux was determined indirectly via $^{1}$H(n,p) protons elastically scattered from the polyethylene target. Previous measurements fall into upper and lower bands, the results of the present measurement are consistent with the upper band.
Lowest energy spectrum of the $^{12}$C nucleus is analyzed in the 3$alpha$ cluster model with a deep $alphaalpha$-potential of Buck, Friedrich and Wheatley with Pauli forbidden states in the $S$ and $D$ waves. The direct orthogonalization method is applied for the elimination of the 3$alpha$-Pauli forbidden states. The effects of possible first order quantum phase transition are shown in the lowest $^{12}$C($0_1^+)$ and $^{12}$C($2_1^+)$ states from weakly bound phase to a deep phase. The ground and lowest $2^+$ states of the $^{12}$C nucleus in the deep phase are created by the critical eigen states of the Pauli projector for the $0^+$ and $2^+$ three-alpha functional spaces, respectively.
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