Resonances to Continuum
51
information on specific resonances, if it becomes available, using the methods of
Ref. [8].
We plan to implement a full R-matrix description of the cross section, which will
take interference between resonances into account. Using the approach described
in Ref. [19], this is straightforward, as level shift effects are removed. Including
interference effects will allow additional phenomena, such as Ericson fluctuations,
to be revealed. This extension will require that the reaction rate be calculated by the
numerical integration of Eq. (10), which will be more computationally intensive.
It should be noted that these type of interference effects are not expected to be
significant for the case of 34 Ar(α, p) 37 K.
In conclusion, the variance in the 34 Ar(α, p) 37 K reaction rate due to the finite
number of contributing resonances has been calculated. It is found to be a nontrivial consideration. We also note that the α + 34 Ar optical potential, which is used
in this and other works to predict the 34 Ar(α, p) 37 K cross section, is poorly known
at astrophysically relevant energies.
Acknowledgments It is a pleasure to thank K.A. Chipps, S.M. Grimes, M.A.A. Mamun,
T. Rauscher, K. Schmidt, and A. Voinov for providing useful discussions and information. This
work was supported in part by the U.S. Department of Energy, under Grants No. DE-FG0288ER40387, DE-NA0002905, and DE-NA0003883.
References
1. T. Rauscher, The path to improved reaction rates for astrophysics. Int. J. Mod. Phys. E 20,
1071–1169 (2011). https://doi.org/10.1142/S021830131101840X. http://www.worldscientific.
com/doi/abs/10.1142/S021830131101840X
2. J.L. Fisker, F.K. Thielemann, M. Wiescher, The nuclear reaction waiting points: 22 Mg, 26 Si,
30 S, and 34 Ar and bolometrically double-peaked type I x-ray bursts. Astrophys. J. Lett. 608,
L61 (2004). https://doi.org/10.1086/422215
3. A. Parikh, J. José, F. Moreno, C. Iliadis, The effects of variations in nuclear processes on type I
x-ray burst nucleosynthesis. Astrophys. J. Suppl. Ser. 178, 110 (2008). https://doi.org/10.1086/
589879
4. C. Deibel et al.: Radioactive ion beam studies of αp process waiting points in x-ray bursts. PoS
(NIC XII) 146, 044 (2013). https://doi.org/10.22323/1.146.0044. https://pos.sissa.it/146/044/
5. A.M. Long et al.: Indirect study of the stellar 34 Ar(α, p) 37 K reaction rate through
40 Ca(p, t) 38 Ca reaction measurements. Phys. Rev. C 95, 055803 (2017). https://link.aps.org/
doi/10.1103/PhysRevC.95.055803
6. A.C. Lauer, Studying the reaction 34AR(ALPHA,P)37K and its impact on XRB nucleosynthesis and observables. Ph.D. thesis (Louisiana State University, Louisiana, 2017). http://
digitalcommons.lsu.edu/gradschool_dissertations/4118
7. P.E. Hodgson, Compound nucleus reactions. Rep. Prog. Phys. 50, 1171–1228 (1987). https://
doi.org/10.1088/0034-4885/50/9/002
8. P. Mohr, R. Longland, C. Iliadis, Thermonuclear reaction rate of 18 Ne(α, p) 21 Na from Monte
Carlo calculations. Phys. Rev. C 90, 065806 (2014). https://doi.org/10.1103/PhysRevC.90.
065806. http://link.aps.org/doi/10.1103/PhysRevC.90.065806
9. P.A. Moldauer, Why the Hauser-Feshbach formula works. Phys. Rev. C 11, 426–436 (1975).
https://doi.org/10.1103/PhysRevC.11.426. http://link.aps.org/doi/10.1103/PhysRevC.11.426
51
information on specific resonances, if it becomes available, using the methods of
Ref. [8].
We plan to implement a full R-matrix description of the cross section, which will
take interference between resonances into account. Using the approach described
in Ref. [19], this is straightforward, as level shift effects are removed. Including
interference effects will allow additional phenomena, such as Ericson fluctuations,
to be revealed. This extension will require that the reaction rate be calculated by the
numerical integration of Eq. (10), which will be more computationally intensive.
It should be noted that these type of interference effects are not expected to be
significant for the case of 34 Ar(α, p) 37 K.
In conclusion, the variance in the 34 Ar(α, p) 37 K reaction rate due to the finite
number of contributing resonances has been calculated. It is found to be a nontrivial consideration. We also note that the α + 34 Ar optical potential, which is used
in this and other works to predict the 34 Ar(α, p) 37 K cross section, is poorly known
at astrophysically relevant energies.
Acknowledgments It is a pleasure to thank K.A. Chipps, S.M. Grimes, M.A.A. Mamun,
T. Rauscher, K. Schmidt, and A. Voinov for providing useful discussions and information. This
work was supported in part by the U.S. Department of Energy, under Grants No. DE-FG0288ER40387, DE-NA0002905, and DE-NA0003883.
References
1. T. Rauscher, The path to improved reaction rates for astrophysics. Int. J. Mod. Phys. E 20,
1071–1169 (2011). https://doi.org/10.1142/S021830131101840X. http://www.worldscientific.
com/doi/abs/10.1142/S021830131101840X
2. J.L. Fisker, F.K. Thielemann, M. Wiescher, The nuclear reaction waiting points: 22 Mg, 26 Si,
30 S, and 34 Ar and bolometrically double-peaked type I x-ray bursts. Astrophys. J. Lett. 608,
L61 (2004). https://doi.org/10.1086/422215
3. A. Parikh, J. José, F. Moreno, C. Iliadis, The effects of variations in nuclear processes on type I
x-ray burst nucleosynthesis. Astrophys. J. Suppl. Ser. 178, 110 (2008). https://doi.org/10.1086/
589879
4. C. Deibel et al.: Radioactive ion beam studies of αp process waiting points in x-ray bursts. PoS
(NIC XII) 146, 044 (2013). https://doi.org/10.22323/1.146.0044. https://pos.sissa.it/146/044/
5. A.M. Long et al.: Indirect study of the stellar 34 Ar(α, p) 37 K reaction rate through
40 Ca(p, t) 38 Ca reaction measurements. Phys. Rev. C 95, 055803 (2017). https://link.aps.org/
doi/10.1103/PhysRevC.95.055803
6. A.C. Lauer, Studying the reaction 34AR(ALPHA,P)37K and its impact on XRB nucleosynthesis and observables. Ph.D. thesis (Louisiana State University, Louisiana, 2017). http://
digitalcommons.lsu.edu/gradschool_dissertations/4118
7. P.E. Hodgson, Compound nucleus reactions. Rep. Prog. Phys. 50, 1171–1228 (1987). https://
doi.org/10.1088/0034-4885/50/9/002
8. P. Mohr, R. Longland, C. Iliadis, Thermonuclear reaction rate of 18 Ne(α, p) 21 Na from Monte
Carlo calculations. Phys. Rev. C 90, 065806 (2014). https://doi.org/10.1103/PhysRevC.90.
065806. http://link.aps.org/doi/10.1103/PhysRevC.90.065806
9. P.A. Moldauer, Why the Hauser-Feshbach formula works. Phys. Rev. C 11, 426–436 (1975).
https://doi.org/10.1103/PhysRevC.11.426. http://link.aps.org/doi/10.1103/PhysRevC.11.426