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Register a new userCoulomb screening correction to the $Q$ value of the triple alpha process in thermal plasmas
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The triple alpha reaction is a key to $^{12}$C production and is expected to occur in weakly-coupled, thermal plasmas as encountered in normal stars. We investigate how Coulomb screening affects the structure of a system of three alpha particles in such a plasma environment by precise three-body calculations within the Debye-Huckel approximation. A three-alpha model that has the Coulomb interaction modified in the Yukawa form is employed. Precise three-body wave functions are obtained by a superposition of correlated Gaussian bases with the aid of the stochastic variational method. The energy shifts of the Hoyle state due to the Coulomb screening are obtained as a function of the Debye screening length. The results, which automatically incorporate the finite size effect of the Hoyle state, are consistent with the conventional result based on the Coulomb correction to the chemical potentials of ions that are regarded as point charges in a weakly-coupled, thermal plasma. We have given a theoretical basis to the conventional point-charge approach to the Coulomb screening problem relevant for nuclear reactions in normal stars by providing the first evaluation of the Coulomb corrections to the $Q$ value of the triple alpha process that produces a finite size Hoyle state.
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The first excited $J^pi=0^+$ state of $^{12}$C, the so-called Hoyle state, plays an essential role in a triple-$alpha$ ($^4$He) reaction, which is a main contributor to the synthesis of $^{12}$C in a burning star. We investigate the Coulomb screening effects on the energy shift of the Hoyle state in a thermal plasma environment using precise three-$alpha$ model calculations. The Coulomb screening effect between $alpha$ clusters are taken into account within the Debye-Huckel approximation. To generalize our study, we utilize two standard $alpha$-cluster models, which treat the Pauli principle between the $alpha$ particles differently. We find that the energy shifts do not depend on these models and follow a simple estimation in the zero-size limit of the Hoyle state when the Coulomb screening length is as large as a value typical of such a plasma consisting of electrons and $alpha$ particles.
The triple-alpha process, whereby evolved stars create carbon and oxygen, is believed to be fine-tuned to a high degree. Such fine-tuning is suggested by the unusually strong temperature dependence of the triple-alpha reaction rate at stellar temperatures. This sensitivity is due to the resonant character of the triple-alpha process, which proceeds through the so-called Hoyle state of $^{12}$C with spin-parity $0^+$. The question of fine-tuning can be studied within the {it ab initio} framework of nuclear lattice effective field theory, which makes it possible to relate {it ad hoc} changes in the energy of the Hoyle state to changes in the fundamental parameters of the nuclear Hamiltonian, which are the light quark mass $m_q$ and the electromagnetic fine-structure constant. Here, we update the effective field theory calculation of the sensitivity of the triple-alpha process to small changes in the fundamental parameters. In particular, we consider recent high-precision lattice QCD calculations of the nucleon axial coupling $g_A$, as well as new and more comprehensive results from stellar simulations of the production of carbon and oxygen. While the updated stellar simulations allow for much larger {it ad hoc} shifts in the Hoyle state energy than previously thought, recent lattice QCD results for the nucleon S-wave singlet and triplet scattering lengths now disfavor the scenario of no fine-tuning in the light quark mass $m_q$.
The Coulomb correction (difference from the 1st Born approximation) to the Moli`{e}re screening angle in multiple Coulomb scattering theory is evaluated with the allowance for inelastic contribution. The controversy between dominance of close- or remote-collision contributions to Coulomb correction is discussed. For scattering centres represented by a Coulomb potential with a generic (not necessarily spherically symmetric) creening function, the Coulomb correction is proven to be screening-independent, by virtue of the eikonal phase cancellation in regions distant from the Coulomb singularity. Treating the atom %more self-consistently, as an assembly of pointlike electrons and the nucleus, and summing the scattering probability over all the final atom states, it is shown that besides the Coulomb correction due to close encounters of the incident charged particle with atomic nuclei, there are similar corrections due to close encounters with atomic electrons (an analog of Bloch correction). For low $Z eq1$ the latter contribution can reach $sim 25%$, but its observation is partly obscured by multiple scattering effects.
The correction to the Coulomb energy due to virtual production of $e^+e^-$ pairs, which is on the order of one percent of the Coulomb energy at nuclear scales is discussed. The effects of including a pair-production term in the semi-empirical mass formula and the correction to the Coulomb barrier for a handful of nuclear collisions using the Bass and Coulomb potentials are studied. With an eye toward future work using Constrained Molecular Dynamics (CoMD) model, we also calculate the correction to the Coulomb energy and force between protons after folding with a Gaussian spatial distribution.
The $gamma$ process in supernova explosions is thought to explain the origin of proton-rich isotopes between Se and Hg, the so-called $p$ nuclei. The majority of the reaction rates for $gamma$ process reaction network studies has to be predicted in Hauser-Feshbach statistical model calculations using global optical potential parameterizations. While the nucleon+nucleus optical potential is fairly known, for the $alpha$+nucleus optical potential several different parameterizations exist and large deviations are found between the predictions calculated using different parameter sets. By the measurement of elastic $alpha$-scattering angular distributions at energies around the Coulomb barrier a comprehensive test for the different global $alpha$+nucleus optical potential parameter sets is provided. Between 20$^{circ}$ and 175$^{circ}$ complete elastic alpha scattering angular distributions were measured on the $^{113}$In textit{p} nucleus with high precision at E$_{c.m.}$ = 15.59 and 18.82 MeV. The elastic scattering cross sections of the $^{113}$In($alpha$,$alpha$)$^{113}$In reaction were measured for the first time at energies close to the astrophysically relevant energy region. The high precision experimental data were used to evaluate the predictions of the recent global and regional $alpha$+nucleus optical potentials. Parameters for a local $alpha$+nucleus optical potential were derived from the measured angular distributions. Predictions for the reaction cross sections of $^{113}$In($alpha,gamma$)$^{117}$Sb and $^{113}$In($alpha$,n)$^{116}$Sb at astrophysically relevant energies were given using the global and local optical potential parameterizations.
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