Speaker
Description
In the present work, a new asymptotical theory is proposed for the peripheral sub- and above-barrier transfer $A(x,y)B$ reaction in the framework of a three-body model, where $x=y+a$, $B=A+a$ and $a$ is a transferred particle. The asymptotic theory is based on the idea of the fact that, firstly, a peripheral reaction is governed by the nearest to the physical region $(-1\le\cos\theta\le 1)$ singularity (ζ) of the reaction amplitude (θ is the scattering angle in the c.m.s.). Secondly, the dominant role played by the nearest singularity is the result of the surface nature of this reaction. The dominant contribution to the peripheral reaction comes from the surface and outer regions of nuclei corresponding to $R \le R_{ch}$, where $R$ and $R_{ch}$ are the relative distance between the center of mass of the colliding nuclei and the channel radius, respectively. The regions for the reaction amplitude decomposed on the partial waves ($l$), correspond to the several lowest partial waves with $l < kR_{ch}$ ( $l=0,1,2,$ and $k$ is a wave number of the colliding nuclei) for sub-barrier energies $(k= (2\mu E)^{1/2}/\hbar \rightarrow 0$, $E\rightarrow 0$ and $\mu$ is the reduced mass of the colliding nuclei) and to the peripheral partial waves with $l\ge kR_{ch}>>1$ for the above-barrier energies ($E =10 -15 {\rm MeV}/N$).
In the proposed asymptotic theory, the main advantage of the dispersion method and the distorted wave Born approximation (DWBA) are combined. There the allowance of the contribution of the three-body ($A$, $y$ and $a$) Coulomb dynamics of the transfer mechanism to the peripheral partial amplitudes, which is determined by the nearest singularity of the reaction amplitude located at $\cos\theta = \zeta$, is done properly.
The explicit form of the differential cross section for the reaction under consideration is derived. This form is expressed in terms of the product of the squared asymptotic normalization coefficients (ANCs) for $y+a x$ and $A+a B$. The ANCs determine the amplitude of the tail of the radial overlap functions for the bound state wave functions of the x and B nuclei in the $(y+a)$ and $(A+a)$ channels, respectively. The asymptotic theory is applied for the analysis of the experimental differential cross sections (DCSs) both of the sub-barrier $^{19}$F($p,\alpha){}^{16}$O reaction and of the above-barrier $^{16}$O(${}^3$He, d)${}^{17}$F, ${}^9$Be(${}^{10}$B, ${}^9$Be)${}^{10}$B and ${}^{11}$B(${}^{12}$C, ${}^{11}$B)${}^{12}$C reactions measured by other authors.
As a result, the values of the squared ANCs for ${}^{16}$O+$t\rightarrow{}^{19}$F, ${}^{16}$O$+p\rightarrow{}^{17}$F,${}^9$Be$+p\rightarrow{}^{10}$B and ${}^{11}$B+$p\rightarrow{}^{12}$C are determined. They are to be equal 583.346.1, 1.350.14, 6216632, 4.350.19 and 311.613.3 fm$^{-1}$ for ${}^{16}$O $+t\rightarrow{}^{19}$F, ${}^{16}$O$ +p\rightarrow{}^{17}$F(g.s), ${}^{16}$O $\rightarrow{}^{17}$F(0.429 MeV), ${}^9$Be$ +p\rightarrow{}^{10}$B and ${}^{11}$B$ +p\rightarrow{}^{12}$C, respectively.
The ANC values for ${}^{16}$O$ +t\rightarrow{}^{19}$F, ${}^{16}$O$ +p\rightarrow{}^{17}$F and ${}^9$Be$ +p \rightarrow{}^{10}$B are used for the estimation of cross section of the nuclear-astrophysical ${}^19$F$(p,\alpha){}^{16}$O reaction at sub-barrier projectile energies 250, 350 and 450 keV. They also used for the estimation of astrophysical S factors corresponding to the nuclear-astrophysical ${}^{16}$O$(p,\gamma){}^{17}$F and
${}^9$Be$(p,\gamma){}^{10}$B reactions at zero energy. The obtained results are compared with those from other authors.
This work has been supported in part by the Ministry of Innovations and Technologies of the Republic of Uzbekistan (grant No. HE F2-14) and by the Ministry of Education and Science of the Republic of Kazakhstan (grant No AP05132062).
