An efficient nonclassical quadrature for the calculation of nonresonant nuclear fusion reaction rate coefficients from cross section data

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• 作者：Bernie D. Shizgal ^{shizgal@chem.ubc.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonclassical polynomials ; Quadrature ; Astrophysical factor ; Nuclear reaction rate coefficient
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：205
• 期：Complete
• 页码：61-68
• 全文大小：583 K

文摘

Nonclassical quadratures based on a new set of half-range polynomials, science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300972&_mathId=si185.gif&_user=111111111&_pii=S0010465516300972&_rdoc=1&_issn=00104655&md5=5cfd8d010561ec90be8e2ceb4c7d3bae" title="Click to view the MathML source">T_n(x)$T_n\left(x\right)$, orthogonal with respect to science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300972&_mathId=si186.gif&_user=111111111&_pii=S0010465516300972&_rdoc=1&_issn=00104655&md5=80166d5d1da5d468737e1b6517c978fe">$w\left(x\right)=e^{-x-b/\sqrt{x}}$ for science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300972&_mathId=si187.gif&_user=111111111&_pii=S0010465516300972&_rdoc=1&_issn=00104655&md5=5332462fd21636029be5889e9c8867d6" title="Click to view the MathML source">x∈[0,∞)$x\in [0,\infty )$ are employed in the efficient calculation of the nuclear fusion reaction rate coefficients from cross section data. The parameter science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300972&_mathId=si188.gif&_user=111111111&_pii=S0010465516300972&_rdoc=1&_issn=00104655&md5=0e27418ed8e411708448ecaea3b73381">$b=B/\sqrt{k_{B}T}$ in the weight function is temperature dependent and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300972&_mathId=si189.gif&_user=111111111&_pii=S0010465516300972&_rdoc=1&_issn=00104655&md5=1275e84fb4879504d82e28dcb529d9db" title="Click to view the MathML source">B$B$ is the Gamow factor. The polynomials science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300972&_mathId=si185.gif&_user=111111111&_pii=S0010465516300972&_rdoc=1&_issn=00104655&md5=5cfd8d010561ec90be8e2ceb4c7d3bae" title="Click to view the MathML source">T_n(x)$T_n\left(x\right)$ satisfy a three term recurrence relation defined by two sets of recurrence coefficients, science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300972&_mathId=si191.gif&_user=111111111&_pii=S0010465516300972&_rdoc=1&_issn=00104655&md5=768e890f70f343cd6239e1f58197a120" title="Click to view the MathML source">α_n${\alpha }_n$ and science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300972&_mathId=si192.gif&_user=111111111&_pii=S0010465516300972&_rdoc=1&_issn=00104655&md5=be3739abba2ff33bef507c067b1bb943" title="Click to view the MathML source">β_n${\beta }_n$. These recurrence coefficients define in turn the tridiagonal Jacobi matrix whose eigenvalues are the quadrature points and the weights are calculated from the first components of the eigenfunctions. For nonresonant nuclear reactions for which the astrophysical function can be expressed as a lower order polynomial in the relative energy, the convergence of the thermal average of the reactive cross section with this nonclassical quadrature is extremely rapid requiring in many cases 2–4 quadrature points. The results are compared with other libraries of nuclear reaction rate coefficient data reported in the literature.