arXiv subjects

A. M. Mukhamedzhanov

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

At least 55 records · Page 3Linked to original sources

arXiv2009

Bound, virtual and resonance $S$-matrix poles from the Schrödinger equation

A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schrödinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$

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arXiv2009

New High-Precision Measurement of the Reaction Rate of the 18O(p,alpha)15N Reaction via THM

The 18O(p,alpha)15N reaction rate has been extracted by means of the Trojan-Horse method. For the first time the contribution of the 20-keV peak has been directly evaluated, giving a value about 35% larger than previously estimated. The present approach has allowed to improve the accuracy of a factor 8.5, as it is based on the measured strength instead of educated guesses or spectroscopic measurements. The contribution of the 90-keV resonance has been determined as well, which turned out to be of negligible importance to astrophysics.

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arXiv2008

Astrophysical S factor for the radiative capture 12N(p,gamma)13O determined from the 14N(12N,13O)13C proton transfer reaction

The cross section of the radiative proton capture reaction on the drip line nucleus 12N was investigated using the Asymptotic Normalization Coefficient (ANC) method. We have used the 14N(12N,13O)13C proton transfer reaction at 12 MeV/nucleon to extract the ANC for 13O -> 12N + p and calculate from it the direct component of the astrophysical S factor of the 12N(p,gamma)13O reaction. The optical potentials used and the DWBA analysis of the proton transfer reaction are discussed. For the entrance channel, the optical potential was inferred from an elastic scattering measurement carried out at the same time with the transfer measurement. From the transfer, we determined the square of the ANC, C^2(13Og.s.) = 2.53 +/- 0.30 fm-1, and hence a value of 0.33(4) keVb was obtained for the direct astrophysical S factor at zero energy. Constructive interference at low energies between the direct and resonant captures leads to an enhancement of Stotal(0) = 0.42(5) keVb. The 12N(p,gamma)13O reaction was investigated in relation to the evolution of hydrogen-rich massive Population III stars, for the role that it may play in the hot pp-chain nuclear burning processes, possibly occurring in such objects.

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arXiv2008

Measurement of the 20 and 90 keV resonances in the ${}^{18}{\rm O}(p,α){}^{15}$N reaction via THM

The $^{18}{\rm O}(p,α)^{15}{\rm N}$ reaction is of primary importance in several astrophysical scenarios, including fluorine nucleosynthesis inside AGB stars as well as oxygen and nitrogen isotopic ratios in meteorite grains. Thus the indirect measurement of the low energy region of the $^{18}{\rm O}(p,α)^{15}{\rm N}$ reaction has been performed to reduce the nuclear uncertainty on theoretical predictions. In particular the strength of the 20 and 90 keV resonances have been deduced and the change in the reaction rate evaluated.

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arXiv2008

Benchmark on neutron capture extracted from $(d,p)$ reactions

Direct neutron capture reactions play an important role in nuclear astrophysics and applied physics. Since for most unstable short-lived nuclei it is not possible to measure the $(n, γ)$ cross sections, $(d,p)$ reactions have been used as an alternative indirect tool. We analyze simultaneously $^{48}{\rm Ca}(d,p)^{49}{\rm Ca}$ at deuteron energies $2, 13, 19$ and 56 MeV and the thermal $(n,γ)$ reaction at 25 meV. We include results for the ground state and the first excited state of $^{49}$Ca. From the low-energy $(d,p)$ reaction, the neutron asymptotic normalization coefficient (ANC) is determined. Using this ANC, we extract the spectroscopic factor (SF) from the higher energy $(d,p)$ data and the $(n, γ)$ data. The SF obtained through the 56 MeV $(d,p)$ data are less accurate but consistent with those from the thermal capture. We show that to have a similar dependence on the single particle parameters as in the $(n, γ)$, the (d,p) reaction should be measured at 30 MeV.

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arXiv2007

Trojan Horse as an indirect technique in nuclear astrophysics. Resonance reactions

The Trojan Horse method is a powerful indirect technique that provides information to determine astrophysical factors for binary rearrangement processes $x + A \to b + B$ at astrophysically relevant energies by measuring the cross section for the Trojan Horse reaction $a + A \to y+ b + B$ in quasi-free kinematics. We present the theory of the Trojan Horse method for resonant binary subreactions based on the half-off-energy-shell R matrix approach which takes into account the off-energy-shell effects and initial and final state interactions.

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arXiv2007

Are spectroscopic factors from transfer reactions consistent with asymptotic normalisation coefficients?

It is extremely important to devise a reliable method to extract spectroscopic factors from transfer cross sections. We analyse the standard DWBA procedure and combine it with the asymptotic normalisation coefficient, extracted from an independent data set. We find that the single particle parameters used in the past generate inconsistent asymptotic normalization coefficients. In order to obtain a consistent spectroscopic factor, non-standard parameters for the single particle overlap functions can be used but, as a consequence, often reduced spectroscopic strengths emerge. Different choices of optical potentials and higher order effects in the reaction model are also studied. Our test cases consist of: $^{14}$C(d,p)$^{15}$C(g.s.) at $E_d^{lab}=14$ MeV, $^{16}$O(d,p)$^{17}$O(g.s.) at $E_d^{lab}=15$ MeV and $^{40}$Ca(d,p)$^{41}$Ca(g.s.) at $E_d^{lab}=11$ MeV. We underline the importance of performing experiments specifically designed to extract ANCs for these systems.

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arXiv2006

Astrophysical factor for the neutron generator 13C(alpha,n)16O reaction in the AGB stars

The reaction 13C(alpha,n) is considered to be the main source of neutrons for the s-process in AGB stars. At low energies the cross section is dominated by the 1/2+ 6.356 MeV sub-threshold resonance in 17O whose contribution is determined with a very large uncertainty of ~1000% at stellar temperatures. In this work we performed the most precise determination of the low-energy astrophysical S factor using the indirect asymptotic normalization (ANC) technique. The alpha-particle ANC for the sub-threshold state has been measured using the sub-Coulomb alpha-transfer reaction (6Li,d). Using the determined ANC we calculated S(0), which turns out to be an order of magnitude smaller than in the NACRE compilation.

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arXiv2006

The Trojan Horse Method: an Indirect Technique in Nuclear Astrophysics

The Trojan Horse (TH) method is a powerful indirect technique that provides information to determine astrophysical factors for rearrangement processes at astrophysically relevant energies. A short coming for understanding the reliability of the technique has been determining the importance of nuclear and Coulomb effects on the energy dependence of the yield. Using a simple model, we demonstrate that off-energy-shell and Coulomb effects in the entry channel and the final state nuclear interactions do not change the energy dependence of the astrophysical factor extracted from the TH reaction. Some examples are presented.

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arXiv2006

Completeness of the Coulomb scattering wave functions

Completeness of the eigenfunctions of a self-adjoint Hamiltonian, which is the basic ingredient of quantum mechanics, plays an important role in nuclear reaction and nuclear structure theory. However, until now, there was no a formal proof of the completeness of the eigenfunctions of the two-body Hamiltonian with the Coulomb interaction. Here we present the first formal proof of the completeness of the two-body Coulomb scattering wave functions for repulsive unscreened Coulomb potential. To prove the completeness we use the Newton's method [R. Newton, J. Math Phys., 1, 319 (1960)]. The proof allows us to claim that the eigenfunctions of the two-body Hamiltonian with the potential given by the sum of the repulsive Coulomb plus short-range (nuclear) potentials also form a complete set. It also allows one to extend the Berggren's approach of modification of the complete set of the eigenfunctions by including the resonances for charged particles. We also demonstrate that the resonant Gamow functions with the Coulomb tail can be regularized using Zel'dovich's regularization method.

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arXiv2005

Indirect techniques in nuclear astrophysics. Asymptotic Normalization Coefficient and Trojan Horse

Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reactions down to astrophysically relevant energies. We explain why there is no Coulomb barrier in the sub-process amplitudes extracted from the TH reaction. The expressions for the TH amplitude for direct and resonant cases are presented.

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arXiv2005

The leading asymptotic terms of the three-body Coulomb scattering wave function

The asymptotic wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A 47, 2004 (1993)] and Mukhamedzhanov and Lieber [Phys. Rev. A 54, 3078 (1996)] has been refined in the region where the pair $ (β,γ)$ remains close to each other while the third particle $α$ is far away from them $(ρ_α \to \infty$, $r_α/ρ_α\to 0)$. The improved wave function satisfies the Schrödinger equation up to the terms of order $O(1/{ρ_α}^{3})$, provides the leading asymptotic terms of the three-body scattering wave function with Coulomb interactions and gives further insight into the continuum behavior of the three-charged-particle wave function and helps to obtain $3\to 3$ scattered wave. This opens up further ways of solving and analysing the three-body Schrödinger equation by numerical means.

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arXiv2005

Scattering of $^{7}$Be and $^{8}$B and the astrophysical S$_{17}$ factor

Measurements of scattering of $^{7}$Be at 87 MeV on a melamine (C$_{3}$N$ _{6}$H$_{6}$) target and of $^{8}$B at 95 MeV on C were performed. For $^{7}$Be the angular range was extended over previous measurements and monitoring of the intensity of the radioactive beam was improved. The measurements allowed us to check and improve the optical model potentials used in the incoming and outgoing channels for the analysis of existing data on the proton transfer reaction $^{14}$N($^{7}$Be,$^{8}$B)$^{13}$C. The resultslead to an updated determination of the asymptotic normalization coefficient for the virtual decay $^{8}$B $\to$ $^{7}$Be + $p$. We find a slightly larger value, $C_{tot}^{2}(^{8}B)=0.466\pm 0.047$ fm$^{-1}$, for the melamine target. This implies an astrophysical factor, $S_{17}(0)=18.0\pm 1.8$ eV$\cdot$b, for the solar neutrino generating reaction $^{7}$Be($p$,$γ$)$^{8}$B.

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arXiv2005

Scattering theory for arbitrary potentials

The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.

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arXiv2005

Understanding low energy reaction with exotic nuclei

Recent developments on the understanding of low energy reactions are highlighted. Emphasis is given to the CDCC framework where the breakup channels of the projectile are included explicitly. Properties of the breakup couplings are presented. Comments are given with regard to the separation between the nuclear and the Coulomb contributions to breakup cross sections as well as the dependence on the optical potentials. A discussion on the sensitivity of the CDCC basis is discussed, by comparing pure breakup results with transfer to the continuum calculations. Finally, some remaining controversies show the need to go beyond the single particle picture for the projectile.

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arXiv2005

Combined method to extract spectroscopic information

Spectroscopic factors (SF) play an important role in nuclear physics and astrophysics. The traditional method of extracting SF from direct transfer reactions suffers from serious ambiguities. We discuss a modified method which is based on including the asymptotic normalization coefficient (ANC) of the overlap functions into the transfer analysis. In the modified method the contribution of the external part of the reaction amplitude, typically dominant, is fixed and the SF is determined from fitting the internal part. We illustrate the modified method with $(d,p)$ reactions on ${}^{208}{\rm Pb}, {}^{12}{\rm C}$, and ${}^{84}{\rm Se}$ targets at different energies. The modified method allows one to extract the SF, which do not depend on the shape of the single-particle nucleon-target interaction, and has the potential of improving the reliability and accuracy of the structure information. This is specially important for nuclei on dripline, where not much is known.

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arXiv2005

Progress on reactions with exotic nuclei

Modelling breakup reactions with exotic nuclei represents a challenge in several ways. The CDCC method (continuum discretized coupled channel) has been very successful in its various applications. Here, we briefly mention a few developments that have contributed to the progress in this field as well as some pertinent problems that remain to be answered.

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arXiv2005

Three-Body Coulomb Final-State Interaction Effects in the Coulomb Breakup of Light Nuclei

Coulomb breakup of a projectile in the Coulomb field of a fully stripped heavy nucleus is at present one of the most popular experimental methods to obtain information on reactions of interest in nuclear astrophysics. Its theoretical interpretation presents, however, considerable difficulties, due to the three-body nature and the infinite range of the Coulomb forces involved. Among the uncertainties affecting present analyses, the possible modification of the dissociation cross section by three-body Coulomb final-state interactions plays a major role. Various methods which have been proposed to deal with it are briefly reviewed. However, none of them is based on a consistent and mathematically satisfactory quantum mechanical treatment, with the exception of the one proposed recently. The latter, being based on the prior form of the dissociation amplitude, makes use of a genuine three-charged particle wave function for the final state which is an exact solution of the three-body Schrödinger equation, albeit only asymptotically, i.e. for large distances. Nevertheless, interesting conclusion can be drawn concerning the influence of three-body Coulomb final-state interactions on quantities of astrophysical interest.

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