# NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION

## Abstract

The resistance coefficients in the screened Coulomb potential of stellar plasma are evaluated to high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of an attractive potential. This may result in a problem for the numerical integral. In order to avoid the problem, I have used a proper scheme, e.g., splitting into many subintervals where the width of each subinterval is determined by the variation of the integrand, to calculate the scattering angle. The collision integrals are calculated by using Romberg’s method, therefore the accuracy is high (i.e., ∼10{sup −12}). The results of collision integrals and their derivatives for −7 ≤ ψ ≤ 5 are listed. By using Hermite polynomial interpolation from those data, the collision integrals can be obtained with an accuracy of 10{sup −10}. For very weakly coupled plasma ( ψ ≥ 4.5), analytical fittings for collision integrals are available with an accuracy of 10{sup −11}. I have compared the final results of resistance coefficients with other works and found that, for a repulsive potential, the results are basically the same as others’; for an attractive potential, the results in cases of intermediate and strong couplingmore »

- Authors:

- Yunnan Observatories, Chinese Academy of Sciences, 396 Yangfangwang, Guandu District, Kunming, 650216 (China)

- Publication Date:

- OSTI Identifier:
- 22663976

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 834; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; COLLISION INTEGRALS; COLLISIONS; COMPARATIVE EVALUATIONS; COULOMB FIELD; DIFFUSION; HERMITE POLYNOMIALS; INTERPOLATION; PLASMA; SCATTERING; STAR MODELS; STARS; STRONG-COUPLING MODEL

### Citation Formats

```
Zhang, Q. S., E-mail: zqs@ynao.ac.cn.
```*NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/834/2/132.

```
Zhang, Q. S., E-mail: zqs@ynao.ac.cn.
```*NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION*. United States. doi:10.3847/1538-4357/834/2/132.

```
Zhang, Q. S., E-mail: zqs@ynao.ac.cn. Tue .
"NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION". United States.
doi:10.3847/1538-4357/834/2/132.
```

```
@article{osti_22663976,
```

title = {NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION},

author = {Zhang, Q. S., E-mail: zqs@ynao.ac.cn},

abstractNote = {The resistance coefficients in the screened Coulomb potential of stellar plasma are evaluated to high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of an attractive potential. This may result in a problem for the numerical integral. In order to avoid the problem, I have used a proper scheme, e.g., splitting into many subintervals where the width of each subinterval is determined by the variation of the integrand, to calculate the scattering angle. The collision integrals are calculated by using Romberg’s method, therefore the accuracy is high (i.e., ∼10{sup −12}). The results of collision integrals and their derivatives for −7 ≤ ψ ≤ 5 are listed. By using Hermite polynomial interpolation from those data, the collision integrals can be obtained with an accuracy of 10{sup −10}. For very weakly coupled plasma ( ψ ≥ 4.5), analytical fittings for collision integrals are available with an accuracy of 10{sup −11}. I have compared the final results of resistance coefficients with other works and found that, for a repulsive potential, the results are basically the same as others’; for an attractive potential, the results in cases of intermediate and strong coupling show significant differences. The resulting resistance coefficients are tested in the solar model. Comparing with the widely used models of Cox et al. and Thoul et al., the resistance coefficients in the screened Coulomb potential lead to a slightly weaker effect in the solar model, which is contrary to the expectation of attempts to solve the solar abundance problem.},

doi = {10.3847/1538-4357/834/2/132},

journal = {Astrophysical Journal},

number = 2,

volume = 834,

place = {United States},

year = {Tue Jan 10 00:00:00 EST 2017},

month = {Tue Jan 10 00:00:00 EST 2017}

}