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A. M. Mukhamedzhanov

Publications and source records attributed to A. M. Mukhamedzhanov.

At least 19 recordsLinked to original sources
arXiv2026

Bayesian Smooth-Fit Extrapolation of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ Astrophysical $S$ Factor

A Bayesian analysis of the astrophysical \(S\) factor for the \(^{12}{\rm C}+{}^{12}{\rm C}\) fusion reaction is presented using available low-energy information at carbon--carbon relative energies \(E <3.5~{\rm MeV}\), including direct measurements and recent inverse-kinematics data. The goal of the global Bayesian fit is not to reproduce the local resonance-by-resonance structure of the \(^{12}{\rm C}+{}^{12}{\rm C}\) system, but rather to constrain the smooth global component of \(S^{*}(E)\) using the direct and inverse-kinematics constraints. The resulting posterior \(S^{*}(E)\) lies systematically below the traditional FCZ75 reference normalization over the energy interval considered. For example, at \(E=1.5~{\rm MeV}\) the median posterior value is \(S^{*}(1.5~{\rm MeV})=1.20\times10^{16}~{\rm keV\,b}\), whereas the Fowler--Caughlan--Zimmerman reference value is \(S^{*}_{\rm FCZ75}=3.0\times10^{16}~{\rm keV\,b}\) [W.~A. Fowler, G.~R. Caughlan, and B.~A. Zimmerman, Annu. Rev. Astron. Astrophys. \textbf{13}, 69 (1975)]. Thus, the updated posterior favors a lower smooth low-energy trend and does not support a sharp increase of \(S^{*}(E)\) as the energy decreases. The astrophysical consequence of the analysis is assessed through the thermonuclear reaction rate \(N_A\langleσv\rangle\). The resulting median rate is lower than the CF88 analytic rate [G.~R. Caughlan and W.~A. Fowler, At. Data Nucl. Data Tables \textbf{40}, 283 (1988)] over the temperature interval considered, with \(R_{\rm present}/R_{\rm CF88}\simeq0.33\)--\(0.46\) for \(0.3\leq T_9\leq1.2\). At higher temperatures, where the Gamow window extends above the upper end of the adopted integration interval, the calculated rate should be regarded as a truncated rate rather than a complete stellar rate.

astro-ph.SR↗
arXiv2025

Bayesian Framework for the E1 and E2 Astrophysical Factors at 300 keV from Subthreshold and Ground-State Asymptotic Normalization Coefficients

The $^{12}\mathrm{C}(α,γ)^{16}\mathrm{O}$ reaction governs the carbon-to-oxygen ratio set during helium burning, shaping white-dwarf structure and Type~Ia supernova yields. At the astrophysical energy $E \approx 300~\mathrm{keV}$, the cross section is controlled by the subthreshold $1^{-}$ (7.12~MeV) and $2^{+}$ (6.92~MeV) states, whose contributions depend on their asymptotic normalization coefficients (ANCs) $C_{1}$ and $C_{2}$, respectively. We perform a Bayesian analysis of the $S_{E1}(300~\mathrm{keV})$ and $S_{E2}(300~\mathrm{keV})$ factors using calibrated $R$-matrix mappings and experimental ANC constraints for the $1^{-}$, $2^{+}$, and $0^{+}$ ground state. For $S_{E1}(300~\mathrm{keV})$, flat prior on the $1^{-}$ ANC lead to broad posterior with $68\%$ credible interval spanning $ [71.4,\,93.4]$~keV\,b, while Gaussian priors concentrate weight near the reported ANC values and yield narrower posteriors. For $S_{E2}(300~\mathrm{keV})$, the analysis includes the interference of the radiative transition through the subthreshold resonance with the direct capture to the ground-state, which depends on the ground-state ANC $C_{0}$, giving broad posterior with $68\%$ credible interval spanning $[30.7,\,50.5]$~keV\,b. The Gaussian priors centered near anchor values. The resulting posteriors quantify both correlations and uncertainties: despite incorporating the published ANC constraints, the $68\%$ intervals remain broad, showing that present ANC determinations do not yet reduce the astrophysical uncertainty. Overall, the Bayesian framework provides statistically robust posteriors for $S_{E1}(300~\mathrm{keV})$ and $S_{E2}(300~\mathrm{keV})$, improving the reliability of extrapolations for stellar modeling and nucleosynthesis.

astro-ph.HE↗
arXiv2024

Asymptotic normalization coefficients for $α+ {}^{12}{\rm C}$ synthesis and the $S$-factor for ${}^{12}{\rm C}(α, \,γ){}^{16}{\rm O}$ radiative capture

The $^{12}{\rm C}(α,γ)^{16}$O reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the $^{16}$O nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, 2$^+$) and (7.12 MeV, 1$^-$), that dominate the behavior of the low-energy $S$-factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. Recently, using a model-independent extrapolation method, Blokhintsev {\it et al.} [Eur. Phys. J. A {\bf 59} (2023) 162] determined the ANCs for the $α$-particle removal taking into account three subthreshold states in $^{16}$O. The goal of this paper is to address four main problems elucidating the impact of the subthreshold ANCs on the low-energy $S$-factor. Firstly, we analyse the connection between variations of the subthreshold ANCs and the low-energy $S$-factor, in particular, at the most effective energy of $300$ keV. Secondly, we calculate contributions to the $S(300\,{\rm keV})$-factor from the subthreshold $1^{-}$ and $2^{+}$ resonances, that are controlled by the subthreshold ANCs. We also evaluate the contribution of the uncertainties of the subthreshold ANCs to the budget of the low-energy $S$-factor uncertainty, especially, the $S(300\,{\rm keV})$-factor. Thirdly, we analyse interference of the subthreshold resonances (SRs) with higher resonances and with the $E1$ and $E2$ direct captures to the ground state. Finally, we investigate a correlated effect of the subthreshold and ground-state ANCs on the low-energy $S$-factor and, in particular, on the $S(300\,{\rm keV})$-factor.

nucl-th↗
arXiv2023

Proton 0.01 MeV resonance width and low-energy $S$-factor of p+10B fusion

{\bf{Purpose}:} In this paper, the proton resonance width of the near-threshold resonance is calculated using two different approaches. The values of the proton width are used to calculate the low-energy $S$-factor. \\ {\bf{Method:}} First, the proton resonance width is estimated using the mirror symmetry of the resonance $ {}^{11}{\rm C}(E_{x}=8.70\, {\rm MeV};\,\frac{5}{2}^{+})$ and the mirror bound state ${}^{11}{\rm B}(E_{x}=9.272\, {\rm MeV};\,\frac{5}{2}^{+})$. In the second approach, this width is estimated using the $R$-matrix definition of the observable resonance width, which is expressed in terms of the $p-{}^{10}{\rm B}$ resonant wave function calculated in the potential approach and the spectroscopic factor. \\ {\bf{Results}:} Depending on the method chosen, the calculated proton resonance width varies from $\,1.03 \times 10^{-19}\,$MeV to $\,2.96 \times 10^{-19}\,$MeV. The role of the near-threshold resonance is determined using fitting of two low-energy $S$-factors from direct measurements [C. Angulo {\it et al.}, Z. Phys. A {\bf 345}, 333 (1993)] and from the indirect Trojan horse method (THM) [ A. Cvetinović {\it et al.}, Phys. Rev. C {\bf 97}, 065801 (2018)]. Within the framework of the $R$-matrix method using the determined proton resonance widths and the modified THM parameters for six low-lying resonances, the low-energy $S$-factors were calculated and compared with the corresponding experimental $S$-factors. The closest agreement with the data is achieved with the proton resonance widths $1.0 \times 10^{-19}$ MeV when fitting the $S$-factor from the THM indirect measurements, and $\,1.68 \times 10^{-19}\,$ MeV and $\,2.5 \times 10^{-19}\,$ MeV when fitting the $S$-factor from [Angulo {\it et al}, Z. Phys. A {\bf 345}, 333 (1993)].\

nucl-th↗
arXiv2023

Asymptotic normalization coefficients of alpha-particle removal from $^{16}$O($3^-,2^+,1^-$)

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In a recent paper [Blokhintsev et al., Eur. Phys. J. A 58, 257 (2022)], we considered the ANC $C_0$ for the virtual decay $^{16}$O$(0^+; 6.05$ MeV)$\to α+^{12}$C(g.s.). In the present paper, which can be regarded as a continuation of the previous, we treat the ANCs $C_l$ for the vertices $^{16}$O$(J^π)\to α+^{12}$C(g.s.) corresponding to the other three bound excited states of $^{16}$O ($J^π=3^-$, $2^+$, $1^-$, $l=J$). ANCs $C_l$ ($l=3,\,2,\,1$) are found by analytic continuation in energy of the $α^{12}$C $l$-wave partial scattering amplitudes, known from the phase-shift analysis of experimental data, to the pole corresponding to the $^{16}$O bound state and lying in the unphysical region of negative energies. To determine $C_l$, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. For a more reliable determination of the ANCs, various forms of functions expressed in terms of phase shifts were used in analytical approximation and subsequent extrapolation.

nucl-th↗
arXiv2022

Determination of asymptotic normalization coefficients for the channel $^{16}$O$\to α+^{12}$C. Excited state $^{16}$O($0^+; 6.05$ MeV)

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC $C$ for the virtual decay $^{16}$O$(0^+; 6.05$ MeV)$\to α+^{12}$C(g.s.), the known values of which are characterized by a large spread $(0.29-1.65)\times 10^3$ fm$^{-1/2}$. The ANC $C$ is found by analytic continuation in the energy of the $α^{12}$C $s$-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the $^{16}$O bound state and lying in the unphysical region of negative energies. To determine $C$, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC $C$ is found by solving the Schrödinger equation for the two-body $α^{12}$C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of $^{16}$O$(0^+; 6.05$ MeV) in the $α+^{12}$C channel. The values of the ANC $C$ obtained within these two methods lie in the interval (886--1139) fm$^{-1/2}$.

nucl-th↗
arXiv2022

Status of deep subbarrier $\mathbf{{}^{12}{\rm C}+{}^{12}{\rm C}}$ fusion and advancing the Trojan horse method

In this paper, I will update the current status of the carbon-carbon fusion research taking into account that after the latest analysis [Beck {\it et al.} Eur. Phys. J. A {\bf 56}, 97 (2020), Letter to the Editor] new important experimental and theoretical results had been published and will discuss how to advance new THM measurements to extract the low-energy astrophysical $S$-factors.

nucl-th↗
arXiv2019

Status on $\mathbf{{}^{12}{\rm C}+{}^{12}{\rm C}}$ fusion at deep subbarrier energies: impact of resonances on astrophysical $S^{*}$ factors

Since the discovery of molecular resonances in $^{12}$C+$^{12}$C in the early sixties a great deal of research work has been undertaken to study $α$-clustering and resonant effects of the fusion process at sub-Coulomb barrier energies. The modified astrophysical $S^{*}$ factors of $^{12}$C+$^{12}$C fusion have been extracted from direct fusion measurements at deep sub-barrier energies near the Gamow window. They were also obtained by the indirect Trojan horse method (THM). A comparison of direct measurements and the THM, which elucidates problems in the analysis of the THM, is discussed in this Letter to the Editor.

nucl-ex↗
arXiv2019

New method of analytic continuation of elastic-scattering data to the negative-energy region and asymptotic normalization coefficients for $^{17}$O and $^{13}$C

A new method is proposed for extrapolation of elastic-scattering data to the negative-energy region for a short-range interaction. The method is based on the analytic approximation of the modulus-squared of the partial-wave scattering amplitude. It is shown that the proposed method has an advantage over the traditional one based on continuation of the effective-range function. The new method has been applied to determine the asymptotic normalization coefficients for the $^{17}$O and $^{13}$C nuclei in the $n+^{16}$O and $n+^{12}$C channels, respectively.

nucl-th↗
arXiv2019

Theory of surrogate nuclear and atomic reactions with three charged particles in the final state proceeding through a resonance in the intermediate subsystem

Within a few-body formalism, we develop a general theory of surrogate nuclear and atomic reactions with the excitation of a resonance in the intermediate binary subsystem leading to three charged particles in the final state. The Coulomb interactions between the spectator and the resonance in the intermediate state and between the three particles in the final state are taken into account. Final-state three-body Coulomb multiple-scattering effects are accounted for using the formalism of the three-body Coulomb asymptotic states based on the work published by one of us (A.M.M.) under the guidance of L. D. Faddeev. An expression is derived for the triply differential cross section. It can be used for investigation of the Coulomb effects on the resonance line shape as well as the energy dependence of the cross section. We find that simultaneous inclusion of the Coulomb effects in the intermediate and final state decreases the effect of the final-state Coulomb interactions on the triply differential cross section.

nucl-th↗
arXiv2018

Extrapolation of scattering data to the negative-energy region. Application to the $p-^{16}$O system

The problem of analytic continuation of the scattering data to the negative-energy region to obtain information on asymptotic normalization coefficients (ANCs) of bound states is discussed. It is shown that a recently suggested $Δ$ method [O.L.Ram\'ırez Suárez and J.-M. Sparenberg, Phys. Rev. C {\bf 96}, 034601 (2017)] is not strictly correct in the mathematical sense since it is not an analytic continuation of a partial-wave scattering amplitude to the region of negative energies. However, it can be used for practical purposes for sufficiently large charges and masses of colliding particles. Both the $Δ$ method and the standard method of continuing of the effective range function are applied to the $p-^{16}$O system which is of interest for nuclear astrophysics. The ANCs for the ground $5/2^+$ and excited $1/2^+$ states of $^{17}$F are determined.

nucl-th↗
arXiv2018

Astrophysical factors of ${}^{12}{\rm C}+{}^{12}{\rm C}$ fusion from Trojan horse method

Carbon-carbon burning plays an important role in many stellar environments. Recently, using the indirect Trojan horse method A. Tumino {\em et al.} reported [Nature {\bf 557} 687 (2018)] a strong rise of the astrophysical factor for the carbon-carbon fusion at low resonance energies. In this paper, we demonstrate that this rise is the artifact of using an invalid plane-wave approximation. It is shown that the calculated renormalization factor decreases the astrophysical factor from [A. Tumino {\em et al.}, Nature {\bf 557} 687 (2018)] at the resonance energies of $E=0.8-0.9$ MeV by as much as $\approx 10^{3}$ times.

nucl-th↗
arXiv2018

Impact of the $^7$Be($α, γ$)$^{11}$C reaction on the primordial abundance of $^7$Li

We calculate the radiative capture cross section for $^7$Be($α, γ$)$^{11}$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.

nucl-th↗
arXiv2018

Three-body Faddeev equations in two-particle Alt-Grassberger-Sandhas form with Distorted-Wave-Born-approximation amplitudes as effective potentials

In this paper, I prove that the sub-Coulomb $A(d,p)B$ reaction amplitude, which is a solution of the three-body Faddeev equations in the Alt-Grassberger-Sandhas (AGS) form, is peripheral if a peripheral is the corresponding DWBA amplitude. Hence the Faddeev's reaction amplitude for the sub-Coulomb $A(d,p)B$ reactions can also be parametrized in terms of the ANC of the $(n\,A)$ bound state. First, I consider the original AGS equations with separable potentials and prove that such equations are peripheral at sub-Coulomb energies. After that, the two-particle AGS equations are derived for the general potentials for sub-Coulomb transfer reactions. The effective AGS potentials are expressed in terms of the DWBA amplitudes for the sub-Coulomb reactions. Again, I demonstrate that the amplitude of the $A(d,p)B$ transfer reaction obtained from the AGS equation is peripheral and can be parametrized in terms of the ANC for the $(nA)$ bound state because the corresponding DWBA amplitude is peripheral. Finally, the AGS equations are generalized by including the optical nuclear potentials in the same manner as it is done in the DWBA. The obtained two-particle AGS equations contain the DWBA effective potentials with distorted waves generated by the sum of the nuclear optical and the channel Coulomb potentials. The AGS equation for the $A(d,p)B$ reactions is analyzed above the Coulomb barrier and it is shown again that the reaction amplitude satisfying generalized AGS equation with optical potentials depends on the ANC if a peripheral is the DWBA amplitude. The two-body AGS equations are generalized by including the intermediate three-body continuum and more than one bound state in each channel.

nucl-th↗
arXiv2018

Cosmological Lithium Problems

We briefly describe the cosmological lithium problems followed by a summary of our recent theoretical work on the magnitude of the effects of electron screening, the possible existence of dark matter parallel universes and the use of non-extensive (Tsallis) statistics during big bang nucleosynthesis. Solutions within nuclear physics are also discussed and recent measurements of cross-sections based on indirect experimental techniques are summarized.

nucl-th↗
arXiv2017

Extrapolation of scattering data to the negative-energy region II

A problem of analytical continuation of scattering data to the negative-energy region to obtain information about bound states is discussed within an exactly solvable potential model. This work is continuation of the previous one by the same authors [L. D. Blokhintsev et al., Phys. Rev. C 95, 044618 (2017)]. The goal of this paper is to determine the most effective way of analytic continuation for different systems. The $d+α$ and $α+^{12}$C systems are considered and, for comparison, an effective-range function approach and a recently suggested $Δ$-method [O. L. Ram\'ırez Suárez and J.-M. Sparenberg, Phys. Rev. C 96, 034601 (2017)] are applied. We conclude that the $Δ$-method is more effective for heavier systems with large values of the Coulomb parameter, whereas for light systems with small values of the Coulomb parameter the effective-range function method might be preferable.

nucl-th↗
arXiv2017

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

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 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 sub-reaction. Finally, we demonstrate how the THM can be used to calculate the astrophysical S-factor for the neutron generator $^{13}{\rm C}(α,\,n)^{16}{\rm O}$ 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.

nucl-th↗