Progress in Nuclear Physics Vol. 5. Edited by Prof. O. R. Frisch. (Progress Series.) Pp. vii + 325. (London and New York: Pergamon Press, Ltd., 1956.) 80s. net; 12.50 dollars.

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Advances in Nuclear Physics

Precision big bang nucleosynthesis with improved Helium-4 predictions

We assess the status of big-bang nucleosynthesis (BBN) in light of the final Planck data release and other recent developments, and in anticipation of future measurements. Planck data fix the cosmic baryon density to 0.9% precision, and determine the helium abundance and effective number of neutrinos with precision approaching that of astronomical and BBN determinations respectively. In addition, new high-redshift measurements give D/H to better precision than theoretical predictions, and new Li/H data reconfirm the lithium problem. We present new ${}^{7}{\rm Be}(n,p){}^{7}{\rm Li}$ rates using new neutron capture measurements; we have also examined the effect of proposed changes in the $d(p,\gamma){}^{3}{\rm He}$ rates. Using these results we perform a series of likelihood analyses. We assess BBN/CMB consistency, with attention to how our results depend on the choice of Planck data, as well as how the results depend on the choice of non-BBN, non-Planck data sets. Most importantly the lithium problem remains, and indeed is more acute given the very tight D/H observational constraints; new neutron capture data reveals systematics that somewhat increases uncertainty and thus slightly reduces but does not essentially change the problem. We confirm that $d(p,\gamma){}^{3}{\rm He}$ theoretical rates brings D/H out of agreement and slightly increases 7Li; new experimental data are needed at BBN energies. Setting the lithium problem aside, we find the effective number of neutrino species at BBN is $N_\nu = 2.86 \pm 0.15$. Future CMB Stage-4 measurements promise substantial improvements in BBN parameters: helium abundance determinations will be competitive with the best astronomical determinations, and $N_{\rm eff}$ will approach sensitivities capable of detecting the effects of Standard Model neutrino heating of the primordial plasma. (Abridged)

Big-Bang Nucleosynthesis after Planck

Big-Bang Nucleosynthesis After Planck

Frontiers in nuclear astrophysics

During the Big Bang, ${}^{6}{\rm Li}$ was synthesized via the ${}^{2}{\rm H}(\alpha,\gamma){}^{6}{\rm Li}$ reaction. After almost 25 years of the failed attempts to measure the ${}^{2}{\rm H}(\alpha,\gamma){}^{6}{\rm Li}$ reaction in the lab at the Big Bang energies, just recently the LUNA collaboration presented the first successful measurements at two different Big Bang energies [M. Anders {\it et al.}, Phys. Rev. Lett. {\bf 113}, 042501 (2014)]. In this paper we will discuss how to improve the accuracy of the direct experiment. To this end the photon's angular distribution is calculated in the potential model. It contains contributions from electric dipole and quadrupole transitions and their interference, which dramatically changes the photon's angular distribution. The calculated distributions at different Big Bang energies have a single peak at $\sim 50^{\circ}$. These calculations provide the best kinematic conditions to measure the ${}^{2}{\rm H}(\alpha,\gamma){}^{6}{\rm Li}$ reaction. The expressions for the total cross section and astrophysical factor are also derived by integrating the differential cross section over the photon's solid angle. The LUNA data are in excellent agreement with our calculations using a potential approach combined with a well established asymptotic normalization coefficient for ${}^{6}{\rm Li} \to \alpha +d$. Comparisons of the available experimental data for the $S_{24}$ astrophysical factor and different calculations are presented. The Big Bang lithium isotopic ratio ${}^{6}{\rm Li}/^{7}{\rm Li} = (1.5 \pm 0.3)\times 10^{-5}$ following from the LUNA data and the present analysis are discussed in the context of the disagreement between the observational data and the standard Big Bang model, which constitutes the second Lithium problem.

Primordial ${\alpha} + d \to {}^{6}{\rm Li} + \gamma$ reaction and second Lithium puzzle

In this paper we discuss the $R$-matrix approach to treat the subthreshold resonances for the single-level and one-channel and for the single-level and two-channel cases In particular, the expression relating the asymptotic normalization coefficient (ANC) with the observable reduced width, when the subthreshold bound state is the only channel or coupled with an open channel, which is a resonance, is formulated Since the ANC plays a very important role in nuclear astrophysics, these relations significantly enhance the power of the derived equations We present the relationship between the resonance width and the ANC for the general case and consider two limiting cases: wide and narrow resonances Different equations for the astrophysical $S$ factors in the $R$-matrix approach are presented After that we discuss the Trojan horse method (THM) formalism The developed equations are obtained using the surface-integral formalism and the generalized $R$-matrix approach for the three-body resonant reactions It is shown how the Trojan horse (TH) double-differential cross section can be expressed in terms of the on-the-energy-shell astrophysical $S$ factor for the binary subreaction Finally, we demonstrate how the THM can be used to calculate the astrophysical $S$ factor for the neutron generator $^{13}\mathrm{C}(\ensuremath{\alpha},\phantom{\rule{016em}{0ex}}n)^{16}\mathrm{O}$ in low-mass AGB stars At astrophysically relevant energies this astrophysical $S$ factor is controlled by the threshold level $1/{2}^{+},{E}_{x}=6356$ keV Here, we reanalyzed recent TH data taking into account more accurately the three-body effects and using both assumptions that the threshold level is a subthreshold bound state or it is a resonance state

Subthreshold resonances and resonances in the R -matrix method for binary reactions and in the Trojan horse method

We calculate the radiative capture cross section for 7Be(?, ?)11C and its reaction rate of relevance for the Big Bang nucleosynthesis (BBN). The impact of this reaction on the primordial 7Li abundance is revised including narrow and broad resonances in the pertinent energy region. Our calculations show that it is unlikely that very low energy resonances in 11C of relevance for the BBN would emerge within a two-body potential model. Based on our results and a comparison with previous theoretical and experimental analyses, we conclude that the impact of this reaction on the so-called "cosmological lithium puzzle" is completely irrelevant.

Impact of the 7Be(α, γ)11C Reaction on the Primordial Abundance of 7Li

We calculate the radiative capture cross section for $^7$Be($\alpha, \gamma$)$^{11}$C and its reaction rate of relevance for the big bang nucleosynthesis. The impact of this reaction on the primordial $^7$Li abundance is revised including narrow and broad resonances in the pertinent energy region. Our calculations show that it is unlikely that very low energy resonances in $^{11}$C of relevance for the big bang nucleosynthesis would emerge within a two-body potential model. Based on our results and a comparison with previous theoretical and experimental analyses, we conclude that the impact of this reaction on the so-called "cosmological lithium puzzle" is completely irrelevant.

Impact of the $^7$Be($\alpha, \gamma$)$^{11}$C reaction on the primordial abundance of $^7$Li

We apply the $R$-matrix method in distorted wave Born approximation (DWBA) calculations. The internal wave functions are expanded over a Lagrange mesh, which provides an efficient and fast technique to compute matrix elements. We first present an outline of the theory, by emphasizing the $R$-matrix aspects. The model is applied to the $^{16}\mathrm{O}(d,p)^{17}\mathrm{O}$ and $^{12}\mathrm{C}{(}^{7}\mathrm{Li},t)^{16}\mathrm{O}$ reactions, typical of nucleon and of $\ensuremath{\alpha}$ transfer, respectively. We illustrate the sensitivity of the cross sections with respect to the $R$-matrix parameters and show that an excellent convergence can be achieved with relatively small bases. We also discuss the effects of the remnant term in DWBA calculations and address the question of the peripherality in transfer reactions. We suggest that uncertainties on spectroscopic factors could be underestimated in the literature.

Shubhchintak

Papers

Primordial ${\alpha} + d \to {}^{6}{\rm Li} + \gamma$ reaction and second Lithium puzzle

Subthreshold resonances and resonances in the R -matrix method for binary reactions and in the Trojan horse method

Impact of the 7Be(α, γ)11C Reaction on the Primordial Abundance of 7Li

Impact of the $^7$Be($\alpha, \gamma$)$^{11}$C reaction on the primordial abundance of $^7$Li

Transfer reactions with the Lagrange-mesh method